Rational Bureau of Standards

ybrary. E-01 Admin. Bldg. l^r.^

APR 2 3 1971

BUILDING SCIENCE SERIES 34

Strength

of Masonry Walls

Under Compressive and

Transverse Loads
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UNITED STATES DEPARTMENT OF COMMERCE • Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Strength of Masonry Walls

Under Compressive and Transverse Loads

F. Y. Yokel, R. G. Mathey, and R. D. Dikkers

Building Research Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Building Science Series 34.'

Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 34, 74 pages (Mar. 1971)

CODEN: BSSNB

Issued March 1971

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Library of Congress Catalog Card Number: 77-608986
Contents

Page List of symbols V

SI conversion units VI Abstract 1

1. Introduction and objective 1

2. Scope 1

3. Materials 2

3.1. Brick 2

3.2. Concrete masonry units 2

3.3. Mortar 3

4. Test specimens 3

4.1. Description of walls 3

4.2. Fabrication of walls 6

4.3. Description and fabrication of prisms 6

5. Testing procedures 7

5.1. WaU tests 7

5.2. Instrumentation for wall tests 8

5.3. Prism tests 9

5.4. Instrumentation for prism tests 9

6. Test results 9

6.1. Wall test results 9

6.2. Description of wall failures 13

6.3. Prism test results 21

7. Theoretical discussion 23

7.1. Introduction 23

7.2. Interaction between vertical loads and moments 23

7.2.1. General discussion "23

7.2.2. Cross-sectional moment capacity. 25

7.2.2.1. Solid prismatic sections 25

7.2.2.2. Symmetrical hollow sections 29

7.2.2.3. Asymmetric sections 30

7.3. Slenderness effects 32

8. Analysis of test results 35

8.1. Introduction 35

8.2. Stress-strain relationships 35

8.3. Cross-sectional capacity 35

8.4. Wall strength 38

8.4.1. General discussion of the test conditions 38

8.4.2. Concrete block walls 39

8.4.2.1. 8-in hollow concrete block walls 39

8.4.2.2. 8-in solid concrete block walls 43

8.4.2.3. Conclusions 44

8.4.3. Brick walls 44

8.4.3.1. Comparison of brick wall systems 44

8.4.3.2. Correlation of test results with theory 48

8.4.3.3. Conclusions 51

8.4.4. Cavity and composite walls 51

8.4.4.1. Comparative strength of walls 51

III
Page

8.4.4.2. 4-2-4-in cavity walls of hollow concrete block 52

8.4.4.3. 4-2-4-in cavity walls of brick and hollow concrete block 54

8.4.4.4. 8-in composite brick and hollow concrete block walls 58

8.4.4.5. Conclusions 60

9. Recommendations and discussion of present design practice 61

9.1. Determination of transverse strength of masonry walls 61

9.2. Discussion of present design practice 62

9.2.1. ANSI building code requirements 62

9.2.2. SCPI standard for engineered brick masonry 63

9.2.3. NCMA and ACT recommendations 65

9.3. Recommended research 66

10. Summary 67

10.1. Conclusions from test results 67

10.2. Comparison of test results with existing design practice 67

11. Acknowledgment 68

12. References 68

IV
List of Symbols

A Area of net section a Flexural compressive strength coefficient

af'm Flexural compressive strength of masonry

b Width of wall

Cm Moment correction coefficient (section 7.3)

c Distance from centroid to outer fiber E Modulus of elasticity

Ei Initial tangent modulus of elasticity

e Eccentricity relative to centroid of uncracked

section

ca- Distance from centroid to edge of kern

Fa Allowable axial compressive stress

fa Computed axial compressive stress Fm Allowable flexural compressive stress

/,„ Computed flexural compressive stress f'm Compressive strength of masonry determined

from axial prism tests

/'( Tensile strength of masonry determined from

modulus of rupture tests g Moment coefficient in the approximate evaluation for Me (section 7.2.2.2)

Ti Unsupported height of wall

/ Moment of inertia of section

/„ Moment of inertia of section based on un- cracked net section

k Reduction coefficient to account for end fixity

kh Unsupported height of wall reduced for end

fixity

M Moment

Mc Cracking moment (section 7.2.2.1) M'c Maximum cracking moment (section 7.2.2.1)

Me Maximum moment capacity, computed using

linear stress gradients (section 7.2.2.1)

Mend Maximum transverse end moment resulting

from fixity at wall supports

Met Total maximum moment capacity of cavity

wall (section 8.4.4.3)

Mk Moment developed by Pk, applied at the edge

of the kern

Mo Maximum moment caused by transverse load

under pin ended conditions

M'o Maximum moment in the direction of the transverse loads caused by these loads

under given conditions of end fixity

Ml Maximum moment considering tensile strength

with zero vertical load (section 7.2.2.1)

m Stiffness ratio in composite section (section

7.2.2.3)

P Applied vertical compressive load; also de- notes resultant force on wall section P' Resultant compressive force acting on wall

section

Pall Allowable axial load

Pc Vertical load capacity when load is applied at the minimum eccentricity at which section

cracking occurs (section 7.2.2.1) Per Critical load for stability induced compression

failure computed on the basis of a modified

EI, accounting for section cracking and re- duced stiffness at maximum stress (section

7.3) Pcro Critical load, computed on the basis of the

initial tangent modulus of elasticity and an uncracked section (section 7.3)

Pk Vertical load capacity when load is applied at the edge of the kern of a wall section (sec- tion 7.2.2.1)

P0 Short wall axial load capacity determined on

the basis of prism strength (section 7.2.2.1)

s Ratio of tensile strength to axial compressive

strength of masonry (f'tlf'm) T' Resultant tensile force acting on cross section

t Thickness of wall

u Uncracked thickness in cracked section (fig- ure 7.2)

V Horizontal reaction

w Distributed transverse load

A Maximum transverse deflection

8 Transverse deflection

A/ Difference in force (figure 7.4)

V
SI Conversion Units

In view of present accepted practice in this country in this technological area, common U.S. units

measurement have been used throughout this paper. In recognition of the position of the USA as a signato

to the General Conference on Weights and Measures, which gave official status to the metric SI system

units in 1960, we assist readers interested in making use of the coherent system of SI units by giving convf

sion factors applicable to U.S. units used in this paper.

Length

1 in = 0.0254*

1 ft = 0.3048* meter

meter

Pressure, Stress

1 psi = 6895 newton/meter1 ksi = 6.895X106 newton/meter^

Area

1 in2 = 6.4516* X 10-^ meter-'

1 ft- =0.09290 meter^

Mass/Volume

1 lb/ft3 (lbm/ft3) = 16.02 kilogram/mete

Moment

Force 1 kip-in = 113.0 newton-meter

1 lb(lbf) = 4.448 newton

1 kip = 4448 newton

'Exactly

VI
Strength of Masonry Walls Under Compressive and Transverse Loads

Felix Y. Yokel, Robert G. Mathey, and Robert D. Dikkers

Ninety walls of 10 different types of masonry construction were tested under various combinations

of vertical and transverse load. It is shown that the effect of vertical load and wall slenderness on trans- verse strength can be predicted by rational analysis. The analysis is based on established theory which

has been extended to account for the properties of masonry. Similar methods of rational analysis have been adopted for the design of steel structures and are presently being considered for reinforced concrete structures.

Key words: Brick; cavity walls; composite walls; compressive strength; concrete block; flexural strength; masonry; mortar; slenderness effects; star dards; structural stability; walls.

1. Introduction and Objective

Until very recently masonry structures were

designed by essentially empirical methods, and only

limited effort has been devoted in the past to the

development of rational design criteria. A literature search of the state of knowledge on

the transverse strength of masonry walls indicated

that research was needed on the effect of vertical

compressive loads on the transverse flexural strength of masonry walls. To this end a research ef- fort was initiated by the National Bureau of Stan- dards to obtain data on the flexural strength of

masonry walls of various types of construction, subjected simultaneously to transverse loads and verti- cal compressive loads. The results of tests of 90 walls of various types

of masonry construction are reported. The data

|i from these tests are used as a basis for the develi opment of analytical procedures to predict the

' strength of masonry walls subjected to combined

< ompressive and transverse loads. A new analytical approach is proposed to evaluate

both strength and slenderness effects in masonry

walls. The application of this approach would lead to new design procedures, closely paralleling similar

procedures recently adopted for steel construction

and presently under consideration for reinforced

concrete. Present design practice is evaluated and

' compared with the proposed approach.

*This work was performed with the aid of a financial grant from the Tri-Service Building Materials Investigational Pro- gram (Office of the Chief of Engineers; Naval Facilities Engineering Command; Headquarters, U.S. Air Force).

2. Scope

To obtain the desired experimental data on the

strength of masonry walls subjected to combined

compressive and transverse loads, tests were con- ducted on the following 10 different tvpes of wall

construction:

1. 8-in hollow concrete masonry units with

masonry cement mortar.

2. 8-in hoUow concrete masonry units with

high-bond mortar.

3. 8-in 100 percent solid concrete masonry

units with masonry cement mortar.

4. 4-in Brick A with portland cement-lime mortar.

5. 4-in Brick A with high-bond mortar.

6. 4-in Brick S with high-bond mortar.

7. 4-in Brick B with high-bond mortar.

8. 4-2-4-in cavity walls of hollow concrete masonry units with masonry cement mortar.

9. 4-2-4-in cavity walls of Brick B and hollow concrete masonry units with masonry ce- ment mortar.

10. 8-in composite walls of Brick B and hollow concrete masonry units with masonry ce- ment mortar. Eight or more wall panel specimens of each of the 10

types listed above were tested by applying uniform

transverse loads, uniform axial compressive loads, or a combination of both types of loading. The wall

specimens were nominally 4-ft wide and 8-ft high.

Two wall specimens of each type were axially loaded

to compressive failure with no transverse loading.

These walls were 4 X 8 ft except for two walls of each

1
of the 4 types of brick walls given in the preceding

list, which were nominally 2-ft wide and 8-ft high.

The capacity of the testing machine used in the tests was not sufficient to develop the compressive

strength of 4 X 8-ft brick wall panels.

For the 10 wall systems listed above, companion

prism specimens were constructed. These prisms were tested to determine their strength in compression and in flexure. In the subsequent analysis in section 8, wall panel

strength is compared to prism strength. The data

from both the wall and prism tests are used to develop analytical methods for the determination of the transverse strength of various types of masonry

wall construction.

The conclusions from this investigation are compared with present design practice in section 9.

3. Materials

All materials used in the wall panel construction were available commercially and were representative of those commonly used in building construction.

3.1. Brick

Three types of brick designated as A, B, and S were used in the construction of the wall panel

specimens. The dimensions and physical properties

of these types of brick are presented in table 3.1, and

brick units are shown in figure 3.1. The three types of brick were selected to cover a reasonable range of compressive strengths and ab- sorption rates that represent high-strength brick cur- rently used in building construction. Brick A were cream colored, extruded, wire-cut units with 3 round

cores. Brick B were gray, extruded, wire-cut units

with 5 oval cores. Brick S were red, extruded, wir

cut units, having no cores.

15 5/8"

o o o

BUCK (

K

' " h

id

' in STRETCHED BISCK llooooo

BUCK I

8 ' in CORNER BLOCK

iis

BRICKS

15 5/8" CD CD CID

e in KERF BLOCK

4 in BLOCK

:i

I

III

k

1

8- in SOLID BLOCK

Figure 3.1. Masonry units. '

3.2. Concrete Masonry Units ['

Three types of concrete masonry units were use

in the construction of the wall panel specimens: ^

1. 8-in, 2-core hollow block

2. 4-in, 3-core hollow block

3. 8-in solid block

The dimensions and physical properties of thes units are given in table 3.2. The units are illustrate

in figure 3.1. The 8-in hollow block, 4-in hollo block, and the 8-in solid block were made c lightweight expanded-slag aggregate and portlan|

cement. Three shapes of 8-in hollow units were use

in the wall panels: 1. stretcher block (two ope

ends), 2. corner block (single open ends), and 3. ke\

Table 3.1. Dimensions and physical properties oj brick '

Brick Gross Net Compressive Motlulus Absorption Saturation

! Initial designation Width Length Height area sohd strength of per cent coefficient rate of 1- area (Gross area) rupture absorption

in in in in- % psi psi 24 -hr 5-hr g per 30 ira^ cold boil per min \ A 3.63 7.97 2.25 28.9 89.7 14,480 850 3.33 5.1 0.65 6.2

s B 3.75 8.08 2.25 30.0 80.8 20,660 760 2.7 3.3 0.82 2.6 j

S 3.62 8.00 2.26 29.0 100.0 17,560 740 7.6 10.5 0.72 19.8 ^

9

if

i

Brick were tested in accordance to ASTM C67-66 [1].' Each value in the table represents the results of tests of measuremenl

of five specimens. <

' Figures in brackets indicate literature references given in sec tion 12.
Table 3.2. Dimensions and physical properties of concrete masonry units '

Masonry

unit designation

Width ?th Height

Minimum

face shell thickness

Gross

area Net solid area Compressivestrength (Gross area)

Weight

of concrete Absorption

in hollow expanded slag

[Tlblock

jj4-in hollow jexpanded slag

I block

^Is-in solid Jexpanded slag

,1 block

75/8

3-V8

75/8

m

I5S/8

15-^8

15=/8

in 7^8

75/8

r/4

in- 119.1

56.6

119.1

%

.52.2

72.4

100.0

psi 1100

1.530

3370

103.0

101.7

14.3

14.9

(")

" Concrete masonry units were tested in accordance to ASTM C140-65T [2]. Each value in the table represents the results of tests or measurements of five specimens.

'' Since the units were acquired at the same time from the same producer of the other two types of expanded slag block, it is assumed

that the weight of concrete and the absorption are approximately the same as for the other two units.

block. The kerf block units were cut into two pieces

jand used at the ends of alternate courses. All values

I for 8 X 8 X 16-in block given in table 3.2 are for stretcher block.

I 3.3. Mortar

I

' Three types of mortar were used in the wall

panels:

' 1. Masonry cement mortar

2. Portland cement-lime mortar

3. High-bond mortar

|i The masonry cement and portland cement-lime

1-imortars were selected to represent conventional

j'Imasonry construction, and serve as a basis for comparison with masonry containing high-bond mortar.

"1^ The masonry cement mortar contained 1 part by

"([volume of masonry cement and 3 parts - by volume

f of masonry sand and met the requirements for type

J-N mortar described in ASTM C270-68 [3]. This

f^mortar will be referred to as 1:3 mortar. The portj land cement-lime mortar contained (by volume) 1

I, part of Type 1 portland cement, 1 part hydrated

lime, and 4 parts of sand. This mortar will be

referred to as 1:1:4 mortar.

' The high-bond mortar contained 1-ft-^ (1 part) of

Type 1 Portland cement, 1-ft' (1 part) fine limestone

(passing a No. 200 sieve), 4-ft'^ (4 parts) of masonry

sand, and 4 gallons of liquid additive. This additive, was a commercially available polyvinylidene

chloride having the trade name of Sarabond.-'

il! ^ Sand was proportioned on the basis of an average (loose volume) unit weight of 90 lb/ft'. A proprietary commercial product produced by fhe Dow

Chemical Company.

The washed river silica sand used in the three

types of mortars had a gradation conforming to the

requirements of ASTM C144-66T [4]. The fineness

modulus of the sand was 1.95. The mortar materials were obtained from the same source during fabrication of the wall panel

specimens, and were essentially uniform.

The mortars were mixed in a conventional barrel

type mixer with rotating blades. Retempering was

permitted, but mortar was not used that was more

than three hours old. Two-inch mortar cubes were made along with the wall panels and prism

specimens. The mortar cubes were air cured in the

laboratory under the same conditions as the wall

panels and prism specimens. Compressive strengths

of the mortar cubes with respect to the type of wall

construction and type of mortar are given in table

3.3. The compressive strengths of the mortar cubes

representing mortar in the prism specimens are given in table 3.4. The mortar cubes were tested at approximately the same age as the corresponding

wall panel or prism specimen.

4. Test Specimens

A detailed description of the wall and prism

specimens and the methods of fabrication of these

specimens are presented in this section.

4.1. Description of Walls

AU the wall panel specimens in this series of tests were constructed in running bond^ and were

* Units in adjacent courses overlap by 50 percent and head

joints in alternate courses are in vertical alignment.

410-021 OL - 71 - 2
Table 3.3. Mortar cube compressive strengths for different wall construction '

8-in 8-in 8-in 4-2-4 in 4-2-4 in

1 8-in

' Hollow Hollow Solid 4-in 4-in 4-in 4-in Cavity Cavity Comp.

block block block Brick A Brick A Brick S Brick B block and brick and brick anc- block block block

"(1:3) (h.b.) (1:3) (1:1:4) (h.b.) (h.b.) (h.b.) (1:3) (1:3) (1:3) '

660 7590 400 900 7410 8010 8210 480 720 530

) 500 9460 490 1500 7580 6640 7490 810 910 510 ( 510 430 1080 6850 6980 7830 660 500 780

430 400 930 8480 8430 490 420 i 470 7410 430 670 ) 6930 380

Average values (

525 8710 440 1100 7280 7530 7720 650 570 580 '

" Mortar cube strengths are given in psi and each value represents the average of 3 tests. The cubes were air cured along with th| wall specimens and tested at ages between 35 and 42 days.

'' Mortar type.

Table 3.4. Mortar cube compressive strengths for prism

specimens

Type of No. of Compressive

mortar specimens Age strength

(lays psi

1:3 3 180 345

1:3 3 38 460 High-bond 3 180 4920

panels depended on the type of masonry units anti the type of construction used. Outside cross-sec

tional dimensions, areas and moments of inertia o) net cross sections for each of the 10 types of mason'

ry walls are shown in figures 4.1 through 4.3. A brie

description for each of the 10 types of walls is as fol lows:

nominally 4-ft wide and 8-ft high with the exception

of eight brick walls which were 2-ft wide and 8-ft high. The thickness and cross section of the wall

WALt TYPE 4 i 5

* = 179 in

In = 195 in' A = 89 in'

WALL TYPE 1.

A = 167 in^

In = 1415 in"*

8-in 2 CORE HOLLOW BLOCK |1:3 MORTAR)

WALL TYPE 2

4. 4-in BRICK A |1:1:4 MORTARI

5.4'in BRICKA |HIGH BOND MORTAR j

WALL TYPE 6,

A = 167 in'

ln= 1415 in"*

J

3 5/e

A = 179 in'

In =195 in'

A = 89 in^

8 in 2 CORE HOLLOW BLOCK |HIGH BONO MORTAR]

WALL TYPE 3.

T

4'in BRICK S |HIGH BONO MORTARI

WALL TYPE 7

7%

A = 362 in

l„= 1 755 in"*

J 3 3/4 A = 187 in

Ip = 219 in* A = 93 in'

8'in SOLIO BLOCK |1 3 MORTAR]

Figure 4.1. Cross-sectional dimensions of block walls.

1

4. in BRICK B (HIGH BOND MORTAR]

Figure 4.2. Cross-sectional dimensions ofbrick walls.
WALITYPE 8 47 1/2"

BLOCK

riVIT V BLOCK 1±.

XT

t = 230 in

In = 354 in*

4 2-4-in CAVITY. BLOCK AND BLOCK 11:3 MORTARI

WALL TYPE 9

BLOCK

BRICK

BLOCK BRICK

A = 115 in' A = 178 in^

In = 177 in"* = 209 in'

4-2-4 in CAVITY, BRICK ANO BLOCK |1:3 MORTARI

WALL TYPE 10

BLOCK

BRICK

BLOCK BRICK

A = 115in^ A = 178in^

8-in composite, brick and block |1:3 mortar]

Figure 4.3 Cross-sectional dimensions of cavity and composite

walls.

1. 8-in hollow concrete block walls with type N (1:3)

mortar

The walls contained 8 X 8 X 16-in whole units having two cores and half-units that were obtained by

cutting kerf block. The walls were constructed in running bond with type N mortar and the bottom

course contained a half unit at each end. The bed

and head-joint mortar was applied only to the face

shells (face-shell bedding) with the exception of the

outside edges at the ends of the walls where mortar was applied to the end webs. Stretcher block were

used in the wall interior. At the ends, corner block

and one-half kerf block, respectively, were used in alternate courses.

2. 8-in hollow concrete block walls with high-bond

mortar

This type of wall was constructed in the same way

as the 8-in hollow concrete block walls previously

described, with the exception that a high bond mortar was used instead of ASTM type N masonry ce- ment mortar.

3. 8-in 100 percent solid concrete block walls with

type N (1 :3) mortar

These walls were constructed in the same manner

as the 8-in hollow block walls except that 100 percent solid block was used. Full bed and head mortar

joints were used in constructing these solid wall

panels.

4. 4-in brick (A) walls with 1:1:4 mortar

The walls were 4-in thick and were constructed

using Brick A and Portland cement-lime mortar. Brick were laid in running bond with full bed and

head joints. These walls were intended to be control

specimens for all four types of single wythe brick

walls, all of which were built in a similar manner.

5. 4-in brick brick (A) walls with high bond-mortar

This group of 4-in thick wall panels were made of

Brick A and high-bond mortar. Brick were laid as previously described.

6. 4-in brick (S) walls with high-bond mortar

These 4-in thick brick walls were constructed

using Brick S and high-bond mortar. Brick were laid as previously described.

7. 4-in brick (B) walls with high-bond mortar

These 4-in thick brick wall panels were constructed using Brick B and high-bond mortar. Brick were laid as previously described.

8. 4-2-4-in cavity walls of hollow concrete block with

type N (1:3) mortar

In these cavity walls 4-in hollow concrete block were laid in running bond and mortar was applied to the entire horizontal surfaces and the vertical end

surfaces of the block. The head joints of opposite

wythes of block were staggered by starting the bot- tom course of one wythe with a half unit and that of

the opposite wythe with a whole unit. Facing and

Lacking wythes were bonded with metal ties in ac- cordance with American Standard A41.1 [5].

Descriptive details of the ties and their locations in the wall are provided in section 4.2 on wall fabrication.

9. 4-2-4-in cavity walls of brick (B) and hollow

concrete block with type N (1 :3 ) mortar

The cavity walls containing brick were made with

a facing of Brick B and a backing of 3-core 4 X 8 X

16-in hollow concrete block. The brick and block were laid in running bond and the mortar joints were made solid in the brick facing wythe and in the

5
concrete block backing as previously described.

Metal ties were provided as in the previous wall

system.

10. 8-in composite brick (B) and hollow concrete block walls ivith type N (1:3) mortar

In the 8-in composite wall panels the facing was made of Brick B and the backing of 4-in hollow concrete block. Bonding consisted of a brick header

course in every seventh brick course.

Full head and bed joints were used in the brick

facing and 4-in block backing. The back of the brick

facing was pargeted'' with mortar and when the

backup block was laid a conscious effort was made

to fill the gap between brick and block with mortar.

4.2. Fabrication of Walls

The masonry wall panels measuring nominally 4

X 8-ft and 2 X 8-ft were fabricated and air cured in a controlled environment laboratory that was maintained at 73 °F±3 °F and 50 percent ±5 percent

relative humidity. All of the wall specimens were

constructed by the same experienced mason using

techniques representative of good workmanship.

The walls were built in running bond with the mortar

joints on both faces of the walls cut flush and not

tooled. The bottom course of masonry was laid in a full bed of mortar in a steel channel of suitable width and

length to facilitate moving and placement of the test panel in the testing machine. Walls were erected

between wooden frames that were braced in two

planes to keep them perpendicular to the floor. The

bed joint locations were marked on the wooden

frames in order to control the thickness of these

joints through the entire series of tests. In controlling the bed joints for the various types

of walls made of concrete block or clay brick at a thickness of f in, the height of 3 brick and 3 joints was taken as 8 in. In a similar manner the height of one concrete masonry unit and one joint was also taken as 8 in. The mason kept the face of the wall which was away from him in alignment using a horizontal line and level. This face was designated as the outer face

of the wall. The near face of the wall to the mason

was designated as the inner face. In aU walls the first unit was laid at the end of the course without head joint mortar. Head joints were

subsequently formed by buttering one end of a unirl*

just before placing it in the wall. In this way all heac *

joints were "shoved" and there were no closure

units or slushed head joints. i Two series of cavity walls were constructed with a 2-in space between inner and outer wythes. One^

series was built of one wythe of brick and one wythe''

of 4 X 8 X 16-in hollow concrete units. The other se^

ries was built with two wythes of 4 X 8 X 16-in hollow^ concrete units. The first course of each wythe wasj

set in a common bed of mortar and for the remaindei

of the wall construction the cavity was kept clear ol mortar droppings.

The top course of the cavity walls to be tested witF no vertical load was bridged with a 2-in thick course

of 8 X 10-in solid units laid in a full bed of mortar, sc' that the upper courses of the wythes as well as th^

lower courses would be connected during the flexu'

ral tests. Cavity walls which were tested in flexure

under vertical load had their upper courses held ir* place by the application of the vertical load and didj*' not require bridging.

j The facing and backing wythes of the cavity wall^ were tied together in accordance with American

Standard A41.1. The commercial ties used in these

walls were ^-in diameter steel rods bent into a completely closed rectangle measuring 2 X 6 in with^ the ends of the rod meeting at the middle of the 2-in sides. The two 6-in sides of the ties contained a i-ir drip crimp** at mid-length. Ties were placed in al: ternate bed joints of block courses starting with the

joint above the second course. Lateral spacing of the! ties along a bed joint was 30-in on centers starting at' points 2 i-in from opposite ends in alternate tied joints. This spacing resulted in a pattern of 2 ties in alternate joints staggered by 15 inches. The waE

panels contained 10 metal ties; therefore, there wa; nominally one tie for each 3.2 ft^ of wall area. Two-inch mortar cubes were made along with the wall specimen's and were air cured in the laboratory

under the same conditions as the wall specimens. |

4.3. Description and Fabrication of Prisms

Tests were carried out on a large number of small

specimens in order to determine the properties of the various types of masonry. Compression tests were conducted on 2-, 3-, and 5-block high prisms

and on 5-brick high prisms. The block prisms were.

^ A coat of mortar was applied to the vertical face. " A triangular vertical dent which drains accumulated water.

6
il ([constructed in stacked'' bond. The brick prisms were

constructed in running bond with a whole unit in the

first, third, and fifth courses and 2 half-units in the

second and fourth courses. The prisms constructed using the 8 X 8 X 16-in

hollow block contained only face-shell mortar

bedding. Full bed joints were used in fabricating the

, prisms in which the 8 X 8 X 16-in solid and 4 X 8 X

d 16-in hollow block were used. The brick prisms were

constructed with full head and bed mortar joints.

Flexural tests were carried out on 2-block high

prisms in accordance with ASTM Standard E149-66

[6]. These prisms were made of both hollow and

solid 8 X 8 X 16-in block and 4 X 8 X 16-in hollow

block and were constructed in the same manner as

the prisms used for compressive tests. Flexural tests were also conducted on 7-course brick prisms tested

as beams with the 8-in dimension of the brick

j horizontal, which were loaded at the third points over a 16-in clear span. These 7-course brick prisms were constructed in stacked bond with full bed mortar joints.

The prisms were constructed from the three types

of mortar described in section 3.3. Two-in mortar

I cubes were made along with the small specimens

and were air cured in the laboratory under the same

j conditions as the prisms.

I The decision on size and type of prisms was

j governed by the following considerations:

Concrete block

(a) Compression: At the present time there is no standard ASTM test for determining the

compressive strength of concrete block

prisms. The National Concrete Masonry Association (NCMA) presently recommends a prism not less than 16 inches in height with

a height-to-thickness ratio of two. It was felt that end restraints may have too much effect on the strength of a two-block high prism.

Most of the tests were, therefore, conducted

on three-block high prisms, but some tests on two-block and five-block high prisms were

also conducted for comparison.

Traditionally, block prisms are built in stacked bond and not in running bond.

This construction is more practical and

stacked bond prisms were, therefore, used

in this program.

' Units in adjacent courses do not overlap, so that all head joints are in vertical alignment.

(b) Flexure: It was decided that flexure tests of

prisms would be conducted in accordance

with estabhshed ASTM Standard E149-66

which requires two-block high prisms laid in stacked bond.

Brick

(a) Compression: At the present time there is no standard ASTM test for determining the

compressive strength of brick prisms. The

Structural Clay Products Institute (SCPI)

presently recommends a prism not less than

12 inches in height with a height-to-thickness

ratio of 5 but not less than 2. The 5-brick high

prisms used in this program had a height-tothickness ratio of 3.5 and a height of 12.8 in.

(b) Flexure: There is presently no standard test for the flexural strength of brick prisms. The

7-brick stacked bond prism which is con- venient for fabrication and testing was

adopted as a specimen for determining the

modulus of rupture of brick masonry.

5. Testing Procedures

5.1. Wall Tests

A wall panel in position for testing is shown in figure 5.1. The vertical load was applied concentrically to the wall and was transmitted from the head

of the 600,000-lb capacity hydraulic testing machine

through a 12 i-in deep loading beam, a 1-in square

steel bar centered along the width of the wall, and a

2-in steel plate that covered the top area of the wall. A piece of i-in fiberboard was used between the top

of the wall and the 2-in steel plate to provide a uniformly distributed load to the top of the wall. The

bottom of the wall was built inside a steel channel

which rested on a i-in fiberboard.

The transverse load was applied uniformly by an

air bag, made of 20-mil polyvinyl sheeting, that was

84 in long and extended across the entire width of

the wall. A steel reaction frame attached to three

wheels provided the support for the air bag on one

side of the wall specimen. On the opposite side of

the wall, upper and lower horizontal reaction bars were spaced 82 i-in apart, and attached to another

reaction frame on wheels.

The two reaction frames were rolled into position on either side of the wall and bolted together at the

four corners. On the loaded side of the wall the air
Figure 5.1. Experimental setup forflexural test.

bag was held against a sheet of plywood attached to the reaction frame. A sheet of rubber on both sides

of the air bag provided protection from abrasion. The

reaction bars on the opposite face of the wall were

1-in wide, extended across the entire width of the

wall specimen, and were faced with teflon over

leather to provide a quarter-inch thick resilient material. The steel reaction frame, which has the

air bag connected to it, is shown in figure 5.2 prior

to its connection to a specimen.

The compressive load was applied vertically to the

wall specimens at a rate of 60,000 lb per minute up

to failure or to a load level that was maintained while

the transverse load was appUed.

The inlet tube to the air bag was connected to a hand-regulated compressed air line (100 psi max- imum pressure) to apply the transverse load. Air bag

pressure was recorded by using a piezo-resistive

pressure transducer connected to the air bag outlet tube. Continuous visual monitoring of the air bag

pressure was accomplished by using a mercury

manometer that was also connected to the outlet tube. The wall specimens were loaded transversely

at a rate of approximately 0.30 to 0.35 psi of air pres- sure per minute.

In all tests where vertical loads were applied, the

vertical compressive load was applied first. When

the desired vertical load level was reached, theji » transverse load was applied and gradually increasedi

until the specimen failed. The walls were tested at an approximate age of 35

days after being air cured in the controlled environ-'

ment laboratory. They were moved from the fabrication area to the testing machine by a forklift truck. In positioning a wall specimen in the testing)

machine, the steel channel in which it was built rested on i-in fiberboard that was placed on top of 4^

in thick steel blocks. The steel blocks can be seen in figure 5.2. The 4-in thick steel blocks bore on the

platen of the testing machine and were spaced 8 in apart to allow the withdrawal of the forklift truck;

prongs after positioning of a wall for test.

y 5.2. Instrumentation for Wall Tests

j Vertical applied loads, horizontal applied loads,

and lateral deflections of the wall specimens were measured and recorded digitally on paper tape by an

automatic electronic multichannel data logging"

system. The vertical loads were measured with a.^ bonded-foil strain gage pressure transducer that was' attached to the hydraulic load measuring system of

the testing machine. The pressure in the air bag that^ was used to apply the uniformly distributed horizon- i
tal load was measured with a solid-state pressure

1 transducer having a range of 0-50 psi.

The lateral deflection of the wall specimens was

i measured with two transformer-type displacement

transducers (LVDT's), calibrated to read increments

f* of ±0.0001 in. which were clamped at mid-height to

6-ft lengths of 1-in diameter aluminum tubing. As

shown in figure 5.1., the tubing was attached along

the centerline of the two vertical edges of the wall at

• points near the reaction bars in a manner that alI lowed it to pivot at each end. The lower end of the

^ j tubing was allowed to slide in a vertical direction

||j without lateral movement. The end of the core of the

j! displacement transducers was threaded and loosely

I screwed into a tapped hole in an aluminum plate that

j was attached to the face of the wall at mid-height,

j The attached plate extended beyond the edge of the

|! wall so that the core of the transducer was free to

j move in or out of the transducer coil. In most wall

tests, the displacement transducers were removed

i:

just prior to failure to prevent damage to equipment.

! However, in most cases, deflections were measured

beyond the maximum load. The output from the pressure transducers and the

I displacement transducers provided signals that were

fj recorded on automatic data-recording equipment. A

[j complete cycle of scanning and recording took 5

,j seconds. Data were recorded at 5-second intervals

ij during transverse loading for walls vdthout any com-

' pressive load or those failing at transverse loads of

Ij 1 psi or less. For the wall tests requiring larger transj verse loads before failure, data were recorded every

ij 30 seconds. The printed tape record was converted

1 to load-deflection plots by use of conventional high

|| speed digital computers.

I 5.3. Prism Tests

\ A description of the various types of prisms it

j given in section 4.3.

I The prisms subjected to compressive tests were

loaded at a rate of 50,000 lb per minute. Most of the

compressive prisms were capped at top and bottom

i| with high-strength plaster. Since fiberboard was

i used at the top and bottom of all wall panels to dis- tribute evenly the compressive load, some of the

j; prisms were tested using fiberboard instead of highi strength plaster to investigate the effect of different

capping materials on the prism strength.

I The flexural strength of the masonry prisms was

determined by a flexural bond test and a beam test

for concrete masonry and brick masonry, respectively. The flexural bond strength was determined by

testing two-block high prisms that were clamped in metal frames at both the top and bottom of the prism

and loaded eccentrically 10 in from the longitudinal

centerline of the prism. This test method is described in ASTM Standard E149-66.

The 7-course brick prisms were tested as beams

with the 8-in dimension of the brick horizontal. The

prisms were supported approximately along the centerline of the two end bricks as simple beams with

16-in spans. Symmetrical loads were applied at the

third points of the beams.

5.4. Instrumentation for Prism Tests

The modulus of elasticity of the concrete masonry was determined by testing 8-in hollow block prisms.

Three-block high prisms constructed in stacked

bond were instrumented. The change in length of the

prisms subjected to compressive loads was measured with LVDT's which were mounted vertically on the sides of the specimens along the centerline.

The gage length extended between the centers of the

top and bottom units and was 16 in. This report also presents test data on the modulus

of elasticity of brick masonry. These tests were per- formed by the National Bureau of Standards in a dif- ferent testing program. Specimens for these tests were 16 X 16-in and 24 X 24-in monowythe brick

piers built in running bond. Brick A with portland ce- ment-lime mortar and Brick A with high-bond mortar were used in two series of pier tests. These piers were instrumented by LVDT's mounted vertically on

both faces along the centerline of the long side of the

piers. Gage lengths of 10 in and 16 in were used for the 16 X 16-in and the 24 X 24-in piers, respectively.

6. Test Results

6.1. Wall Test Results

A summary of results of the wall tests is given in tables 6.1 through 6.5. Values of the transverse load

and midspan deflection corresponding to the point

where the load-deflection curves deviated from

linearity and values of the maximum transverse load

and deflection corresponding to that load are given

for various levels of imposed compressive vertical load. It may be noted that the maximum transverse

load usually does not represent the final failure load,

since transverse loads dropped off before failure. 9
Table 6.1. Summary of test results on 8-in hollow concrete block walls

Wall

panel

desig. Typeconstruction Typemortar Compressive

vertical load

Deviation from a linear load-deflection curve occurred at: Maximum

transverse

load

Midspan deflection at maximum

transverse load Transverse

load Midspan

deflection

lb psi in psi in 1-1 o-in liollow 1:3 A

U 0.12 0.00 0. 12 0.23

1 — '> block Z\).\)\J\) 1.82 0.02 2.63 0.83

/I A AAA 3.05 0.05 4.65 0.86 1-4 60,000 4.28 0.07 6.03

l-.S 120.000 6.31 0.13 6.31 0.13 1—0 1 Q C AAA " 95.000 0.01 "135,000 0.06

1 7 1 /

1 /I O AAA 14-o,UUU "115,000 0.00 "148,000 0.06

Z 1 o-in hollow 111 high-bond AU 1.90 0.02 1 .90 0.02

z z DloCK A

1.54 0.02 1.58 0.02 z—

0

AU 2.00 0.03 2.00 0.03 z—

4

40,000 4.48 0.05 5.17 0.91 Z—.D 75,000 6.93 0.08 6.93 0.08 2-6 130,000 6.13 0.09 6.30 0.09 2-7 150.000 4.41 0.07 5.27 0.08 2-8 150,000 5.32 0.05 5.41 0.05 2-9 150,000 "150,000 0.01

"Walls were tested by application of only vertical loads. Values given are for vertical loads.

Table 6.2. Summary of test results on 8-in solid concrete block walls

Wall

panel

desig. Type

construction Typemortar Compressivevertical load

Deviation from a linear load-deflection curve occurred at:

Transverse

load Midspandeflection

Maximum

transverse

load

Midspan deflec- tion at maximum

transverse load

3-1 3-2

3-3 3-4

3-5

3-6

3-7 3-8 3-9

3-10

3-11

3-12 3-13

-in solid block1 :3

lb00

25,000

50,000

100,000

150,000 200,000

300,000

400,000

500,000

530,000

490,000

597,000

psi 0.15

0.22

1.66 3.07

2.23 6.79

7.65

7.65 11.43 5.04

in 0.00

0.01 0.05 0.06

0.02

0.07 0.10

0.04

0.13 0.08

psi 0.34

0.29

3.29

5.94

8.17

15.12 15.26

" 13.80

" 15.59 6.10

13.70

" 395,000 0.04 "597,000

in 0.34

0.91 0.49

0.61 0.23

0.79 0.40

0.20

0.19

0.29

0.03

" WaOs were tested by application of only vertical loads. Values given are for vertical loads.

' Specimen did not fail, testing was halted because the loading mechanism capacity was exceeded.

Deflections at the actual point of failure are in most

cases not recorded, since the instrumentation was

removed prior to this point. In some of the wall tests the transverse loading

had to be terminated due to the limited capacity of

the plastic air bags. Loading was halted for this reason at a horizontal load of approximately 15 psi.

Three wall tests which were stopped in this manner

are noted in table 6.2, and one such test appears in table 6.5. The brick wall specimens subjected only to compressive load had a nominal width of 2 ft because of

limited testing-machine capacity. In the test data

given in t-ables 6.3 and 6.4 the results were adjusted

to correspond to the other wall data, which were ob- tained from 4-ft wide wall panels, by doubling the

measured test loads. For most of the different types of wall panels at least two specimens of each type were tested at zero compressive load to determine flexural tensile strength.

Table 6.6 contains a summary of computed

average compressive stresses and moduli of rupture

for the 10 different wall systems. Figures 6.1 through

10
Table 6.3. Summary of test results on brick A walls

WaU

desig. Type

construction Typemortar

UI II JJI "S5l V tr vertical load

Deviation from a linear load-deflection curve occurred at: Maximum

transverse

load

Midspan deflection at maximum

transverse load Transverse

load Midspandeflection

lb psi in psi in 4-1 1:1:4 0 0.12 0.01 0.20 0.02 4-2 4-in brick A 0 0.20 0.03 0.20 0.03 4-3 100.000 2.21 0.12 3.38 0.51 4-4 200.000 3.70 0.18 5.20 0.54 4-5 250,000 2.82 0.16 5.48 0.61 4-6 300.000 3.90 0.31 5.14 0.58 4-7 350,000 1.78 0.10 4.47 0.55 4-8 " 562.000 4-9 " 576.000

5-1 high-bond 0 0.60 0.02 0.80 0.03 5-2 4-in brick A 0 0.58 0.02 0.80 0.03 5-3 100.000 2.70 0.11 3.88 0.42 5-4 200.000 4.88 0.20 6.84 0.65 5-5 250,000 4.90 0.21 7.00 0.53 5-6 300,000 5.62 0.31 6.90 0.59 5-7 350,000 5.44 0.31 6.73 0.59 5-8 400,000 5.10 0.23 8.29 0.67 5-9 " 844,000 5-10 " 872,000

" Actual test was performed on 2-ft wide panel and values were adjusted for 4-ft width.

Table 6.4. Summary of test results on brick B and brick S walls

Wall

Deviation from a linear load-deflection curve Maximum Midspan deflec- panel Type

construction Type Compressive

vertical load occurred at: transverse

load

tion at maximum

transverse load desig. mortar Transverse

load Midspan

deflection

//, psi ;>! psi in 6-1 high-bond 0 0.40 0.02 0.40 0.02 6-2 4-in brick S 0 0.45 0.02 0.54 0.03 6-3 140,000 2.95 0.20 3.94 0.,S8 6-4 220,000 4.02 0.28 7.10 0.72 6-5 290,000 4.08 0.24 7.10 0.72 6-6 350,000 4.94 0.29 7.13 0.60 6-7 400.000 3.99 0.22 6.94 0.69 6-8 " 1.088,000

" 1,050.000

0

6-9

7-1 high-bond 1.10 0.03 1.10 0.03 7-2 0 1.34 0.04 1.34 0.04 7-3 4-in brick B 160.000 4.67 0.13 6.91 0.56 7-4 320.000 7.98 0.21 11.29 0.59 7-5 320.000 6.54 0.25 9.68 0.70 7-6 600.000 6.52 0.23 11.21 0.63 7-7 "948.000 7-8 " 970.000

" Actual test was performed on 2-ft wide panel and values were adjusted for 4-ft width.

410-021 OL - 71 - 3 11
Table 6.5. Summary of test results on cavity and composite walls

Wall

panel

desig. Type

construction Typemortar Compressive

vertical load

Deviation from a linear load-deflection curve occurred at: Maximum

transverse

load

Midspan deflection at maximum

transverse load Transverse

load Midspandeflection

/6 psi / /? psi in O 1

/l- V in /^Qi/itv TP-Z. T" 111 LdVliy 1 . o 0 0.23 0.01 0 23 0 01 o z block- block 0 0.21 0.01 0 91 0 39

o o

1 7/1 0U.UVOQ 0 '^7 o.o t fl— O d.4- Z.o / n 1

Q

d. 97 0U.40d^ 8-5 150,000 /I on n 90 5.42 0.56 8-6 200,000 /I ^^0 nu.ozQ9 5.02 0.39

ft7

O ( 93Q 000 o ni ^' 9^8 000 0 02

ft-S o o

9i;d, 000 '/ 1 ono n 09 " 9=^4 Z04',WVJO 000

y L

/I. V /l in /^Qi/it^r

T' T" 111 CdVliy 1

• ^ Q 0.26 0.01 0 26 0 01 0—9 brick- block 000 1.15 0.08 9 90 0 7fi 7 O 70i u,vwo 000 9 01^ 0 Oft ^ Q7

Q—d. 1 00 000 o.oo 0 10 1ft O. iO 0U.40dS 9-5 200,000 n 1 /I 7.50 0.40 9-6 250,000 o.oo n no 8.18 0.34 9-7 •^00 000 o.o / U.l'* 6.53 0.36

Q-ft 7 o ^fXS 000 f/ 1 7Q 000 n ni U.Ul " ^(SO OOfl 0 11^ O. lO

Ifl—

1

IVJ 1 o-in composite n U.o / n n9 U.UZ 0 7^ 0 0^

1 0—9 bnck-block AO 000 3.04 0.05 d4. 7^4 O 11.14" Id

ft^ 000 5.46 0.05 10.16 0.76 QO 000 5.92 0.10 1010.04"^d 0 M

10— 1 ^0 000 6.38 0.06 1 9 7fi u.oo 10-6 180,000 6.83 0.03 " 14.59 0.28 10-7 OCn AAA 9.11 0.09 13.87 0.21 10-8 400,000 "315.000 0.06 " 400,000 0.10 10-9 465,000 "355,000 0.09 " 465,000 0.26

" Walls were tested by application of only vertical loads. Values given are for vertical loads. Specimen did not fail, testing was halted because the loading mechanism capacity was exceeded.

Table 6.6. Summary of average compressive and flexural strengths of walls "

Wall panel

desig.

Average

compressive

load

Average

compressive

strength

Average modulus of rupture

Type of construction

Partial

fixity assumed

Pin ended assumed

1 8-in hollow block, 1 : 3 mortar

l.,p 141.5

l>si 847

psi6psi9

2 8-in hollow block, high-bond mortar 150.0 898 130 191

3 8-in solid block. 1 : 3 mortar 543.5 1500 15 22

4 4-in Brick A, 1 : 1 : 4 mortar 569.0 3187 50 75

5 4-in Brick A, high-bond mortar 858.0 4806 210 310

6 4-in Brick S, high-bond mortar 1069.0 6050 120 180

7 4-in Brick B, high-bond mortar 959.0 6140 300 440

8 4-2-4 in cavity block-block, 1 : 3 mortar 246.0 1071 23 34

9 4-2-4 in cavity brick-block, 1 : 3 mortar

8-in composite brick-block, 1 : 3 mortar

360.0 1229 (")

10 432.5 1476 '30 '44

" Average stress on net cross section; see figures 4-1, 4-2, and 4-3.

* No meaningful average stress can be computed. Based on I of transformed section.

12
li.lO are plots of transverse load versus vertical compressive load for aU the wall systems. The curves

jjhown in these figures approximately represent the

general trend of the maximum load data.

6.2. Description of Wall Failures

A brief, general description of the manner in

which the walls failed is given hereafter for each

type of waU construction. As indicated previously,

the walls were loaded axially with a uniform load and

the transverse load was applied uniformly over the

face of the wall that normally is considered the exterior face. The walls were loaded in compression

only, flexure only, or a combination of compression

and flexure.

500,000

400.000

300,000

200,000

100,000

O DEVIATION FROM LINEAR LOAD DEFLECTION CURVE • MAXIMUM LOAD

J t I I I I L

6 8 10 TRANSVERSELOAD.PSI

12 14

|Figure 6.1. Relationship between vertical compressive load and transverse load for 8-in hollow concrete block walls with Type N{1:3)

500,000

400,000

300,000

200,000

100,000

O DEVIATION FROM LINEAR LOAD DEFLECTION CURVE • MAXIMUM LOAD

10 12 14 TRANSVERSE LOAD, PSI

Figure 6.2. Relationship between vertical compressive loadand transverse loadfor8-in hollow concrete blockwalls with high bond mortar.

13
600,000 I

500,000 ,

O DEVIATION FROM lINEtR LOAD DEFLECTION CURVE • MAXIMUM LOAD

52 400,000 Q

300,000

200,000

Figure 6.3. Relationship between vertical compressive load and transverse load for 8-in solid concrete block walls with Type N(l:3)

mortar.

1,000.000

800,000

600,000

^ 400,000

200,000

o DEVIATION FROM LINEAR LOAD DEFLECTION CURVE • MAXIMUM LOAD

o

O i o

o

^ 1 1 1 1 1 1

6 8 10 12 TRANSVERSE LOAD,P$l

Figure 6.4. Relationship between vertical compressive load and transverse loadfor 4-in Brick A walls with 1:1:4 mortar.

14
1,000.000

800.000

600.000 -

400.000

200,000

0 2 4 6 8 10 12

TRUNSVERSE L0*D,PSI

LIRE 6.5. Relationship between vertical compressive load and transverse loadfor 4-in Brick A walls with high bond mortar.

1,000.000

800.000

600,000

^ 400,000

200,000

O DEVIATION FROMLINEARLOAD DEFLECTION CURVE • MAXIMUM LOAD

6 8 10 TRANSVERSE LOAD, RSI

IRE 6.6. Relationship between vertical compressive load and transverse loadfor 4-in Brick S walls with high bond mortar.

15
500,000

400,000

"S, 300,000 -

200,000

100,000

O DEVIATION FROM LINEAR LOAD DEFLECTION CURVE • MAXIMUM LOAD

6 8 10 TRANSVERSE LOAD. PSI

Figure 6.8. Relationship between vertical compressive loadfor 4-2-4-in cavity block and block walls with Type N(l -.3) mortar.

16
] 900,000 O DEVIATION FROM LINEAR LOAD DEFLECTION CURVE • MAXIMUM LOAD

400.000 -

TRANSVERSE LOAD. PSI

Figure 6.9. Relationship between vertical compressive load and transverse load for 4-2-4-in cavity brick and concrete block walls with Type N(l :3) mortar.

0 2 4 6 e 10 12 14 TRANSVERSE LOAD, PSI

Figure 6.10. Relationship between vertical compressive load and transverse loadfor 8-in composite brick and concrete block walls with Type N(1 :3 ) mortar.

17
1 . 8-in hollow concrete block walls ( 1 :3 mortar)

Under combined compressive and flexural loads,

the walls failed by tensile cracking along horizontal

joints near midspan when the vertical compressive

load ranged from 0 to 60,000 lb. For vertical compressive loads greater than 60,000

lb, vertical splitting occurred along the ends of the

walls near the top or the bottom. Generally the end

splitting extended from 4 to 6 courses from the top

of the wall. This type of end splitting failure was also observed in the 3-block high prism tests. The failure of wall 1-4 is shown in figure 6.11. This wall was subjected to a 60,000 lb compressive load prior to the application of the transverse uniform load.

WALL SPECIMEN 1-4

Figure 6.11. Failure of8-in hollow concrete block wall.

2. 8-in hollow concrete block walls (high-bond mortar)

Tensile failure occurred along a horizontal joint at midspan or near midspan in walls under combined

loading in which the vertical compressive load

ranged from 0 to 75,000 lb. Walls that were subjected to vertical compressive loads greater than

'

75,000 lb failed by splitting of the end webs of the concrete masonry units near the top or near the bot- tom of the wall. The failure of wall 2-8 is shown in figure 6.12. This wall had a compressive load of

150,000 lb prior to the application of the transverse

load.

j. 8-in solid concrete block walls (1:3 mortar)

Cracking along a horizontal joint at midspan or^ near midspan occurred in all wall panel specimens

under combined loading in which the superimposed

vertical compressive load ranged from 0 to 200,000

lb. At vertical compressive loads of 25,000 lb and

200,000 lb, initial cracking was observed at trans- verse air pressures of 2.8 psi and 11.4 psi, respectively. Walls subjected to vertical compressive loads

ranging from 300,000 to 400,000 lb did not exhibit

any cracking prior to stopping the application of transverse loads. In all wall tests in which the

compressive load ranged from 200,000 to 400,000 lb, the transverse loading was stopped because of either

excessive deflection of the wall or limitations on the

capacity of the transverse loading system. The

system was capable of applying a uniform load of 15

psi over the face of the walls. In walls subjected to vertical compressive loads greater than 400,000 lb, failure occurred by crushing accompanied by

splitting in the top one to three courses. Typical

failures for 3 different vertical compressive loads are shown in figure 6.13.

4. 4-in brick (A ) walls (1 :1 :4 mortar)

5. 4-in brick (A) walls (high-bond mortar)

6. 4-in brick (S) walls (high-bond mortar)

7. 4-in brick (B) ivalls (high-bond mortar)

The following general comments apply to the four

types of brick walls listed above. Under combined

loading conditions with low vertical compressive

loads, failure occurred on the tensile face of the waU

by cracking along a horizontal joint near midspan as shown in figure 6.14. An increase in the vertical compressive load resulted in flexural failures that were

initiated on the compressive side of the wall panel

specimen. At very high vertical loads, failure oc- curred suddenly by crushing. A typical crushing

failure is shown in figure 6.15.
OVERALLVIEW CLOSE UP VIEW

Figure 6.12. Failure of8-in hollow concrete block wall {specimen 2-8).

WALL SPECMEN 3-6 WALL SPECIMEN 3-8

Figure 6.13. Failures oj 8-in solid concrete masonry walls.

WALL SPECIMEN 3 12

410-021 OL - 71 - 4 19
Figure 6.14. Typical failure of brick walls with low vertical FIGURE 6.1S. Typical failure of brick walls with h compressive loads. compressive loads.
WALLSPECIMEN9-6 WALL SPECIMEN 9-7

Figure 6.17. Failures of brick-block cavity walls.

\ 8. 4-2-4-in cavity walls of hollow concrete block

I (1:3 mortar)

Tensile failure due to combined loading occurred

I in walls in which the applied compressive loads

I ranged from 0 to 100,000 lb. This type failure was in the horizontal joint on the tensile face of both wythes

ij of the wall near midspan. In tests where the comjj pressive load was greater than 100,000 lb, failure of

i the wall occurred by crushing. These crushing-type

failures generally occurred near the top of the wall. The tensile face and compressive face of wall 8-5 are shown in figure 6.16. This wall was subjected to a

I vertical compressive load of 150,000 lb prior to trans-

' verse load application.

I|

j: 9. 4-2-4-in cavity walls of brick (B) and hollow

j| concrete block (1:3 mortar)

ij

I Tensile failure due to combined loading occurred

I in walls in which the applied compressive load

ranged from 0 to 100,000 lb. For the wall subjected

to 200,000 lb compressive load, failure occurred by

buckling of the ties and subsequent crushing of the

masonry. In tests in which the compressive load ex- ceeded 250,000 lb, failure occurred by crushing accompanied by some splitting of the concrete masonry units near the top of the wall. The failures of walls

9-6 and 9-7 are shown in figure 6.17. These walls were loaded with vertical compressive loads of

250,000 and 300,000 lb, respectively, prior to application of transverse loads.

10. 8-in composite brick and holloiv concrete block

walls (1:3 mortar)

Under combined loading, tensile failures occurred on the block face along a horizontal joint near midspan for walls having vertical compressive loads that ranged from 0 to 130,000 lb. In wall tests where the

vertical compressive load exceeded 130.000 lb. the

walls either failed by crushing of the concrete masonry units or flexural loading had to be sus- pended because of the capacity of the horizontal

loading equipment. The failures of walls 10-4 and

10-5 are shown in figure 6.18. The vertical compressive loads on these walls were 90,000 and 130,000

lb, respectively.

6.3. Prism Test Results

The results of tests of masonry prisms in compression and flexure are presented in tables 6.7 and 6.8,

21
Table 6.7. Summary of compressive tests of prisms

Capping

material Number of Age at Compressive Compressive

Specimen designation Mortar type specimens

tested time of test strength (Gross area)" strength (Net area)''

davs psi psi 3" b1 c k li 1 §li prisms

ft-iii yj 111 injinjvv nnllnw 1 : 3 plaster 3 180 440 840

8-in hollow high-bond plaster 3 180 760 1460

8"in liollow high-bond fiberboard 4 66 420 800

8-in hollow higli-bond plaster 1 66 780 1490

8-in hollow 1 : 3 plaster 2 37 400 770

8-in hollow hi*^h-bond plaster 2 37 760 1460

8-in O III <;nliri oUlIU 1 : 3 plaster 3 180 1560 1560

8-in solid 1 : 3 plaster 2 37 1790 1790

4-in hollow 1 : 3 plaster 3 180 860 1190

^-in hollow 1 : 3 fiberboard 4 66 1020 1410

4'-m hollow 1 : 3 fiberboard 4 66 960 1330

2-block high prisms

8-in hollow high-bond plaster 3 180 780 1490

5"block high prisms

8-in hollow hi^'^h- bond fiberboard 4 66 440 840

5- course brick pnsms'

brick A, 1:1:4 plaster 3 35 5400

Krlnl: A 1111^11 1 cTn- ij\JiiyA nitn H plaster 3 35 6240

1 : 3 plaster 3 180 3010

1 : 3 plaster 2 63 4870

brick B 1 :3 fiberboard 3 63 4520

brick B 1 : 3 plaster OZ OO OlOU 1 (^n

brick B high-bond plaster 3 35 7650

brick S high-bond plaster 3 35 7320

Values were based on measured gross cross-sectional area.

'' Values were based on measured net cross-sectional area.

Table 6.8. Summary offlexural tests of prisms

Number of Age at Flexural Flexural Specimen designation Mortar type specimens time of test modulus of modulus of tested rupture '' rupture

^'

(lays psi psi 2-block high prisms

8-in hollow 1 :3 3 180 6 9

8-in hollow high-bond 5 38 192 231

8-in solid 1 :3 5 180 25 25

4-in hollow 1 :3 8 180 26 27

7-course brick prisms " brick A 1:1:4 3 35 35

brick A high-bond 3 35 370

brick B 1:3 5 180 54

brick B high-bond 3 35 430

brick S high-bond 3 35 220

" Tested over 16-in clear span and loaded at the third points.

'' Values were based on the gross cross-sectional area.

^' Values based on the net cross-sectional area.

22
Table 6.9. Values of average strengths of prisms

Specimen designation Mortar type Number of specimens

tested

Compressive

strength

(gross area)

Compressive

strength

(net area)

Flexural

strength

(gross area)

Flexural

strength

(net area)

3-block high prisms

8-in hollow

8-in hollow

8-in solid

4-in hollow

5-course brick prisms

brick A

brick A

brick B

brick B

brick S

2-block high prisms

8-in hollow

8-in hollow

8-in solid

4-in hollow

7-course brick prisms

brick A

brick A

brick B

brick B

brick S

1 :3 high-bond

1 :3

1 :3

1:1:4

high-bond

1:3

high-bond

high-bond

1 :3 high-bond

1 :3

1 :3

1:1:4

high-bond

1 :3 high-bond

high-bond

5

6

5

11

3

3

73

3

3

55

8

3

3

53

3

psi

420

760

1650 950

5400 6240

3580

7650

7320

psi

810

1460

1650 1320

psi [>si

6

192

25

26

35 37054 430

220

9

231

27

respectively. Table 6.9 summarizes average values

of strength that were used in the evaluation of the

correlation between wall and prism tests. From the values given in table 6.7, the compressive strength of the 3-block high prisms of 8-in hol- low block with high-bond mortar was 44 percent less when fiberboard was used as a capping material in- stead of high strength plaster.

It is also noted from table 6.7 that the compressive

strength was approximately the same for both the 3- block and 5-block high prisms constructed from 8-in hollow block and high bond mortar when fiberboard was used as a capping material. The type of capping

material had little effect on the compressive strength

of the 3-block high prisms constructed of 4-in hollow

block and the 5-course prisms made of Brick B. When fiberboard was used as a capping material,

failure occurred in the prisms constructed of 8-in hollow block and high bond mortar by vertical

splitting along the middle of the end webs of the

block. Vertical splitting accompanied by crushing

occurred in similiar specimens capped with high

strength plaster. Failure cracking in 3- and 5-block

high prisms constructed of hollow block is shown in figure 6.19.

7. Theoretical Discussion

7.1. Introduction

The theoretical approach developed in this section

parallels similar methods recently adopted for the

design of compression members in steel structures,

and proposed for reinforced concrete structures. The theory is subsequently used in the analysis of

the test results in this investigation and it is demonstrated that the general trend, as well as the magnitude of these test results, are closely predicted.

7.2. Interaction Between Vertical Loads and

Moments

7.2.1. General Discussion

Equilibrium conditions of short prismatic walls

acted on by a combination of vertical and horizontal

loads are shown in figure 7.1. The effect of deflections on the short-wall equilibrium condition is of

second-order magnitude and can, therefore, be

disregarded. The horizontal forces in this case act normal to the plane of the wall. Flexural tensile

strength is assumed to be relatively low when compared with compressive strength. Flexural compressive strength is assumed to equal af,'„, where f,'„, is
WALL SPECIMEN10-4

WALL SPECIMEN 10-5

Figure 6.18. Failures of composite walls.

Figure 6.19. Failure cracking in 3- and 5-block high prisms

constructed with hollow block.

I

iires

ek = t/6

6000

4000

2000

BRICK A, 1:14 MORTAR

BRICK A

HIGH BOND MORTAR,

K A, 114 MOR

/A'' e-iN HOLLOW BLOCK, TYPE N MORTAR

0.001STRAIN

0.002

Figure 7.1. Equilibrium conditions of a short wall under' combined transnerse and axial loads and stress-strain curves for masonry.

the compressive strength of masonry as determined

by tests on axially loaded three-block or five-brick

prisms. It will be demonstrated in section 8.3 that the flexural strength factor "o" is not necessarily

equal to unity and may depend on strain gradient. In figures 7.1(a) and 7.1(b) the simplified assumption is made that the stress-strain relationship of

masonry is linear up to the point of failure stress. Typical stress-strain curves for brick and concrete block masonry used in the test specimens of this ex- periment are shown in figure 7.1(c). The dotted lines drawn from the origin to the end points of these curves correspond to a stress-strain relationship that would lead to the linear stress block shown in figures

7.1(a) and (b). Note that while the stress-strain rela- tions observed in the specimens are not linear, the

linear approximation does not depart very much

from the actual curves. A stress block similar to the

actual curves would in all cases result in an ultimate

moment greater than the elastic moment

represented by figures 7.1(a) and (b). The linear ap- proximation to the stress block will therefore result

in a conservative prediction of moment capacity.

24
It must be emphasized that the conclusions drawn

from figure 7.1(c) are hmited to the information

available for masonry used in this testing program.

Figure 7.1(c) is not necessarily typical for all types of

masonry. Neither can it be stated with certainty that

stress-strain relationships derived from axial loading

of walls are similar to the stress-strain relationship

in flexure, when there is a strain gradient. However,

within the limits of the present state of knowledge,

the linear stress block represents a reasonable and

conservative approximation.

In figures 7.1(a) and (b) a free body is shown for a

section of a wall from its top to mid-height. Figure

7.1(a) illustrates the case of a cracked section at midheight. Figure 7.1(b) illustrates the case of an un- cracked section, where the vertical resultant force

at mid-height acts at the edge of the kern". If the wall

is assumed pin connected at its ends and therefore

does not develop any moments at its end supports,

the horizontal force V acting at the top of the wall can be determined as V = whl2. The internal forces

at mid-height must resist a moment: M = wh-jS. All compressive forces P' and tensile forces T' acting on

the base of the free body shown in figure 7.1(a) can

be replaced by a single resultant compressive force

which is equal and opposite to the axial force P and

acts at an eccentricity with respect to the line of action of P, such that: Pe = wh'-j8.

Moments produced by linear stress blocks with a maximum stress of afm as illustrated in figures

7.1(a) and (b) will be referred to as "elastic ultimate

moments" (Me).

7.2.2. Cross-Sectional Moment Capacity

7.2.2.1. Solid Prismatic Sections

It has been noted in the previous section that ob- served stress-strain properties of the masonry tested

justify the conservative assumption of a linear dis- tribution of flexural bending stresses at failure. This

proposition is also based on the assumption that plane sections remain plane under flexure and that the presence of strain gradients will not materially

affect the linearity of the stress-strain relationships

shown in figure 7.1(c). Equations for the moment

capacity of solid prismatic sections derived herein

are based on the above assumptions.

* The kern is the portion of the area of the cross section through which a resultant compressive force must pass if it causes no tensile stress in the cross section.

Figure 7.2(a) shows a solid prismatic section of

width b and thickness t, acted upon by a vertical load

P at an eccentricity e relative to the section centroid

as shown in the figure.

NEUTRAL AXIS

fm COMPRESSION

(o) WALL SECTION PLAN VIEW

I b) AXIAL LOADING

COMPRESSION M, ^

> pi

T

TENSION

ft T Ofjr

I K- CRACK

t/2

(c) FLEXURE (d) CRACKED SECTION

Figure 7.2. Stress distrib ution.

Figure 7.2(b) shows the stress distribution at failure under axial compressive load. The axial load

capacity Po can be derived by equihbrium:

Po =f'mbt = Af',n (7.1)

where: /m = Compressive strength of masonry de- termined from axial prism test, ^ = Area of net section.

Figure 7.1(b) illustrates the stress distribution

when a section is loaded to capacity by a vertical

load, applied at the edge of the kern. At this stress distribution there will be zero stress at the outer

fibers on one side of the section.

Thus: PkCkC ^Pk

In A

InAc 6

where: e/, = Distance from centroid to edge of kern. Pa = Vertical load capacity when load is apphed at the edge of the kern,

c = Distance from centroid to outer fiber,

/„ = Moment of inertia of section based on uncracked net section.

25
The vertical load capacity Pk is:

(7.2)

The moment capacity at eccentricity e^, M^, can

be derived in terms of f*A and eA-:

Ma- kek aPpt

12

(7.3)

bu

The stress distribution at flexural failure, when no

resultant vertical load acts on the section, is illus- trated in figure 7.2(c). Since the flexural tensile strength of masonry is generally very low compared

to the flexural compressive strength, failure will be

controlled by tensile strength. The moment capacity

at this stress distribution, M^, is derived below:

• c ft

ii: 5 = TT

/"I

where: f\ = Tensile strength of masonry determined

from modulus of rupture test.

/// hec 6

Substituting (1) into (2), Me can be expressed inf terms of P:

("rom (1):

and

M,=/'(|^;;)+6./;,, u6

IP

afr'n -ft

, _aPo

bt

^' ~ ht

(3)l'i

but: f'mbt^Po

:. M, _sPot

(7.4)

When the tensile strength at the extreme fiber of a section is exceeded the section will crack. However, initial cracking does not necessarily constitute

structural failure, since the ultimate moment of the

cracked section at any particular axial load may ex- ceed the cracking moment. Equations for the ulti- mate moment of cracked sections are derived below.

Figure 7.2(d) shows the stress distribution on a cracked section at maximum tensile and flexural compressive stresses. Length "u" is the uncracked

depth of the section and P the resultant vertical compressive force acting on the section. The following

equation can be written for P: p= (of:„+/;) j-fbu

(1) bu , // =Y("y, -/;)

from (4):

•. bu

2Pbt

Po(a-s)

2Pt

Po{a-s)

and buf^

3 3Po {a-s)

, u 1 sPo 2Pbt

(4)

2Pt

6 6 bt Po(a-s) Poia-s)

2 P2 ts 3 Po {a-sySubstituting (4) and (5) into (3):

(5)

Pi

' 2

Pt

4 P 1 3 Po ia-s)

1

2 3Po {a-sY

4P

3Po a — s {(i — s)-

The resultant moment acting on the section. Me,

can be defined in terms oi afm-, ft , and w, as:

Pt P

1.33-

r 0

a — 2s _{a-sy-_ (6)

26
I For masonry with no tensile strength or negligible

tensile strength {s — 0), eq (6) reduces to:

(7)

It is also interesting to examine eq (6) for relatively

small tensile strength, which is typical for most

kinds of masonry:

a -2s

the term:

a-2s

can be rewritten as:

fl2 — 2as + 5^ but if s is very small, s'- is of second order magnitude,

and:

a — 2s ^ a — 2s _ 1 (a — s)- a(a — 2s) a

thus: 25

( a — 5 ) a

for most practical cases. This result indicates that the tensile strength of masonry has a relatively

minor effect on the moment capacity of cracked sections. The equation for the moment capacity of

cracked sections can thus be written as:

Pt i P a — 2s

Pi

2 1-1.33

(a-s)2j

aPo

(7.5)

As noted above the ultimate cracked moment is not necessarily the greatest moment that a section can support at a given vertical load. For instance, at P = 0 the ultimate moment capacity of a cross section equals Mt 0, while eq (7.5) converges to 0 as P

goes to 0. Figures 7.3(a) and (b) show two different

modes of stress distribution which have a resultant

force P and a resultant moment Pe. In both cases the

moment shown at the top of the figure is the maximum moment at which section cracking is about to occur, Mc , which occurs at the cracking load Pc- In figure 7.3(a) this vertical load is gradually de- creased and always placed at an eccentricity which

will generate the maximum tensile stress // at the outer fiber but not cause section cracking. In

figure 7.3(b) the vertical load is also decreased,

but it is placed at an eccentricity at which maximum tensile and compressive stresses are de- veloped simultaneously. The moments developed

(c) DERIVATION OF Mc

Figure 7.3. Moments at P s P,..

by the stress distribution shown in figure 7.3(b) can be computed by eq (7.5). An equation for the stress distribution shown in figure 7.3(a) can be derived by resolving the stress block into two

separate components as shown in figure 7.3(c). This

moment, which is hereafter defined as the cracking

moment {Mc), is given as:

Mc = M(i, = M(2) + M(3)

M^2) = Mr = sPQ ^

(from eq 7.4)

since the resultant force P is applied at the edge of

the kern.

therefore:

but:

Thus:

Mc = Pe,+

sPiit

Mc = 2 isPo + P)

0

(7.6)

410-021 OL - 71 - 5 27
For masonry with no tensile strengtli: Mc = f^tl6. Since eq (7.5) converges to 0 at P = 0, and eq (7.6) converges to M, al P = 0, there is a range of vertical loads between P = 0 and some value of P where the

cracking moments exceed the ultimate cracked mo- ment computed by approximate eq (7.5). The complete equation for Me for axial loads

smaller than the cracking load (Pc) can therefore be

written as follows:

Mp = — 1-1.33-5-

2 [ Po lia-s)-

Pt 1-1.33

aPo

or: Me = 2 (sPo + P)

o

(7.7)

whichever is greater.

At loads greater than P,- the section will not crack.

Figure 7.4 shows a typical stress block at such a

load. The load P acting on the section will be:

T

JL

Figure 7.4. Moment at P > Pc.

p=bt{<if;n-Y)

= aPo —

The ultimate moment will be:

/\fbt ^.fbt t

but:

2 2 6

aPo-P

therefore at P ^ Pc: M.= (aPo-P) eA-(aPo-P)^ (7.8)

It is evident from the equations developed abovi

that cross-sectional moment capacity is a function o the vertical load acting on the cross section. An in teraction diagram can therefore be constructed b' plotting ultimate moments (Me) against vertical load

Figure 7.5 shows an interaction diagram foj solid prismatic sections. In order to make this plo

generally applicable, axial loads and moments wert

plotted in non-dimensional form. Axial loads P wer^

divided by the axial load capacity Po=//h bt, while

moments were divided by the moment capacit)|

when the vertical load is applied at the edge of the kern, M/, = Po?/12, which corresponds to the stress, distribution in figure 7.1(b). Figure 7.5 has been; developed on the assumption that "a", the flexural compressive strength factor, equals unity. This is c(| conservative assumption which will be further

discussed in section 8.3.

10

0.8 -

wad

aluf

»[

0.6 -

CL

Q. 0.4 -

0.2 -

0.2^ 04 0.6 0.8 1.0 1.2 1.4 M/Mk

Figure 7.5. Cross-sectional capacity of solid prismatic section

at f; =0.1/:,^.

Figure 7.5 shows the interaction diagram for masonry capable of developing a tensile strength // = 0.1 /,;,. The hne connecting/!/, at P = 0 with M;; at P = Pc is the locus of all moments which will bring

the section to the verge of section cracking. This

line, which was computed by eq (7.6) will be referred

to as the "cracking line". The curve connecting the

origin with M'c is the locus of the cracked moments

computed by approximate eq (7-5). From P= 0 to the

intersection of the cracking line with the curve, mo

ment Mc exceeds the cracked moment and therefore

represents, for all practical purposes, the section

capacity. Between this intersection point and M'e the section capacity is for all practical purposes

represented by the cracked moment [eq(7.5)]. Thus

a general expression for Me between P = 0 and P =

Pc is provided by eq (7.7). The straight line connect- 28
ing Mc with A/ = 0 at P/Po = 1 is a plot of eq (7.8) and

represents section capacity above Pc- The efifect of tensile strength on section capacity

is illustrated in figure 7.6. This figure shows an in- teraction curve forfi' — O. Note that in this case the

cracking line connects the origin with Ma. The

dotted lines show M,. for the case of // = 0.1 which would represent a masonry of relatively high

tensile strength. Note that the interaction curves

differ appreciably only between P=0 and a very low

value of P where the cracking line intersects the curve for cracked moments. Above this point the dif- ference between the two curves is not significant.

Approximate eq (7.5) which does not consider tensile

strength is therefore sufficiently accurate for all practical purposes.

Mr AT s =0 1

Me AT S=0.|:

V P!(|.|33P OJ)

Figure 7.6. Cross-sectional capacity of solid prismatic section atf; = 0.

7.2.2.2. Symmetrical Hollow Sections

Equations developed in section 7.2.2.1 cannot be

directly applied to walls which do not have a solid cross section. Similar equations can be derived for the case of hollow symmetrical cross sections (hol- low block walls).

The distance from the section centroid to the edge

of the kern, e^, can be expressed as:

Ac

2h

At (7.9)

The load capacity when a vertical load is applied at the edge of the kern, P/,, as illustrated in figure

7.1(b), can be determined by symmetry:

2

(7.10)

Similarly, A//,, the ultimate moment associated with

the stress block in figure 7.1(b) equals:

Mk = Pkek =

aPJn

At

(7.11)

An exact continuous equation for the cracked moment, applicable to all hollow symmetrical sections, can not be derived because of the discontinuities in these sections. However, an approximate equation,

sufficiently accurate for all practical purposes and

applicable to any cross section, is developed below:

Eq (7.5) can be rewritten as follows:

TIT =''Ml-«

aPf)/

where c = distance from centroid to outer fiber, and ^ = a constant dependent on section geometry.

Jt /> = />, , M = M, =/>Ki

eA = c l-g

aPo

aPo [ ., Ck

For symmetrical sections:

aP,

Pa-

' and —=

At^

^=2 1-^4^

Af^

A general approximate equation for the cracked mo- ment can therefore be written as:

Me Pc l-g

aPo,

/here:

gPo

Pa

(7.12)

and for symmetrical sections:

g=2 1 4^

'At^

29
Ml, the ultimate moment at P = 0, can be computed

from the tensile strength of the material:

M,=f;

^-f = sP,e, = 2sP,j-^ (7.13)

It should be noted that, for hollow block with faceshell bedding, the moment of inertia /„ to be used in combination with tensile stress should be based on

the face-shell area alone. However, the difference

between /„ based on the face-shell area alone and /„

based on the entire net section of the masonry unit

is not very great for most hollow block. In this report,

/„ for the entire net section of the block is therefore

used throughout.

The equation for the cracking line, can be derived

from figure 7.3(c) as:

Mc = M> + Pek - sPoek + Pe,

^e,{sPo + P)=^ [sPo + P] (7.14)

The approximate equation for M(. between P = 0

and P — Pi; can therefore be written:

where: ^=2 1- 4^

or:

/xt

(7.15)

whichever is greater.

An equation for Me for vertical loads greater than P( can be derived, as in the case of solid sections, from

figure 7.4:

if: P^Pr

2In Me = e,{aPo-P)^^ iaPo-P) (7.16)

Note that eq (7.15) covers the range of vertical

loads from 0 to Pk, while eq (7.16) is valid from Pc to P. Pc is slightly lower than Pa and the range between

Pr and Ph is covered by both equations. This

redundancy results from the approximate nature of

eq (7.15), which does not account for tensile strength. Eq (7.15) is a conservative approximation.

8-IN HOLLOW 2-CORE BLOCK

Mk = I,II Po

M. OF CRACKED SECTION

Figure 7.7.

1.2s

Cross-sectional capacity of symmetrical hollow

section. Figure 7.7 shows an interaction diagram for a symmetrical hollow wall section. This particular figure

illustrates the case of 2-core hollow masonry block.

The curve is plotted for // = 0, since only the loca- tion of the cracking line would be significantly af- fected by tensile strength. The curve is plotted for the case where a/»', =/,',: {a= 1). As in the soHd section. Ml; occurs at one half the maximum axial load

(Po). However, the eccentricity of the vertical load

'corresponding to that moment (e^) will be greater

han was the case for the solid section. Note that in

this case the maximum cracked moment only

slightly exceeds Mk (1.02 Mk), while in the solid section the maximum cracked moment was 1.12 Ma- (see

fig. 7.5). The interaction curve shown by the solid line in

this figure has been developed by computing axial

loads and moments associated with various stress blocks and is thus theoretically correct. The broken

line is a plot of eq (7.12) which purports to approximate the interaction curve. Note that up to P/Po =

0.2 there is good agreement. For higher values of

P/Po, eq (7.12) begins to deviate on the conservative

side; however, the maximum deviation never ex- ceeds 8 percent. Considering that in present design

practice the maximum allowable axial load is 0.2Po

it may be concluded that for all practical purposes

eq (7.12) is sufficiently accurate.

7.2.2.3. Asymmetric Sections The third case of interest in addition to symmetrical solid and symmetrical hollow walls is that of an asymmetric wall cross section. In this investigation

30
this case is represented by the composite brick and

block walls. Figure 7.8 shows an ideahzed asymmetric section,

with the neutral axis closer to one face of the wall. Such a section would result by transforming a section composed of two kinds of masonry which have

different stiffness. In the case of figure 7.8 the stiffer material would be on side 1. Transformation would

be made in accordance with the ratio of the moduli

of elasticity: m = E]IE2.

SIDE I

SIDE 2

NEUTRAL

AXIS

Figure 7.8. Asymmetrical section.

The area of side 1 would be multiplied by "m".

Compressive strengths associated with the trans- formed section would be aif,'„Jm and fn/m on side

1 and a2f,n2 and ft'2 on side 2. The distances from the neutral axis to the edge of

the kern, Ck-, can be computed as follows: When a load P is applied at the kern eccentricity, the stress

at the outer fiber opposite to that eccentricity will be zero. Therefore:

A In

Loads Pa, the load capacities at kern eccentricity,

which will be different for sides 1 and 2 can be deter- mined from ca as:

eA i

' Jn_

AC2

Similarly:

therefore:

n ri Ac2

' ~ m ~T

Pin ^ aifnn _ £2 Pb2 muzf'mt Cx (7.18)

Values for Ma , the ultimate moment at kern eccentricity, can be derived from equations (7.17) and

(7.18):MD // AC\ In // III k2 = Pk2eh2 = a2j ml -7— — OLij m2 —

t Aci '

Similarly:

and:

mt

Cllfml Mk2 mciif'nri (7.19)

The ultimate moment of a cracked section for this case can be computed by approximate eq (7.12) as:

M,, = Pc, [l-gx

aP,n

^here:

fliPoi /i = ek\

I i ^' PkX \ c,

and M.2-Pc2(l-g2 - ^)

^here

(' 2P02 , 1 ek: Co (7.20)

Values for Poi and Po^ are hypothetical values of

axial strength based on the respective material components on sides 1 and 2. An actual specimen would

develop only the lower of these two computed

strengths.

Equations for ultimate tensile moments M, at P =

0 can also be derived as:

Similarly ek2 ' Aci

,., _ Pk2 , Pk2ek2C2 «2/m2— ^ +

J

(7.17)

Mr.

C2

__f;jn

mCl

(7.21)

p

,Ir,C2 \_Pk2(Cx + C2 ^''^A^AIncJ- A [ cx

. 1^2 — (IZJ m2

Expressions for the cracking lines will therefore be:

Mci^Mn + Peki

Mc2^M,2 + Pek2 (7.22)

31
Equations (7.18) through (7.20) have been derived

for the general case where the ratio of the moduh of

elasticity of the two materials differs from the ratio of the flexural compressive strengths (EJE-z 7^

difmilo-^fm-z)- However, in the particular case of the

composite brick and block walls tested in this study,

and also for a wide range of different masonry

systems, the expression:

E2

a\f'm

a^fm

is approximately correct, or E is approximately pro- portional to a/„',.. This relationship makes it possible

to greatly simplify equations (7.18) to (7.20). These

simplified equations are summarized below:

Loads Pk: Pki =

aPo

1 +

(A

C-2 1 +

C2

Cl

Pjn.

Pk2

£2

Cl (7.23)

and side 2 applies to moments that cause brick compression. It will be seen later in this report that mo- ment capacity in both directions must be considered

in order to predict the strength of this wall system.

Cracking lines were drawn for f't=0. Note that Pk

depends on the direction of eccentricity; however,

for the case where //„ is proportional to E the values

for Mk and Po are unique. Accurately computed in- teraction curves are drawn as solid lines. These are compared with interaction curves which are computed by approximate eq (7.25). Note that the agree- ment for brick compressive moments is excellent. For block compressive moments the approximate

equation closely predicts moments up to P/Po = 0.15. For higher values of P moments are slightly overestimated; however, the largest discrepancy does not exceed 5 percent. Again it may be concluded that

the approximate equation is sufficiently accurate for

all practical purposes.

7.3. Slenderness Effects

Moments Ma-:

Mki = Mk2 = Pkieki = Pk2ek2

Cracked Moments:

wnere:

/ P Mei^PcAl-gi--^

\ Clio aPo 1-

where:

rki

M.2 = PC2

aPo /, ek2 ''=-h:2V'~2

(7.24)

7.25)

An interaction diagram for an asymmetric section

is shown in figure 7.9. This figure applies to the composite brick and block walls used in this program. In

this case the ratio of the moduli of elasticity approximately equals the ratio of the masonry strengths,

and simplified equations (7.23), (7.24) and (7.25) are

applicable. The conservative assumption was also made that a = 1. The diagram shown on side 1 applies to moments which cause block compression

Slenderness effects on the moment capacity of walls are illustrated in figure 7.10. This figure shows

the free body of the upper half of a deflected wall

subjected to axial and transverse loads. The effective moment at any point along the height of this wall

will be determined by the location of the line of ac- tion of the vertical force, relative to the location of

the deflected centerline of the wall. Hence, the mo- ment acting on any section of the wall is magnified

by an added moment equal to the product of the

axial force and the centerline deflection.

A similar problem has been analyzed for the case

of eccentrically loaded reinforced concrete columns

[7], where it has been shown that the external mo- ments acting on a column are magnified and that this effect can be predicted quite reasonably by the fol- lowing equation:

Cn

1 P_

Per

(7.26)

where Cm is a moment correction factor, depending

on the ratio of the end moments and the shape of the

primary moment diagram and Pcr = Tr''EII(kh)'- is the

axial load that will cause a stability-induced compression failure. This method of computing the total moment is designated as the "Moment Magnifier

Method". A similar method may be applied to the

loading conditions of the tests reported herein.

32
p/p,

SIDE I BLOCK COMPRESSION

M|^= 0.69 Pq

Pk,= 0.33Po

Me BY EQ 7.25

8- IN COMPOSITE BRICK AND HOLLOW CONCRETE BLOCK WALL

SIDE 2 BRICK COMPRESSION

Mk=0.69 Po

Me FOR CRACKED SECTION

I \ L

Me AT CRACKED

SECTION

Me BY EQ 7.25

1.6 1.2 0.8 0.4 0.4 0.8 1.2 1.6

Figure 7.9. Cross-sectional moment capacity of asymmetrical section.

T p.e=|l-W§i.PA

=Mo+PA

j! Figure 7.10. Slendemess efiects on equilibrium.

Figure 7.11(a) shows the moment diagram acting

jlj on a wall which is subjected to combined axial and

' transverse loading. If it is assumed that the wall section is pin-ended, the moment due to transverse load

)| will be parabolicaUy distributed over the height of

the wall with a maximum moment at mid-height, Mo = {ll8)wh'-. If it is in turn assumed that the deflection curve of the waU is also parabolic,^ the added mo- ment caused by the action of the axial load on the

' A parabolic curve is a close approximation to the actual

deflection curve.

w—>

p fv

kh -PA

-P8

(o) MOMENT DISTRIBUTION (b) PARTIAL END FIXITY

Figure 7.11. Slenderness effects.

deflected wall, PS, will also be distributed parabolicaUy with a maximum moment PA at mid-height.

Thus the maximum total moment acting on the waU

at mid-height, which at failure will equal the section

capacity Me, equals Me = Mo + PA. If it is assumed

that the stiffness EI is constant over the height of the

wall the following equation can be written for A, the

mid-height deflection:

^=11 (*'«+''^'
The maximum added moment acting at mid-height,

PA, can be expressed in terms of A:

If it is now assumed that the maximum moment: Me = Mo + PA, then:

48£/

.-. Me = Mo

but: 48£/

5/? 2

1 5Ph^

48£/

The equation for section capacity for pin-ended conditions can therefore be rewritten:

Me^Mo

1 5Ph^

48£/

Mo [1:21]

1-

Under conditions of partial end-fixity the deflection curve, and thus the magnitude of the added moment, will change. For the particular case of trans- verse loading, the equation for pin-ended conditions can be modified by substituting the "effective" wall

height, kh, at which a pin-ended member of equal

stiffness {EI) would develop similar slenderness ef- fects, for the wall height h. Effective heights for dif- ferent conditions of end-fixity for braced members,

as well as members which are free to sway at the top,

may be conveniently determined by referring to the

Jackson and Moreland Alignment Charts [8]. Partial end-fixity is illustrated in figure 7.11(b), and eq

(7.26) thus becomes:

Me = M'o1

1 P_

Per

(7.28)

^here: Per —

n-EI

{khV

and M'o is the maximum moment in the direction of

the transverse loads at the given end-fixity.

The equation must be modified for section

cracking (change in /), and change in E with increasing stresses. For a material with a relatively small

tensile strength, the section will be cracked withir

the range of vertical loads where section capacity h

governed by the ultimate moment for a cracked sec

tion. Thus, the stiffness (EI) of the section is a func

tion of vertical load. Consequently, EI in the momen

magnification equation is a function of P/Po.

It has been shown for lightly reinforced concret<i

columns [7] that slenderness effects can reasonablt

be approximated by using an "equivalent" EI ol P;/h/2.5. Observation of the magnitude of deflections

of the slender brick walls tested in this study in- dicates that at axial loads up to about 0.25Po an "equivalent" EI of £',7»/3 will fit the test results reasonably well. For this case eq (7.28) can thus be

modified as: M,;=M„(i-£)

where: Per -

TT^EJ,,

(7.29)

Sikh)''

This equation accounts also for partial end-fixity.

The above equation is a good approximation for the range of vertical loads between P — 0 and P =

0.25Po. For higher vertical loads section capacity is underestimated by eq (7.29). Closer examination of

the test results on brick walls indicated that an

equivalent EI of:

EI Eil„ (0.2 + ^

O.lEJn (7.30)

will approximate the actual test results of slender

walls over the entire range of vertical loads. Reduced interaction curves can be developed by

plotting Me — PA for each value of P. Such reduced

curves will show the value of M'o, the moment that can be imposed on the wall by external forces at any ^ particular value of P. These interaction curves can be used to determine

the moment capacity of slender walls since they

have been in effect corrected for effects of deflections. Reduced interaction curves using equations

(7.29) and (7.30) are compared with test results in the

following sections.

Figure 7.12 illustrates the effect of different slen- derness ratios on an interaction diagram for a solid prismatic section. While slenderness is traditionally

expressed by the parameter khjt, slenderness ef- fects, computed by the moment magnifier method,

depend on the parameter PojPcro

where: Pcro (kh)'

34
FOR BRICK A WITH I M 4 MORTAR

kh/t 0 0

10 03

18 1.0 22 1.5

SECTION CAPACITY

Figure 7.12. Slenderness effects on moment capacity of solid prismatic section.

The figure illustrates the order of magnitude of

slenderness effects for different kh/t ratios of Type

A Brick with 1:1:4 mortar. Note that the location of

the cracking line is also affected by slenderness.

8. Analysis of Test Results

8.1. Introduction

In this section the test results are analyzed and

compared with the theory developed in section 7. Section 8.2 deals with the observed stress-strain

properties of the different types of masonry tested in this investigation. In section 8.3, section capacity is evaluated on the basis of test results on small prism

specimens. In section 8.4 the strength and rigidity of the wall panels tested are evaluated. The magnitude

of measured slenderness effects is determined and

compared with theoretically predicted slenderness

effects.

8.2. Stress-Strain Relationships

Stress-strain curves for concrete block and brick,

developed from tests of axially loaded block prisms

and brick piers are shown in figures 8.1, 8.2, and 8.3. Figure 8.1 shows the stress-strain curve obtained

from an axially loaded 8-in hollow block prism with

1:3 mortar. An initial tangent modulus of elasticity of 1.5 X 10** psi was developed, and at failure a se- cant modulus of elasticity of 1.3 X lO** psi and a tan- gent modulus of elasticity of 650,000 psi. It should be

reaUzed that stress-strain relations may be different

if masonry is subjected to strain gradients associated

with flexural stress. Nevertheless, on the basis of

this information, which is the only information

' Figure 8.1. Stress-strain diagram from axially loaded

8 X 8 X 16-in hollow block prism with Type N(l:3) mortar.

available for the concrete block test specimens used,

it appears that the simplified assumption of linear

stress distribution at failure is a reasonably good and

slightly conservative approximation.

Stress-strain curves obtained from a series of tests on 16 X 16-in and 24 X 24-in piers made of Brick A

with 1:1:4 mortar are shown in figure 8.2.'"' The

average initial tangent modulus of elasticity from

these tests is 3.65 X 10** psi, and the average secant modulus of elasticity at failure is 3.25 X 10** psi. The

results from these tests are reasonably consistent,

except that one specimen appeared to have significantly less stiffness. Again, the assumption of a

linear stress distribution at flexural failure appears

justified, even though strain gradients may have an

effect on stress-strain relationships in compression.

Figure 8.3 shows a similar family of curves for specimens made of Brick A with high-bond mortar.*" The average initial modulus of elasticity of these

specimens was 4.2 X 10^ psi and the average secant modulus at failure was 3.6 X 10'' psi. Some of these

specimens developed significantly more deformation

than other specimens, but on the whole it again ap- pears that the approximation of a linear stress dis- tribution at flexural failure is justified.

8.3. Cross-Sectional Capacity

It has been noted in section 7.2 that compressive

strength of masonry in flexure does not necessarily

equal the compressive strength in pure compression.

A study of high-bond mortars, conducted at the National Bureau of Standards in June 1968. 35
This relationship can be investigated by examining

the cross-sectional capacity of short walls where

slenderness effects are negligible.

STRAIN

Figure 8.2. Stress-strain diagrams from axially loaded piers. Brick A with Type N(l:l:4) mortar.

STRAIN

FiGUrtE 8.3. Stress-strain diagrams from axially loaded piers. Brick A with high bond mortar.

Short-wall section capacity for hollow concrete

block, solid concrete block, and brick was in- vestigated in a series of tests on eccentrically loaded

prisms. The masonry units used in these tests had

somewhat different properties than the masonry

units used in the full scale walls. The information

conveyed therefore, is of a qualitative, rather than a

quantitative nature. Other prism tests with masonry

units and mortars similar to the ones used in the wall

specimens were conducted while the testing pro- gram was in progress and were used to determine

section capacity of the wall systems tested, however,

these prisms were subjected only to axial loads. The results of tests on eccentrically loaded prisms

made of hollow 8 X 8 X 16-in concrete block, solid 8

X 8 X 16-in concrete block and 4-in brick are shown

in figures 8.4, 8.5, and 8.6, respectively.

Figure 8.4 shows a plot of 12 tests that were con- ducted on three-block prism specimens made of hol- low 8-in concrete masonry units using type N mortar.

Vertical loads were applied at different eccentricities, as shown in the sketch, in order to determine

the cross-sectional capacity to resist combined verti- cal loads and moments. The solid curve is a theoreti- cal interaction curve developed on the assumption

that f'm = af'm or o.= \. Comparison of this interaction curve with test results indicates that the load

capacity under eccentric loading exceeds the capacity predicted on the assumption that a = 1 by a considerable margin.

A second theoretical curve, shown by the dashed

line is the theoretical interaction curve corresponding to the average apparent flexural compressive

strength developed at the tjdi eccentricity, which ex- ceeds the compressive strength under axial load by

40 percent [a = 1.4). Comparison of this second in- teraction curve with the test results at eccentricities

smaller than ?/3 indicates that apparently factor "a"

increases with increasing strain gradients.

The observed mode of failure in these tests was

generally vertical splitting of the webs which

originated at the corners of the intersection between

the webs and the face shells, followed at the larger

eccentricities by crushing of the face shells. Figure 8.5 shows a plot of 12 tests on eccentrically

loaded 8 X 8 X 16-in solid concrete block prisms. In these tests the strength increase at increasing load

eccentricity is even greater, since the apparent compressive strength developed at maximum load ec- centricity exceeded the compressive strength under

axial loading by 145 percent. Tests results from eccentrically loaded brick

prisms are illustrated in figure 8.6. A similar

phenomenon can be observed in this case, where ap36
100

f m IN AXIAL COMPRESSION 1600 psi APPARENT afm AT MAXIMUM ECCENTRICITY 2250 psi "^>^ AT afm =

• -PRISM TEST RESULTS

= 2250 psi

2 STEEL

.

PLATE^

AT af ' = 1600 psi

^"<^ STEEL HALFROUND

STEEL PLATE

LOADING

100 MOMENT, kip-in

150

Figure 8.4. 8-in holloiv concrete block prisms with Type N mortar under eccentric loading.

200

fm IN AXIAL COMPRESSION 1520 psi APPARENT afm AT MAXIMUM ECCENTRICITY: 3720 pSiX

M, AT aim' 1520 psi

t/6

\ Me AT afm '3720 psi

\

-PRISM TEST RESULTS

200 MOMENT, kip-in300

Figure 8.5. 8-in solid concrete block prisms with Type N mortar under eccentric loading.

parent compressive strength developed under max- imum eccentricity exceeds compressive strength

under axial loading by 144 percent.

It should be noted that the preceding test results may be affected to some extent by end fixity conditions. It is also important to note that in all the

preceding cases the apparent compressive strength

in flexure was computed on the assumption of a

linear stress distribution at flexural failure. If the

stress distribution at failure was not linear, flexural compressive stresses may have been overestimated.

But even had the specimens developed a fuUy plastic

moment, compressive flexural strength would ex- ceed compressive strength under axial loading by a considerable margin. It is also apparent from figures

8.4, 8.5, and 8.6, that in all cases "a" increases with

increasing strain gradients. This can be seen by

comparing the test results with the dashed interaction curves, which were computed for the average

flexural strength at the tl3 eccentricity.

It has been noted above that prisms constructed

during this testing program as companion specimens

to the wall panels were tested in axial compression

only. While the test results illustrated in figures 8.4,

8.5, and 8.6 provide qualitative information to the ef- fect that a/,'„ > /,'„ and that the factor "a" seems to increase with increasing strain gradients, the magnitude of factor "a" for the wall panels tested cannot

be estimated on the basis of available information.

In the subsequent interpretation of test results, wall

panel strength will be analytically predicted on the

basis of prism strength, making the conservative as- 37

I
80(1-

IN AXIAL COMPRESSION; 2500 psi APPARENT of^ AT MAXIMUM

ECCENTRICITY: 6,100 psi

<" of'= 2,500 psi y

t/6

M„ of af'" 6,100 psi \

\

lt/4

t/3

• PRISM TEST RESULT

* A 11,000 psi BRICK

J I I _L

0 20 40 60

MOMENT, kip-in

Figure 8.6. 4-m brick* prisms with 1 :1 :4 mortar under eccentric loading.

sumption that a = 1, and that wall panel strength will therefore equal or exceed the strength predicted on

the basis of compressive tests on axially loaded

prisms.

(a) PINNED END (b) FIXED END

M, =060Mo

M2=0.e6Mo

(d)

(c) PARTIAL FIXITY

M| =0.68 Mo Mg^O.eSMo

(c) (b)(a) • • •

M, OR M2

p

''ma*

8.4. Wall Strength

8.4.1. General Discussion of the Test Conditions

Figure 5.1 illustrates the test setup and the loading

conditions. The top of the wall is free to rotate but is restrained from lateral movement and may be con- sidered as pin connected. The bottom of the wall

rests on a fiberboard which does permit rotation, but

may impose some restraint on the rotation, particularly under large vertical loads. While these test conditions attempt to simulate actual conditions in a

structure, they also impose a varying degree of restraint on the wall base, which will tend to reduce

the maximum moment caused by superimposed

loads when compared to a wall with a pinned base.

Figure 8.7 illustrates the approximate influence of end conditions on moments due to superimposed

lateral loads for three hypothetical cases. In figure

8.7(a), the wall base is free to rotate and the max- imum moment due to lateral load is developed.

Figure 8.7(b) illustrates the case of complete fixity of

the wall base. In the latter case, the maximum mo- ment occurs at the wall base and equals approximately 86 percent of the maximum moment in figure

8.7(a)."

Figure 8.7. Influence ofend conditions.

" The magnitude of, this moment will be influenced by the ef- fects of the vertical load, section cracking, and changes of the modulus of elasticity with changing stress. These factors were not considered when the approximate fixed ended moment was deter- mined.

38
Figure 8.7(c) illustrates the case of partial restraint

of the wall base which produces the least possible

moments due to superimposed lateral loads. Note

that in this case the lateral load produces only 68

percent of the moment that is produced in the case

of a pin connection at the bottom of the wall. Figure

8.7(d) illustrates the effect that the assumed end conditions would have on the determination of the mo- ment that acted on the waU at a given lateral load. End conditions will also significantly influence slen- derness effects as discussed in section 7.3. In the subsequent interpretation of results it has

been assumed that partial end restraint reduced moments in the walls to 68 percent of the pin-ended moments. Slenderness effects for the conditions illus- trated in figure 8.7(c) were assumed to correspond to an "effective" wall height of 80 percent of actual

height (A- = 0.8). WaU strength computed in this way

wUl be the lowest strength that the walls could have

developed.

300 -

200

O- HIGH-BOND MORTAR

SPECIMEN TEST

HIGH-BOND MORTAR

PRISMS SET IN •- TYPE N MORTAR _ PLASTER SPECIMEN TEST

<4— AVERAGE AXIAL PRISM STRENGTH

2-8 SPECIMEN DESIGNATION

WALLS WITH HIGH-BOND_ MORTAR

HIGH-BONO MORTAR PRISMS ON FI6ERB0AR0

:-8

100 150 200

APPLIED TRANSVERSE MOMENT, kip-in

Figure 8.8. Comparative strength of 8-in hollow concrete block

walls with Type N and high bond mortars.

8.4.2. Concrete Block Walls

8.4.2.1. 8-in Hollow Concrete Block Walls

Figure 8.8 shows a comparative plot of the test results on hoUow 8-in concrete masonry walls with

ASTM type N (1:3) mortar, and walls built of the same masonry units using high-bond mortar. Moments plotted in the figure are the moments imposed

by transverse loads, assuming partial fixity as illus- trated in figure 8.7(c). The curves shown in the figure

show the average trend of the test results. Note that at P = 0 the three high-bond mortar

walls tested developed moments of 42.3 kip-in, 52.2

kip-in and 54.8 kip-in while the wall with type N mortar developed a 3.3 kip-in moment. These moments

correspond to an average masonry tensile strength

of 130 psi for high-bond mortar walls and a tensile strength of 6 psi for the regular mortar wall tested. (Correction has been made for the weight of the

wall.) The average tensile strength for these wall

systems, as determined by flexure tests on two-block

prisms, was 231 psi for high-bond mortar and 9 psi

for regular mortar. Thus the full-scale walls

developed at least 50 percent of the tensile strength

determined by prism tests for high-bond mortar, and

60 percent of the tensile strength for regular mortar. Further comparison of the test results for the two

wall systems indicates that, at higher vertical loads,

the moment capacities of the two wall systems did

not differ significantly and that the maximum axial load bearing capacity of the two systems was about

equal.

Wall strength in pure compression, computed on

the basis of the average strength obtained from

prism tests, is also shown in figure 8.8. Note that there is good agreement between compressive

strength of conventional mortar prisms and strength

of the full scale wall system. In the case of high-bond

mortar, the strength of prisms set in plaster ex- ceeded wall strength by a considerable margin. The

strength was correctly predicted by prisms set on

fiberboard. This difference in strength may be

caused by the added lateral restraint imposed by the

friction between the prism support and the capping.

The combined effect of the stronger high-bond mortar and the end restraints will prevent failure of the

masonry units by vertical splitting, which is the

usual mode of failure. It should also be noted that in the test panels, fiberboards were set at the top and

bottom of the waU panels.

In order to make a meaningful comparison

between the interaction curve, predicted for a short

wall on the basis of prism strength, and the strength

of a more slender wall, the added moment attributa- ble to deflections must be taken into consideration.

This can be done approximately by adding to the mo- ment imposed on the wall by transverse loads an additional moment which equals the axial load times

39

J
p/p.

160 —

140 —

120 —

^\oo —

<

980- <

O60 • H

tr

UJ>40

20 —

0 —

COMPUTED REDUCED MOMENTS

8-IN HOLLOW 2 CORE BLOCK

M,, = l.ll Po

f' =910 psi 1\ : PRISMS 9 psi WALLS 5 psi

EQ (730) El= Ej in(0.2+^)£0.7Ejln

12 14 M/M|,

I I I I I 0 4 0 80 120 200 MOMENT, kip- In

Figure 8.9. 8-in hollow block u>alls with Type N mortar, correlation with prism strength.

the maximum deflection of the wall at failure, rela- tive to the line of action of the axial load. Figure 8.9 compares the experimental strength of

the 8-in walls constructed using conventional mortar

with an analytical prediction based on prism tests. In this analytical prediction the prism strength

under axial compression was used as a basis of computing /;„(a/;„ =/J.

To bring prism tests and wall tests to a common

denominator, and to afford comparison, all vertical

loads are divided by Po, the load-bearing capacity

under axial loading computed on the basis of the

average prism strength, and aU moments are divided

by the maximum theoretical moment capacity if the

vertical load is applied at the edge of the kern of the

section (Ma), based on the assumption that flexural compressive strength is equal to compressive

strength in pure compression. The actual magnitude

of loads and moments is also shown in figure 8.9 by

additional scales. For each test point, both the moment imposed by

transverse loads and the added moment imposed by

deflection are shown. The part of the moment at- tributable to deflection is shown by the solid black

horizontal lines. These lines illustrate the magnitude

of the measured slenderness effect. The soHd curve in figure 8.9, (Me), is a short-wall

interaction curve, computed on the basis of axial prism strength. The two dotted curves represent

reduced interaction curves, computed by eq (7.29)

and (7.30), respectively. Note that the theoretical

short-waU interaction curve underestimates wall

strength for all panels. The reduced interaction curves predict moment capacities equal to or smaller than the observed reduced capacity.

For wall 1-4, for which no deflection reading is available at failure, the first solid line of the broken

horizontal line is the magnitude of the added mo- ment at the last measured deflection. The great

strength developed by most walls, particularly wall

1-5, tends to indicate that the flexural compressive

strength exceeded f,'„ by a substantial margin.

Added moments due to deflections are in general

not very great compared with the total wall strength.

Nevertheless, they are of a greater order of magnitude than the predicted added moments. This dif- ference is in part attributable to the great loss in mo- ment of inertia, associated with section cracking of

hoUow block. Eqs (7.29) and (7.30), which were

developed on the basis of brick data, do not account

for this effect and may also not account sufficiently

for the decrease in the modulus of elasticity of concrete block with increasing stress. Since no data on more slender hollow block walls are available, it was not feasible to develop a special relationship for slenderness effects on hollow block walls within the

scope of this investigation. Note that most of the

specimens exceeded the computed reduced moment

by a rather narrow margin while developing cross- sectional capacities which were considerably greater

than the predicted capacity.

It is also interesting to compare the points at which the load-deflection curves deviated from

linearity with the location of the theoretical cracking

40
line. Both lines are shown in figure 8.9. It appears

that cracking moments reduced for slenderness ef- fects could be used to closely predict this point.

Since the cracking line is a function of the shape of

the cross section and the flexural strength in tension,

the flexural compressive strength has no effect on

the magnitude of cracking moments.

XT N

, MAXIMUM LOAD 6.03 psi NO DEFLECTION READING

120 Kip VERTICAL LOAD (1-5)

60 kip VERTICAL LOAD

(1-4) 20 kip VERTICAL LOAD (1-2)

0.2 0.4 0.6 0.8 1.0 DEFLECTION, in

Figure 8.10. Load-deflection curves for 8-in hollow concrete block walls with Type N mortar.

real ductility of the materials. Thus, great additional

deflections will develop without a significant in- crease in moment. At higher compressive loads,

failures tend to be more brittle because of the large

added moments associated with each increment of

added deflection. This behavior is illustrated by the

dashed-dotted line which shows the deflections at a 120-kip vertical load. The test strength of 8-in hollow block walls with

high-bond mortar is compared in figure 8.11 with

analytical predictions, based on the results of prism

tests. The short-wall interaction curve was

developed on the basis of the strength of axiaUy

loaded prisms with fiberboard capping. This

strength was used since it is realized that the prisms

with plaster capping develop deceptively higher

strength than the walls. The solid curve in figure 8.11 shows theoretical

short-waU capacities. Up to an axial load of 0.2 Po,

the capacity is controlled by the cracking hne, which

is based on the average tensile strength developed

by the walls. Wall strength, rather than prism

strength was used, since flexural tests on high-bond

160 —

P/Po

0—0

2^ Mk = l.ll Po

f'm= 915 psi

f't = PRISMS 230 psi WALLS 110 psi 2-6 COMPUTED REDUCED MOMENTS

EQ (7.29)EQ (7.30)

0.2 0.4

I I I 40 80

0.6 0.8 1.0 1.2 l.4M/Mk

I I I I I

I I I 120 160 200 240 MOMENT, kip-in

Figure 8.11. 8-in hollow concrete block walls with high bond mortar, correlation with prism strength.

Figure 8.10 shows load-deflection curves for some

of the wall specimens. The dashed curve shows the

deflections at 20-kip vertical load. Note that at this low vertical load the walls exhibit considerable ap- parent ductility. This is attributable to the sudden

loss in stiffness with section cracking and not to any

mortar prisms developed a tensile strength approximately 70 percent higher than the tensile strength

developed by wall panels. Note that the tensile strength of this type of construction is so high that the interaction curve at low axial loads can be

adequately approximated by the cracking line. 41
Comparison of test results with the theoretical in- teraction curves in figure 8.11 shows that all specimens exceeded the predicted strength. In general, added moments due to deflections were

small when compared with the total moments

developed, and tended to be smaller than in the case

of 8-in hoUow block walls with conventional mortar. An exception to this behavior is specimen 2-4. Unfortunately no load-deflection curve is available for this specimen, since the instrumentation became

jammed at the beginning of the test and only the ulti- mate deflection was measured. The vertical load on

this specimen was within the range of vertical loads

such that the ultimate moment occurs at a cracked

section. Specimens 2-6, 2-7, and 2-8 indicated that

flexural compressive strength is substantially higher

than compressive strength under axial load. Indeed,

specimens 2-7 and 2-8 carried a vertical load as large as the failure load under axial loading alone.

_ /

75 kip VERTICAL LOAD (2-5)

/(

/

-130 kip VERTICAL LOAD (2-6)

I h 6

-150 kip VERTICAL LOAD (2-7)

plotted since only maximum deflection readings are* available. ' Figure 8.13 shows a comparison of load-deflection curves of 8-in hollow block walls built with type N

and with high-bond mortar and subjected to vertical loads of 120 and 130 kips, respectively. Note that the

high-bond mortar wall is slightly stiffen

8-IN HOLLOW BLOCK- HIGH BONO MORTAR

130 kIp VERTICAL LOAD

8-IN HOLLOW BLOCK-TYPE N MORTAR

120 kip VERTICAL LOAD

(1-5)

a I 02 03

DEFLECTION, in

Figure 8.13. Relative stiffness of8-in hollow concrete block walls.

Initial tangent moduli of elasticity may be computed from the initial slopes of these load-deflection curves which are not significantly affected by section cracking. To account for some uncertainty

about the degree of base fixity, moduli were computed for the extreme cases of partial fixity as in figure 8.7(c) and of pin-ended condition at the base

of the wall. The following values were derived in this manner: 0«-

0

1 1 1 1 0.1 0 2 0.3 0.4 DEFLECTION, in

Partial

fixity Pin ended

8.12. Load-deflection curves for 8-in hollow concrete block wall with high bond mortar.

Hollow block with type N

mortar Hollow block with high-bond

E = 0.9x 10«- 1.6 X 10" psi

mortar E = 1.1 X 10"- 2.0 X 10<^ psi

Typical load-deflection curves for these tests are

illustrated in figure 8.12. Note that in this case the

load-deflection diagrams are essentially linear until a brittle failure occurs at maximum load. Only

specimen 2-4 showed a large deflection at maximum

load (0.56 in). The curve for this specimen is not

Values for the type N mortar walls are between 0.9 X 10*^ and 1.6 X 10« psi. The initial modulus of

elasticity derived from figure 8.1 for the same type

of masonry is 1.5 X 10'' psi which is within the computed range and closer to the value corresponding to the pin-ended condition. The value for the high bond

42
mortar walls appears to be approximately 20 percent

higher.

8.4.2.2. 8-in Solid Concrete Block Walls

Figure 8.14 shows a plot of the test results on solid concrete block walls with type N mortar. Moments

plotted are the moments imposed by transverse

loads (reduced moments). Test results on hollow

concrete block walls with type N mortar are plotted

in the same figure for comparison, illustrating the

„„„n PRISM TEST RESULTS

APPLIED TRANSVERSE MOMENT, kip-in

Figure 8.14. Test results for 8-in solid concrete block walls with Type N mortar.

great difference in strength between the two

systems. The solid curves approximately represent

the trend of the data. The average prism test results predicted about 10

percent higher strength than the average of the axial wall test results. This predicted strength is also plotted in figure 8.14. The two specimens tested at zero vertical load

developed moments of 8 kip-in and 9.3 kip-in,

respectively. This corresponds to an average tensile

strength of 15 psi which may be compared with the

average 25 psi tensile strength developed by flexure

tests on prisms. Thus the fuU-scalp walls developed

approximately 60 percent of the tensile strength

computed from two-block prism tests. Figure 8.15 compares the observed transverse

strength of the wall system with an interaction dia- gram analytically derived from the average prism

strength. The solid curve (Me) shows computed section capacity. Specimens 3-7, 3-8, and 3-9 did not fail since their strength exceeded the capacity of the

loading mechanism. Specimens tested at a vertical

load of 150 kips or higher in general exceeded the

predicted moment capacity by a considerable margin, particularly specimen 3-11 for which no deflection was measured. This behavior again points to the

phenomenon that the flexural compressive strength

exceeds the axial strength. At smaller axial loads,

panels developed capacities which were equal to or

slightly smaller than predicted capacity.

Theoretically predicted slenderness reductions by

eq (7.29) and (7.30) are also shown in the figure by

43
the two dashed curves. Except for specimen 3-5,

which failed at 90 percent of the predicted strength,

all panels developed or exceeded the reduced mo- ment capacity predicted on the basis of axial prism

tests. Typical load-deflection curves for solid 8-in concrete block walls are shown in figure 8.16. These

curves indicate that at low axial load there was a significant increase in deflections before the ultimate

load was reached.

The load-deflection curves for specimens 3-7, 3-8 and 3-9 must be considered incomplete since their

strengths exceeded the loading mechanism capacity.

400 kip VERTICAL LOAD (3-9) ./~_/^200 kip VERTICAL LOAD (3-7) y T1_ 300 kip VERTICAL LOAD (3-8)

-100 kip VERTICAL LOAD (3-5)

25 kip VERTICAL LOAD (3-3) ^

04 0.6 DEFLECTION, in

Figure 8.16. Load-deflection curves for solid 8-in concrete block walls with Type N mortar.

8.4.2.3. Conclusions The following conclusions can be drawn from the

test results on concrete block walls:

(1) The transverse strength of concrete masonry

walls was approximately and conservatively

predicted by determining cross-sectional mo- ment capacity and reducing that capacity for slenderness effects by the moment magnifier

method.

(2) Theoretical moment capacity computed on

the basis of axial prism strength and a linear

stress-strain relationship correctly predicted

the trend of the experimental data. The pre- diction of moment capacity was conservative, since flexural compressive strength is underestimated by axial prism tests.

(3) Slenderness effects computed by the mo- ment magnifier method, using a modulus of

elasticity as derived from experimental

results, have orders of magnitude and show

trends which are in good agreement with the

experimental data.

(4) The ultimate compressive strength of three- block prism specimens made of concrete

block and type N mortar and capped with

plaster correlated well with the compressive

strength of the full scale walls tested under

axial loading. Prism specimens made of 8-in hollow block and high-bond mortar and

capped with plaster developed significantly

greater compressive strength than the full scale walls. However, the same prisms, when

set on fiberboard, developed compressive

strength which correlated well with the

strength of full-scale walls, which were also tested on fiberboard. The added strength of

the capped prisms is probably caused by the

influence of end restraint.

(5) Full-scale walls, when tested in flexure with no axial load, developed flexural tensile strength in excess of 50 percent of the tensile strength as determined from two-block prism

tests in flexure.

(6) Hollow 8-in block walls with high-bond mortar developed significantly higher tensile strength than similar walls with type N mortar. However there was no noticeable dif- ference in compressive strength.

8.4.3. Brick Walls

8.4.3.1. Comparison of Brick Wall Systems

Figure 8.17 shows a comparison of the test results on two wall systems. The solid circles are test results of type A brick walls with 1:1:4 mortar and the hol- low circles are test results of type A brick with highbond mortar. Moments plotted are the moments imposed by transverse loads. The curves show the

average trend of the test results. Note that the walls

with high-bond mortar developed significantly

higher load capacities. This behavior contrasts with

that of the hollow block walls, where the wall

44
800 -

600 -

400 -

4-1 5-1 100 200 300

4-2 5-2 APPLIED TRANSVERSE MOMENT, kip-in

Figure 8.17. Comparative strength of Brick A walls with 1:1:4 and with high bond mortars.

Strength may have been limited by the relatively low

strength of the masonry units. At zero vertical load the two walls with 1:1:4 mortar developed moments of 5.5 kip-in, which cor- respond to tensile strengths of 50 psi. This value

compares with an average tensile strength of 35 psi

developed by the seven-brick beam specimens. The

two high-bond mortar walls tested at zero compressive loads developed moments of 22 kip-in, which

correspond to tensile strengths of 210 psi. This compares with an average tensile strength of 370 psi pre- dicted by seven-brick beam tests. Thus, in this case,

the high- bond mortar walls developed 57 percent of the tensile strength predicted by prism tests, and the

regular mortar walls exceeded the prism strength.

Figure 8.17 also lists the short-wall axial load

capacity predicted from the average prism strength

for the two waU systems. The values were not plotted

since one lies off the figure. The walls with 1:1:4 mortar developed an average axial load capacity of

567 kip. Short-wall axial load capacity computed on

the basis of prism strength would be 965 kip. This

result indicates that the wall developed only 59 per- cent of the short-wall compressive strength. The

high-bond mortar walls developed an average axial

load capacity of 858 kip or 77 percent of the short- wall axial load capacity of 1105 kip computed from

prism tests. These results lead to the conclusion that the axial load capacity of these walls is probably

limited by stability induced compression failure.

brick b prism strength

brick s prism strength

1200 -

1000

800 -\

600 -

400 -

aoo -

0 200 400

APPLIED TRANSVERSE MOMENT, kip-in

Figure 8.18. Influence of brick units on the strength of high bond mortar walls.

rather than by the compressive strength of the

masonry.

The effect of the properties of the brick units on

the transverse strength of high-bond masonry walls

is illustrated in figure 8.18, which shows a comparative plot of the interaction curves for Brick A, Brick

S, and Brick B walls. The curves show the approximate trend of the test results. Compressive

strengths of the brick units are 14,480 psi for Brick

A, 17,560 psi for Brick S, and 20,000 psi for Brick B. Tensile strengths of the walls, computed from trans- verse load capacity with zero vertical load and compressive strengths computed from wall failures

under axial compressive loads are tabulated with the

average prism strengths for each wall system:

Wall

tensile strength

Prism

tensile strength

Wall

compressive

strength

Prism

compressive

strength

(psi) (psi) {psi) (psi) Brick A 210 370 4800 6240

Brick S 120 220 60.50 7320

Brick B 300 430 5140 7650

Comparison of the tensile strength data for both,

wall tests and prism tests, indicates that Brick S

masonry was weakest in tensile strength. Since in 45
compression Brick S is stronger than Brick A, there

appears to be no correlation between brick compressive strength and the tensile strength developed by

high-bond mortar. It is quite conceivable that other

brick properties, for instance, the initial rate of ab- sorption, may effect the tensile strength developed

by the mortar. The relative weakness of Brick S

masonry in tension may also be related to the fact that Brick S is not cored. There is definite correlation between the tensile strength derived from prism

tests and the tensile strength of the walls; however,

it is evident that the flexural prism tests overestimate the tensile strength of the walls. Brick S walls

developed 55 percent of the prism tensile strength;

Brick A walls, 57 percent; and Brick B walls, 70 percent. Comparison of compressive strength data from

full-scale wall tests and from prism tests indicates

that while in the prism tests masonry compressive

strength increased with the compressive strength of

the brick units, the full-scale walls behaved in a dif- ferent manner. Brick S waUs developed the highest

compressive strength (the same walls had the lowest

tensile strength), which was 83 percent of the prism

strength, while Brick B walls developed only 67 per- cent of the prism strength. As previously noted, the

walls probably failed by stability induced compression failure rather than by compression.

In the latter case the axial load capacity of the

walls would be a function of the modulus of elasticity

and not of masonry compressive strength, and moduli of elasticity do not necessarily increase with compressive strength of masonry. To date, no extensive

experimental study on moduli of elasticity of brick

masonry with high bond mortar has been conducted.

Data available from another research program con- ducted at the National Bureau of Standards, as shown in figures 8.2 and 8.3, indicate the following

average initial tangent moduli of elasticity: Brick A

with 1:1:4 mortar, Ei = 3.65 X lO*' psi; and Brick A

with high-bond mortar, Ei = 4.2 X 10'' psi. In the fol- lowing table, axial failure loads are listed together

with critical loads (Euler) computed on the basis of

"pin ended" wall conditions as well as the partial fix- ity conditions illustrated in figure 8.7(c). Stiffness EI

at failure is assumed to equal 0.7 EJ,, in accordance

with eq (7.30).

It appears that axial failure loads tend to occur

within the range of computed critical loads and are considerably lower than predicted short-wall

strength. It can therefore be assumed that wall

failures are attributable to stability rather than

strength.

Mortar

type

Avg.

axial

load

Computed critical load Short-wall

axial failure load based

on prism test

Pin ended Partial fixity

a-ip) (kip) ikip)

1:1:4 567 540 840 960

High-bond 858 640 990 1110

Further comparison of the three interaction curves in figure 8.18 shows that at low axial loads

Brick S, shown by the solid curve, developed lower

transverse strength than Brick A which is shown by

the dashed curve. This relationship tended to be

reversed at high axial loads, even though the Brick

A specimen at the 400-kip vertical load developed

very high transverse strength. This general trend is consistent with the observation that Brick S masonry

had lower tensile strength and higher compressive

strength. Brick B walls, shown by the dashed-dotted

curve, developed considerably higher transverse

strength than the other two wall systems.

Typical load-deflection curves for the four wall

systems tested are shown in figures 8.19, 8.20, 8.21,

and 8.22. In all cases the initial slope of these curves, which is basically a function of the modulus of

VERTICAL LOADS

A 100 kip B 250 kip C 350 kip ^ BM-5)

!c(4-7)

. A (4-3) X

- /

- ft.

A 1 1 1 1 1 1 0 0.2 0.4 0.6 DEFLECTION, in Figure 8.19. Load-deflection curves for Brick A walls with 1:1:4 mortar. 46
0.4 0.6 DEFLECTION , in

1 .0

Figure 8.20. Load-deflection curves for Brick A walls with high

bond mortar.

VERTICAL LOADS

A 140 kip B 290 kip C(6-7) ^ "'P

0.4 0.6 DEFLECTION, in

Figure 8.21. Load-deflection curves for Brick S walls with high bond mortar.

._ 8

S 4 -

VERTICAL LOADS

A 160 kip B 320 kip C 600 kip

0.2 0 4 06 OB 1.0 1.2 DEFLECTION, in

Figure 8.22. Load-deflection cun>es for Brick B walls with high bond mortar.

Note that some of the curves do not start at the

origin. This behavior is caused by accidental initial eccentricity of the vertical load. If the initial vertical

load eccentricity imposes an added moment on the

specimen the curve starts to the right of the origin.

If initial eccentricity tends to reduce the moments

acting on the specimen the curve will start to the left of the origin.

The relative stiffness of the different wall systems

is illustrated in figure 8.23, which shows a comparative plot of load-deflection curves for the four wall

systems at approximately equal vertical load. Brick

I elasticity of the masonry, is similar and seems to be

jl independent of the magnitude of the vertical comI pressive loads. The subsequent point where the

I load-deflection curves depart from this initial slope,

which is probably the point where section cracking

occurs, depends on the magnitude of the vertical

load up to the load at which walls fail in compression

before section cracking occurs. Above that load an

increase in vertical load seems to have no effect on

the load-deflection curve. An exception to this is the curve for the 350-kip vertical load in figure 8.19

where inelastic deformations, caused by high compressive stresses, lowered the stiffness of the wall. Curve "D" in figure 8.20 shows the curve for specimen 5-8. which developed higher transverse

strength than the other specimens.

BRICK B, HIGH-BOND MORTAR, 320 kip VERTICAL LOAD

/

BRICK A, HIGH-BOND MORTAR,

300kip VERTICAL LOAD BRICK S, HIGH-BOND MORTAR, 290 kip A VERTICAL

LOAD

0.4 DEFLECTION, in

Figure 8.23. Comparative stiffness of brick ivalls. 47
I A walls with 1:1:4 mortar were somewhat less stiff than the other wall systems. There is no noticeable

difference in stiffness between high-bond mortar

walls made of Brick A and Brick S. The Brick B

walls, which also developed much higher transverse

strength, developed significantly smaller deflections

than all other wall systems. This added stiffness must be caused by a higher value of EI which is probably due to the combined effect of a higher

modulus of elasticity and a high moment of inertia because of reduced section cracking due to higher

tensile strength. This observation is not supported

by the relative magnitude of critical loads which was

previously discussed, even though reduced section

cracking may affect deflection without materially af- fecting critical loads.

Initial tangent moduli of elasticity may be computed from the initial slope of the load-deflection curves. Since there is some doubt about the degree

of end fixity, moduli were computed for the extreme

cases of partial fixity as in figure 8.7(c) and of pin

ended condition as in figure 8.7(a) at the base of the

wall. The following tabulated values were derived in

this manner.

Partial

fixity Pin ended

Brick B (liigh-bond mortar) Brick S (high-bond mortar) Brick A (high-bond mortar) Brick A (1:1:4 mortar)

£' = 7.3x 10'=-12.0X 10'= psi

£' = 3.0x 10'=- 5.0 X 10'= psi

£' = 3.6x 10'=- 6.3 X 10'= psi E = 2.2x 10'=- 3.9 X 10'= psi

Values for Brick A with high-bond mortar are between 3.6 X 10'' and 6.3 X 10" psi. The average

value of tangent modulus of elasticity derived from

figure 8.3 is 4.2 X 10" psi. These values appear

reasonably consistent and seem to indicate that fixi- ty may have been somewhat less than the partial fixi- ty which was conservatively assumed in the in- terpretation of test results. A similar comparison can

be made for Brick A with 1:1:4 mortar, even though

in this case the specimens on which figure 8.2 is based had a somewhat higher compressive strength

than similar prisms taken from the walls tested, and

therefore also had a higher modulus of elasticity.

The tangent modulus derived from figure 8.2 is 3.6 X 10" psi, while the modulus for Brick A with 1:1:4 mortar computed from deflection curves is between

2.2 X 10" and 3.9 X 10" psi. Again it appears that the

values are reasonably consistent and that end fixity was probably somewhat less than the assumed partial fixity. The values of the moduli for the above

mentioned masonry walls are also reasonably consistent with observed critical loads. The value for Brick B, on the other hand, appears extremely high

considering the low capacity of these walls under

axial vertical loads.

8.4.3.2. Correlation of Test Results with Theory

The correlation between prism strength and the

strength of full-scale walls for the four wall systems

tested is illustrated in figures 8.24, 8.25, 8.26, and

8.27. Again vertical loads are divided by Po which is the short wall axial failure load, computed on the

basis of prism strength, and moments are divided by

Ml; = Po^/12, which is the theoretical maximum

elastic moment resulting when a vertical load is ap- plied at the edge of the kern of the section. A dual

scale is used to show actual magnitude of loads and

moments. The part of the moment caused by deflection is shown by a sohd horizontal line. The left end

of this line represents the moment caused by trans- verse loads alone. The right end represents the ulti- mate moment acting on the wall at failure. Thus, the

magnitude of the measured slenderness effect can

be clearly seen by the length of the solid lines. The

figures illustrate the great magnitude of the added

moment caused by deflection, which represents the j slenderness effect. Figure 8.24 shows the test results on Brick A walls with conventional mortar. The

right-hand end of the solid horizontal lines represents ultimate moment capacity and should be

compared with the solid curve marked Me which was computed on the basis of prism strength. Note

that the total ultimate moments developed by the

walls closely follow the predicted short wall interaction curve. Theoretical reduced moments were computed by

the two methods represented by the following equations:

M.;=M.(i-£)

and (1) EI = ^

(7.29)

or (2) EI = EiI„ (o.2 + ^^^0.7EiI„ (7.30)

48
P/Po

MOMENT, kip-in

Figure 8.24. Brick A walls with 1:1:4 monar, correlation with prism strength.

P„t/I2 4 lO^psi 6,240 psi

f', = WALLS 210 psi PRISM 370 psi

300 MOMENT, kip-in500

Figure 8.2.5. Brick A walls with high bond mortar, correlation with prism strength. These theoretical curves were developed by reducing the ultimate value of Me shown by the solid curve

in figure 8.24. For Brick A, values of /,'„ and E used

in arriving at these reduced curves were independently derived on the basis of prism tests and the

stress-strain values in figures 8.2 and 8.3, except that the value of E; for Brick A with 1:1:4 mortar was

slightly modified as noted below. For Brick S and B

values for were available only from physical

tests. Values for E were assumed to equal the value

for Brick A with high-bond mortar. The theoretical

reduced curves thus computed, which are shown in figure 8.24 by the dashed and the dashed-dotted

curves for eq (7.29) and eq (7.30), respectively.

should be compared with the left end of the solid horizontal lines. Examination of these two theoretical curves shows that eq (7.29) slightly overestimates

the moments at low axial loads and underestimates

the moments at high axial loads. This difference

should be expected since cracking will increase with

decreasing axial loads, causing a reduction in the

moment of inertia, while at high axial loads the total gross section will be effective. Eq (7.30) was derived

to fit the test results of all the brick wall systems and

in general shows good agreement. Nevertheless, eq

(7.29) shows reasonably good agreement with test results within the range below 0.2 Po, which is the

maximum axial load presently permitted in conven49
Figure 8.26. Brick S walls with high bond mortar, correlation with prism strength.

1200-

Ei=4-I0®psi

t'n,= 7650 psi

f't= WALLS: 300psi

PRISMS; 430psi

7-1 7-2 0.2 0.4 0.6 0.8 10

I I I I I I I I I I 100 200 300 400 500 MOMENT, kip-in

1.4 M/Mi< 600

Figure 8.27. Brick B walls with high bond mortar, correlation with prism strength.

tional design, and it has the advantage of greater

simphcity. All calculations were based on partial end

fixity, as illustrated in figure 8.7(c). The magnitude

of moments at a deflection of 0.2-in which is 1/480 of

the wall height, has also been shown on the plot by

the dotted curve. This would be a reasonable value

for a maximum permissible deflection under service

loads in present design practice. The position of that

line relative to ultimate load capacity of the wall in- dicates that even though deflection does not seem to be critical in this case, maximum deflection should

be given some consideration, since, at a load level of

0.2 fo, it occurred at less than 2/3 of the ultimate moment.

For the moment reduction computations for Brick

A walls with 1:1:4 mortar, an of 3 X 10" psi, rather

than the 3.65 X 10'' psi previously mentioned has

been used. The data shown in figure 8.2, which were

developed in another testing program came from

specimens with a compressive strength over 6000

psi, compared with a 5400 psi strength of prisms

tested in this program. This fact, as weU as the measured load-deflection curves, seem to indicate that

the masonry in the waUs used in this program had a 50
lower modulus of elasticity than the masonry used to develop the stress-strain curves shown in figure 8.2. Test results on high-bond mortar walls are plotted

in figures 8.25, 8.26, and 8.27 in a similar manner.

For all these wall systems, theoretical reduced-moment interaction curves were computed using a modulus of elasticity of = 4 X 10** psi. In general,

these specimens developed or exceeded the theoretical moment capacity computed from compressive

prism strength, indicating that "a" was greater than

1. Computed theoretical reduced curves show

reasonably good correlation with test results, except

that the strengths of the Brick B walls (figure 8.27) were underestimated. These walls developed deflection curves corresponding to a much higher modulus

of elasticity, but their buckHng load was rather low.

These walls also exceeded their predicted section

capacity by a substantial margin.

8.4.3.3. Conclusions The following conclusions can be drawn from the

test results on brick walls:

(1) The load capacity of the brick walls tested was

closely predicted by the moment magnifier method,

using compressive prism strength as the basis for predicting short-wall section capacity, and a stiff- ness EI in accordance with eq (7.29) or (7.30). The

trend of the relationship between vertical loads and

moments was correctly predicted by theoretical in- teraction curves and the order of magnitude of observed slenderness effects shows good agreement

with the predicted slenderness effects.

(2) All brick walls tested behaved as slender

walls. They failed by stability induced compression

and their moment capacity was significantly reduced

by slenderness effects.

(3) Compressive and flexural tensile strengths of

prisms built from Brick A with 1:1:4 mortar were

smaller than the strengths of prisms from the same

brick built with high-bond mortar. Compressive

strength of high-bond mortar prisms increased with

the compressive strength of the brick units. Flexural

tensile strength of high-bond mortar prisms did not

correlate with the compressive strength of the brick

units.

(4) FuU-scale walls built with 1:1:4 mortar

developed flexural tensile strength which exceeded

the average tensile strength determined from prism

tests. FuU-scale high-bond mortar walls developed 50

percent or more of the prism tensile strength.

(5) Walls built of Brick A with high-bond mortar

developed significantly higher ultimate load capacity

under combinations of vertical and transverse loads

than walls built of the same brick with 1:1:4 mortar.

(6) Walls built with high-bond mortar and Brick B

developed significantly higher transverse strength

than the high-bond mortar walls built with lower

strength brick. However, under compressive loads

alone these walls did not develop increased strength.

(7) Maximum permissible deflection as well as wall strength should be considered when permissible transverse service loads are determined for brick

walls with slenderness ratios similar to or greater

than the ratios of the walls tested.

8.4.4. Cavity and Composite Wails

Cavity and composite wall systems consist of

separate wythes which may or may not act monolithically. The strengths of these systems de- pend not only on the strengths of the wythes of

which they are composed but also on the manner in which these wythes interact.

8.4.4.1. Comparative Strength of Walls Figure 8.28 shows a plot of the three composite

and cavity wall systems tested. In addition. Brick A

walls with 1:1:4 mortar and 8-in solid concrete block

walls are shown for the sake of comparison. As ex- pected, the 4-2-4-in hollow concrete block cavity wall

had the least strength. The difference in strength

between the 4-2-4-in brick and the hollow concrete

. BLOCK

,400 0-

\. . .BRICK A WITH 1. 1:4 MORTAR '^"^^^ 8-IN SOLID CONCRETE \ 8-IN COMPOSITE \ BRICK AND HOLLOW

\ ---....^CONCRETE \

' BLOCK

\

\

4-IN HOLLOW CONCRETE BLOCK

.• CAVITY WALL

200 400

APPLIED TRANSVERSE MOMENT, kip- in

Figure 8.28. Comparative strerifith of cavity and composite

walls.

51
block cavity walls shown by the solid curve and the

8-in composite brick and block walls shown by the

dashed-dotted curve, which consist of brick and

block components of equal dimension and strength,

is an indication that the composite walls acted as monoHthic composite sections while there was no

composite action by the cavity walls. Another in- teresting comparison can be made between the in- teraction curve for Brick A with 1:1:4 mortar shown

by the dashed curve, in figure 8.28 and the 4-2-4-in brick and hollow concrete block cavity wall. The

curve for Brick A has been plotted even though the

brick in the cavity wall is Brick B, since no observed

interaction curve for Brick B with conventional mortar is available. Note that the Brick A walls acting

alone developed almost as much moment capacity

as the cavity walls and higher axial load capacity

than the cavity walls. It is evident from this comparison that the cavity walls will develop greater

axial load capacity and almost the same moment

capacity if the entire vertical load is supported by

the brick alone instead of resting on both wall components.

Figure 8.29 shows the comparative stiffness of

these walls under transverse loading. The load- deflection curves were measured at shghtly different

load levels, since the systems were not tested at equal vertical load levels. As expected, the concrete

0 0.2 0 4 0.6 0 8 1.0 DEFLECTION, in

Figure 8.29. Comparative stiffness of cavity and composite

walls.

block cavity wall was the least stiff and the composite 8-in wall was much stiffer than the cavity

walls. In the subsequent sections it is attempted to predict the strength of these composite walls on the

basis of section properties, slenderness and the

prism strength of the different material components.

Prism tests were conducted on brick and block

prisms separately, and no composite short-wall sec- tions were tested. The results of these prism tests are utilized to predict wall strength analytically, and f actual test results are compared with predicted j strength.

8.4.4.2. 4-2-4-in Cavity Walls of Hollow Concrete Block The ties connecting the two wythes across the

cavity in this system are not capable of transmitting

shear in the plane of the walls. The wall cross section can, therefore, not be considered a monolithic

section. The walls were loaded vertically at their

geometric center line and it may be assumed that the

vertical load was evenly distributed between the two

|^ j wythes. It is also assumed that the ties were capable

j of transmitting horizontal loads from one wythe to the other, causing both wythes to participate in re- sisting transverse loads. , The results of tests on 4-2-4-in block cavity walls

^ are plotted in figure 8.30 together with interaction curves computed on the basis of prism tests. The as- , sumption was made that each block wythe takes one

half the vertical load and one half the moment. Po . was computed on the basis of the average strength

obtained from the prism tests on the 4-in hollow

block. Moments were computed conservatively, as- , suming that partial top and bottom fixity existed

which produced about one half the pin-ended moment. While it is difficult to determine the actual mo- , ments acting on the wall it may be noted that, since , there were in effect two walls, and the vertical load was applied through a pin connection at the center

^ between the two walls, there could have been partial

j fixity at the top as well as at the bottom. This condi- , tion is illustrated in figure 8.30(a). The additional

| vertical load imposed by this end condition on one of , the wythes and the vertical load reduction in the

other wythe, as illustrated in figure 8.30(a), will | somewhat affect the moment capacity of each of the , wythes. ; Study of the mode of failure of these walls in-, dicates that walls 8-1 through 8-4 failed by mid-
300 —

§ 200 • O

<

O

Ia:LU> 100-

0 —

(a) ASSUMED END CONDITIONS

M2

P/2+AP P/2-AP M|+ M2 = dAP

MOMENT, kip-in

Figure 8.30. 4-2-4-in concrete block cavity walls, correlation with prism strength.

height flexure, whereas walls 8-5 through 8-8 failed by compression near the top. This study suggests

that at lower vertical load the amount of end-fixity was less, causing a larger positive moment, whereas

at higher vertical load the amount of end-fixity was

more than that assumed for the minimum moment

condition, causing a specimen failure by negative

moment, which in this case occurred near the top.

A study of figure 8.30 reveals that the analytically

derived curve for section capacity reflects the trend

of the tests reasonably well. This conclusion can be

verified by comparing the right end of the horizontal

lines with the solid curve. The great strength of specimens 8-5 and 8-6 can be explained by the fact

that a/m exceeds /„', by a considerable margin. This

particularly affects the magnitude of ultimate moments at vertical loads greater than Po/2. It may be

seen from the magnitude of the observed added moments due to deflection at failure, which are represented by the length of the horizontal Hnes, that slenderness effects are an important factor in this wall system. Theoretical reduced interaction curves developed by eq (7.29) and (7.30), which are shown

by the dashed and the dashed-dotted curve, respectively, underestimate somewhat slenderness effects

at low vertical loads. This difference again indicates,

as in the case of the 8-in hollow block walls, that eq

(7.30) underestimates slenderness effects for hollow

sections where cracking causes a greater reduction

in I. The low wall strength under axial load, relative

to the prism strength (75 percent of prism strength)

cannot be explained by the slenderness, and may be

the result of eccentricity caused by unequal load dis- tribution between the wythes. As in the case of the

brick walls, moments causing a 0.2-in deflection are shown in figure 8.30. At zero axial load the walls developed tensile strengths of 24 and 22 psi, or about 74 percent of the

average 31 psi tensile strength developed by the 2- block prisms.

Figure 8.31 shows typical load-deflection curves

for these walls. As in the cases previously discussed,

VERTICAL LOADS A 50 kip B ISO kip C 200 kip

0.4 0.6 DEFLECTION, in

Figure 8.31. Load-deflection curves for 4-2-4-in concrete block cavity walls. 53
load-deflection curves tend to have similar initial slopes and tend to depart from these slopes at section cracking, when axial loads are low, while at higher axial load the effect of vertical load on stiff- ness is not very significant.

8.4.4.3. 4-2-4-in Cavity Walls of Brick and Hollow Concrete Block

It was noted in the previous section that the ties in cavity walls are capable of transmitting transverse

forces from wythe to wythe, but that the stiffness of the ties in the plane of the wall is relatively small, so

that shear forces acting parallel to the plane of the

wall cannot be transmitted. The cavity walls therefore, do not act as monolithic sections. This conclusion is also substantiated by referring to figure 8.28

and comparing the strength of the brick and block

cavity walls with that of the composite walls, which

developed a much greater moment capacity. In the brick and block cavity wall there are two

wythes of different stiffnesses. The strength of this system can be analyzed by assuming that the ties will cause both wythes to assume the same deflection curve. Equations for the strength of cavity walls

are derived using the following assumptions:

(1) Both wythes have equal lateral deflection at

all stages of loading.

(2) The moment developed by each wythe is a function of the deflection.

(3) Failure is defined as flexural or compressive

failure of one wythe, even though the system

may have reserve strength beyond this point

by transfer of all the load to the wythe that did not fail.

WYTHE I, STIFFNESS EI

WYTHE 2 . STIFFNESS Elg

Figure 8.32. Pin-ended cavity wall.

Figure 8.32 is a schematic sketch of a pin-ended

deflected cavity wall. The outside wythe is acted on by the axial force Pi and by the uniformly distributed transverse load w. The inside wythe is acted on by

axial force Pi. Both wythes deflect equally, with a maximum deflection of A. The stiffness of the out- side wythe is EI\ and that of the inside wythe EI2. If

it is assumed that the outside wythe develops a max- imum internal moment Mx and the inside wythe a moment M-?, and that the transverse moment due to load w, as well as the added moments due to axial \ %

loads Pl and P2 are distributed parabolically along

the height of the wall, an equation for the relation- ship between moments Af1 and M-z can be derived.

The mid-height deflection, A can be computed in terms of Mi or Mo:

\

llien

A =

5h'

4SEh

5h'

48£/2

Moments Mi andM2 are therefore related as follows: EI2

M. = Mi Eh

Eh

Eh

i2n

The following expressions can be written for the

total maximum moment (Met) acting on the wall:

M,, = ^+(Pi+P2)A

o

=Mo+aP)^

Moment Met can also be expressed in terms of the

moments acting on each wythe:

Eh'

Me, = Mi + Mo=Mi 1 +

Eh

(4)

From (1) and (3) and the equation for A, the midheight deflection can be rewritten:

A= Mi = • Met

1 48£/i 48£/i

1 +

Eh

Eh

The added moment acting on the wall at mid-height,

(SP)A can be expressed as:

5 h'lP

aP)A = Me,

48 Eh[l +

Eh

Eh

54
5 A-SP

48 lEI

but: 48 ^EI tt'XEI

h- h- = VP

(5)

(6)

therefore: {^P)^ = Met

tP

IPcr

The moment due to transverse loads, Mo, is therefore: Mo = Me,-aP)A

(7)

The following general equation for the section

capacity of a cavity wall can therefore be written:

Met^Me, 1 +

or Met = Me2 1 +

Eh

Eh

Eh

Eh

whichever is smaller.

(8.i;

Slenderness effects can be computed by a moment

magnifier equation:

Mo = Met l- IP

IPc,

(8.2)

Eq (8.1) impUes that one of the two wythes will probably fail first. The other wythe, at the same

time, may or may not have reached its ultimate

strength. Since the ultimate moment of each wythe

depends on its strength and on the axial load component acting on it, this assumption does not exclude

the possibihty that after failure of one wythe the

second wythe may be able to support all the external

loads on the wall and thus prevent collapse at this point. Eq (8.2) indicates that slenderness effects can

be evaluated as a function of the total load acting on

the wall and the sum of the critical loads of both

wythes.

It should be noted that wythe-interaction, as well

as slenderness effects depend on the value of Eh

and that the value of EI for each wythe is a function

of P/Po for the wythe. The relationship between the

EI values of the two wythes is therefore not fixed and

will change with loading conditions.

Hereafter, a theoretical interaction curve for the

4-2-4-in brick and block cavity wall is computed,

using the preceding equations. The following masonry parameters are used.

/,'„ brick = 3580 psi

/;„ block = 1400 psi

£"/ brick = 3.0 X 10«psii^

block = 1.3 X 10« psi

Using the above values of /,'„ and the cross-sectional

areas, the following values for axial load capacity

result:

Po brick = 637 kip

Po block = 161 kip

Moments of inertia computed from cross-sectional

dimensions are:

brick wythe /„ = 209 in* block wythe /„ =177 in*

Partial top and bottom fixity as illustrated in figure

8.30(a) for the block and block cavity walls has been

conservatively assumed in the interpretation of the

test results of the brick and block cavity walls. The same assumption is made in the computations

for evaluating slenderness effects using a "A" value

of 0.7. Thus:

TT'^EI

1Pcr =

(0.7/!)2

Me for the brick wythe is computed by eq (7.7): Pt ( P

For the brick wythe this becomes:

Me^ 1.875P fl-1.33

Po

Me for the block was evaluated by approximate eq

(7.12):

if (1-^.0

where:

The only parameter that was not derived from tests is the modulus of elasticity of brick masonry, which was arbitrarily as- sumed to be 3-10'' psi similar to the modulus of Brick A with 1:1:4 mortar. It is realized however, that the lower strength of this brick masonry (3850 psi, as compared with 5400 psi for Brick A) is probably associated with a lower modulus of elasticity. 55
for the 4-in block:

thus:

c = -= 1.81 in

M^=1.81P 1-1.07

Met is computed using eq (8.1):

Met = Mei fl+l^

The smaller value of Met thus computed will control and is designated by a check mark. Note that up

to XP — 100 kip, brick strength controls while block

strength controls for axial loads above 2P= 100 kip.

Slenderness effects are computed in table 8.2. M'q

is the total net moment capacity of the wall, which in the case of the test specimens corresponds to the

maximum moment imposed by the transverse loads.

For F>^, Me^{Po-P)ek

for the 4-in block: e/c = 0.85in

thus: Me-0.85 {P-Po

Table 8.1 shows the steps for computing the section capacity Met for various combinations of axial loads and moments. Me for each wythe is computed

for its appropriate value of PjPo by the equations

developed above. Then Me,, the total section capacity for the cavity wall, is computed on the basis of each of the wythe capacities, using the appropriate

stiffness EI, as computed by eq (7.30):

EI = EiIn 0.2 +

Po

0.7 EJn

Table 8.2. Computation of slenderness reduction for brick and block cavity tvalls IP M,, ^Pcr 'V/o

kip — in kip kip — in 50 70 509 63

100 140 643 118

150 159 772 128

200 124 843 95

250 79 898 57

300 25 953 17

A comparison between computed and observed

strength is shown in figure 8.33. Specimen tests are plotted by soHd bars. The left end of the bars in- dicates the magnitude of externally applied mo- ments and the length of the bars shows the magnitude of the added moments {PA). Moments were computed conservatively, assuming end fixity that would produce 50 percent of the pin-ended moment.

Table 8.1.. Section capacity computation for brick and block cavity walls

Brick Block

IP PlPo EI Per Mr , EI block EI brick

Mr, based on

brick PlPo EI Pr, Mr

EI brick

* £•/ block*

Me, based on

block

kip psi X in-* k,p kip — in kip — in psi X in^ kip kip — in kip — in 0 0 125 X lOe 6.15 1.37 8.4 V 0 46 X 106 2.65 3.7 9.8

50 0.04 150 X 106 330 45 1.55 70 V 0.1,55 82 X 106 179 38 2.83 108

100 .08 175 X lO** 385 84 1.67 140 V .310 117X 106 2.58 61 2.50 1,52

150 .117 198 X 10** 436 119 1.77 211 .465 1.53 X 106 336 69 2.30 1,59 V

200 .157 223 X 106 490 148 1.72 255 .620 161 X 106 353 52 2.39 124 V

250 .196 248 X 106 545 173 1.65 286 .775 161 X 106 353 31 2..54 79 v' 300 .235 273 X 106 600 194 1.59 308 .93 161 X 106 353 9.4 2.70 25 V

56
400

100 200 MOMENT, kip-in

I Figure 8.33. 4-2-4-in brick and concrete block cavity walls,

j correlation with prism strength.

At zero vertical load, the predicted moment, based

on the brick, is 8.4 kip-in. This compares with a moj ment of 5.25 kip-in or higher developed by the

specimen. Thus, the wall developed about 60 peril cent of the moment capacity predicted on the basis

I of prism strength.

I The dashed Hne in figure 8.33 shows computed

j reduced moment capacity and should be compared

j with the left end of the sohd bars. Note that this

J curve is correct or conservative for all the test

;! results except specimen 9-4, where capacity is

I overestimated by about 7 percent. Up to P= 100 kip,

j the moment capacity is controlled by the brick. In

I this range the computed reduced moment capacity

is in good agreement with the tests. The total mo-

, ment capacity, which is shown by the solid hne and

!! should be compared with the right end of the solid

l| bars, is somewhat less than observed capacity and

consequently, the magnitude of the measured slenI derness effects is larger than that of the computed

effect. This apparent discrepancy is caused by two

reasons: First, as noted before, the assumed initial

I modulus of elasticity probably overestimates

I somewhat the stiffness of the brick wythe. The

j second reason is apparent when figure 8.34, which

7

tfi 6

a. q'o

^

_]LU

CO 4

LiJ >

<

tr

I- 2

- / ^ — -

VERTICAL LOADS

A-35kip

B-iOO kip C-300 kip

A

' ~~— (9-4) / A (9-2) O T_

ll jO^^'^ o test points il^r • DEFLECTIONS FROM

EQ 8 2

'loQ 1I 1I 1I 1I— 0 0.2 0.4 0.6 0.8 DEFLECTION, in

Figure 8.34. Load-deflection curves for 4-2^-in brick and

concrete block cavity walls.

shows typical load-deflection curves for the brickblock cavity walls, is examined. Note that walls 9-2 and 9-4 show considerable apparent ductility. This

behavior is not due to the proximity to a stability

failure, since the axial load is small. The cause is a rather significant loss of stiffness due to cracking,

combined with the fact that after the beginning of

crushing in the brick the wall does not collapse,

since added moment capacity is available in the

block. The actual deflections associated with the

computed failure for these walls are shown in the

plot as solid points. These deflections are very small

compared with the observed deflections at failure. At these deflections, however, the wall developed

from 80 to 90 percent of its ultimate strength.

Above the axial load of 100 kip (figure 8.33), the

computed strength underestimates observed wall

strength by a very large margin. In this range

it is predicted that strength is controlled by the

block. Since in this range PIPq of the block exceeds

0.5, the assumption that the flexural compressive

strength in bending equals the axial strength be- comes extremely conservative, as can be seen by ex- amining figures 8.4 and 8.6. A similar trend can also be observed for specimen 8-6 in figure 8.30, which

shows tests of 4-2-4-in block-block cavity waUs.

Strength in this range could be more accurately

estimated by determining the real value of a/„', in *lexure for this type of masonry.

Axial compressive' strength was computed on the

basis of prism strength of the block and underestimates actual wall strength by approximately 10 per- cent. Observation of actual failures indicates that
above 150 kip specimens failed by block compression near the end. This behavior indicates that, at failure, load was controlled by the block as pre- dicted, but in some cases end fixity probably ex- ceeded the assumed partial fixity.

Figure 8.34 shows typical load-deflection curves

for these walls. The relationships between vertical

load and stiffness are quahtatively similar to the

relationship observed for concrete block cavity

walls. However, the brick and block cavity walls

developed greater initial stiffness.

8.4.4.4. 8-in Composite Brick and Hollow Concrete Block Wall: The composite brick and hollow concrete block

walls studied in this investigation consisted of twc

separate components: a 4-in thick brick wythe and

a 4-in thick concrete block wythe. In order to act as a monoHthic section, shear forces acting in the plane

of the wall between these two components of the

wall must be effectively resisted. In the test specimens, resistance to shear forces was provided

by header courses of brick in every seventh brick course and by the mortar in the collar joint. Analysis

of the test results indicates that the walls did act as monoUthic sections.

The modulus of elasticity of the brick used in the

experimental specimens was between 3 X 10^ to 4 X

10^ psi, and the modulus of elasticity of the concrete

block, based on gross section, was approximately

900,000 psi. Thus the simplifying assumption has

been made that, under equal strain, the brick component of the wall will carry four times the load of

the block component. On the basis of this assumption, a transformed section was developed foi analytical purposes. This idealized transformed sec-| tion is illustrated in figure 8.35(a). i For the sake of simplicity, it has been assumed

that the block area is concentrated in the center-line^ of the two face shells, since stresses must be trans-i mitted through the mortar bed under the face shells. The interaction diagram of vertical force and mo- ment developed in figure 8.35 is based on the trans- formed section shown in figure 8.35(a) and has been

developed in accordance with eq (7.23) throughl s (7.26). It should be noted that in this case the trans- » formed section is not a symmetrical section. Two in-: teraction diagrams, therefore, have to be used, de-i p

pending on the direction in which the moment is ap

plied. In figure 8.35, the interaction diagram shownj

by the solid curve to the right of the origin is developed for moments which tend to impose compressive stresses on the brick side of the wall. These

moments are defined herein as brick compressive

moments. They are the moments which are induced

by the transverse loads. The interaction diagram

shown by the solid curve to the left of the origin is for moments which tend to impose compressive stresses

in the block components of the wall. These latter mo- ments are defined herein as block compressive moments. Note that in this case interaction diagrams

are developed for moments with respect to the section centroid, rather than the geometric centerline

of the section. When section capacity is evaluated

with the aid of these interaction diagrams, all mo- ments must be computed with respect to the section

centroid.

BLOCK COMPRESSIVE MOMENT

M - BLOCK COMPRESSION

ECCENTRICITY OF

APPLIED VERTICAL

jO-9 LOAD, I 32 P^

\l0-8

"niO-7,

P/„ BRICK

Pq compressive MOMENT

(o) transformed section BRICKl CENTROID

M/M^ 12

I ' BLOCK COMPRESSIVE

MOMENT, kip-in

3({^FACESHELLS

0 = BLOCK AREA (gross)

Mg- BRICK COMPRESSION

BRICK COMPRESSIVE MOMENT, kip-in

Figure 8.35. 8-in brick and concrete block composite walls, correlation with prism strength. 58
fori Figure 8.35(a) shows the centroid of the trans- ^wjormed section which is located within the brick

lomponent of the wall at a distance of 1.32 -in from

he geometric center between the brick wythe and

'it^he block wythe. A vertical force acting through this geometric center will therefore impose a block comDressive moment on the wall. The magnitude of this iioment equals 1.32P kip-in. Figure 8.36 illustrates ichematically the experimental loading conditions,

t should be noted that under conditions of end fixity ransverse loads may induce block compressive mo-

•|ments in excess of the initial moment Pe shown in

Eigure 8.36. However, since the base fixity of the test )anels was only partial it is assumed that the max- imum moment at the base of the specimens did not

iiexceed Pe.

Figure 8.36.

M= P e =1 32 P kip-in

End moments acting on 8-in composite brick and

block walls. A dual scale is used in figure 8.35 to show the total magnitude of loads and moments actually developed

in a scale which is superimposed on the nondimensional scale. The dashed radial Hne drawn from the

origin in the direction of the left-hand interaction

diagram is the locus of the block compressive mo- ments (1.32P) exerted by the axial loads which are applied through the geometric center between the

brick wall and the block wall. The theoretical maxI imum axial load acting at that location which can be

I supported by this wall system can be determined

j from figure 8.35. It will occur at the intersection of

the radial hne with the block compressive interaction diagram. This intersection indicates that the

magnitude of the maximum load applied at the

geometric center is limited by the block compressive

moment capacity and equals 0.39Po- If a load had

been applied at the elastic centroid of the wall,

y

presumably the wall could have supported an ulti- mate load of However, under test conditions the

vertical load was applied at the geometric center. Specimen tests are plotted in figure 8.35 and can

be compared with the theoretical interaction curves which were developed on the basis of axial prism

strength. To account for brick compressive and

block compressive moments, each specimen test has

been plotted in figure 8.35 on both interaction dia- grams. The right side diagram shows net brick compressive moments acting on the specimens which

equal the total moment due to transverse load less a moment of 1.32P to account for vertical load eccentricity. The points at the left side diagram show

block compressive moments acting on the

specimens, which are greatest near the end supports

where they equal 1.32P. Added moments caused by

deflections (PA) which magnify the brick compressive moments, are shown by solid horizontal lines on

the right side diagram.

For instance, specimen 10-5, which was subjected

to a vertical load of 130 kip, is plotted on the radial

hne in the left side diagram at a block compressive

moment of 130 X 1.32 = 172 kip-in. This value

represents the maximum block compressive mo- ment acting on this wall. However, reference to the

left-hand interaction curve will indicate that at this vertical load level the wall was capable of resisting a block-compressive moment of about 440 kip-in.

This specimen therefore did not fail by block compression. The brick compressive moment due to

lateral load, acting on this specimen wiU be the left end of the solid horizontal line plotted on the righthand side of the diagram. The length of the solid horizontal line represents the added brick compressive moment acting on this specimen, which equals

the product of the vertical force and the maximum

deflection. Thus the right end of the horizontal line labeled 10-5 represents the total brick compressive

moment acting on this specimen at failure. It can be

seen that this moment slightly exceeded the max- imum moment capacity predicted by the interaction curve for brick compressive moment. Thus this specimen, in accordance with theoretical prediction,

should have failed by brick compression. This is borne out by observation, which indicates a flexural

failure at mid-height in the direction of brick compressive moments, as described in section 6.2. Observation of the mode of failure of the

specimens indicates that specimens 10-1 through 10- 5 failed by flexure at mid-height (i.e. brick compres59
sive moment). Specimen 10-6 did not fail since the

capacity of the transverse loading system was ex- ceeded. Specimens 10-7 through 10-9 failed by block

compression near the supports. This observation is confirmed by the plot of the test results in figure

8.35, which shows that specimen 10-1 through 10-5 exceeded the computed section capacity for brick

compressive moment. Specimen 10-6 could have

developed additional capacity, and specimens 10-7 through 10-9 exceeded the computed section capacity for block compressive moment while not developing the section capacity for brick compressive moment.

Specimens 10-8 and 10-9 failed by axial load alone. These specimen tests have been plotted on the dia- gram at their proper eccentricity. Inspection of these

plots indicates that the compressive strength

developed by the wall system exceeds the predicted

compressive strength of 0.39f*o by a considerable

margin, probably because of greater flexural compressive strength (a/,/,) than predicted for the 4-in block by axial prism tests. The plot of specimen 10-7 clearly indicates that this specimen failed by block

compressive moment, a fact that is confirmed by the

observed mode of failure. The plot of specimen 10-1 indicates that the mo- ment capacity developed at zero vertical load

produced a tensile stress of 30 psi at the block face. This value compares with a 31 psi average tensile strength of the prism specimens.

It was noted at the beginning of this section that, for monolithic action, shear forces between the brick

component and the block component of the wall

must be effectively resisted. Observation of figure

6.18, which illustrates the failure of wall 10-5, in- dicates that horizontal shear did play a role in the

failure of this specimen. However, the records in- dicate an observed flexural failure at mid-height, and

the plot of the test results shows that maximum flex- ural capacity was developed and that the assumption

of a monolithic section is justified.

Typical load-deflection curves for the wall system

are shown in figure 8.37. Note the large block compressive moment that was imposed on the specimen

tested under 350 kip vertical load. (The curve starts

to the left of the origin.)

8.4.4.5. Conclusions

(1) The strength of slender cavity walls was ap- proximately predicted by assuming that the ties between the two wythes are capable of transmitting

DEFLECTION, in

Figure 8.37. Load-deflection curves for 8-in composite brick and block walls.

transverse loads from wythe to wythe, but are not

stiff enough to transmit shear forces parallel to the

plane of the wall. Theoretical section capacity was computed on the basis of axial prism strength, and

slenderness effects were predicted by the moment ' magnifier method. The general trend of observed I relationships between vertical loads and moments |i and observed slenderness effects was correctly pre-

;

dieted by theory. The actual strength of the walls 'i was closely predicted for axial loads up to ^0/3. For|5

higher axial loads the theoretical prediction based on

the assumption that the axial compressive strength

of the masonry equals the flexural compressive

strength was very conservative.

(2) The capacity of composite brick and concrete

block walls was approximately predicted by assuming that the two wythes of this wall system acted as

a monolithic section. The theoretical section capacity was evaluated by assuming that the ratio of the

stiffnesses of the brick and block components ap- proximately equals the ratio of the flexural compressive strengths of these components. It was demonstrated that end moments, as well as mid-height moments, must be considered when the strength of this wall system is evaluated and that the location of the

line of action of the vertical load with respect to the

elastic centroid of the monolithic section must be

taken into consideration. The general trend of the

relationship between vertical loads and moments as well as the actual strengths of the walls were

reasonably closely predicted on the basis of these

theoretical assumptions and of observed prism

strengths of the brick and the block component of

the wall system, as determined separately for each

of the two components.

60
(3) All of the walls tested at zero vertical compres-

'sive load developed tensile strength which equaled

or exceeded 50 percent of the tensile strength preI dieted on the basis of flexural tests on prisms.

9. Recommendations and Discussion

of Present Design Practice

j 9.1. Determination of Transverse Strength of

I Masonry Walls

Two wall properties must be evaluated in order to determine the transverse strength of masonry walls:

1. The capacity of the wall cross section to resist combined bending and axial loads.

2. The effect of wall slenderness on load

capacity.

It has been shown in section 7.2 that the moment

capacity of a wall cross section is not only a function

of the tensile and compressive strength of the

masonry but also of the vertical load acting on the

cross section. Thus an interaction curve can be

j developed which shows the maximum moment

capacity as a function of vertical load. Such an in- teraction curve can be developed if flexural tensile and compressive strengths and the stress-strain pro- perties of the masonry are known.

It has been shown that cross-sectional capacity can be conservatively determined by assuming a

flexural compressive strength equal to the compressive strength of prisms under axial loading, a linear

stress-strain relationship for masonry, and a flexural

tensile strength equal to 50 percent of the modulus

of rupture as determined by prism tests. This

procedure is conservative since it appears that most

specimens developed flexural compressive strengths

in excess of the strength of axially loaded prisms,

and that the assumption of a linear stress-strain rela- tionship will underestimate the moment that the

cross section is actually capable of developing.

In this study, the capacity of wall cross sections

has been evaluated directly by testing eccentrically

loaded prism specimens and indirectly by adding the

moment exerted by the axial load on the deflected

wall to the moment exerted by transverse loads. Slenderness effects are caused by the additional

moments which the vertical loads impose on the

deflected waU. Not only will the vertical load impose

added moments on the walls, which will equal the

product of the vertical load and transverse deflections relative to the line of action of the vertical load,

but the vertical load will also act to increase the magnitude of transverse deflections. These slenderness

effects, which will magnify the moments acting on

the walls, can be approximately predicted by the mo- ment magnifier method, provided that EI, the stiff- ness of the wall, is correctly estimated.

Slenderness effects have been successfully and

conservatively predicted for slender brick walls by

using the moment magnifier equation with an

equivalent stiffness which may be predicted either

by eq (7.29) or by (7.30). Equation (7.29) is somewhat

simpler, while eq (7.30) shows better agreement with

test results for the entire range of vertical loads that the wall can support. No extensive data are available on slender concrete block walls. Transverse strength can be reasonably weU predicted, however, by using

eq (7.29) or (7.30) to predict slenderness effects for

solid block walls, and by conservatively assuming for hollow block that the cracking line represents ulti- mate strength.

The moment magnifier equation [eq (7.28)] uses

a coefficient Cm, which accounts for the shape of the

deflection curve and a coefficient k, which accounts

for end fixity. In the special case where moments are caused by transverse loads, the coefficient C,n is taken as 1. However, in the case where transverse moments are caused by eccentric vertical loads, a case which was not covered by this investigation, the

moment magnifier equation is also applicable, with

a factor C,„ which will depend on the relationship

between vertical load eccentricities at the wall supports. Thus the moment magnifier method could be

applied to determine transverse strength under all practical loading conditions.

The practical procedure in an actual design

problem would be to determine cross-sectional

capacity on the basis of flexural compressive and

tensile strengths, cross-sectional geometry, and the

vertical load at which transverse strength is to be

determined, and then to reduce this capacity to ac- count for slenderness, on the basis of wall length,

end-support conditions, and wall stiffness "fT' at the

design vertical load. The following equations may be used to predict ul- timate and cracking strength. The ultimate trans- verse moment imposed on the wall in the direction

of transverse loads. Mo', can be taken as:

61
The maximum end moment opposite to the direction

of transverse loads. Mend, will be: Mend — Me

where:

Me — maximum moment capacity of the wall in the direction of transverse loads,

Me = maximum moment capacity of the waU

opposite to the direction of transverse

load,

P — applied axial load, Per — critical load for stability-induced compressive failure, computed on the basis of a modified EI, accounting for section

cracking and reduced stiffness at maximum stress, where:

EI = EiIn-(o:2 + y^^0.7 EJn or EI = ^

Ei = initial tangent modulus of elasticity of

masonry.

In = moment of inertia based on uncracked

net section, Po = short-wall axial load capacity (section

7.2.2.1). The transverse cracking strength of a wall, Mc, can be determined by the following equation:

where:

Mc = moment at which cracking occurs (section 7.2.2.1),

Mt = maximum moment considering tensile strength with zero vertical load (section

7.2.2.1), Ck = distance from centroid to edge of kern,

Pero = critical load for stabihty-induced compression failure computed on the basis

of Ei and /« (section 7.3); 0.7 Pero is rec- ommended as critical load for uncracked

walls.

In view of the loss of moment of inertia after cracking of hollow block walls, it is recommended

that the ultimate strength of slender hollow concrete block walls equal the cracking strength.

9.2. Discussion of Present Design Practice

Present masonry design is based entirely on working stresses. Even though design provisions were

developed with specific margins of safety relative tj ultimate strength in mind, comparison of hypothet

cal ultimate strength computed on the basis i design practice standards with ultimate strength a^ tually achieved is not necessarily the only criteric by which these should be judged.

Three different design standards will be coi sidered:

(1) The ANSI Standard Building Code Requin

ments for Masonry [5]

(2) Building Code Requirements for Engineere

Brick Masonry developed by SCPI [9]

(3) Design Specifications for Load-Bearin{

Concrete Masonry developed by NCM !

[10] and proposed recommendatioi

developed by ACI Committee 531 [11;

9.2.1. ANSI Standard Building Code Requirements I The ANSI building code requirements (A41.]i

1953) limit allowable slenderness as follows:

Type of masonry hjt Ratio (based on

nominal dimensions)

Hollow unit walls 18

Solid unit walls 20

Cavity walls 18 '3

These limits may be

24 for the brick wall

compared with a nominal hjt c

5, and a nominal hjt of 12 for th block walls as well as the cavity walls tested in thi

!

program. Consequently, these design requirement

j

permit the construction of walls that will be subjecl

to considerable slenderness effects, particularly ii the case of cavity walls. On the other hand, this star dard does not contain any provisions for stres reduction to account for these slenderness effects To assure a safe design, permitted allowabL

stresses are extremely low, compensating for poten

tial slenderness effects. Such a procedure, whicl

does not account for such an important variable

requires a very high margin of safety which penal

izes short walls and therefore leads to uneconomica

design.

For composite waUs, this standard limits the al lowable stress to that permitted for the weakest o the combinations of units and mortars of which tht member is composed. There are no provisions foil considering the location of the vertical load witl respect to the weakest wall materials.

t in cavity walls is the sum of both wythe thicknesses. 62
9.2.2. SCPl Standard for Engineered Brick Masonry

In the present SCPI Standard (1969), the following

equation is used for the computation of allowable

vertical loads on nonreinforced brick walls: P = CeCsi0.20f,:,)A>,

-where Ce and Cs are determined from the following

equations:

For e

For-<e - r =

6' 1^1

6e 2

1 +

20

1-

0 6 t)'^2{t 20

where: e = maximum eccentricity,

ei = smaller eccentricity at lateral supports,

^2 = larger eccentricity at lateral supports,

t= wall thickness.

Value of ei/e2 is positive for walls bent in single cur- vature and negative for walls bent in double or

reverse curvature. For members subjected to trans-

""I verse loads greater than 10 psf, Ci/e-z is assumed as + 1.0 in the computation of Cp.

Cs=1.20

h

t 300

5.75+ ( 1.5 + — 1.0

Loads and moments at eccentricities in excess of i/3 are Hmited by allowable flexural tensile stresses. Test results on Brick A walls with 1:1:4 mortar are compared in figure 9.1 with hypothetical ultimate

strength curves based on the 1969 SCPI Standard.

These curves were developed on the assumption

that the ultimate loads are equal to CeCsf,'„A,i.

The dashed curve applicable to eccentric vertical

loads was based on eje-i — —0.4 (assuming partial

fixity at one end and a pinned condition at the other

end). The axial load capacity predicted by this curve

is in fair agreement with the test results obtained in this investigation and the capacity predicted by eq

(7.30). However for smaller values of vertical load,

there is considerable difference in the moment

capacities. The reasons for these differences are discussed in the following paragraphs.

Figure 9.2 shows a comparison between the load- ing condition on the tested wall panels and the load- ing conditions which were used in SCPI tests. As

shown, brick walls were subjected to eccentric verti- cal loads in the SCPI tests. If the moment magnifier

method is apphed to these two cases of loading, the

following coefficients would be used:

Lateral loading: C,„ =l,k — 0.8 Vertical loading: C„, = 0.5, A' = 0.8 The resulting predicted slenderness effects would

be quite different for the two cases. Figure 9.3 compares the SCPI curve with trans- verse strength predicted by the moment magnifier

800

600

PRISM STRENGTH T

INTERACTION CURVE BY EQ |7.30|

CURVE BASED ON SCPI 1969 STANDARD

(ECCENTRIC VERTICAL LOADS!

r ^ CURVE BASED ON SCPI 1969 STANDARD

(TRANSVERSE LOADS!

200

2 4-2 MOMENT, l(ip in

Figure 9.1. Comparison of design recommendations for brick walls with test results on Brick A walls with 1 :1 :4 mortar.

63
TEST CONOITIOKS

IN THIS PROCRAM

P

' > PIK

SCPI 1969

PARTIALLY

FIXED

P

PIN

1

PARTIALLY

FIXED

K = 0,8

Cm = 0,5

K = 0 8

Figure 9.2. Comparison of loading and end conditions.

method using the coefficients Cm = 0.5 and k = 0.8. The predicted interaction curve for lateral loading is also shown for the sake of comparison. It can be

seen that the moment magnifier curve for vertical

load eccentricity approximately agrees with the

SCPI curve.

It should be recognized that the SCPI test curve was developed on the basis of tests with eccentric

vertical loads only. When slenderness effects are analyzed by considering added moments caused by

deflections, it can be demonstrated that the case of

lateral loading is not correctly simulated by eccentric vertical loads. However, this difference is generally not recognized in present design practice.

Thus the moment magnifier method provides a more

flexible approach for the prediction of slenderness

effects under all loading conditions.

| In the 1969 SCPI Standard, the case of transverse loading has been recognized as a result of the in vestigation presented in this report. This loading

condition corresponds to the dashed-dotted curve ir figure 9.1 and is in reasonable agreement with the.

L results obtained in this investigation. i The shaded area in figure 9.1 shows the allowable

loads and moments in accordance with the case oil transverse loading specified in the SCPI 1969 stanJ dard. These values are safe, however the margin of safety seems to decrease with increasing e/t. It is ob- vious that these recommendations provide a margin

of safety by "scaling down" a hypothetical ultimate

strength curve- This scaling down is along constant

elt lines. At the eccentricity of elt = 1/3 the interaction curve is scaled down radially, which provides a'' rather slim margin of safety at that eccentricity. For

loads larger than P> (fig. 9.1), the margin of safety for transverse moments gradually increases. At load Pi no moment is permitted, while actually a wall wouldji

be capable of supporting a much greater moment at! that load than at load P2, where the maximum trans-j verse moment is permitted. The philosophy behind

the method of scaling down the ultimate interaction curve is questionable and should be reexamined,

considering all possible combinations of vertical loads and moments at ultimate loads, as well as at service loads.

EQ 17.301 • C„ = l.K = 0.8

EQ |7.30| • = 0.5, K = 0.8

SCPI 1969 STANDARD

.2 M

Figure 9.3. Prediction ofSCPI 1969 conditions byeq 7.30. 64
9.2.3. NCMA and ACI Recommendations

These recommendations account for slenderness

effects, but do not account for end or loading conditions. The following equations are recommended by

NCMA and ACI for nonreinforced walls:

Axial load: p=o.20/; An

where: A„ = net cross-sectional area of the masonry.

Eccentric loads: ^+

^ shall not exceed 1.

where: /« = computed axial compressive stress, p

Fa = —= allowable axial compressive stress, An

/m = computed flexural compressive stress, Fm = 0.3/ni = allowable flexural compressive

stress. Up to an eccentricity of e/t = 1/3, a cracked section

^ may be assumed to compute bending strength in

solid unit walls, neglecting the flexural tensile strength. In hollow unit walls, eccentricity is limited

to a value which would produce tension.

In figure 9.4 allowable axial load {P,iii) computed

by the NCMA standard is compared with critical axial load computed for the 8-in solid concrete block

walls used in this program, where critical axial loads were assumed to equal 0.7 Pco, (eq 7.30). Critical loads were computed for different h/t ratios for the

pin ended case and for partial fixity as assumed in the interpretation of test results. It appears that the

pin ended case is fairly close to the NCMA equation.

The slenderness reduction equation used by

NCMA and ACI, which is also termed "empirical

equation," considers only the geometry of the wall gross section. Variables which influence slenderness

effects and which are not considered by the equation

are: f'mIE, cross-sectional geometry, end fixity, and

loading conditions. The justification for not considering some of these variables may be in part attributed

to the fact that there is a linear relationship between

f'm and E within a certain range of masonry strength,

and that end conditions are similar for most conventional masonry structures. It is questionable

whether, with the increasing use of high strength

masonry and of high rise masonry construction, it is

[ill

1.0

0.8

0.6

0.4

0.2

NCMA STANDARD

Figure 9.4. NCMA expression for slenderness effects. 65
0 3-2 200 300 MOMENT, kip-in

i

i

Figure 9.5. Comparison ofNCMA recommendations with test results on solid 8-in concrete block walls.

still possible to disregard these variables without the use of unduly high margins of safety.

Interaction curves for ultimate and allowable

loads are compared in figure 9.5 with test results and

with interaction curves constructed in accordance

with the analysis in section 8. It should be noted that the NCMA allowable flexural stress is O.S/m and the

allowable compressive stress only 0.2/,'n. These

stresses when multiplied by 5, which may be con- sidered the axial load margin of safety and assumed

constant throughout the elt range, will result in a short-wall interaction curve. This curve assumes an "a" value greater than 1 for large ejt values, with a peak at fo and a distortion which will result in greater ultimate moments at higher ejt ratios. This

short-wall interaction curve is modified for slen- derness by reducing the part of the total stress due

to axial load {PIA), without at the same time reducing

the stress caused by moments (Mcll).

For the slenderness of the walls tested, the modification of the interaction curves is relatively minor.

Curves were therefore constructed for an h/t ratio ol 30. to provide a better comparison between eq (7.30)

and the NCMA equation.

For the small slenderness ratio the moments pre- dicted by the NCMA equation are greater, accounting for an "a" value which is greater than 1. These

increased moments are less conservative than the

moments predicted by the interaction curve at a =

1, and seem to show fairly good agreement wit some of the tested panels, while overestimating th

strength of other specimens.

Comparison of the two theoretical curves for h/ = 30 shows that the NCMA curve predicts a smalle

axial load, but greater moments. While no slende concrete masonry walls were tested, it appears oi the basis of the agreement between predicted am

observed strength of the more slender brick wall

that the NCMA curve probably overestimates thi transverse strength of transversely loaded slende

walls, even though the curve plotted by eq (7.30)

which assumes a= l,is very conservative. However

the NCMA equation is probably conservative for the' case of eccentric vertical loads. Allowable moments by the NCMA equation for ar

hit ratio of 13 are shown in the shaded area in figure

9.5. As in the case of the SCPI equation, the, philosophy of scaling down predicted ultimate inter

action curves should be reexamined.

9.3. Recommended Research

Based on this program the following research is recommended to supplement and expand this in^, vestigation.

(1) Investigation of stress-strain properties q/( masonry and short-wall section capacity. The objective of this investigation would be to develop an in 66
leraction curve for short-wall section capacity on the

basis of short specimen tests. This study should in- clude a thorough investigation of the relationship

between compressive strength in one-dimensional

compression and in flexure and investigation of the

stress distribution corresponding to linear strain

gradients.

(2) Investigation of slenderness effects on transverse strength with particular emphasis on concrete masonry. The purpose of this investigation would be

to study the strength of slender walls with the slen- derness ratio as a variable.

(3) A mathematical study of the effects of section

cracking and the change in E with increasing stress. The purpose of this investigation would be to mathematically determine the relationship between stiff- ness EI and the level of vertical loading at failure for

different wall systems.

(4) Investigation ofwalls resisting transverse loads

as two-way slabs, by studying walls supported along

three andfour edges.

(5) Investigation of walls subjected to a combination of transverse and eccentric vertical loads. The

purpose of this investigation would be to evaluate

the difference between slenderness effects on walls

loaded by eccentric vertical loads, by combined axial

vertical and transverse loads and by combinations of

these two modes of loading. The feasibility of using

the moment magnifier method to predict wall

strength under all these modes of loading would also be investigated.

10. Summary

The following conclusions can be drawn from this investigation:

10.1. Conclusions from Test Results

(1) Transverse strength of masonry walls is reasonably predicted by evaluating the cross-sectional capacity and reducing that capacity to account

for the added moment caused by wall deflection.

The general trend of the test results is in good agree- ^ ment with theory, and the magnitude of individual

test results is conservatively predicted.

(2) Cross-sectional moment capacity of wall

panels was conservatively predicted by a theoretical

interaction curve which was based on compressive

prism strength and linear strain gradients.

(3) Slenderness effects, computed by the moment

magnifier method as modified to account for section

cracking, predicted closely the slenderness effects observed in the 4-in thick brick walls, and

reasonably predicted these effects for concrete masonry walls, concrete block cavity walls, and

brick and block cavity walls.

(4) The qualitative observation was made that at large eccentricities, the flexural compressive

strength of masonry exceeds the compressive

strength developed in pure one-dimensional compression by a significant margin, and that flexural compressive strength increases with increasing

strain gradients.

(5) The transverse strength of cavity walls was

conservatively predicted by assuming that each

wythe carries its proportional share of vertical loads

and moments, and that transverse loads, but not shear forces parallel to the plane of the wall, are transmitted by the ties.

(6) The transverse strength of composite brick

and block walls was approximately predicted by as- suming that the walls act monolithically.

(7) Whenever walls did not fail by stability-induced compression failure, their axial compressive

strength was reasonably predicted by prism tests. In

the case of concrete masonry with high-bond mortar,

compressive tests with prisms capped with high

strength plaster overestimated wall strength, while

prisms set on fiberboard showed good correlation

with wall strength.

(8) Flexural tensile strength of all the wall panels

tested equaled or exceeded 1/2 of the flexural strength as determined by prism tests.

10.2. Comparison of Test Results with

Existing Design Practice

(1) The ANSI American Standard Building Code

Requirements for Masonry do not take into account

slenderness and end-conditions and compensate for variability in wall strengths by high margins of

safety.

(2) The design equations in the 1969 SCPI Stan- dard account for end conditions as well as slen- derness. The equations were developed on the basis

of eccentric vertical load tests but also provide for the case of transverse loading.

(3) The NCMA and ACI recommendations consider slenderness but not end conditions. The

NCMA equations probably overestimate wall

strength under transverse loading conditions.

(4) The interaction diagrams for ultimate trans- verse strength as a function of lateral loads. 67
developed by SCPI and NCMA were scaled dowii

radially to determine allowable working load. This

scaling down in some cases results in extremely low

factors of safety in bending, while the factor of safety

under vertical loads is very high.

(5) Neither the NCMA nor the SCPI standard pro- vide for the design of composite (brick and block)

walls. This type of construction is widely used.

(6) While existing design standards are primarily

intended for the case of eccentric vertical loads, and

in most cases do not account for end conditions, the

moment magnifier method, if used for the prediction

of transverse wall strength, could cover both the case of eccentric vertical loading and the case of transverse loading and could also account for end

conditions.

11. Acknowledgment

The contribution of the following persons is acknowledged:

Louis E. Cattaneo, Research Engineer, was in charge of the laboratory testing program.

Dallas G. Grenley, Research Associate from The

Dow Chemical Company, at the National Bureau of Standards, 1966-67, was in charge of construction

and testing of the high bond mortar specimens.

Frank A. Rankin, was the Mason Contractor in charge of construction of the specimens.

Timothy Miles, Jr. and Harvey M. Shirley, Laboratory Technicians, assisted in the preparation of specimens for testing.

James W. Raines, was the Electronic Technician

in charge of instrumentation.

Edward O. Pfrang, Chief of the Structures Section, participated in the analysis of test results and

made many contributions to this report.

John E. Breen, Professor of Civil Engineering, at the University of Texas, critically reviewed this re- port and contributed to the analysis of test results.

12. References

[ 1] Standard Methods of Sampling and Testing of Brick, ASTM

Designation C67-66 (1966).

[2] Tentative Methods of Sampling and Testing Concrete Masonry Units, ASTM Designation C140-65 (1965). [3] Standard Specifications for Mortar for Unit Masonry, ASTM

Designation C270-68 (1968). [4] Tentative Specifications for Aggregate for Masonry Mortar, ASTM Designation C144-66T (1966). [5] American National Standards Institute, American Standard

Building Code Requirements for Masonry (National Bureau of Standards, 1953). [6] Standard Method of Test for Bond Strength of Mortar to

' Masonry Units, ASTM Designation E149-66 (1966). [7] McGregor, J. G., Breen, J. E., Pfrang, E. O., Design of; Slender Concrete Columns, Journal of the American

| Concrete Institute, V. 67, No. 1, pp. 6-28 (January 1970). \ [8] Column Research Council, Guide to Design Criteria for' Metal Compression Members (John Wiley and Sons, Inc., New York, 1966). ; [9] Structural Clay Products Institute, Building Code Require- ments for Engineered Brick Masonry (August 1969). [10] Natiorial Concrete Masonry Association, Specification for the Design and Construction of Load-Bearing Concrete Masonry (1968). [11] American Concrete Institute, Committee 531, Concrete Masonry Structures — Design and Construction, Journal

of the American Concrete Institute, V. 67, No. 5, pp. 380- 403, (May 1970), and V. 67, No. 6, pp. 442-460, (June 1970).

68
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entitled, Standardization of Data Elements and Codes

in Data Systems.

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