AlllQQ ^^2fi=ll

Structural Performance

of Masonry Walls

Under Compression

and Flexure

TA -

.U58

NO, 73
The Building Science Series

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building materials, components, systems, and whole structures. The Series presents research results, test methods, and performance criteria related to the structural and environmental functions and the durability and safety characteristics of building elements and systems. These publications, similar in style and content to the NBS Building Materials and Structures Reports (1938-59),

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[See mailing list announcement on last page]
structural Performance of Masonry Walls

Under Compression and Flexure

» > > )

S. G. Fattal and L. E. Cattaneo

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Sponsored by

Brick Institute of America

1750 Old Meadows Rd. McLean, Va. 22101 National Concrete Masonry Assoc., 1800 North Kent Street Arlington, Va. 22209 The Departments of the Army, the Navy,

and the Air Force

and

The National Bureau of Standards

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secrefary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued June 1976
Library of Congress Cataloging in Publication Data

Fattal, S G

Structural performance of masonry walls under compression and

flexure. (NBS Building Science Series ; 73)

Bibliography: p. Supt. ofDocs. No.: € 13.29/2:73.

1. Masonry-Testing. 2. Walls-Testing. I. Cattaneo, L. E., joint author. II. Brick Institute of America. III. Title. IV. Series: United

States. National Bureau of Standards. Building Science Series ; 73. TA435.U58 no. 73 [TA670] 690' .08s [693.2'1] 75-619305

National Bureau of Standards Building Science Series 73

Nat. Bur. Stand. (U.S.), BIdg. Sci. Ser. 73, 65 pages (June 1976) CODEN: BSSNBV

U.S. GOVERNMENT PRINTING OFFICE

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Contents

Notation v SI Conversion Units , vi

1. Introduction and Objective 1 2. Scope 1 3. Materials 2

3.1. Brick Units 2

3.2. Concrete Block Units 2

3.3. Mortar 2

3.4. Ties 3

4. Test Specimens 3

4.1. Description and Fabrication of Prisms 3

4.2. Description of Walls 6

4.3. Fabrication of Walls 6

5. Test Procedure and Instrumentation 7

5.1. Prism Tests 7

5.2. Instrumentation for Prism Tests 7

5.3. Wall Tests 7

5.4. Instrumentation for Wall Tests 9

6. Test Results 10

6.1. Prism Test Results 10

6.2. Prism Failures 11

6.2.1. Brick Prisms 11

6.2.2. Block Prisms 13

6.2.3. Composite Prisms 13

6.3. WaU Test Results 23

6.4. Description of WaU Failures 25

6.4.1. Brick WaUs 25

6.4.2. Block WaUs 25

6.4.3. Composite Walls 27

7. Analysis and Synthesis of Test Results 30

7.1. Introduction 30

7.2. Constitutive Relations 30 10.

7.2.1. Brick Masonry 30

7.2.2. Summary of Findings and Conclusions 34

7.2.3. Concrete Block Masonry 35

7.2.4. Summary of Findings and Conclusions 37

7.2.5. Composite Masonry 37

7.2.6. Flexural Rigidity of Masonry 38

7.3. Capacity of Short WaU Sections 38

7.3.1. Analytical Basis 38

7.3.2. Capacity of Brick Prisms 39

7.3.3. Capacity of Concrete Block

Prisms 40

7.3.4. Capacity of Composite Prisms... 41

7.3.5. Failure Hypothesis for HoUow

Concrete Block 42

7.3.6. Summary of Findings and Conclusions 43

7.4. WaU Capacity 43

7.4.1. Capacity of Brick Walls 43

7.4.2. Capacity of Concrete Block

Walls 44

7.4.3. Capacity of Composite WaUs ... 45

7.4.4. Summary of Findings and Conclusions 46

Conclusions and Recommendations 47

8.1. Conclusions 47

8.2. Recommendations 48

Appendix 48

9.1. Flexure — Compression Interaction 48

9.2. Numerical Analysis of HoUow Concrete Block Unit in Compression 50

References 57

ill

Notation

A Area of net section a Flexural compressive strength coefficient

af'm Flexural compressive strength of masonry

b Width of wall

c Distance from centroid to outer fiber E Modulus of elasticity in compression normal to bed joint

Ei Initial tangent modulus of elasticity

EI Flexural rigidity of masonry at failure

e Eccentricity relative to centroid of section

efc Distance from centroid to edge of kern

f'm. Compressive strength of masonry determined from axial prism tests

ft' Tensile strength of masonry determined from modulus of rupture tests g Coefficient in the evaluation of Me

h Unsupported height of wall

/, /„ Moment of inertia of section based on uncracked net section

L Height of wall between lateral supports

M Resultant moment on cross section

Me Maximum moment capacity, computed using linear stress gradients

Mk Moment developed by Pk applied at the edge of the kern

Mo Maximum moment capacity exclusive of slenderness effect m Ratio of elastic moduli in composite section

P Resultant compressive force on cross section

Per Critical buckling load for walls with pinned supports

Pk Vertical load capacity when load is apphed at the edge of the kern of a wall section

Po Short-wall axial load capacity determined on the basis of prism strength

t Thickness of wall

w Distributed transverse load

A Maximum transverse deflection

v
SI Conversion Units

In view of present accepted practice in this technological area, U.S. customary units of measurement

have been used throughout this report. It should be noted that the U.S. is a signatory to the General Conference on Weights and Measures which gave official status to the metric SI system of units in 1960. Readers

interested in making use of the coherent system of SI units will find conversion factors in ASTM Standard

Metric Practice Guide, ASTM Designation E 380-72 (available from American Society for Testing and

Materials, 1916 Race Street, Philadelphia, Pennsylvania 19103). Conversion factors for units used in this paper are:

Length Pressure, Stress

1 in =0.0254*

1 ft =0.3048*

meter

1 psi=6895 pascal

1 psf= 47.88 pascal

meter

Area

1 in2 = 6.4516 X 10-4 meter^

1 ft2 = 9.2903 X 10-2 meter^

MasslVolume

1 lb/ft3 (lbm/ft3)= 16.02 kilogram/meter^

Moment

1 lbf-ft= 1.3558 newton-meter

1 lbf-in= 0.1130 newton-meter

Force

1 lb (lbf)=4.448 newton

1 kip = 4448 newton

Temperature

°C = 5/9 (Temperature °F-32)

* Exactly.

vi
Structural Performance of Masonry Walls Under Compression and Flexure*

S. G. Fattal and L. E. Cattaneo

Ninety-five prisms and 56 walls of brick, concrete block and composite brick and block masonry

construction were tested under various combinations of compressive and transverse loads. Constitutive relations for masonry are developed from test results. By using rational analysis it is shown

that prism strength can be predicted on the basis of linear behavior at failure. It is also shown that wall strength can be predicted on the basis of prism strength when an appropriate allowance is made

for the effect of wall slenderness on sectional capacity.

Key words: Brick; buckling; composite walls; compressive strength; concrete block; constitutive

relations; Hexural strength; masonry; masonry walls; mortar; slenderness ratio; standards; stiffness; structural stability; walls.

1. Introduction and Objective

An analytical approach recently proposed [1, 2,

17], • was used to demonstrate that the strength of

masonry walls can be predicted by using the

strength of prisms of similar construction together

with moment-amplification factors to account for the slenderness of the walls. The objective of this investigation was to expand

and supplement the earher study by exploiting new

experimental evidence on constitutive relationships

and the strength of masonry prism and wall speci- mens of brick, concrete block and composite brick

and block construction.

The results of tests of prisms and walls of various

types of masonry construction are reported in sections 1 through 6. The interpretation of test results and the analytical approach to predict the strength

of masonry walls on the basis of experimental evi- dence is presented in section 7. Conclusions and

recommendations are summarized in section 8. On the basis of available test results from many

different types of masonry construction, it is rea- sonable to assume that the consistent rational pro- cedure, which is corroborated by the experimental

evidence obtained in this and other programs, can

be applied to types of masonry construction not

yet tested, with appropriate allowance for their

physical and mechanical characteristics.

2. Scope

Tests were conducted on prisms and walls having

the following nominal thicknesses and material

compositions:

1. 4-in brick

2. 6-in hollow concrete block

3. 10-in brick and block composite.

"^This work was partly supported by financial jirants from ihe Brick Institute of America. National Concrete Masonry Association and the Tri-Service Building Materials Investigational Program (Office of the Chief of Engineers: Naval Facilities Engineering Command; Headquarters, U.S. Air Force).

' Figures in brackets indicate the literature references at the end of this paper.

All specimens were constructed using portland

cement-hme mortar. For each type of construction,

a minimum of 30 prisms and 14 walls were tested. In order to obtain correlation between prism and wall

strengths, companion prism specimens were con- structed for each wall tested, using similar cross- sectional dimensions and masonry composition, and

were tested under similar support conditions. As

indicated in table 2.1, a total of 95 prisms and 56

walls were tested. The prisms were subjected to vertical compressive loads appUed at various equal, top and bottom

eccentricities with respect to the centroid of the cross section. Prisms were also tested in bending,

using uniformly distributed transverse load; onethird point, transverse loading; and in accordance

with the ASTM E149-66 [3] standard test method.

Walls were tested under transverse load, and

different combinations of transverse and vertical

load.

Table 2.1. Scope and number of tests

Type of specimen

Vertical loading Transverse

loading

Vertical and

transverse

loading

Number

of speci- mens

Centerline Eccentric

Brick prisms 8 12 10 30

Hollow concrete

block prisms 8 12 10 5 35

Brick-block composite

prisms 7 13 10 30

Brick walls 4 6 2 2 14

Hollow concrete

block walls 4 14 2 6 26

Brick block composite

walls 2 6 4 4 16

Total number of specimens 151

1
3. Materials

All materials used in the construction of test specimens were commercially available and were

typical of those commonly used in building

construction.

3.1. Brick Units

One type of brick was used; its dimensions and

physical properties are given in table 3.1. The brick were extruded, wire-cut units with three round

cores as shown in figure 3.1.

3.2. Concrete Block Units

The concrete block units were nominally 6 X

8 X 18-in two-core hollow block. The units are shown in figure 3.1 and their dimensions and physical properties are given in table 3.2. Two shapes of

hollow units were used in the test specimens: kerf

block and corner block (two square ends). The

kerf block units were cut into two pieces and used at the ends of courses requiring a half-unit.

3.3. Mortar

The mortar used in all specimens was type S

mortar, mixed in accordance with the proportion

specifications of ASTM C270-68 [6]. Type I port3-5/8'

7-5/8

o o o

BRICK

5-5/8"

T

1.

15-5/8

6 in. KERF BLOCK

6 in. CORNER BLOCK

Figure 3.1. Masonry units.

Table 3.1. Dimensions and physical properties of brick

Width

in Lengthin Heightin Grossarea

inNet

solid area percent

Compressive

strength

(gross area)

psi

Absorption

percent Saturation

coefficient

Initial rate of absorption

24-h g/30 in^/min

cold

5-h

boil

3.56 7.62 2.25 27.13 79.7 13,085 7.1 9.1 0.76 21.1

Brick was tested in accordance with ASTM C67-66 [4]. Each value in the table represents the average of the results for five specimens.

Table 3.2. Dimensions and physical properties of concrete masonry units

Unit Width

in Height

in Lengthin

Minimum

thickness

in Grossarea

in

Net

area

Compressive

strength

psi Ovendry

weight

lb

Concrete

weight

Ib/cu ft

Water

absorption

Ib/cu ft Face

sheU Web

percent Gross

area Netarea

Corner

block Kerf block5.60 5.60

7.60

7.62 15.60

15.60

1.05

1.05

1.05 1.05 87.36

87.36

56.3

60.2 1243

1462 2210

2429

23.06

25.56

106.95

110.37

12.97

11.31

Concrete masonry units were tested in accordance to ASTM C 140- 70 [5]. Each value in the table represents the average of the

results for five specimens.

2
Table 3.3. Compressive strength of mortar cubes for prism

specimens'^

Batch test numberAge

days Specimen number

Average

compressive

strength

psi

1

1 A 9 A lA, ZA

z

A A oA

o

A A oAQ A 1 /^91 lOzl

A CO Id 1 C/1

1

1041

c0 Oo 1lr>, R ZD9R 1004

0

lf\ /O OD 1 A 7Q 14/0

7( /U OD 1 '^9Q lOZb

Qo 1 0 OD 1041

Qb

or> ^R

lU ^R)D, 1IL^C

lib 1IL., C ZL. 9P

1 9IZ /1

1

41 1 Q oL-1 o 10/0

lo /1

1

41 oL-4, o lOVO

1 /I 00 1 RA— 1

n

1 DO 1

U

1 t^l fl lOlU

10 00 ZdO lU lOUl

10 / 0 QRA 7 odO» /

1 AQQ lOoo

1 71 i / 0 ot>O^V QRA_Q looy

10 7c: /O ODo, y lOUZ

1 QIV 7/1 /4 IP1L.0A—inlU, OlSlU QRin louy

^7 9ni— ZUl 0,^ iP/^in n_.o^iu 114^4 A.QA 91Zl oO o(_.u lU 1 /1 1 Q i4iy

99 OO OL-O lU 1400 23 59 lBll-15 1532 24 36 2B11-15, 1B15 1467 25 72 3B11, 12 1335 26 72 3B11-14 1425

27 76 3B13, 14 1368

28 76 3B15 1344

Avg. 1513

^ Each value of mortar cube strength represents the average

of three test results. Test data not available.

land cement (ASTM C 150- 70) [7], type S hydrated

lime (ASTM C207-49) [8] and sand were propor- tioned 1 : V2 : 4V2 by volume. Sieve analysis of the

sand showed that its fineness modulus which ranged

from 1.6 to 1.8 conformed to the requirements of ASTM C144-70 [9]. Although the mortar was pro- portioned by volume, the measurement of materials

used in each batch of mortar was by weight. The

mixer used was electrically driven and had rotating

blades on a horizontal axis. It was used at half its capacity of 3-ft^. Upon discharge from the mixer,

flow of the mortar was determined in accordance

with ASTM Method C185-59 [10]. The values of mortar flow averaged 133.8 percent between the

limits of 119.4 percent and 154.3 percent. Air content of the freshly mixed mortar was determined

by the pressure method in ASTM Method C231-68

[11] and averaged 7.7 percent between limits of 5.8 percent and 9.5 percent.

A total of 111 batches of mortar were made during the fabrication of prism and wall specimens.

Two-inch mortar cubes were made for each batch

of mortar used in the prisms and walls, and were

air-cured in the laboratory under the same conditions (73° F, 50% R.H.) as the masonry specimens.

The mortar cubes were tested at approximately

the same age as respective prism and wall speci- mens. Compressive strengths of the mortar cubes

and the identification of the specimens to which

they apply are given in tables 3.3 and 3.4 for the

respective prism and wall specimens. The average

strength of mortar was 1513 psi (between the limits of 1335 and 1676 psi) for the prisms, and 1562 psi

(between the Hmits of 1198 and 2360 psi) for the

walls. Since several batches of mortar were required

to construct the walls, the mortar strength varied

at different levels in the wall.

3.4. Ties

Galvanized steel ties were used to bond the

brick and concrete block wythes of composite

masonry specimens. These were of a continuous

truss design and consisted of two parallel longitudinal rods welded to a continuous, diagonally

folded, cross rod as shown in figure 3.2. The configuration had an outside width of 8 inches and was

prefabricated with No. 9 gauge wire.

16"

8"

No. 9 GAUGE GALVANIZED

STEEL WIRE

Figure 3.2. Steel ties used in composite construction.

4. Test Specimens

This section describes the wall and prism speci- mens and the method of their fabrication. The

designations, dimensions, masonry composition,

and support conditions of all test specimens are

listed in table 4.1. In this table and in the text of the report, the specimens are identified by their nominal dimensions. Actual cross-sectional dimensions are shown in figure 4.1. The net cross-sectional area and the net moment of inertia of each

section are given in the same figure. To calculate

these properties, a mortar joint thickness of % in, and a minimum face shell and web thickness of

1.05 in for the hollow block have been assumed.

4.1. Description and Fabrication of Prisms

The prism and wall specimens were fabricated in the same laboratory using similar construction

593-885 0 - 76 -2
Table 3.4. Compressive strength of mortar cubes for prism specimens '•'

Batch number

Age

days

Specimen number

Average

compressive

Strength

psi

Batch number

Age

days

Specimen number

Average

compressive

strength

psi

29 95 4A1 1455 72 149 4A10 1459 30 95 4A1, 4B1 1422 73 149 4A11 1468

31 119 4B1, 4C1 1382 74 148 4A12 1501 32 118 4C1 1373 75 148 4A12, 13 1396 33 118 4C1 1332 76 154 4A13 1535 34 94 4A2 1372 77 153 4A14 1549 35 118 4A2, 4B2 1228 78 153 4A14, 15 1399 36 115 4C2 1198 79 153 4A15 1671 37 115 4C2 1264 80 71 4B10, 11 1458 38 115 4C2, 4A3 1363 81 71 4B12, 13 1419 39 115 4A3 1257 82 71 4B14, 15 1476 40 115 4A3 1236 83 83 4B16, 17 1435

41 109 4B3, 4C3 1499 84 83 4B18, 19 1423 42 116 4C3 1450 85 90 4B20, 21 1521 43 116 4C3 1417 86 90 4B22, 23 1474 44 108 4C3, 4A4 1486 87 94 4B24, 25 1642 45 111 4A4. 4B4 1323 88 97 4B26, 27 1548 46 114 4B4, 4C4 1379 89 105 4C9, 10 2015

47 114 4C4 1315 90 100 4C9, 10 2100

48 114 4C4 1383 91 100 4C9, 10 1946 49 133 4A5 1492 92 100 4C9, 10 1922 50 133 4A5 1631 93 100 4C9, 10 1820

51 134 4B5, 4C5 1584 94 111 4C11 1460 52 134 4C5 1555 95 111 4C11 1604

53 134 4C5 1612 96 111 4C11 1792 54 133 4A6 1478 97 110 4C12 2360

55 133 4A6, 4B6 1475 98 110 4C12 2142

56 133 4B6, 7 1587 99 110 4C12 2222

57 130 4C6 1527 100 112 4C13 2192

58 130 4C6 1639 101 112 4C13 1765 59 135 4C6, 4A7 1602 102 112 4C13 1824 60 161 4A7 1447 103 111 4C14 1524

61 160 4A7, 4C7 1602 104 111 4C14 1494 62 160 4C7 1722 105 111 4C14 1551 63 160 4C7, 4A8 1516 106A 112 4C15 1587 64 160 4A8 1612 106B 112 4C15 1648

65 162 4A8 1640 107A 112 4C15 1591 66 161 4C8, 4B8 1386 107B 112 4C15 1710 67 161 4C8 1452 108A 112 4C15 1609 68 161 4C8 1509 108B 112 4C15 1743 69 160 4A9 1406

70 160 4A9, 4B9 1393

71 150 4A10 1645 Avg. 1562

completion of this testing program. The 4 X 8 X 16-in brick prisms identified by the symbol lA in their designation were built in stacked bond - using six units in as many courses. This gave a height of 15.5

in and a height-to-thickness ratio of 4.4. The 6 X

16X24-in hollow concrete block prisms identified

by the symbol 2A in their designation were built in stacked bond using three units in as many courses. The National Concrete Masonry Association

(NCMA) [13] at the time of testing recommended a prism height not less than 16 in and a height-tothickness ratio not less than 2. The 23.6-in height

and 4.2 height-to-thickness ratio satisfied the NCMA

recommendation. The 10X16X32-in composite

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

Each value of mortar cube strength represents the average

of three test results.

methods, workmanship, types of masonry units and

mortar. For each of the three types of masonry

walls described in section 4.2 (brick, block and

brick-block composite), there correspond 15 prisms

of the same nominal cross-sectional dimensions as the respective wall types. In table 4.1 these prisms

are identified by the letter B appearing in their

designation.

At the time of testing, there was no standard

ASTM test for determining the compressive strength

of masonry prisms. The Brick Institute of America

(BIA, formerly Structural Clay Products Institute)

[12] at that time recommended a prism not less than

12 inches in height with a height-to-thickness ratio of not more than 5 nor less than 2. Similar recom- mendations are currently provided by ASTM

Standard E 447-72 [14] which was issued after the

4
Table 4.1. Description and number of lest specimens

Type of specimen DesignationNominal

dimensions

in

Nominal

height

in

Vertical load at eccentricity Transverse

loads Transverse and vertical loads

End

condition 0 f/12 tl6 t/4 «/3

Brick lAl to 1A5 4X 8X16 16 5 "'Flat prisms IBl to 1B15 4X32X 16 16 3 3 3 3 3 Pin ICl to ICIO 4 X 8 X 27 24 10 •-"in

Hollow 2A1 to 2A5 6 X 16 X 24 24 5 Flat concrete 2B1 to 2B15 6 X 32 X 24 24 3 3 3 3 3 Pin block 2C1 to 2C5 6 X 16 X 16 16 5 Fin prisms 2D1 to 2D10 6 X 16 X 32 32 10 Fin

Brick-block 3A1 to 3A5 10 X 16 X 32 32 "5 Flat composite 3B1 to 3B15 10 X 32 X 32 32 "2 '4 "7 "2 Fin prisms 3C1 to 3C10 10 X 16 X 32 32 10 Pin

Brick 4A1 to 4A6, 4 X 32 X 96 96 2 2 2 2 Pin

walls 4A9, 4A10

4A7, 4A8 2 Flat 4A11, 4A12 2 Pin 4A13, 4A14 2 Pin

Hollow 4B1 to 4B6, 6 X 32 X 96 96 2 2 3 2 2 Pin concrete 4B11 to 4B15

block

walls 4B8, 4B9 2 Flat 4B10, 4B16 2 Pin 4B17 to 4B22 '6 Pin 4B23, 4B24 "2 Pin 4B25, 4B2o, ^3 Pin 4B27

Brick-block 4C1 to 4C4, 10 X 32 X 96 96 "2 '2 '2 Pin composite 4C7, 4C8

walls 4C5, 4C6 "2 Pin 4C2, 4C9 to 4 Pin 4C11 4C12 to 4C15 '4 Pin

Load applied at mid-thickness of specimen.

Vertical load positioned at the centroid of transformed composite section. Load applied at 0.82 in from centroid toward the brick face in one prism and at 1.55 in from centroid toward the block face in three

prisms. Loads applied at 1.64 in from centroid toward the brick face in four prisms and at 3.10 in from centroid toward the block face in three prisms.

Load applied at 4.10 in from centroid toward the block face.

' On two of the specimens the vertical load was applied with an eccentricity of £/4.

" Vertical load eccentricities of t/3 and 0 at top and bottom, respectively.

^ Vertical load eccentricities of f/3 and — t/3 at top and bottom, respectively.

' Vertical load applied at 1.55 in from centroid toward the block face.

' Vertical load applied at 3.10 in from centroid toward the block face. Vertical load applied at 0.82 in from centroid toward the brick face.

' Two specimens with vertical load applied 0.82 in from centroid toward the brick face. " Flat and pin refer, respectively, to restraint and freedom of end rotation described in section 5.

prisms, designated by the symbol 3A, were fabri- cated using three courses of hollow block in stacked

bond and nine courses of brick in running bond.

The procedure followed in the compressive testing

of axially loaded prisms was in accordance with

ASTM Test Method E447-72 [14]. ASTM Standard E-518 [23] prescribes a hori- zontal flexural test method for determining bond

strength of masonry. Although this document was

not available at the time of testing, the procedures

therein described are similar to those used in this

test program. The 10-brick prisms of stacked bond,

designated by the symbol IC, were convenient to fabricate and test as simply supported beams in order to determine the modulus of rupture of brick

masonry. The two-block hollow concrete prisms

(designation 2C) were fabricated for testing flexural bond strength according to ASTM Standard

E149-66 [3]. The 6Xl6x32-in hoUow block

prisms (2D) and 10Xl6x32-in composite prisms

(3C) were constructed and tested in flexure in a manner similar to that used for the brick prisms.

5
1—7.62"—

I

-3.56 _i_

-3.56

A= 27.1 in2

I = 28.6 in4 A = ll2.5in2

I = 118.8 in4

4x8in BRICK PRISMS 4 X 32 in BRICK WALLS AND PRISMS

15.6

5.6 1.

31.6 "T

k5.6"

A= 43.8 in2

I = 184 in^ A= 88.4 in2

I = 372 4 in''

6x16 in BLOCK PRISMS 6 X 32 in BLOCK WALLS AND PRISMS

2.97 ~r663"

-CENTROIDAL

AXIS

31.6 297

663"

A=l950in2

1= 1188 in'' A= 394.8 in2

I = 2402 in''

I0xl6in COMPOSITE PRISMS 10x32 in COMPOSITE WALLS AND PRISMS

Figure 4.1. Cross-sectwnal dimensions of test specimens.

4.2. Description of Walls

All walls were constructed in running bond ^ to a height of approximately 8 ft and were nominally

32 -in wide.

The brick walls were of 4-in single-wythe construction with average dimensions of 3.56 X 31.6-in. The brick were laid with fuU bed and head mortar

joints.

The hollow concrete block walls were of 6-in single-wythe construction with average dimensions

of 5.6 X 31.6-in. The walls contained 6x8xl6-in

whole corner block units having two cores, and half

units that were obtained by cutting a kerf block.

The bed- and head-joint mortar was applied only

to the face shells (face-shell bedding).

The 10-in composite brick and hollow concrete block walls were constructed with 4-in brick facing

and 6-in block backing. Full bed and head mortar

joints were used in the brick facing and face-shell bedding was used for the horizontal and vertical

'Units in adjacent courses overlap by 50 percent and head joints in alternate courses

are in vertical alinement.

mortar joints in the hollow block backing. The collar

joint was slush-filled with mortar and consolidated

in the joint with the aid of a trowel. The brick and

block wythes were bonded by continuous truss- type ties (fig. 3.2) imbedded in horizontal joints at a

vertical spacing of 16 in. The length of the ties was

equal to the width of the specimens.

4.3. Fabrication of Walls

The wall specimens were constructed and air- cured in a laboratory environment maintained at approximately 73° F and 50 percent relative humidity. All specimens were constructed by exper- ienced masons using techniques typical of good

workmanship and supervision. The mortar joints on both faces were cut flush and not tooled. In all wall specimens, the first course was laid directly on a polyethylene sheet placed on the

laboratory floor. Walls were erected between wood

guides braced in two perpendicular directions to keep them in proper vertical alinement. To control the thickness of bed joints, their locations were marked on the wooden frames at 8-in intervals

6
which corresponded to the height of one block and

one ^/s-in joint. Each 8-in interval was further

divided into three equal intervals each corresponding to the height of one brick and one joint. Since

the average height of the brick units was 2V4-inch,

the average bed joint thickness for brick specimens was approximately Vie-inch. The mason kept the outer face of the wall in alinement using a horizontal

hne and level. The construction of 8-ft wall speci- mens is shown in figure 4.2.

Figure 4.2. Eight-ft brick, hollow concrete block and composite

wall specimens.

5, Test Procedure and

Instrumentation

5.1. Prism Tests

All prisms subjected to compressive tests were

capped, top and bottom, with high-strength plaster

and were tested at a loading rate of 50,000-lb per

minute in a 600,000-lb capacity testing machine.

The experimental setup used for testing wall panels

in vertical compression, as described in greater

detail in section 5.3, was closely followed in the

compression testing of the prism specimens.

The flexural strength of the masonry prisms was

determined by a beam test for brick, concrete block

and composite masonry and by a flexural bond test for concrete block masonry. The bond strength in the last test was determined by testing two-block

high prisms that were clamped in metal frames at the top and at the bottom of the prism and loaded

eccentrically 10 in from the longitudinal centerline

of the prism. The test method is described in ASTM

Standard E 149-66 [3]. The 10-course brick prisms were tested as beams

with the 27-in dimension horizontal. The prisms were supported approximately along the centerline

of the two end bricks. The 4-course concrete block

prisms were tested as beams with the 32-in dimension horizontal and were supported along Unes

approximately half a block height from the ends.

Equal numbers of these specimens were tested with

the concrete face and the brick face in tension,

respectively.

Prisms were tested at an average age of approximately 60 days, within a range of 35-75 days.

5.2. Instrumentation for Prism Tests

Test loads on prisms were measured by force

transducers of an electrical resistance type or fluid pressure transducers, as required by the various

test arrangements.

The prism specimens tested in vertical compression were instrumented with displacement trans- ducers which were linear variable differential trans- formers (LVDT's) mounted on the specimens to record vertical deformations. The gage length ex- tended between the centers of the top and bottom

units and in each case, depended on the height of

the specimen. In general, these prisms were instru- mented with three LVDT's on each face. The smallest brick prisms (4 X 8 X 16-in: designation lA) were instrumented with one LVDT at the centerline

of each face and each edge. The output signals from

the load transducer and aU displacement trans- ducers, except two, were recorded on automatic

data-recording equipment for later processing by a

digital computer. The signals from two central dis- placement transducers and the load transducer were

monitored by two x-y recorders which provided

continuous plots of the load-displacement curves for the opposite sides, of the prism.

Two types of transverse loads were separately

used on prisms tested in flexure: third-point con- centrated loads and uniformly distributed loads

induced with an air bag under pressure.

5.3. Wall Tests

A brick wall panel, positioned for testing in vertical compression, is shown in figure 5.1. The

experimental setups for compression tests of concrete block walls and composite walls were also similar to that shown in figure 5.1. The vertical load was applied by the head of a hydraulic testing

7
Figure 5.1. Experimental setup for the vertical compression

test ofa wallfree to rotate at its top and base. machine of 600,000-lb capacity through a 12V2-in

deep loading beam, a 4V2-in diameter half-round

steel bar with the flat side toward the loading beam

and a 2-in thick steel plate that was bedded in highstrength plaster on the top surface of the wall. In

a similar manner, the bottom surface of the wall was seated in plaster on a 2-in thick steel plate

positioned over a 4V2-in diameter half-round bar

with the flat side bearing against the platen of the

testing machine. To keep the wall in vertical aline- ment, temporary wedges were inserted between

the bottom steel plate and the floor on opposite

sides of the half-round bar. These wedges were removed when the loading head was brought into contact with the loading assembly.

The test setup of figure 5.1 was designed to permit rotation at the top and at the base of the

wall. Figure 5.2 shows the setup used for brick and

hollow block wall tests designed to prevent end

rotation.^ A concentric vertical load was appUed

through the loading beam directly to the 2-in thick

steel plate attached to the top of the wall. The load was transmitted to the platen through a 2-in thick

steel bearing plate at the base of the wall. The test program included walls tested under

uniformly distributed transverse load applied singly or in combination with vertical compressive load.

* The two end cunaitions described here are called, respectively, "pin end" and

"flat end" for brevity in this report.

Figure 5.2. Experimental setup for the vertical compression

test of a wall in which the rotation at its top and base is prevented.

Figure 5.3 shows the test assembly. The transverse load was applied through an air bag, made of 20- mil polyvinyl sheeting, which was 84-in long and

extended across the entire width of the wall on one side. The air bag was mounted on a sheet of plywood attached to a steel frame which served

as a reaction when the bag was pressurized. The

frame was mounted on three wheels for ease of

movement. On the opposite side of the wall, upper

and lower horizontal reaction bars were spaced with

their centerhnes 82V2-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 near the four corners. A sheet of rubber between the air bag and the

specimen provided protection to the bag 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. Figure 5.3 shows the assembly

with both reaction frames bolted in place, positioned

in the 600-kip testing machine which was used to apply the vertical load. The inlet tube to the air bag was connected to a hand-regulated compressed air line (100 psi maximum pressure). Air pressure was monitored by a piezoresistance pressure transducer connected

^ Trade names are identified in order to adequately specify the experimental pro- cedures. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material identified

is necessarily the best available for the purpose.

8
Figure 5.3. Installation of the apparatus for wall tests under

transverse uniform load and vertical compressions.

to the bag outlet tube. Continuous visual monitoring of the air pressure was also accomplished as an

alternate backup system, using a mercury manometer which was also connected to the outlet tube. The wall specimens were loaded transversely at a

rate of approximately 0.30 to 0.35-psi per minute.

In all combined loading tests, the vertical load was

applied, first, at a rate of 60,000-lb per minute.

When the desired vertical load level was reached,

it was maintained constant while a transverse load was applied and increased gradually until the

specimen failed. The walls were tested at an average age of

approximately 120 days within a range of 70-160

days. They were moved approximately 30 yards from

the fabrication area to the testing machine by a fork

lift truck. Before moving, the walls were carefully

braced with wooden boards strapped to the edges to prevent damage to the specimen.

5.4. Instrumentation for Wall Tests

Vertical loads, transverse loads, vertical de- formations, transverse deflections, and transverse

strains of the wall specimens were measured and

recorded by an automatic electronic multichannel

data logging system. The vertical loads were measured with a pressure transducer that was

attached to the hydrauhc load measuring system of

the testing machine. In specimens subjected to

transverse uniformly distributed load, the pressure

in the air bag was measured with a pressure trans- ducer having a range of 0-50 psi.

Transverse deflections of the wall specimens were measured at V4-height, mid-height and

^/4-height with two displacement transducers

(LVDT's) at each level, calibrated to read incre- ments of ± 0.0001 in. These LVDT's were attached

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 1 ft away from the upper and lower

ends of the specimen by hinges to prevent bending of the pipe by out-of-plane rotation of the wall. The lower end of the tubing was allowed to slide

in the vertical direction without transverse movement. The ends of the cores of the displacement

transducers were attached to aluminum plates that were mounted on the face of the walls at the three

levels where deflection measurements were

recorded.

Vertical deformations at both faces of the wall

specimens were measured with four LVDT's

clamped to the lower ends of 1-in diameter

aluminum tubing over a 4-ft gage length installed

symmetrically with respect to the height and 4 in inside the edges of the specimen. At the upper end,

these tubes had a pinned connection to the wall and

at the lower end they were attached to a guide which

kept the tubes in vertical alinement but permitted

them to slide downward when the wall contracted

under the load. The centerline of the transducer

core was offset at a distance of P/s-in from the face

of the wall. Two of the instruments attached to the near face of the wall are shown in figure 5.1. In the composite wall specimens, 6-in electrical resistance strain gages were attached horizontally across the collar joint at mid-height on both edges

to record the transverse strains due to axial compression. In specimens subjected to transverse uniform load, LVDT's for vertical deformation

measurement were clamped to the lower ends of the

6-ft aluminum tubing along the edges of the wall

since the pressure bag did not permit instrumentation of one face of the wall. The air-pressure transducer and the displacement

transducers provided signals that were recorded on

automatic data-recording equipment. Instrument

readings were electronically scanned at equal load

increments. The tape record was processed by a

digital computer. The output consisted of tabulated

test results and plotted curves of load versus

deformation.

AU walls were instrumented with two additional

LVDT's which provided an independent set of

measurements of the transverse deflection at midheight and vertical deformation of the specimen. As

shown in figure 5.1, the transverse deflection was measured against a stationary cross-bar attached to the legs of the loading frame. The data from these

instruments and the corresponding load cell trans9
ducers were monitored with x-y recorders which

provided continuous plots of displacement versus

applied load.

6. Test Results

6.1. Prism Test Results

A summary of prism test results is given in tables

6.1 through 6.3. Table 6.1 lists results for brick and

block prisms tested in vertical compression. Table

6.2 lists results of composite prisms tested in vertical

compression. Table 6.3 gives a summary of flexural

test results for prisms of the three types of masonry

construction.

The compressive strength values in the last column of table 6.1 were calculated using the

sectional properties given in figure 4.1 and an as- sumed linear stress distribution for prisms with the

vertical loads apphed within the kern eccentricity.

For prisms subjected to vertical loads applied at eccentricities greater than the kern eccentricity of the section, the compressive strength was calculated on the basis of sectional properties of the area of contact for the cracked section of the specimen

assuming no tensile strength and linear stress dis- tribution. For composite specimens, the last two

columns of table 6.2 Ust the maximum compressive

stress at failure in the brick and the block specimens

respectively. This stress was calculated on the basis

of sectional properties in figure 4.1 for vertical load

eccentricities equal to, or less than, the kern

eccentricity; or on the basis of cracked-section

properties assuming no tensile strength and linear

stress distribution for vertical load eccentricities

larger than the kern eccentricity. The transformed

section was obtained using a modular ratio of 2.6 between brick and concrete masonry (consult sec.

7.2.5). This ratio was obtained from average values

of initial elastic moduU derived from the test reTable 6.1. Summary of vertical compression tests of brick and holloiv block prisms

Prism Height Width End Eccentricity Age Maximum Compressive

designation in in conditions in days load strength " kip psi

4-in Brick prisms

lAl 15.7 7.6 Flat 0 31 120.0 4423 1A2 31 126 0 4644 1A3 32 122^0 4497 1A4 32 120.0 4423 1A5 32 124.5 4589 Avg 122.5 4515

IBl 15.7 31.6 Pin 0 44 497.0 4418 1B2 45 408.5 3631 1B3 45 450.0 4000

Avg 451.8 4016

1B4 15.7 31.6 Pin 0.297 52 465.0 6200 1B5 52 462.0 6160 1B6 50 495.0 6600

Avg 474.0 6320

1B7 15.7 31.6 Pin 0.593 53 353.0 6275 1B8 53 356.5 6329 1B9 53 331.5 5893 Avg 347.0 6166

IBIO 15.7 31.6 Pin 0.890 54 267.0 6329 IBll 57 243.5 5772 1B12 57 267.0 6329 Avg 259.2 6143

1B13 15.7 31.6 Pin 1.187 58 152.0 5404 1B14 58 145.0 5155 1B15 58 151.8 5394 Avg 149.6 5318

10
suits for axially loaded brick and block prisms. Some

of the specimens did not fail under vertical loads

applied axially or at low eccentricity. These tests were terminated when the 600-kip capacity of the

testing machine was reached.

Figures 6.1 through 6.18 show approximate re- gression curves through average test data of

vertical strain versus vertical load for all prisms

tested in vertical compression. For eccentrically

loaded specimens, these plots show two curves

representing the strains at the two opposite faces

of the specimens. It should be noted that vertical deformation measurements actually were recorded

at the centerlines of the vertical gages placed

P/s-in from the faces of the specimens. These data were corrected to provide the strains at the specimen faces by assuming a linear strain distribution

Table 6.1. Summary of vertical compression tests of brick and hollow block prisms — Continued

Prism Height Width End Eccentricity Age Maximum Compressive

designation in in conditions in days load strength " kip psi

6-in Bloclc prisms

2A1 23.7 15.6 Flat 0 35 54.5 1245 2A2 36 63.4 1448

O^7I 2A4 38 75.0 1713 2A5 38 64.5 1473 Avg 64.5 1473

2B1 23.7 31.6 Pin 0 48 127.7 1444 2B2 49 122.5 1385 2B3 49 122.5 1385

Avg 124.2 1405

2B4 23.7 31.6 Pin 0.467 50 120.0 1778 2B5 51 87.8 1300 2B6 49 160.0 2371

Avg 122.6 1816

2B7 23.7 31.6 Pin 0.933 54 115.1 2109 2B8 56 108.9 1996 2B9 56 117.1 2146

Avg 113.7 2084

2B10 23.7 31.6 Pin 1.400 57 82.5 1801 2B11 56 84.4 1843 2B12 56 82.3 1797

Avg 83.1 1814

2B13 23.7 31.6 Pin 1.867 59 62.2 1611 2B14 59 77.0 1994 2B15 62 68.0 1761

Avg 69.1 1789

" Based on gross area of brick units and net area of concrete block units.

11

between the respective centerlines of the gages at opposite faces of the specimens.

6.2. Prism Failures

In general, the trend of prism failures was similar

to those observed in wall specimens of comparable

cross section, end conditions and loading configuration. A brief description of prism failures is given in the following sections according to type of specimen.

6.2.1. Brick Prisms

The five-brick stacked bond prisms, tested under

axial compression, with flat ends, failed by crushing

and sphtting in the vertical plane through the

circular cores of the units as shown in figure 6.19.

593-885 0 - 76 -3
Table 6.2. Summary of vertical compression tests of composite prisms

Prism

designation

Height

in Widthin Endconditions

Eccentricity

in Age

days

Maximum

load

kip

Maximum compressive

stress at failure ^ DnCK

psi olock

psi 3A1

3A2

3A3

3A4

3AS

Avg

31.8 15.6 Flat = 1.230<= 42

44

43

39

43

169.0 070 A

190.0 220.8

178.2

899

1450

1008

1172

951

2024 3268

2274

2644

2133

206.2 > 600

577.5 > 590

600.0 600.0 >600

678 > 1520

1463 > 1491

5533

5533 > 5533

2468 >3951

3803 >3877

1399

1399 > 1399

3B1 3B13

Avg.....

31.8 31.6 Pin 0 70

76

3B1 3B2 3B3

Avg

31.8 31.6 Pin 6* = 0.820 70

71

71 >600

341.0

404.0

363.0

>5533

2583 3060

2750

> 1399

2323

2752

2472

3B4

3B5

3B6

Avg

31.8 31.6 Pin ec= 1.550 72

7374

369.3

177.5

150.0 213.5

2798

1398

1181 1681

2516

1811 1530 2178

OD i 3B8

3B9

Avg

O i -O Oi.O Pin 1 in p — ^ 1 nn to 76

76

180.3 007 O 382.0

340.0 418.0

1420

6146

5913 5263

6471

1840

325

313

278

342

363"

3B10

3B11 3B12

Avg

31.8 31.6 Pin e„= 1.640 7174

75

75

384.2

1 1 7 A

100.0

5948

616

527

314

1846

1578

or>14 3B15

Avg

61.0 ol.o r^in Cc — 4.0DU 77

108.5 572 1712

^ Values were based on measured net cross-sectional area. The notation Cc and designates eccentricities of vertical load from the centroid of the composite section toward the concrete block and brick faces, respectively. Estimated value (basis of derivation explained in sec. 7.3.4).

* Specimen which did not fail previously under an axial load equal to the 600-kip capacity of the testing machine was reused for this test.

12
This failure mode was also observed in axially

loaded prisms pinned at the ends. Vertical loads

apphed at large eccentricities produced specimen

failure by crushing at the compression face and by

bond separation at the tension face as indicated in figure 6.20. The typical failure of brick prisms tested

as beams was by tension in the bond between mortar

and brick as shown in figure 6.21.

6.2.2. Block Prisms

The three-block stacked prisms, tested in axial compression, with flat ends, failed by vertical splitting in the web and face shell as shown in figure 6.22. This type of failure was also observed in specimens

with pinned ends with vertical loads applied axially or at small eccentricity. As vertical load eccentricity was increased, failure by web splitting was ac- companied almost simultaneously by cracking in the horizontal mortar joints on the tensile face of the

specimen. This is shown in figure 6.23. Prisms

tested as beams failed by tensile cracking in the

block as shown in figure 6.24, or, by tensile or bond

splitting along the mortar joint.

6.2.3. Composite Prisms

The 10X32Xl6-in prisms, tested in vertical compression, failed by vertical splitting in the web

of the blocks as shown in figure 6.25. It should be

noted that the loading head was positioned symmetrically with respect to the thickness of these

specimens, resulting in a vertical load eccentricity

toward the block face measured with respect to the

centroid of the transformed section. The 600-kip

capacity load of the testing machine was not

sufficient to cause failure in axially loaded composite

prisms.

Vertical eccentric loads applied near the block

face produced failures initiated mainly by web

splitting in the block for the case of small load eccentricities. At large load eccentricities, failure was

initiated by cracking along a mortar bed joint at the brick face accompanied by web splitting and

face-shell crushing of the blocks as shown in fig- ure 6.26. SpeciUioiis in which the vertical eccentric

load was applied near the brick face failed by

splitting and crushing of the brick as shown in figure 6.27. Prisms tested as beams failed typically

by tensile cracking in the masonry unit or by bond

splitting along the mortar joint at the tension face.

Table 6.3. Summary offlexural tests of prisms

Prism

designation

Nominal

length

of specimen

in

Age

days

Type and description of maximum load

Transverse

uniform

ib

Transverse

concentrated

lb

Axial eccentric '

lb

Eccentricity

4-in Brick prisms

ICI 1C2 1C3

1C4

ICS

Avg

,

1C6

1C7

1C8

1C9

ICIO

Avg..

27 f (24)

27 (24)

6-in Block prisms

2C1 2C2

2C3

2C4

2C5

Avg

16

29

2929

29

29

31

31

3131

31

2828

28

2828

490 4S8

500 460

452

478

600

664

122 516 404

546

660 630

580 620

662

630

10

13
Table 6.3. Summary offlexural tests ofprisms— Continued

Prism

designation

Nominal

length

of specimen

in

Age

days

Type and description of maximum load

Transverse

uniform

lb

Transverse

concentrated '

lb

Axial eccentric "

lb

Eccentricity

2D1 2D2

2D3

2D4

2D5

Avg

.

32 (24;

2D6

2D7

2D8

2D9

2D10

Avg ..

32 (24)

10-in Composite

(brick in tension)

3C1

3C2

3C3

3C4

3C5

Avg.

32 (24)

10-in. Composite

(block in tension)

3C6

3C7

3C8

3C9

3C10

Avg

32 (24)

30

3030

30

30

30

3030

30

31

29

29

2932

32

28

28

2828

29

340

658

720

700

100

563

1332 772

1200 946

918

1032

8200

8100

8640

7500 7650

8018

4490

4160

4270

4220

3700

4168

^ Includes effect of specimen dead weight (avg. = 48.5 lb). Excluded from average. Includes effect of specimen dead weight (avg. = 99 lb). * Represents the sum of two loads positioned at third points.

" Based on gross area of brick units and net area of concrete block units.

' Bracketed figure represents clear span length.

" Tested in accordance to ASTM E149-60 [5]. " Includes effect of specimen dead weight (avg. = 235 lb).

14
150

0 0001 0,002 0,003 VERTICAL STRAIN Figure 6.1. Relationship between vertical compressive load and

vertical strain for 4 X 8 X 16-in brick prisms at e=0.

500

0 0001 O002 O003

VERTICAL STRAIN

Figure 6.2. Relationship between vertical compressive load and

vertical strain for 4 X 32 X 16-in brick prisms at e=0.

15
-0001 0.002 VERTICAL STRAIN

Figure 6.6. Relationship between vertical compressive load and vertical strain for

4 X 32 X 16-in brick prisms at e= t/3.

16
80 240

17
Figure 6.11. Relationship between vertical compressive load FIGURE 6.12. Relationship between vertical compressive load and vertical strain for 6X32'X24-in hollow block prisms at and vertical strain for 6x32x24-in hollow block prisms at e=t/4. e=t/3.

18
- o

o

o

o

oo

o

o

0

0 o

o - 0 •

O - Ay

° ^BLOCK FACE U

T

^BRICK FACE

o •

1 ^ 7

* — o» A si*

0*

o •

0 •0«

o*

A 46 •

A Oa/ •

A o/« A o4*

A 381

• 3B2

o 3B3

J. AVERAGE LOAD

AT FAILURE

o» A cm

n\ A Oi^

1

|eb=0.82in|

0 0001 VERTICAL STRAIN

480

o" 360 —

240 —

• 3B4 A3B5

o 3B6 L AVERAGE LOAD

AT FAILURE

ec=l.55in |

0.001 0.002 VERTICAL STRAIN Figure 6.15. Relationship between vertical compressive load and vertical strain for 10 X 32 "X 32-in composite prisms at et.= 1-55 in. Figure 6.14. Relationship between vertical compressive load and vertical strain for 10x32'X32-in composite prisms at

ei, = 0.82 in.

< 360 q

120 —

A 387

• 388

o 389

J. AVERAGE LOAD

AT FAILURE

8L0CK FACE

-0.001 0 0.001 0.002 VERTICAL STRAIN Figure 6.16. Relationship between vertical compressive load and vertical strain for 10X32X32-in composite prisms at

ec = 3.10 in.

19

593-885 0 - 76 -4
-0.003

360

BLOCK FACE

-0.002

3BI0

381

1

3812 AVERAGE LOAD

AT FAILURE

leb=l.64iri|

-0.001 0 VERTICAL STRAIN

0001

Figure 6.17. Relationship between vertical compressive load and vertical strain for 10 X 32 X 32-in composite prisms at ei,= 1.64 in.

20
PRISM SPECIMEN 1B15 PRISM SPECIMEN 1B15

Figure 6.20. Failure of brick prism under eccentric vertical loading.
Figure 6.23. Failure of hollow block prism under eccentric vertical compressive load.

PRISM SPECIMEN 3A3

Figure 6.25. Typical failure of composite prisms with flat ends under vertical compression.

22
Figure 6.26. Typical failures of composite prisms under

eccentrically applied compressive loads. Figure 6.27. Typical failures of composite prisms

eccentrically applied compressive loads. %der

6.3. Wall Test Results

A summary of test results for wall specimens is given in tables 6.4 and 6.5. The results in table

6.4 are for walls tested in vertical compression. The

results in table 6.5 are for walls tested under various

combinations of vertical compressive and trans- verse uniform loads. Included in the latter group

are specimens, of each of the three types of masonry

construction, that were subjected only to transverse

loads in order to determine the modulus of rupture. In some of the tests, the midspan deflections at the actual time of failure were not recorded since in- strumentation was removed prior to this stage to avoid possible damage. For each of these specimens, the value of the largest measured midspan

deflection and the corresponding load value are shown in both tables. Specimens in which deflections were recorded for the entire loading range

are identified by the fact that the magnitude of the

load tabulated in the last column is equal to the

magnitude of the tabulated load at failure. In these

instances the tabular value of the midspan deflection occurs at the maximum tabulated load level. The vertical load eccentricities for the composite

specimens listed in table 6.4 are measured from

the centroid of the transformed section having the

properties given in figure 4.1. The tests for each of two concentrically loaded

composite walls are shown in table 6.4. Both tests were terminated after the 600-kip capacity of the

testing machine was reached without failure of either specimen. Figures 6.28 through 6.31 are plots

of transverse, or vertical, load versus the mean

transverse midspan deflection for the wall speci- mens of each of the three types of masonry

construction.

23
Table 6.4. Summary of vertical compression tests for walls

WaU

designation

End

condition Agedays

Maximum Axial Load

Magnitude Eccentricity

kip in

Largest measured

midspan

deflection

0 0.220 0 .168

0 .206 0 .147

0.297 .380 .297 .410

.593 .159

.593 .213

1.187 .178 1.187 .220

0 .015 0 .007

0 .033 0 .186

0.467 .100

.467 .162

.933 .210

.933 .212

4-in Brick 4A7

4A8

Flat

Flat

4A1 Pin 4A2 Pin

4A9 Pin 4A10 Pin r III

4A3 Pin

Pin 1 111

4A5 Pin 4A6 Pin

U ill IIUIIU vv block 4B8 Flat

r lat

4B1 Pin

/I DO rin

4B3 Pin

Pin r m

''4B7 Pin r ill Pin r in

4B12 Pin 4B15 Pin

4B13 Pin 4B14 Pin

4B23 Pin 4B24 Pin

4B25 Pin 4B26 Pin 4B27 Pin

10-in Com

posite walls 4C1 Pin 4C2 Pin

4C3 Pin 4C4 Pin

4C5 Pin 4C6 Pin

4C7 Pin 4C8 Pin

128

132

9294

164

133

113

106

113

123

154 154

96

110

109 110

126

129

72

7776

78

79

91

92,

94

94

97

112 110

113 113

132 128

159

160

501.0

500.0

307.0

321.5

168.5

167.3

108.0

112.0

39.9 23.0

130.0

148.0

137.0

128.2

133.5

119.3

93.2 57.0

120.0

99.0

99.8

60.0

72.0

105.0

100.0

80.0

110.1 111.4

> 600 > 600

320.0 351.0

541.5 596.0

170.0 190.0

^top

"

ebot

'

^bot

'

.933

1.400 1.400

1.867

1.867

1.867 0

1.867 1.867

0

0 "60= 1.550 ec= 1.550

'ec = 0.820

eb = 0.820

ec = 3.100

ec = 3.100

.164

.270

.273

.340

.440

.330

.336

.044

.013 .060

0.198

.060

.112 .136

.264

.227

.163

.145

^ The notation Cc and es designates eccentricities of vertical load from the centroid of the

posite section towards the concrete block and brick faces, respectively.

Specimen damaged during handling and moving.

24
Table 6.5. Summary of combined load tests for walls

Vertical compressive load Maximum

transverse

load

psi

Largest measured

midspan

deflection

in

Corresponding

transverse load

psi

Wall

designation

End conditions Age

days

Magnitude

kip

Eccentricity

in Midspan

deflection

in

4-in. Brick 4A11 4A15

Pin

Pin

147

152

00

0.200

.085

0.0.50 .260 0.200

.085

4A13 4A14

Pin Pin

160

165

70

70

0

0

0

0

2.660

2.400

.450

.306 2.660

2.400

6-in. Hollow

block

,\}0\J .030 .200

/I D 1 A 4d1U

4B16

r in Pin

7178

0

0 .200

4d1 / 4B18

rin Pino/83

2020

0

0 00

1X. 770 I IK) 1.780 .0681 77n

1.700

4B21 4B22Pin

Pin 89

90

20

20

1.400

1.400 0.004.050

.730 .700.148 .220

.730 .700

4B19 4B20

Pin Pin 85

87

4040

0

0

0

0

3.240

3.000

.248

.246 3.240

3.000

10-in. Composite 3.18

2.25

a dp'? MC9

Pin

Pin 29097

0

0 _ 3.18

2.28

.072 .066

''4C10 MCll

Pin

Pin 99100

0

0 - 1.04

1.08

.150

.038

1.04

1.08

"4012 HC13

Pin

Pin

106 108 80

80

II0

0.009 0107.15 7.00

.290

.290 6.96

6.96

"4014

"4015

Pin

Pin

109

111 160

160

el = 0.800

66 = 0.800

.076

.063 6.306.60

.550

.570 6.306.60

^ Transverse uniform load applied to the hoUov*r block face. Transverse uniform load applied to the brick face. The notation et designates eccentricity of vertical load from the centroid of the composite section tov^ards the brick face.

6.4. Description of Wall Failures

Wall failures are described in this section ac- cording to type of construction and type of loading.

As indicated previously, walls were loaded in

vertical compression, transverse flexure, or a combination of both.

6.4.1. Brick WaUs

Walls tested in vertical compression generally

failed by sudden crushing and collapse. Concentrically loaded specimens exhibited face spalling

and vertical cracking across the thickness. In- creased load eccentricity caused greater shattering

of specimens at failure. Typical compression fail- ures are shown in figure 6.32. Under transverse loads, or combined vertical and transverse loads, tensile bond-failure occurred

between the mortar and the brick along horizontal

joints near mid-height. A typical failure is shown in figure 6.33. This wall was subjected to a 70,000-lb

compressive axial load appHed prior to and maintained during the application of transverse uniform

load.

6.4.2. Block WaUs

Hollow concrete block walls, tested in vertical

compression, generally developed verticcd cracks

in the web or in the face shell with fciilure being

accompanied by crushing and spalling of the blocks

usually in the three top and bottom courses of the

specimen. Vertical loads applied at large eccentricities caused horizontal spUtting along mortar

joints near wall mid-height, together with vertical

splitting of the webs extending from the bottom

courses upward. Typical wall failures under vertical compressive loads are shown in figure 6.34. Under transverse loads, failure occurred by cracking along a horizontal joint near wall mid-height in specimens with little or no vertical load. Larger

vertical loads caused substantial web splitting,

usually in the lowest three or four courses of the

specimen. A typical failure of a horizontal joint at mid-height under combined loading is shown in figure 6.35. This wall was under a 40,000-lb compres25
175-

BRICK(e=t/l2)

BLOCK (e=t/3)

BRICK (e = t/3)

0.2 0.3 0.4 0.5 TRANSVERSE DEFLECTION, in Figure 6.28. Relationship between vertical compressive load and transverse midspan deflection for brick and hollow block

walls."

''Each curve represents the mean of the results of two tests.

3.20

2.80-

2,40-

2.00

L60-

1.20

0.80

0.40

BL0CK*(P=40kip)

BRICKS/(P=70kip)

-BLOCK (P = 20 kip)

0.1 0.2 0.3 0,4 TRANSVERSE DEFLECTION, in

0.5 0,6

Figure 6.30, Relationship between transverse uniform load and transverse midspan deflection for brick and hollow block

walls.

"Each curve represents the mean of the resuhs of two tests.

400

300

CO 200 —

100 —

0.1 02 0.3 04

TRANSVERSE DEFLECTION, in Figure 6.29. Relationship between vertical compressive load and transverse midspan deflection for composite walls."

"Each curve represents the mean of the results of two tests.

7.0

6.0

5.0

i2 3.0

20

1.0

P= 160 kip-'

e(, = 0.820in

0 0.1 0.2 0.3 0.4 0.5 0.6 TRANSVERSE DEFLECTION, in Figure 6.31. Relationship between transverse uniform load and transverse midspan deflection for composite walls."

"Transverse uniform load applied to the brick face.

26
WALL SPECIMEN 4A1

WALL SPECIMEN 4A7

Figure 6.32. Failure of brick walls under vertical compression.

sive load during the application of the transverse uniformly distributed load.

6.4.3. Composite Walls

As in the case of composite prisms, composite

walls under axial compression supported the 600- kip capacity load of the testing machine without

complete failure. At this load level, web cracking was observed in the edge blocks at the lowest three courses of the specimens as shown in figure 6.36

(4C2). Specimen 4C2 was later tested in transverse

flexure. Specimens in which the eccentricity of

WALL SPECIMEN 4A14

Figure 6.33. Failure of brick wall under combined vertical and transverse loading.

vertical loading was toward the block face, ex- hibited sudden failure by vertical spUtting in the

webs of blocks at the top or bottom three courses of

the specimens as shown in figure 6.36 (4C7). Speci- mens tested with eccentric load applied near the

brick face, failed by sudden crushing of the brick. Examination of failures of specimens loaded in vertical compression did not reveal any significant

cracking or separation occurring at the interface

between brick and block. In specimens tested under

transverse load, failure occurred in bond between

mortar and masonry units along horizontal joints near mid-height of the walls as shown in figure 6.37. This mode of failure was also observed in trans- versely loaded specimens under an 80-kip axial

load. Specimens under a 160-kip vertical load, and

subjected to transverse uniform load apphed to the brick face, failed by crushing of the brick and

tensile cracking of the block at mid-height as shown in figure 6.38.

27

593-885 0 - 76 -5
WALL SPECIMEN 4B8 WALL SPECIMEN 4B12

Figure 6.34. Failure of concrete hollow block walls in vertical compression.

WALL SPECIMEN 4B19

Figure 6.35. Fallure of concrete hollow block masonry wall under vertical and transverse loading.

28
WALL SPECIMEN 4C9 WALL SPECIMEN 4C10

Figure 6.37. Failure of transversely loaded composite walls.

29
WALL SPECIMEN 4C15 WALL SPECIMEN 4C15

Figure 6.38. Failure of composite walls under transverse and vertical loads.

7. Analysis and Synthesis

of Test Results

7.1. Introduction

In this section, the experimental results are in- terpreted and compared with analytical results based on failure theory for masonry walls under

the simultaneous action of bending and compression. The constitutive relations for brick, concrete

block and composite masonry specimens used in the tests are discussed in section 7.2. The inter- action relations between compressive axial load

and bending moment for short masonry piers are discussed in section 7.3. In section 7.4 the effect of wall slenderness on these interaction relations

is discussed.

7.2. Constitutive Relations

7.2.1. Brick Masonry

Average stress-strain curves obtained from the

axial compression tests of brick masonry specimens

are shown in figure 7.1. These curves have been

developed on the basis of average calculated

stresses on the sections specified in figure 4.1 and

of average strains obtained by dividing measured

vertical deformations by the corresponding gage

lengths of the recording instruments.

In figure 7.1, it is shown that the average stress- strain relations for prism and wall specimens with

flat end supports^ (curves A and B, respectively) are approximately Unear and virtually identical

up to a stress level which is about 50 percent of

the calculated average failure stress of the prisms.

Above that level, the prisms as a group developed

less stiffness than the walls although this divergence

does not appear to be very significant. As shown in figure 6.1, the test results from individual prisms were reasonably consistent with somewhat greater

scatter at higher loads. Curves C and D in figure 7.1 show average stress- strain relationships for prism and wall specimens

with pinned supports. The average stress-strain curve for 4 X 32 X 16-in prisms had a noticeably

lower slope in comparison with the rest of the curves. A possible source for this discrepancy is the influence of end effects, such as localized conditions at the ends of the specimens due to lack of

fit between load bearing surfaces, and stress con- centration under the line loading. These effects would be more pronounced in specimens with low

aspect ratios such as the 4 X 32 X 16-in prisms and

would be more evident when the deformation gages

are mounted close to the ends of the specimens.

"The test setup designed to inhibit end rotations is described in section 5.3 and

illustrated in figure 5.2. 30
0 0.001 0,002 0.003

VERTICAL STRAIN

Figure 7.1. Relationship between vertical compressive stress and

vertical strain of axially loaded brick specimens.

The proximity of curves B and D is probably due

to the gage points being sufficiently remote from

the end plates of the walls to minimize the effect of

such end conditions on deformation measurements.

The elastic moduli derived from axial compression tests on brick specimens are summarized in table 7.1. The notation Ei, Eg, and Et has been in- troduced to designate the initial tangent modulus

of elasticity, the secant modulus of elasticity at failure, and the tangent modulus of elasticity at

failure, in that order; designates the average

compressive strength as determined by tests on

axially loaded prisms with flat supports (4515

psi). The secant and tangent moduli at failure for the wall specimens could not be obtained from test results since instrumentation was removed before

the masonry developed its capacity. The tabulated

values for masonry walls with flat supports were

estimated at the highest load level prior to such

removal. As will be explained later, walls with

pinned supports failed by instability. For these

walls, the tangent modulus of elasticity at failure shown in table 7.1 was calculated using the Euler

buckUng formula

where Pc is the Euler buckling load, h is the height

of the wall and / is the moment of inertia of the cross section about its centroidal axis. The values

of Eg and Et are both dependent on the stress level

at failure. In order to investigate stress-strain relationships

in flexure where a strain gradient is present on the

section, a series of eccentric load tests was con- ducted on short prisms in which the effect of trans- verse deflections on cross-sectional stress dis- tribution is of second order magnitude and can

therefore be neglected.

Figures 6.3 through 6.6 show a family of curves

relating vertical loads to vertical strains derived

from test results on eccentrically loaded brick

prisms with pinned support conditions. The vertical loads were applied at four, equal top and bot- tom, eccentricities (producing single curvature) of

^/12, tl6, tl4, and ?/3, where is the thickness of the specimen. At each eccentricity, prisms were

tested in triplicate and the results were averaged

to develop curves for outer fibers at opposite faces

of the specimen. In each figure, the curve on the

right refers to the face subjected to maximum vertical compressive strain while the curve on the

left refers to the opposite face. Generally, these

Table 7.1. Modulus of elasticity of axially loaded brick masonry specimens

{fin =451 5 psi)

Description of fiX 10-« ii fi'sX 10-" Es £,x 10-6 specimen psi

f'.n psi

f'm

psi

f'm

4 X 8 X 16-in Prisms

flat ends 2.8 620 1.8 400 0.8 180 4 X 32 X 96-in WaUs,

flat ends 2.8 620 2.4 530 1.7 376

4 X 32 X 16-in Prisms,

pinned ends 2.3 510 1.6 350 1.2 270 4 X 32 X 96-in WaUs,

pinned ends 2.8 620 2.5 550 2.2 490

31
curves are linear for loads of up to about 40 to 50

percent of capacity and are similar to those derived

from axial loading (fig. 7.1), indicating, at first glance, that the stress-strain characteristics of

brick masonry are not materially altered by the

presence of a strain gradient. Assuming a linear

stress-strain relationship and an uncracked section, stresses at the opposite faces of a specimen

may be obtained using superposition of flexural and axial stresses as follows: P . {Pe)c

A I

(7.2)

where A

I

c =

net area of cross section

moment of inertia about centroidal axis of net cross section

eccentricity of applied load from centroidal axis

distance from centroidal axis to outer

fibers compressive load

stress at outer fibers.

In eq (7.2), c is positive if it is on the same side

of the centroidal axis as e. Also, / and P are taken

to be positive when compressive. For masonry

with no tensile strength or negligible tensile strength

eq (7.2) is valid only when the vertical load ec- centricity is equal to or less than the kern eccentricity (fig. 7.2b). Since a load applied at the kern

produces zero stress in the outer fibers on one side

of the section, the magnitude of the kern eccentricity Ck may be obtained from eq (7.2),

ek J_

Ac (7.3)

For a solid rectangular section eqs (7.2) and (7.3) assume the simpler form.

-CENTROIDAL AXIS

(a) WALL SECTION PLAN VIEW

F

>

^max

f

. (b) STRESS DISTRIBUTION FOR UNCRACKED SECTION

(c) STRESS DISTRIBUTION FOR CRACKED SECTION

Figure 7.2. Stress distribution.

Initial tangent moduli of elasticity may be computed from the Unear portion of load-strain rela- tionships and eqs (7.4) or (7.6). The following tabulated values were derived in this manner.

J~m

fn

ek 6'

(7.4)

(7.5)

For vertical loads applied at eccentricities greater

than the kern eccentricity, the section wiU be

partially cracked and, assuming tensile strength

is negUgible, the stress distribution will be as shown

in figure 7.2c. In this case, the maximum stress for a solid rectangular section and a Unear stress block

is given by the equation,

fn

P

A

4/3

1 - {2elt)

(7.6)

Table 7.2. Initial modulus of elasticity of eccentrically loaded

brick prisms f/i, = 4515 psi

)

Vertical load

at eccentricity tlU tie tl4 tl3

Ei X 10 -« psi 2.5 2.3 1.9 2.6 Eifm 550 510 420 580

Table 7.2 indicated an average initial tangent

modulus of elasticity in flexure of about 2.3 X 10^

psi which is equal to the value derived for the

axially loaded prisms (table 7.1). It should be noted,

however, that values derived from eccentric load

tests tend to become more sensitive to factors such as accidental deviations in eccentricity, degree

32
of precision of deformation measurements and

specimen imperfections. Since the ratio of strains

at opposite outer fibers is constant in the linear range, actual eccentricities may be estimated using

the curves in figures 6.3 to 6.6 on the basis of

the assumption that the combined effect of other

factors is not significant. For instance, at an in- tended load eccentricity of the magnitudes of

strains'^ at opposite face fibers of the specimens

should have a ratio of 3. The ratio of 2.4, derived

from figure 6.5, indicates a probable actual eccentricity larger than f/4. Likewise, the actual strain

ratio obtained from figure 6.6 is 1.2 compared with a

ratio of 1 which would result from an eccentricity of

t/S. The initial tangent modulus of elasticity calculated on the basis of actual test-derived strain ratios would be about 2.1 X 10^ psi in both of these cases. While results of eccentric-load tests can be uti- lized to develop stress-strain curves for nonlinear

regions, the procedure would be approximate be- cause the curves often fall short of the ultimate

load level, and would involve construction of partially nonUnear stress blocks in a manner that would

satisfy the equilibrium conditions. Nonetheless,

to establish some basis of comparison with axial load test results, the stress-strain curve for the

fuU loading range was developed for prisms loaded

at an eccentricity off/12. Tiie resulting approximate

secant and tangent moduli of elasticity at failure were 1.7X10^ psi and 1.1 X 10^ psi respectively.

These values compared closely with the corre- sponding values of 1.6 X 10^ psi and 1.2 X 10^ psi

indicated in table 7.1, which were derived from axial load tests of prisms of similar geometry, composition and end support conditions.

Elastic moduli of slender masonry walls subjected

to eccentric compressive loads may also be derived

from available test data on load-deflection relation- ships. Average plots of eccentric load versus midspan transverse deflection for 4 X 32 X 96- in high

brick walls pinned at the ends, are shown in figure

6.28. The wall specimens were tested in dupUcate

at load eccentricities of f/12, f/6, and tIS. Yokel [15] obtained an analytical solution for walls of solid rectangular cross section subjected

to compressive loads applied at equal top and

bottom eccentricity. The graphical form of that

solution, relating vertical load to midspan deflection,

is shown in figure 7.3 for ready reference. Relevant

notation is defined in the same figure. The derivation is based on the assumption of a constant modulus of elasticity in compression and zero tensile strength for the material, and is valid in the

region f/6 ^ e < f/2. It was subsequently shown

[16] that for practical purposes the relationship

^The word "strain" as applied to a cracked surface is used here to designate average

vertical deformation per unit length, even though cracks actually represent discon- tinuous localized length changes.

provides a good approximation in the region

0 =S e ^ f/6. The following tabulation of initial tangent moduH of eccentrically loaded walls was

derived using the load-deflection curves from indi- vidual wall tests and the analytically derived curve

of figure 7.3.

0.30

INSTABILITY: P=PcR = 0,285 Pgc

- iii\i<;tari f foiiii irriiim U yraRi FFcyiii irrium.

P

0.20 / \

\ h /o \ /

/ /

h/2 \

/ 0.10 /

/ p

2.25-rr2 / 'ec - 2 /

"

1

1

Ebu

1

3

_L1 0.

Figure 7.3. Graphical presentation of brick wall failure by

instability.

Note that the values of elastic moduh, predicted on the basis of load-deflection curves for walls

with load eccentricities equal to or less than the

kern eccentricity, fell within the range of values

predicted on the basis of vertical deformations.

At greater load eccentricities, it becomes vir- tually impossible to obtain meaningful estimates

since slight deviations in eccentricity, either as a

result of lack of planeness or inaccurate positioning of test specimens, are hkely to produce a sig- nificant change in deflection and wall capacity as evidenced by the test results from walls 4A5 and

4A6 shown in table 6.4. In addition, larger load ec- centricities will produce an apparent increase in the modulus of elasticity (table 7.3) since, in this range, tensile strength significantly influences

stiffness and the curve in figure 7.3 was derived for the case of zero tensile strength.

Elastic properties of masonry waUs may also be

derived from the test results of wall specimens

subjected, simultaneously, to axial load and trans33
Table 7.3. Initial modulus of elasticity of eccentrically loaded

brick walls (fm = 4515 psi)

Vertical load Wall Ei X 10-s Ei

eccentricity UcSlg,Ila.llUII psi jmf

(/12 4A9 2.3 510 4A10 2.2 490

tie 4A3 2.8 620 4A4 2.9 640

tl3 4A5 8.1 1790 4A6 3.4 750

verse uniform load. Figure 7.4 shows the deflected

shape of a wall under combined loads. The broken

curve designates the deflection under uniformly

distributed transverse load w, while the sohd curve

designates the deflection produced by the simultaneous action of axial load P and transverse load

w. The latter, acting alone, produces the following

deflections:

A^, = Ai + A. =

384£/ 48£/ {h-L). (7.7)

The addition of axial load P produces the deflected

shape given by the sohd curve, which is also the

shape of the moment diagram produced by the

axial load. Assuming the moment curve to be

parabolic,* the deflection, produced by the axial

load, is given by [2]

Ap =

Noting that 48£/

(7.8)

A = Ai„ + Apand 48^7 TT^EI 5h'

-Pc

where Pc is defined by eq (7.1), the total midspan

deflection relative to the ends of the wall is ap- proximately given by

A-—^-A.. (7.9)

1 -

Using Au,, obtained from tests on brick walls

loaded transversely and with a 70-kip axial load

(fig. 6.33), eq (7.9) gives an average initial modulus

of elasticity of 3.0 X 10** psi. This value is in good

agreement with 2.9 X 10** psi in table 7.3 obtained

from test results of walls subjected to loads ap- plied at the kern, and with 2.8 X 10** psi in table

7.1 obtained from test results for axially loaded

waUs.

L/2

L/2

h/2

h/2

Figure 7.4. Wall deflection under combined loads.

* A parabolic curve is a close approximation to the actual deflection curve.

On the basis of the information discussed in

this section, the brick masonry used in this program

developed an average initial modulus of elasticity

of approximately 620 fm or 2.8 X 10^ psi. This value

is corroborated by data derived from a variety of

test loading conditions producing flexural as weU

as axial deformations. The current issue of "Building

Code Requirements for Engineered Brick Masonry"

developed by BIA (formerly SCPI) [12] stipulates a design modulus of elasticity of 1000 fm with an upper Umit of 3 X 10^ psi for inspected brick

masonry construction. This discrepancy does not necessarily apply to aU brick masonry since the

modulus of elasticity is dependent on many parameters. However, results from previous tests [17] on brick masonry, involving other types of brick

and mortar, confirm the experimental trend of a lower modulus of elasticity than that presently

stipulated by BIA.

7.2.2. Summary of Findings and Conclusions

(1) The brick masonry specimens used in this program developed an average initial modulus of

elasticity of 2.8 X 10^ psi or 620 fm- This was considerably less than that stipulated by the present

BIA Standard [12]. A similar trend has also been

34
observed in the results of previous tests [17]. Since

a reliable prediction of the modulus of elasticity

is essential in brick masonry design which generally

requires consideration of deflections and slender- ness effects, there is a need to reconcile provisions

of the present standard with experimental evidence.

(2) The initial modulus of elasticity of brick

masonry walls can be reasonably predicted on the

basis of axial load tests on companion prisms with

flat ends and of the same material composition as the walls. The method has particular merit in view

of the relative simplicity of the testing procedure

and because errors due to accidental load eccentricity or geometric imperfections can be effectively controlled by averaging deformations of the outer fibers at opposite faces of the specimens.

(3) Flexure-induced strain gradients had no ap- preciable effect on the stress-strain characteristics

of brick masonry walls.

(4) Prisms with the smaller height-to-width ratio

{hi10=^^2) developed a lower modulus of elasticity

in relation to the other specimens. This is probably

attributed to the influence of localized stress conditions at the supports. Mounting of instrumentation

in a manner that would keep vertical deformation

measurements free of end zone effects would

require test specimens to have a greater height-towidth ratio than that of the 4 X 32 X 16-in prisms.

(5) The specimens exhibited nearly Unear stress- strain properties under load intensities of up to approximately 50 percent of the load at failure. Thus, the value of the initial modulus of elasticity

would provide a reasonably good estimate of the

modulus of elasticity within the region of practical

design loads. The average secant and tangent

moduli of elasticity at failure for the axially loaded

specimens were approximately in the order of 80

and 50 percent, respectively, of the value of the

initial modulus of elasticity.

7.2.3. Concrete Block Masonry

Figure 7.5 shows average stress-strain relations

for prisms and walls of hollow concrete block

masonry tested in axial compression. The curves shown are based on the idealized sectional properties of figure 4.1 and test data relating vertical

deformations to appUed loads. Figures 6.7 and 6.8 show average results derived from individual prism

tests. A comparison of the curves in figures 7.1 and 7.5 indicates a common trend in shape and degree of

linearity of compressive stress-strain curves of brick

and of concrete block masonry specimens. There

are other similarities. Note, for instance, the lack

of stiffness exhibited by the pin ended 24-in prisms

relative to the other specimens and the good agree- ment between the initial elastic moduli of the flat ended 24-in prisms and wall panels.

Table 7.4 gives a summary of elastic moduli of

axially loaded concrete block specimens. The values

VERTICAL STRAIN Figure 7.5. Relationship between vertical compressive stress and

vertical strain of axially loaded concrete block specimens.

of Elf'm appearing in the table have been calculated using an average compressive strength

/m=1473 psi for prisms with flat ends (table 6.1). Due to the absence of test data on displacements

near peak loads, tangent and secant moduli at failure could not be predicted for the prisms with

pinned supports.

The results of eccentric load tests on 6 X 32 X 24-

in hollow concrete block prisms were used to derive

the curves shown in figure 6.9 through 6.12 which

relate the compressive loads to the vertical strains

in the outer fibers. The vertical loads were applied

at equal (single curvature) top and bottom eccentricities of f/12, tl6, tj^, and t/S where t designates

the thickness of the specimens. In each figure the curve on the right represents outer fibers under

maximum compression and the curve on the left represents outer fibers on the opposite face of the

specimens.

The test data from 6 X 32 X 24-in eccentrically

loaded prisms provide a means of examining compressive stress-strain characteristics of concrete block masonry in flexure. In the region where the

strain is proportional to the external load, the

maximum fiber stress may be calculated using eq

(7.2) provided the load is apphed within the kern of the section. An exact continuous equation for the

maximum stress of cracked hollow sections cannot

be derived because of discontinuities in sectional

geometry. For such cases maximum fiber stress may

35
Table 7.4 Modulus of elasticity of axially loaded concrete block masonry specimens

(f'm = 1473 psi)

Description of specimenfiX 10-"

psi Ei

f'n,

i'sX 10-«

psi

f'm

£,X 10-«

psi

f',n

6 X 16 X 24-in Prisms

flat ends

1.5 1020 0.7 4S0 0.3 200

6 X 32 X 92-in Walls

flat ends

1.5 1020 1.4 950 1.0 680

6 X 32 X 24-in Prisms

pinned ends

0.8 540

6 X 32 X 96-in WJ's

pinned ends

1.5 1020 1.0 680 0.5 340

be calculated by trial and error procedures using

equilibrium of the resultant of a linear stress block on the cracked section with the external load. Stresses calculated in the manner described

above and the corresponding strains obtained from

figures 6.9 through 6.12 have been used to evaluate

the initial elastic moduli in table 7.5. While these

average values are consistently smaller than the

initial elastic modulus of like-size prisms tested in axial compression (table 7.4), the elastic modulus

appears to be independent of load eccentricity

which is a measure of the flexural strain gradient on

the cross section. Secant and tangent moduh at failure cannot be reliably predicted on the basis of

available test data on eccentrically loaded prisms

because of nonlinear effects and, in certain in- stances, absence of deformation measurements

near peak loads. However, the shapes of the curves shown in figure 6.9 through 6.12 suggest that for all practical purposes, it would be reasonable to assume

stress-strain characteristics of concrete block

masonry in flexure to be similar to those under axial compression.

1 (7.10)

where

Peh^

8EI

(7.11)

is the deflection produced by two equal and opposite

moments of magnitude Pe applied at the ends of the

specimen. The derivation of eq (7.10) is similar to that of eq (7.9) except that eq (7.7) is replaced by

eq (7.11). Table 7.6 lists the initial modulus of elasticity of concrete block walls as determined by equations

(7.10) and (7.11) and load-deflection test data. The

values obtained are generally in good agreement

with test results of walls under axial compression

and higher than those derived from eccentrically

load prisms having pinned supports.

Table 7.5. Initial modulus of elasticity of eccentrically loaded

6 X 32 X 24-in concrete block prisms (f|„= 1473 psi)

Vertical load at eccentricity

tjU f/6 f/4 f/3

Ei X 10-6

Ei

fin

1.0

680

1.2

810

1.1

750

1.0

680

Test results of eccentrically loaded masonry

walls provide an alternate means of deriving the

modulus of elasticity of concrete block masonry in compression. For the case where e 0, eq (7.9) applies with the following modification:

Table 7.6. Initial modulus of elasticity of eccentrically loaded

concrete block walls (f'm = 1473 psi)

Vertical load WaU Ei X 10-6 Ei

eccentricity designation psi

f'm

«/12 4B3 1.4 950 4B4 1.4 950

Avg. 1.4 950

tie 4B5 1.2 810 4B7 1.3 880 4B11 1.4 950

Avg. 1.3 880

«/4 4B12 1.8 1220

4B13 1.6 1090 4B14 1.8 1220

Avg. 1.7 1150

36
Concrete block masonry other than the pinned

prisms developed an initial modulus of elasticity of 810/4 to 1220 fm with an average value of 1020fm

based on the average compressive strength of 1473

psi obtained from axial tests on prisms with flat support conditions. The values derived from the

pinned prism tests were, on the average, about 30

percent less. The current edition of NCMA Specification for Concrete Masonry [13] recommends a modulus of elasticity of 1000 fU with a specified

upper limit of 3 X 10^ psi. NCMA recommends a compressive strength which is the test strength

modified by a correction factor. This factor is dependent on the height-to-thickness ratio of the

test specimen. If a compressive strength of 1768 psi

(= 1473 X 1.2, [13]) calculated in accordance with

this provision is used as a basis of comparison, the

initial modulus of elasticity obtained from tests would be between 675 fm and 1200 /,'„ with an

average of 850 /,'„. Thus, for the masonry used in

this investigation, the modulus of elasticity derived

in accordance with NCMA is, on the average, 17 per- cent greater than the experimentally derived values.

7.2.4. Summary of Findings and Conclusions

The following conclusions can be drawn on the

elastic properties of hollow concrete block masonry

specimens:

(1) On the average, the concrete block masonry

specimens developed an initial modulus of elasticity

which was significantly less (= 15%) than that prescribed by the present edition of the NCMA

Standard [13]. Thus, it appears, there is a need to reconcile present provisions with experimental

evidence.

(2) The initial modulus of elasticity of walls can

be reasonably predicted on the basis of load- deformation relationships of prisms with flat ends

tested in axial compression. The size and geometry

of these specimens should be governed by requirements of a minimum height-to-width ratio (preferably greater than which is that of the 6 X 32 X

24 in prisms) that would keep the influence of end

zone effects on test results within tolerable limits.

(3) Flexure-induced strain gradients have no

appreciable effect on the stress-strain relations of concrete block walls as evidenced by eccentric

load tests on the prisms.

7.2.5. Composite Masonry

The composite masonry used in this program

consisted of a 4-in-thick brick wythe and a 6-in- thick hollow concrete block wythe. Galvanized

steel ties and mortar-filled coUar joints were used

to insure integral action in flexure. Inspection of

test specimens during and after failure indicated

that the assembly performed monolithically. In order to study the capacity of composite walls a knowledge of the stiffness parameters (elastic constants and sectional properties) of its constituents is required. Based on test results of brick

and concrete block specimens, a modular ratio of

2.6 has been assumed for the purpose of developing

the transformed section used in this investigation.

This value falls within the limiting modular ratios of

2.9 for the pinned prisms and 1.9 for all the other

specimens (consult tables 7.1 and 7.4). The sectional

properties of composite walls listed in figure 4.1 have been determined in accordance with this ratio. The kern eccentricities relative to the centroid of the transformed section are e/fc = 2.04 in and

eA:6 = 0.92 in so that a vertical load applied at e^c (the kern nearest the block face) or at eia, (the kern

nearest the brick face) should produce zero stress

in the extreme brick fibers, respectively.

Figures 6.14 through 6.18 show a family of curves developed from tests on composite prisms subjected

to vertical loads applied at various eccentricities. Noting that load eccentricities close to the kern

eccentricities of the section (i.e.,: 66 = 0.82 in versus

e/c& = 0.92 in, and ec=1.55 in versus eA:c=2.04 in) produce near zero strains in respective opposite

fibers, the assumed transformed section appears to be reasonable. It should also be noted that the re- sults of 10 X 16 X 32 -in composite prism tests shown

in figure 6.13 are not indicative of the true strains

in these specimens because during testing the

specimens could not be prevented from partially

rotating at the top. This condition, ^/hich resulted

in variable curvature along the height, is taken into consideration in section 7.3.4 where the correlation

of the interaction diagram of composite specimens

with test data is interpreted.

The eccentric load tests of composite prisms

offer an alternate means to check the initial elastic moduli of masonry. In the region Cku ^ Ckc, the

maximum fiber stress is determined using the

sectional properties of the uncracked section shown

in figure 4.1. When the vertical load is applied out- side the kern, the maximum fiber stress may be

determined on the basis of a cracked section

analysis using a linear stress distribution on the

uncracked portion of the cross section. These

stresses and the corresponding strains obtained

from figures 6.14 through 6.18 were used to derive

the elastic moduli listed in table 7.7. These values

are higher than indicated for the non-composite

prisms of similar size and end condition (consult

tables 7.1, 7.2, 7.4, and 7.5), while the modular ratio of 2.1 is less than 2.6 (which was based on all the

prism tests) used in its derivation.** Despite these

differences, the computed values in table 7.7 suggest the feasibility of developing criteria for predicting composite behavior from tests of non- composite constituents if a more substantial bank

of experimental research data were to become

available.

" Successive trials made these modular ratios converge to a value of about 2.4 (i.e.: an assumed ratio less than 2.6 yields a computed ratio greater than 2.1, etc.) so that the computed elastic moduli of brick and block were respectively higher and lower than

the values appearing in table 7.7.

37
Table 7.7. Initial modulus of elasticity of eccentrically loaded

composite prisms

X nsm Qcsign3.tion Vertical load

eccentricity

in

Ei X 10"^

psi

3B1-3B3 ei, = 0.82 (uncracked) 3.0 (brick) 3B10-3B12 eb = 1.64 (cracked) 2.8 (brick) 3B4-3B6 ec = 1.55 (uncracked) 1.6 (block) 3B7-3B9 ec = 3.10 (cracked) 1.4 (block) 3B14, 3B15 ec = 4.65 (cracked) 1.3 (block)

7.2.6. Flexural Rigidity of Masonry

A reliable prediction of the modulus of elasticity

of masonry is essential in the analysis of composite

sections or in calculations involving the axial rigidity EA and the flexural rigidity EI of the section.

The magnitude of EI depends on the intensity and

distribution of stresses on the cross section; the

modulus of elasticity decreasing with increasing

stress; and the moment of inertia / decreasing with

flexural cracking.

An empirical expression for EI which accounts for change in E, as well as in /, is given by

EI^EiIn(^0.2 +

~-J

^0.7 Eiln (7.12)

where /« designates the moment of inertia of an un- cracked net section, P designates the compressive

load at failure, and Po is the axial load capacity

derived from prism tests with flat support conditions.

This equation was proposed in a study on the ca- pacity of brick masonry walls tested under various

combinations of flexure and axial compression [2]. The authors demonstrated that the proposed expression will adequately approximate a substantial

amount of test data on brick walls over the entire

range of vertical loads. The accuiacy of eq (7.12) for short-wall sections of brick and possible application

to concrete block masonry can be examined in rela- tion to the curves for eccentrically loaded prisms

from this experimental investigation (figs. 6.3 through 6.6 and 6.9 through 6.12). In short walls,

the moment PA produced by vertical load P acting on transverse deflection A, is negligible compared

to the moment Pe and therefore the specimens may

be assumed bent in constant curvature. From

moment-curvature relation the following equation

for the flexural rigidity at failure is derived:

Pet EI^-^ (7.13)

€1 — 62

where Ci and designate maximum (compressive)

and minimum strains associated with the two

opposite face fibers of the specimen. The values of

EI obtained for brick and concrete block specimens

in this manner are plotted on the nondimensional

chart shown in figure 7.6 which also shows a plot of eq (7.12). It is noted that better agreement with

brick prism data are obtained while EI for concrete block prisms is underestimated. Obviously, these

results should be viewed in Ught of the limited

available test data, particularly in the region where

P/Po < 0.50. In the subsequent sections (7.4.1) and

(7.4.2) it is demonstrated that the use of the bilinear curve for EI given by eq (7.12) results in moment

ampHfication factors which, when applied to brick

as well as concrete block prism test data, give wall

capacities comparable to those obtained from tests of large-size wall specimens in which stability effects are not insignificant.

1 .0

2BI0-I2

2B7-9

0.8 E0.(712)^

• o

28^3-15 '^^-^ ZS%.e

0.6 ,8*4.6

liT

1-4 UJ

0.4 /

yiBis-is • BRICK PRISMS

0 BLOCK PRISMS

02

1

1 1 1 1 C) 0.2 04 0.6 0,8 1.0 P/Po Figure 7.6. Flexural rigidity of brick and concrete block prisms

at failure.

7.3. Capacity of Short Wall Sections

In order to investigate the strength of full-scale wall panels, it is first necessary to consider the

capacity of short prisms in which deflections are

small. In this section, the test results of prisms are discussed and compared with an analytical approach

which closely parallels the procedure used to predict the test results of other experimental pro- grams [1,2]. A summary of the interactive relations

between compression and flexure at failure, from

these previous studies, is given in section 9.1 for convenient reference.

7.3.1. Analytical Basis The analytical approach described in section 9.1 has been developed to predict the capacity of masonry piers under various configurations of load38
ing producing compression and flexure. Equations

(9.1) through (9.8) have been derived from consideration of equilibrium conditions and are based

on the assumption that the stress-strain relation- ships for masonry are approximately linear and

therefore the stress distribution on the critical section at failure can be approximated reasonably well

by a linear stress block. The test results from

previous experimental programs [1, 2, 17, 19] have

been used to demonstrate that cross-sectional

capacity determined in accordance with the pro- posed analytical approach is in close agreement with

that developed from test data. The constitutive relationships discussed in section 7.2 provide a means to examine the approximation involved in the assumption of linear stress distribution across the section at fciilure. In connection with the curves shown in figures 7.1 and 7.5,

it is observed that the lower halves of the stress- strain curves for brick and concrete block masonry

are approximately linear. While the upper halves

of these curves are, in general, not linear, a linear

approximation for the entire loading region would

not depart significantly from these curves. It is noted that a stress block at failure, similar in shape

to the area under the actual stress-strain curve, can

be closely approximated by a statically equivalent

hnear stress block without significantly changing the

position of the resultant force. In the following

sections, it is shown that .such an approximation

gives predicted capacities which are reasonably

consistent with the test results.

7.3.2. Capacity of Brick Prisms

A total of fifteen 4 X 32 X 16-in prisms were tested

under vertical loads appHed at equal top and bottom

eccentricities of 0, t/12, tl6, ^/4, and t/S in a manner

that would permit end rotations (pinned ends). In

addition, five prisms were tested in axial compression in a manner that would inhibit end rotation (flat ends), and ten 4 X 8 X 24-in prisms were tested as beams subjected to transverse loading.

Figure 7.7 shows plots from individual test results

of eccentrically loaded prisms. The compressive

loads at failure are taken from table 6.1 while the

moments are computed from the product M= Pe. The 509-kip load plotted on the P-axis is the equivalent average failure load of five stacked-bond prisms

tested in axial compression, the equivalence being

established on the basis of common cross-sectional

area.

It is evident, from figure 7.7 and table 6.1, that the apparent compressive strength of masonry in flexure is significantly greater than that in axial compression. A similar behavior of clay masonry

has been reported in references [1] and [2] which

introduced the coefficient "a" to distinguish compressive strength in flexure, designated by afm,

from the compressive strength fm, obtained from

50 100 150 200 250 MOMENT, in-kip

Figure 7.7. Cross-sectional capacity of brick prisms.

axial load tests on prisms with flat supports. The

values of "a" given in table 7.8 have been calculated

by taking the ratio of flexural compressive strength

to axial compressive strength. It is interesting to note that "a" is approximately constant for vertical load eccentricities of i/4 or less, and decreases by

only about 14 percent at e — tjS. Thus, the statement

in reference [2] that "a" appears to increase with

eccentricity is not substantiated by these test results.

Table 7.8. Coefficient "a." for brick prisms

elt 1/12 1/6 1/4 1/3

"a" for /; = 4515 psi

(flat ends)

1.40 1.37 1.36 1.18

"a" for /; = 4016 psi (pinned ends)

1.57 1.54 1.53 1.32

The solid curve shown in figure 7.7 is a theoretical

interaction curve developed from eqs (9.5) and (9.6) and the average compressive strength under kern

loading (i.e., a/; = 1.37 X 4515 = 6140 psi). The

sohd line e = f/6 marks the boundary between

cracked and uncracked sections. Note that the

theoretical interaction curve is in good agreement

with test results for e ^ f/12 but slightly over39
50 100 150 MOMENT, in- kip Figure 7.8. Cross-sectional capacity of concrete block prisms.

estimates the capacity at e — tl3. It should also be

pointed out that the theoretical interaction curve

overestimates axial load capacity in situations

where coefficient "a" is greater than unity (since by

definition a = 1 for axial loading). From a practical

viewpoint, this inconsistency may be readily re- solved by limiting the compressive load capacity to that obtained from axial load tests of prisms with

flat supports. This criterion would then confine the

interaction diagram to the portion below the solid horizontal line passing through the hollow circular

point on the P-axis shown in figure 7.7. The specimens tested as beams developed an

average tensile capacity of 128 psi under transverse concentrated loads applied at third points of the

span and 111 psi under transverse uniform loads. The results for the individual specimens are listed

in table 6.3. Since these values correspond to a moment capacity of about 2 in-kip, which is very

small, the cracking hne for 0 has been omitted

in figure 7.7.

7.3.3. Capacity of Concrete Block Prisms

Fifteen 6 X 32 X 24-in prisms were tested with

pinned support conditions under vertical loads

apphed at equal top and bottom eccentricities of

0, f/12, tie, and f/3. Five 6 X 16 X 24-in prisms

were tested under axial compression and with flat support conditions. Flexure tests included five 6 X 16 X 16-in prisms tested in accordance with

ASTM-E149 [3] and ten 6 X 16 X 32-in prisms tested

as horizontal beams.

Figure 7.8 shows plots from individual test results of eccentrically loaded prisms using failure loads from table 6.1 and corresponding moments,

Pe. The average 130-kip failure load of the five 6 X 16 X 24-in specimens with flat ends, computed

on an equal area basis, is plotted on the same figure.

Considering the results in figure 7.8 and table 6.1, once again it is evident that a significant increase in the apparent compressive strength occur as a result of flexure. Magnitudes of coefficient "a" calculated

for various vertical load eccentricities are shown in table 7.9.

Table 7.9. Coefficient "a" for concrete block prisms

e/t 1/12 1/6 1/4 1/3

"a" for

/;;,= 1473 psi

(flat ends)

1.23 1.41 1.23 1.21

"a" for /^=1405 psi (pinned ends)

1.29 1.48 1.29 1.27

40
The solid curve shown in figure 7.8 is a theoreticed

interaction diagram based on the compressive

strength under kern loading (i.e., e/t ~ f/4, afm —

1.23X 1473=1814 psi). The portion of the curve above the cracking hne eA = l-50 in, is developed

from eq (9.6) which appUes to uncracked sections;

the curved portion below the cracking hne is ob- tained from equihbrium of the resultant of a linear

stress block on the uncracked portion of the cross section with external loads; the straight portion shown intersecting the moment axis near the

origin is the cracking Une developed from eq (9.8) assuming an average modulus of rupture // — SS psi, for the small specimens tested in bending (table 6.3). For comparison, the approximate interaction equation (9.5) for the cracked section is indicated by the

broken curve on the same figure. This approximation

introduces a maximum error in the moment of about

11 percent and is on the conservative side. Equation (9.5) offers the added advantage of being much

simpler to use for design purposes than a cracked

section analysis.

Consistent with the approach considered for brick

masonry, the compressive load capacity of the

section may be conservatively assumed to be

Umited to the capacity developed by the axially

loaded prisms with flat ends. The sohd horizontal

Une shown in figure 7.8 would then be considered

as the maximum useful capacity of the section.

7.3.4. Capacity of Composite Prism

Fifteen 10 X 32 X 32-in composite prisms were

tested under vertical loads appUed at equal top and

bottom eccentricities (including e=0) in a manner

that would permit rotation at the supports. In

addition, ten 10 X 16 X 32-in prisms were tested as horizontal beams and five 10 X 16 X 32-in prisms were tested under axial compression. The intended

test setup for the latter specimens was one that would simulate flat support conditions. As previously

noted (sec. 7.2.5), these specimens could not be

entirely constrained against rotation at the top while

testing was in progress, and therefore, the effective load eccentricity at the top is not known precisely. In table 6.2, the maximum compressive stress at

fciilure for specimens 3A1 through 3A5 was calcu- lated using an estimated eccentricity of ec= 1.23 in derived by Unear interpolation between compressive

load capacities at e = 0 and ec= 1.55 in, taking into account the difference in cross-sectional areas. Figure 7.9 shows plots from individual test results

of eccentrically loaded composite prisms obtained

from the failure loads hsted in table 6.2 and the

corresponding moments calculated from the product Pe. The results of 10 X 16 X 32-in prism compression tests are also plotted on the basis of an

estimated eccentricity of ec-= 1.23 in and a common

equivalent area of 394.8 in- (fig. 4.1). Note that one

of the three specimens loaded at 6^ = 0.82 in and

one of the two specimens loaded at e = 0 did not

CONCRETE BLOCK

COMPRESSION

f,'=2l8psl(BRICK)-

\ BRICK \ COMPRESSION

a = I. 37

400 200 0 200 MOMENT, in-kip

J I L 400 600

Figure 7.9. Correlation of wall strength with prism strength of

composite masonry.

fail under the 600-kip capacity of the testing

machine. This condition is indicated by arrows drawn at the appropriate points in the figure.

The analytical prediction of the sectional capacity

of short composite walls in accordance with the

equations in section 9 requires the use of compressive strength values in flexure for the brick and

concrete block masonry components. The theoretical interaction diagram shown by the sohd hues in figure 7.9 is based on the respective compressive

strengths of brick and concrete block prisms under

kern loading as previously determined (figs. 7.7 and

7.8). The plot on the right appHes to moments that cause compression in the brick, and the plot on the

left appHes to moments that cause compression in the block. The diagram for eccentricities smaller

than the kern eccentricity (eAc~2.04 in and 6^-6 =

0.92 in) is developed from eq (9.2) apphcable to un- cracked sections. The curved portions of the dia- grams for larger eccentricities are obtained by

statics assuming a hnear stress block on the un- cracked portion of the cross section. The two

moment capacities based on flexural tensile strength

fines for fl 9^ 0, shown intersecting the interaction curves at low compressive loads, are developed from

eq (9.4). The intercepts of these fines with the

moment axis are calculated on the basis of average

41
// values obtained from flexure tests of brick and

block prisms (table 6.3). Interaction curves for the

cracked section developed from the approximate

simplified equation (9.1), are shown by the broken

curves. It is noted that in this case the approximation

slightly overestimates the capacity, the maximum

error introduced being less than 10 percent.

Figure 7.9 indicates that, in general, when failure occurs in the brick there is good agreement between

the analytically derived capacity and the test results. On the other hand, at certain eccentricities

{ec = 1.55 in, for instance), the block side of the composite wall developed capacities considerably in excess of those predicted on the basis of tests on

block prisms. This increased capacity is probably

attributable to the confining effects of the brick

wythe and the ties and should be further investi- gated. It should be pointed out that at ec=1.55 in and, in general, at smaU load eccentricities towards

the block face, failure occurred by vertical cracking

in the web of the block, indicating the type of tensile

failure mode described in section 7.3.4. At 66 = 0.82 in, the theoretical capacity was

probably in excess of the average test capacity

(600 kip or greater) by a small margin. The average

axial load capacity was greater than 590 kip. This

is shghtly more than the average capacity of 582

kips which is equal to the product of the compressive capacity of concrete block specimens {fln= 1473

psi) and the transformed concrete area of the composite section (394.8 in- ), but it is probably less than

the average capacity of 685 kip which is equal to the product of the compressive capacity of brick

specimens (/m = 4515 psi) and the transformed brick area (394.8/2.6=152 in-) of the same composite

section.

By reference to figure 7.9, it is noted that the condition of dual axial load capacities occurs as a

result of having used different values of coefficient

"a" for the brick and concrete block components of the composite section. In addition, as in the case

for the noncomposite prisms, the use of a > 1 gives

theoretical capacities in excess of the test values at small or zero eccentricities. In a practical design

situation these conditions may be satisfactorily and

conservatively resolved by requiring the compressive load capacity not to exceed the axial load

capacity of the weaker component (583 kips in this case). This hmit is displayed in figure 7.9 by the

horizontal lines intersecting the ordinate at P = 582

kip.

7.3.5. Failure Hypothesis for Hollow Concrete Block

In the foregoing analysis it was demonstrated that interaction curves based on a flexural compressive

strength coefficient "a" evaluated at the kern

eccentricity, provide reasonably good approximation

to short wall capacity except that in cases where

the compressive load is appfied at small or zero

eccentricity the capacity is overestimated since "a"

is greater than unity. It should be noted that eqs (9.2) and (9.6) are based on the premise that failure will occur when the maximum stress in the extreme fiber equals the apparent compressive strength in flexure,

af'm, derived from an assumed hnear stress distri- bution on the cross section. HoUow concrete block

walls built with face shell mortar typically fail by

vertical tensile spUtting of the web under compressive loads appUed axially or at small eccentricity

(figs. 6.22 and 6.23, and fig. 6.19 of ref. [2]). Furthermore, a substantial body of experimental evidence

from this and previous studies (figs. 7.7 and 7.8 and

refs. [1, 2]) indicates that compressive load capacity

is not significantly altered by variations in positioning of vertical load at small eccentricities when

the characteristic failure mode is tensile. To study the behavior of a hoUow block unit in compression, a finite element analysis is presented

in section 9.2 using a 100-kip load placed at various

eccentricities on the 6 X 32-in section shown in figure 4.1. The load was assumed to be transmitted

to the face shells and through shear action to the

webs. The numerical results are shown in figures

9.3 through 9.8. Subject to the limitations of the idealized model

described in section 9.2, certain inferences may be

drawn from these results. For instance, it is observed

that a condition of maximum uniaxial tensile stress

exists at the top of the web midway between the

two face shells under a concentrically applied load

(fig. 9.3). According to maximum normal stress

failure theory, initiation of failure by cracking of

the web at this location might therefore be expected.

This prediction would corroborate the observed

mode of failure of hollow block masonry test speci- mens. It is further noted, by reference to figures 9.4

to 9.7, that increasing the vertical load eccentricity

does not appreciably alter the magnitude of this tensile stress; a condition which may explain the

insensitivity of the average sectional capacity to variations in the positioning of vertical loads within

the central third region of the specimen as indicated

in figure 7.8 (e = ±f/6). At larger eccentricities, the

maximum positive normal strain near the face shell (element 1) is considerably in excess of the maximum

uniaxial tensile strain in the web (figs. 9.7 to 9.9). This condition could cause initiation of web failure near the face shell junction.

The foregoing example was used to provide

qualitative information on the behavior of masonry

specimens built with hollow block units and face

shell mortar. The procedure can be effectively

utihzed to study parametric relationships to better

predict the cross-sectional capacity on the basis

of experimentally observed failure mechanisms.

Furthermore, a study on the optimum shape of a hollow block unit could offer the potential of

improvements in the strength characteristics of concrete block masonry construction.

42
7.3.6. Summary of Findings and Conclusions

The following compares analytically predicted

and experimentally derived properties of short wall

sections obtained from the current test series and

relates to similar documented studies based on

previous test results [1, 2, 17, 19].

(1) The moment capacity of short masonry walls

under compressive loads can be reliably predicted

by rational analysis based on linearly elastic be- havior at failure. This conclusion is consistent with

that drawn from the previous studies. The constitutive relations developed in section 7.2 provide fur- ther indication that the response of masonry walls

at failure may be considered as being essentially Unear.

(2) The previous studies indicated an apparent

increase in the compressive strength of masonry

from f'm under axial compression to af'm under combined compression and flexure, where "a" is a

coefficient greater than unity. The results from the current test series corroborate this trend. For in- stance, within the range of eccentricities used

{tj\2 ^ e ^ f/3) , and on the basis off'm derived from

axial tests on prisms with flat supports, the average

value of coefficient "a" was 1.33 for the brick speci- mens and 1.27 for the concrete block specimens,

with the values at other eccentricities not being

appreciably different from these averages. Thus,

the hypothesis advanced in the previous studies

that compressive strength increases with flexural

strain gradient was not corroborated by the current

test results.

(3) The theoretical interaction diagrams for brick

and concrete block prisms were developed on the

basis of the corresponding compressive strengths

at the kern eccentricities, noting that the values of

1.37 and 1.23 of coefficient "a" at these eccentricities (shown underlined in tables 7.8 and 7.9), were

nearly equal to the respective average values. The

feasibility of a standard prism test using kern

loading to evaluate coefficient "a" has considerable

practical significance in the design of masonry walls on the basis of ultimate strength theory. Since "a"

is greater than unity, however, an ultimate design

approach should simultaneously stipulate limitation

of the maximum compressive load capacity at the

level obtained from standard prism tests under

axial loading.

(4) The possibility of a tensile failure mode in the

web of concrete block units in compression speci- mens constructed with face shell bed mortar was

explored by means of a finite element analysis. The

results indicated that when the axial compressive

load is transmitted to the units through the face

shells, peak uniaxial tensile stress conditions de- velop near the unmortared top and bottom surfaces

of the web. This situation could account for the

vertical cracking pattern frequently observed in compression tests of small specimens. The analysis

also indicated that the same load applied at a range

of eccentricities (approximately confined within the

kern of the section) did not appreciably alter the

magnitude of the peak tensile stress in the web.

Thus, a tensile mode of failure would provide a

plausible explanation of the experimental trend of undiminished compressive strength of prisms within a certain range of low vertical load eccentricities.

(5) The interaction diagram for the composite

specimens developed on the basis of noncomposite

prism test data, generally showed good correlation

with composite test results. However, when the

strength of the composite section was governed by

compressive failure of the concrete block wythe,

analytically predicted values tended to become quite

conservative at small load eccentricities. This trend

is probably attributed to an increase in the strength

of the concrete block component as a result of its confinement by the brick and the presence of

horizontal steel ties in the assembly.

7.4. Wall Capacity

In section 7.3, the test results of short wall sections were predicted reasonably well by the analyti- cal approach discussed in section 9.1. In this section,

the interaction diagrams developed in that analysis are compared with the experimentally observed load

capacity of 8-ft wall panels, taking into consideration

the additional effects of wall slenderness.

7.4.1. Capacity of Brick Walls A total of sixteen 4 X 32 X 96-in brick walls were

tested under various loading conditions. The test results for walls subjected to vertical loads are given in table 6.4. The test results for waUs subjected

to concentric load and transverse uniform load are

listed in table 6.5. The load-deflection curves of

brick walls are plotted in figures 6.28 and 6.30. Walls tested under transverse uniform load and

zero vertical load developed moments of 5.4 in-kip

and 2.3 in-kip corresponding to flexural tensile strengths of 80 psi and 34 psi, respectively. These

values compare with an average tensile strength of

120 psi developed by the 4 X 8 X 27-in beam spec- imens. Thus, on the average, the walls developed

about 50 percent of the tensile strength obtained

from prism tests. The correlation between prism strength and wall

strength is shown in figure 7.10. The part of the

moment attributed to horizontal deflection is shown

by a horizontal line. The left end of this line repre- sents the maximum moment excluding the effect of

the vertical load acting on the horizontal deflection. Where the line is solid, the right-hand end repre- sents the total maximum moment at failure. Thus,

the length of the solid horizontal Line is a measure

of the magnitude of the slenderness effect. The

right-hand end of the solid horizontal fines should

be compared to the soUd interaction curve on the

43
100 200 300 MOMENT , in-kip

Figure 7.10. Correlation of wall strength with prism strength of

brick masonry.

right which was derived from the prism tests. However, by reference to table 6.4, it is noted that instrumentation on all specimens tested under

vertical load was removed prior to failure. For such

cases the sohd portion of the horizontal hne is the

magnitude of the added moment at the last measured deflection while the dotted hne merely in- dicates that such removal occurred. Therefore, in general, a direct comparison with prism moment

capacity represented by the solid interaction curve

cannot be made.

As an alternate basis of comparison between

prism and wall strength, the theoretical interaction

diagram for the prisms may be modified by using a moment magnification factor [2]. The modified

interaction diagram shown by the dotted curve on

the left-hand side in figure 7.10 is developed using

reduced moments calculated from the following

equations:

Mo = Me(l-^) (7.14)

Pcr = ^

(7.15)

where Me is the moment capacity of the prisms

obtained from eqs (9.5) and (9.6), Mo is the reduced

moment capacity, P„ is the Euler buckhng load for specimens pinned at the ends, h is the height of the

wall and EI is the flexural rigidity determined from

eq (7.12). The value of £i = 2.8xl0« psi used in

- eq (7.12) was taken from table 7.1. The reduced interaction curve developed in this manner should be compared with the left ends of

the sohd horizontal hues. Figure 7.10 indicates

generally good correlation between theory and

experimental results.

The walls with flat end supports developed a 500-

kip axial load capacity. This compares closely with

the 500-kip equivalent average axial capacity of the

prisms with flat end supports and is about 10 per- cent greater than the average value of 452 kip

developed by the prisms with pinned support

conditions. The fact that these walls could develop

the fuU short wall capacity is attributed to the

rotational constraints induced by the flat support

condition at the ends. The axially loaded walls with

pinned support conditions failed by stabihtyinduced compression at an average load of 314 kip.

The moment capacity of aU other walls except the

two specimens with zero axial load was significantly

reduced by slenderness effects.

7.4.2. Capacity of Concrete Block Walls

Twenty-six 6 X 32 X 96-in hollow block masonry

walls were tested under various load combinations.

Table 6.4 shows the test results of 18 walls subjected

to compressive loads apphed at the specified eccentricities. The remaining eight walls were subjected

to various combinations of transverse uniform load

and vertical load. These results are shown in table

6.5. The load-deflection history of block walls is illustrated by the curves shown in figures 6.28 and

6.30. The two walls tested under transverse uniform

load and zero axial load developed tensile strengths

of 18 psi and 40 psi. The 6X16X32-in prisms,

tested as beams, developed average tensile strengths

of 51 psi under uniform loading and 38 psi under

third-point concentrated loads. Thus the full-scale walls developed, on the average, approximately 60

percent of the average tensile strength of the prisms

although the number of rephcate wall tests (two

specimens) was too small to permit a stochastic

assessment of scatter which appears to be con- siderable in this case. In order to compare wall strength to the inter- action curves for the prisms, the additional moment

attributable to the wall slenderness must be taken

into consideration. Figure 7.11 correlates the strength

of the full-scale wall specimens to the predicted

strength of the prisms. The moment attributable to wall slenderness effect is given by the product of

the maximum vertical load and the corresponding

maximum transverse midheight deflection in the

wall and is shown by the horizontal fines in the

figure. In cases where such deflection measurement

is not available, the solid portion of the horizontal

hne is the magnitude of the added moment at the

last measured deflection.

The solid curve in figure 7.11 is the interaction curve previously developed for concrete block

prisms (fig. 7.8). The broken curve is the reduced

interaction curve developed from eqs (7.12), (7.14), and (7.15) and an initial modulus of elasticity of

1.5X10^ psi as previously derived in section

7.2.3 and fisted in table 7.4. The predicted moment

44
MOMENT , in- kip

Figure 7.11. Correlation of wall strength with prism strength of hollow concrete block masonry.

attributed to wall slenderne§s, which is represented

by the horizontal interval bounded by the original

and reduced interaction curves at any particular

load level, is, in general, reasonably consistent with

the magnitude of the corresponding measured value

from wall test results as indicated in the figure by

the length of the soHd horizontal lines. In the region below the cracking line, e = f/4, the

short-wall interaction curve closely predicts wall

capacity. Above this line, wall capacity exceeded

predicted values, often by considerable margins.

This difference is probably attributed to a tensile mode of failure prevalent at smaller eccentricities

as described in section 7.3.5. Also, the walls were

tested at twice the average age at which the prisms were tested and it is likely that some strength gain

occurred as a result of this difference. It should be

noted that specimen 4B7 was damaged during handling and, therefore, its strength should not be

considered indicative of waU strength at e = tl6. WaUs tested in axial compression developed a strength equal to or greater than the average axial load capacity of the prisms.

The wall tests included two sets of specimens

which were subjected to compressive loads applied

at unequal top and bottom eccentricity. In speci- mens 4B23 and 4B24, the top and bottom eccentricities were 1.867 in and zero, respectively. In speci- mens 4B25 through 4B27, the top and bottom eccentricities of 1.867 in were equal, but opposite, causing the waUs to bend in double or reverse curvature.

Since, in all these specimens, the maximum moment

occurred at the ends, their capacity was not altered

by slenderness effects. Figure 7.11 compares the

test values plotted as points with the short-waU

interaction curve. It is seen that all but one specimen

tested more than twice the predicted moment

capacity. However, since the critical section at the

supports is laterally confined by the steel bearing

plates, the capacity of the section, as governed by

tensile splitting of the web, would increase significantly. The cracked specimen shown in figure 6.22 provides corroborative, visual evidence on the

extent of lateral confinement at the ends.

7.4.3. Capacity of Composite Walls Sixteen 10 X 32 X 96-in brick and hoUow concrete block composite waU were tested under various

load combinations. Table 6.4 shows the test results

for eight composite walls subjected to vertical loads applied ar~the designated eccentricities. The

test results for waUs under combined transverse and axial loads (including P = 0) are shown in table

6.5. Figures 6.29 and 6.31 show plots of transverse

deflection versus vertical load and transverse uni- form load, respectively.

The two composite walls tested in axial compression did not fail under the 600-kip load capacity of

the testing machine. As previously noted, one of the composite prisms also did not fail at this load

level while the other prism developed an axial load

capacity of 577 kip. The two walls, tested under a transverse uniform load applied to the hollow block

face and zero vertical load, developed tensile

45
strengths of 104 psi and 74 psi. These should be

compared to the average value of 218 psi obtained

from tests of similarly loaded composite prisms, and

to the average value of 120 psi obtained from beam

tests of brick prisms. Note that the walls developed

74 percent of the average tensile strength of brick

prisms and 41 percent of the tensile strength of the

brick component of composite prisms. The two

composite walls under uniform transverse load and

zero vertical load developed almost equal tensile strengths of about 76 psi, which is equal to the

average tensile strength of concrete block prisms

tested in accordance with ASTM E149 [3] , but

greater than the average values of 38 psi and 51

psi derived from respective concrete block beam

tests under third-point concentrated loads and

transverse uniform loads. This strength is about 79

percent of the average tensile strength of the block

component of composite prisms tested as beams.

The moment amplification approach may also be

used to compare composite wall strength to pre- dicted short-wall capacity. The slenderness effect

is small in the composite masonry walls because

they are stiffer than either the brick or the concrete block walls. In figure 7.12, the strength of full-scale walls is compared with the predicted strength of the prisms.

Again, the moments attributed to wall slenderness

are indicated by horizontal lines, the soHd portion

of which is the moment increment corresponding to the last measured deflection or the deflection at maximum load at failure in cases when such

deflection measurement is available.

The outer sohd curves in figure 7.12 represent

the interaction diagram of the composite prisms

(fig. 7.9). This diagram was developed on the basis

of different compressive strengths for the brick and

concrete block components of the composite section. The inner broken curves represent the reduced

interaction diagram developed from eqs (7.12),

(7.14), and (7.15) and an initial elastic modulus of

£',= 1.5X10^ psi for concrete to account for the

effect of wall slenderness. A comparison of the re- duced diagram with the ends of the horizontal lines closest to the load axis (unampUfied moment capacities of the walls derived from tests) indicates a smaller predicted capacity than that derived from

wall tests in cases where failure was governed by

the compressive strength of the concrete block

masonry component. As noted earher, the increased

capacity of the concrete block component is probably attributed to the confinement effect of the brick

wythe and the metal ties used in the construction

of composite specimens. When failure was governed

by the compressive strength of the brick component,

the capacity of the section was predicted more

closely but somewhat less conservatively. The

maximum difference occurred for specimen 4C5,

with the predicted test-derived moment capacity

exceeding the (unampHfied) test-derived moment

MOMENT, in-kip

Figure 7.12. Correlation of wall strength with prism strength of

composite masonry.

capacity by about 26 percent. This is probably

attributed to the considerable difference in strength

and in stiffness between the brick and concrete block components. Under certain loading conditions, the flexural compressive strength in the concrete fibers interfacing with the brick may develop

before the outer face fibers in the brick attain their

maximum compressive strength, and thereby contribute to the reduction in the load capacity of the

composite assembly.

7.4.4. Summary of Findings and Conclusions

The following conclusions are drawn from the

test results of the three types of masonry walls

subjected to various combinations of vertical and

transverse loads:

(1) The capacity of brick walls was closely and

conservatively predicted by analytically derived

interaction equations for short-wall sectional

capacity, modified in accordance with eqs. (7.12),

(7.14), and (7.15) to account for the effect of wall

slenderness. This agreement is rather significant in view of the substantial reduction in moment capacity

caused by wall slenderness and demonstrates the

feasibihty of utihzing the approximate moment

amphfication factor given by eq (7.14) together with

the empirical relationship (7.12) for estimating the

flexural rigidity of the wall.

46
(2) The reduction in capacity attributable to slenderness effects was also evident in the results

of tests on full-size concrete block wall specimens.

However, compared to the brick walls, the influence

of wall slenderness was small. This is attributable to the fact that the compressive strength and height-tothickness ratio of concrete block walls were less than the corresponding values for brick walls. Nevertheless, the trend of the experimental results

for the concrete masonry walls was correctly pre- dicted on the basis of the same analytical approach

as was used for the brick walls. The moment

capacity derived from theory and experiment were

in close agreement in the region of small compressive loads, while at larger loads, the test-derived

capacity of the walls, which often exceeded that of

the comparable prisms, were conservatively predicted. As noted elsewhere in the report, the average

age of the walls was twice that of the prisms. Thus,

to a certain extent, the observed strength gain of the

walls is probably attributed to this age difference.

(3) Generally, good agreement was obtained between predicted and test-derived capacities of brickblock composite walls. The experimental trend in composite construction, both in the prisms and the

walls, seemed to indicate a definite increase in the

strength of the concrete block component and a

slight decrease in the strength of the brick component, in relation to the values indicated by

independent tests of each component. Since the

theoretical interaction diagram was developed on

the basis of noncomposite prism tests, the predicted

capacity tends to be more conservative when failure

is governed by the strength of the concrete block

constituent.

(4) On the average, the walls subjected to lateral loads and zero axial compression developed approximately 50 percent of the flexural tensile strength

of the prisms. This size effect would be significant

in design which, from a practical standpoint, will probably have to be based on tensile bond strength

measurements obtained from small prism tests with

appropriate modifications to account for wall size. However, the results indicate the need for additional

test replication of large-scale specimens to permit

a more reliable assessment of this trend.

8. Conclusions and Recommendations

8.1. Conclusions

The diverse combinations of loads and the differ- ent types and sizes of masonry specimens used in

this experimental program provided the means for a comprehensive study of the constitutive relation- ships of masonry. Initial elastic moduli of brick and

concrete block specimens, developed independently

from prism and wall test results, showed generally

good agreement but were consistently smaller than

those stipulated by the current masonry standards

[12, 13, 22]. The difference was sufficiently significant to indicate the need to reconcile current

practice with experimental evidence.

The stress-strain curves developed from compressive tests on prisms were observed to be insensitive

to flexure-induced strain gradients on the cross

section. The initial modulus of elasticity of masonry

walls was reliably predicted on the basis of axial load test results on prisms with flat support conditions but was consistently greater than that ob- tained from prisms with pinned support conditions.

The tangent modulus of elasticity at failure was of

the order of 30 to 50 percent of the initial elastic modulus. In general, the stress-strain relationships were sufficiently Unear to permit a close analytical

prediction of test-derived sectional capacity by

assuming a linear stress block on the cross-section

at failure. An empirical relationship for the flexural rigidity

EI, proposed by the authors of reference [2] for brick masonry, was checked for correlation with

prism test data for brick as well as concrete block

masonry. It was subsequently shown that the use

of this expression in the analytical derivation of sectional capacity gives predicted values which are consistent with experimental results for the three

types of masonry walls considered in this program.

In previous experimental studies [1, 2] the observation was made that compressive strength in flexure (a/m) derived from a linear stress distribu- tion in the cross section at failure, exceeds the

compressive strength (/,'„) developed in axial compression by a significant margin. This observation was quantitatively corroborated by the results of the present experimental program. In the case of

kern loading, for instance, coefficient "a" was

calculated as 1.23 and 1.37 for the respective concrete block and brick specimens using f'm of flat- ended prisms as a datum; an increase of 23 and 37

percent in respective strengths. It was further

observed that these values did not significantly

change at other eccentricities, and, therefore, a prism test with kern loading should permit a reliable calculation of coefficient "a". With certain modifications proposed in this study,

the theoretical approach developed by the authors

of reference [2] was used to predict the capacity of short masonry walls. The modifications were intro- duced in order to take full advantage of the increased

compressive strength in flexure. Specifically, the

theoretical interaction diagrams for short wall ca- pacity of brick and concrete block masonry were

developed using a constant coefficient a > 1, based

on the compressive strength of the prisms loaded

at the kern or at the centroid, whichever resulted in a smaller total axial load capacity. In general, the

interaction curves developed in this manner showed

consistently good agreement with experimentally

derived short-wall capacity. In the case of brickblock composite construction, the interaction curves, developed on the basis of flexural compressive

47
strengths of the respective brick and concrete block

components, showed reasonably good correlation

with test data on component wall strength.

The capacity of full-size, brick, concrete block

and brick-block composite walls was reasonably

predicted by means of short-wall interaction rela- tionships modified to account for amplification of

internal moments attributed to slenderness effects

[2]. In the case of walls where flexure was induced

by lateral loads singly or in combination with eccentrically applied compressive loads, the agreement

between theory and experiment constitutes a generahzation of the basic theory proposed in the

earlier studies [1, 2, 17, 19].

Brick masonry specimens under compressive

loads applied at small or zero eccentricity typically

failed by in-plane vertical cracking. Similarly

loaded concrete block masonry specimens failed by vertical cracking through the webs. The stresses

in the webs of a hollow concrete block masonry

unit under face-shell compression were investigated

by means of a finite element analysis. The results of this analysis indicated probable locations of

critical tensile regions in the web that would cause

a tensile failure mode similar to that observed ex- perimentally, particularly in cases where the ap- plied eccentricity was close to the centroid of the

section.

8.2. Recommendations

A substantial body of structural test data on masonry, acquired through three separate experimental research programs at the National Bureau

of Standards, has been utilized to develop a rational

analytical procedure for the prediction of the capacity of masonry walls under diverse configurations of transverse and compressive loads. The approach was found to be applicable to aU the types of clay, concrete block and composite masonry tested. From

a practical design standpoint, the proposed analytical approach offers the following advantages:

(1) It provides a consistent and unified method

for ultimate design of masonry.

(2) The method is based on the same principles

of elastic analysis that are used in working

stress design recommended by the present

masonry codes and standards, and a moment

amplification factor similar to that now used

in concrete and steel design.

(3) The method lends itself to direct consideration of the increased compressive strength

of masonry in flexure and of requirements for consistent safety margins against failure. In view of the large body of corroborative experimental data, the inclusion of the proposed analytical

approach in masonry design standards should be

given serious consideration. It is also recommended

that the present provisions for determination of the

modulus of elasticity of masonry be revised to reflect the findings of this study.

9. Appendix

9.1. Flexure — Compression Interaction

The equations in this section have been developed

by the authors of reference [2] to predict the moment

capacity of short masonry walls subjected to compression and bending. The governing equations

are given without derivation.

SIDE I

SIDE 2 NEUTRAL

Figure 9.1. Asymmetrical section.

Assuming masonry has no tensile strength, the

approximate flexure-compression interaction equations for the general case of nonsymmetric trans- formed section shown in figure 9.1 (masonry units

of dissimilar composition), are given by the following

equations:

For a cracked section

g2

g2

Pcz (1

"kl Ci aPp Q _ £fr2^ Pk2 C2 aPo

aPo'

1+^

C2

ek2 =

1 +

/

AC2

I Aci

Ci

(9.1)

48
where

a — Flexural compressive strength coefficient defined below

A — Net area of transformed section

Ci, C2 = Distances from neutral axis to outer- most fibers in maximum compression

cai, eA2 — Kern eccentricities from centroid of

transformed section in directions 1 and 2, respectively

f'j„ = Compressive strength of masonry under

axial load

/ = Moment of inertia of net transformed

section about its centroidal axis

Mei,Me2— Moment capacity of masonry, producing maximum compressive stress in outer fibers on sides 1 and 2, respectively

P — Axial compressive load on the cross

section

Pk\-! Pkz — Compressive loads capacity of masonry

apphed at kern eccentricities ca-i and

eA2, respectively

f*o = Axial load capacity of masonry.

A note of explanation is needed with regard to the compressive strength fm- For a composite construction, such as a brick-block wall assembly,

the axicd compressive strengths of the two wythes

may have different values. The lower of these two

values defines /',« to be used in these equations.

Coefficient "a" is a factor equal to, or greater

than, unity to account for an apparent increase in masonry compressive strength from fm under axial compression to afm under combined flexure and

compression. The expressions for Pk\ and Pa 2 in eqs (9.1) are based on the simplifying assumption

that the ratio of the moduli of elasticity of the two

materials comprising the composite section is the same as the ratio of the flexural compressive

strengths. In addition, the expressions for M,,\

and Me-i in eqs (9.1) are approximate when the

load is appHed at an eccentricity greater than the

kern eccentricity. However, for the case of sohd

rectangular section of noncomposite masonry, ^

assumes a value of 4/3 and the expression for Me

is no longer approximate.

For an uncracked section

Mel = PkxCkx

Me2 = P

aP^-P

aPo - Pki

aPo-P

aPo - Pk2

(9.2)

The cracking hne which separates the uncracked

and cracked regions is defined by the equations

Mkx = Mk2 = PkiCki = Pk2ek2 (9.3)

Equations (9.1) are appUcable in the regions

P ^ Ph\ and P ^ Pk2 and equations (9.2) are applicable in the regions P > P^^ and P ^ Pa-2- An interaction diagram based on a=l for an asymmetric composite section of 4-in brick and 4-in hollow block is reproduced from reference [2] and

is shown in figure 9.2. Note that the Me curve for a cracked section, obtained from eq (9.1), agrees

reasonably well with the solid curve developed

from cracked section theorv.

49
Equations (9.1) were derived on the basis of zero

tensile strength of masonry. For large M/P ratios, failure will occur when the maximum flexural tensile strength of the specimen is developed. As- suming a nonzero tensile strength for masonry,

the expressions for the cracking hues will become.

C2

Me2 = —+ Pe,2

mci

m

El

E2

(9.4)

where.

fti , ft-z — Flexural tensile strength of masonry on

sides 1 and 2, respectively

£1 , £2 — Modulus of elasticity in direction normal

to bed joints of masonry on sides 1 and 2,

respectively.

The moment capacity for the cracked section

is the larger of the two values determined from eqs

(9.1) and (9.4). For a symmetric section, the interaction equations become considerably simpler. Thus, for a cracked section.

21 AtaPo

Po=^Af'm

and, for an uncracked section,

Me = i- (aPo - P).

The cracking Une is given by

Ma- = P,ek

or, in the case where // > 0, by

f'l M,^i^+ Pe,.

(9.5)

(9.6)

(9.7)

(9.8)

The moment capacity for the cracked section is the larger of the two values obtained from eqs

(9.5) and (9.8).

9.2. Numerical Analysis of Hollow Concrete

Block Unit in Compression

A finite element analysis of a hollow concrete block unit is made using a 100-kip compressive

load applied at various eccentricities to the 6 X 32-in

section shown in figure 4.1. The load is assumed to be transmitted from the face shells to the web

through shear action. A Poisson ratio of 0.2 is as- sumed for the material. The results are displayed

in figures 9.3 to 9.8. The analytical model for the upper half of a block unit consists of 12 face shell beam elements

and 48 rectangular plane stress web elements of

equal size as indicated in figure 9.3. The web

thickness is equal to the sum of web thicknesses

of the actual section. Principal stresses and their

orientation are plotted at the centroids of web

elements as shown. Stresses are expressed in psi

units and tension is assumed positive. The follow- ing differences between the ideafized model and

the actual specimen should be taken into consideration in the interpretation of the numerical

results:

(1) In an actual block, face shell and web thick- ness varies with height and is on the average

about 25 percent greater than assumed in the idealized model.

(2) Mortar was assumed to be confined to the

face shell area. Examination of actual test specimens indicates a 25 to 50 percent mortar

penetration over the web area.

(3) In an actual block, the joints between face

shells and webs have smooth transitional

fillets which were not considered in the

idealized model.

In general, these assumptions will tend to over- estimate and somewhat distort stresses in the

web. In particular, the second assumption will amphfy tension at the top while the effect of the

third assumption would be to amplify stresses near

the face shells relative to stresses elsewhere.

Figure 9.3 shows principal stresses in the web

under concentric loading. At the top of the block,

the two outer shells are under equal compression.

Through shear transfer, a near uniform compression develops on the entire section halfway down

the block as indicated by the lower stress diagram.

The diagram on the right shows the stress distribu- tion on the vertical plane of symmetry and describes

a condition analogous to flexure in deep beams of

rectangular cross section reinforced with vertical flanges at the supports [18]. The minimum principal tensile stress occurs at the top of the web in the horizontal direction midway between the two

50
50 kip

^ FACE^

SHELL

HALF- WIDTH OF WEB

= l.75in.

FLANGE-WEB JUNCTION v—TOP OF WEB

283.6 -M93

236 .2 -1 199

102.4

-1 151

13

17-6 -1127

-19.3

-1118

. 357.8 A -320.4

239.9

-931 .4

146.9

-937 .3

10

14 .9 -9S7 .6

14

-51 .2 -978 ..

18

-80.3

-992 .7

22

449.9

"-1 17.3

169 .8 -466.6

20.1 -693.1

-70.

S

-787.2

15

-1 13.S -859.4

19

-127.

S

-896 .6 23

S24.3

--45 .9

, 70.8

\ -246.0

-95 .4 -484 .f

-141.7

-675-3

T 20

-151 -0 -791 -1

153.3

-- -645.1 24

-1119 -993 1 -897 -845

CXDIOI

i

IN WEB SECTION AT MID- DEPTH

-114

-143

-152

154

NORMAL STRESS

DISTRIBUTION IN VERTICAL SECTION

THROUGH HALFWJDTH OF WEB

Figure 9.3. Stress distribution in concrete web block at e=0.

51
60.2 kip

100 kip

.467" 39.8 kip

,496.7

-1573.4

\ -4Z8.5

323.9 -1144.7

421 .5 -148.9

196.

9

579.8

514.6

--51 .0

, 93 .2 \ -296.5

534.7 —41 .7

25

61 .8 -208.8

481 .5 —88.9

26

, 146.0 -356-7

, 388-2 V,--ZZ3.2

27

Z56.9

-719-2

315.3

119.

28

/391 .7 -1012.

29 30 31 32

297.

9

-1440-5 \ 203.8 \ 6 V -1124.8 \ -i67.6 825.8

58.

2

S4B.9

I -113.1

f -440-1 / -24.9 / 94. Z /

/ -563.0 / -750.0 f

174.4

0 t -957.

10 33 34 35 36

169.7 -1370.5 70-3

-1 126 .8 -26-0-901 -7

\ -116.4 I -154. 1 / -111 -9 / -40. Z / t -725. 0 + -638-5

f -676.0 / -788-6 / 35.0

-931 .

13 16 37 38 39 40

64.

Z

-133Z.5

17

\ 0-4 \ -78.4 \

\ -113Z.3 \ -957.5 +

19 20

-136-1

-827.1

-161 .3

- -759.8 I -146.8 / -10Z.6 / -49.1 + -753.1 t -824.6 / -9ZZ.:

41 42 43 44

44 .0 -1316.6 -33.3

-1 133.0 -9S.3 -985.7 -143.7

-875.4 -163.5-815.4

-156-6

-807.7 -127.3-847.3 -8Z.7-920-

21 22 23 24 45 46 47 48

Figure 9.4. Stress distribution in concrete block web at e = 0.467 in.

52
100 kip

70.5 kip

0.933 In 29.5 kip

V 3?6 .

1

\-5ii.2 396.1 -183.7

SOS. 7 --S6.8 546.0 ^38.1

516.3 —63.5433.2 .-140.4 3SS.8

-752.

^549.5 -1654.4358.6

1359.0 \ 225.8

>< -69S.0

122.

8

-354 .3

, 73.2

t -192.1

128.9 -253.3

/ 226.1

y- -508.9

339.8

732.

359.8

-1682.3 258 .9 -1312.8

1 18.4 -959.9 \

10.9 623.0-99.8 -426.6-63.8

-438 .9 40.1 -563.

0

112.

S

-715.

)

237.2

-1590.1

126 .0 -1226- 20.4 -1018 - \

-82.2 -783.6

-149.5

-618.7 -146.5-571 .5 -94.7-620.1 -32.4 -712.3

151 .0 -1538.052 .2 -1286-7

-42.2 -1056.9-117.4 -866.9

I -165.8 I -176.9 I -153.4 / + -734.2 + -659.9 + -671.2 f-lis.

-716.

E

107.5 -1515.213.9 -1283.7

-68 .8 -1075.1-133.1 -906.2 I -172.5 I -185.3 I -174.3 | T -786.2 + -719.1 + -701.9 +-146.

-721 .

Figure 9.5. Stress distribution in concrete block web at e = 0.933 in.

53
100 kip

80.8 kip

1.4 in

19.2 kip

\, 319.2 , 373.7 X^-664.9 A" -221.4

497 .6 --63.5 557.9

--35.3

554 .0 —41 .

1

495.

S

—75.1

415.8

-405.

\02.S \,393.7 \ 255.7 >, 156.5 2135.2 ->C - 1573.4 >f -811.1 \ -416.1

106.2 -196.9127.

1

-165.4

, 200.7 > -304.1

f 28 y.-4

421 .6 -1923.9314.1 -1500.6 \166.0 \ -1094.6 \41 .4 -702.3-55.2 -444.2-83.8 -333.7

SO-7

-474.

304.6

-1809.5

181 .7 -1466.2 \67.8 \ -U35.3 \ 42 .4 847-3-126.3

-617.5

-165-2

-482.9

-146-8

-454.1 -99.8-432

104. Q \ \ -95-7 + -1743.4 ' -1441-0 -1156.8 -909.5

170.3 61-0 -39.2 -122.1 -1713.5 -1429.

1

-1164.5 -937.3

-163.7

-715-3 -200-6-583-2 -202.5-519.6

-IBZ

-511.

1 -lBO-8 I + -757-7 -|- 213.3

631 .3 -221 -0 -556-7

-209.

5

-523 .

S

Figure 9.6. Stress distribution in concrete block web at e=1.4 in.

54
100 kip

.867 in.

91.0 kip 9.0 kip

315.8

-789.

Z

, 354.1 A' -261 .9 490.3

--71 -0 570.

5

--33.2 594 .4 ^21.4

575.8 —27.6

523.1 —105.

286.3

927-9

192 .4 -480.2

^ 154.3 \ -216.8

157.2 -103.2193.1 -117.0

, 242.1 -179

483.5 -216S-5369.3 -1688.5 \215.9 \ 96.6 -1229.7 \ -784.3 \8.9

-481 .4

. -49.3

\ -253.0

-54.4

-203.1 / -232

372.0 -2028.9

237.4 -1635.9

1 15.9 -1253.2

284.4

-IS48.7

155.9 -IS9S.332.1 -1257.3

234 .3 -1911 -8 108.1 -1574.6

-9.6 -1253.9

\^ -916-0 \^

\ -71.8 \

\ -954.5 +

I -110.9 1 t -968-6 +

-86.7

-632.6 -148-4 -429-8

-182.6 \ -304.2

, -167- + -273.

-154.2

-703.7 -210.7

-510-0

( -242.2

-X -377.4 I -248

-f- -306-

-188.3

-730-1 239-8 544 .9 -266.7

-412.6

, -Z73. + -325

Figure 9.7. Stress distribution in concrete block web at e = 1.867 in.

55
e = 2.275 in.

Figure 9.8. Stress distribution in concrete block web at e = 2.275.

56
face shells. The maximum positive normal strain

(extension) also occurs at the top of the web but near the face shell junction (element 1). Figures 9.4 to 9.8 show the effect of eccentricity on the stress distribution in the web. Within the

range of eccentricities considered, the change in the maximum tensile stress is small while a substantial increase in the maximum compressive

stress occurs (element 1) with increasing eccentricity. Because tensile stresses are affected by

factors such as partial presence of mortar on the

web and possible dimensional differences in the

blocks, considerable scatter could occur in tested

capacity such as those observed in figures 7.8 and

7.9, and figure 6.3 of reference [1].

It is noted that with increasing eccentricity the

maximum compressive stress in the web (element 1) increases at a much faster rate than the maximum

tensile stress. Therefore, at larger load eccentricities, the maximum positive normal strains near

the face shells are considerably in excess of normal

tensile strain away from the face shells.

The contributions made by the following persons

are gratefuUy acknowledged by the authors:

Robert D. Dikkers planned and executed the re- search program, and critically reviewed the

report.

Felix Y. Yokel participated in the analysis of test results and critically reviewed the report.

Robert A. Crist, H. S. Lew, and Norman F. Somes

critically reviewed the report.

Robert Livingston, from the Brick Institute of

America, was the mason in charge of the construction of specimens.

Frank A. Rankin was in charge of all laboratory test- ing activities.

James Seller, James Warfield, Lymus Payton,

Mark LeMay, David Eichman, Harvey Shirley,

Edward Butler, and Michael Hawkins collaborated

in the testing of specimens.

Charles BuHk was responsible for coordination of

instrumentation and data acquisition activities.

Randolph Williams was in charge of computer data

processing.

WiUiam Appleton, Thomas Ruschell, and James

Owen collaborated on electronic instrumentation.

Connie Roth, and Becky Hocker typed the several

drafts of the report manuscript.

10. References

[IJ Yokel, F. Y., Mathey, R. G., Dikkers, K. D., Compressive

strength of slender concrete nnasonry walls, Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 33, 32 pages (1970).

[2] Yokel, F. Y., Mathey, R. G., Dikkers, R. D., Strength of masonry walls under compressive and transverse loads, Nat. Bur. Stand. (U.S.), Bldg. Sci. Ser. 34, 74 pages (1971).

[3] Standard Method of Test lor Bond Strength of Mortar to Masonry Units, ASTM E149-66 (1966).

[4] Standard Methods of Sampling and Testing of Brick, ASTM C67-66 (1966).

[5] Tentative Methods of SampUng and Testing Concrete Masonry Units, ASTM C140-65 (1965).

[6] Standard Specifications for Mortar for Unit Masonry,

ASTM C270-68 (1968).

[7] Standard Specifications for Portland Cement, ASTM C150-

70 (1970).

[8] Standard Specifications for Hydrated Lime for Masonry

Purposes, ASTM C207-49 (1949).

[9] Standard Specifications for Aggregate for Masonry Mortar ASTM C 144-70 (1970).

[10] Standard Method of Test for Air Content of Hydraulic Cement Mortar, ASTM C185-59 (1959).

[11] Standard Method of Test for Air Content of Freshly Mixed

Concrete by the Pressure Method, ASTM C231-68 (1968).

[12] Structural Clay Products Institute, Building Code Require- ments for Engineered Brick Masonry (August 1969).

[13] National Concrete Masonry Association, Specifications for the Design and Construction of Load-Bearing Concrete Masonry (1970).

[14] Standard Methods of Test for Compressive Strength of Masonry Assemblages, ASTM E447-72 (1972).

[15] Yokel, F. Y., Stability of Load Capacity of Members with No Tensile Strength, Journal of the Structural Division, Proceedings of the American Society of Civil Engineers

(July 1971).

[16] Yokel, F. Y., Closure on StabiUty and Load Capacity of Members with No Tensile Strength, Journal of the Structural Division, Proceedings of the American Society of

Civil Engineers (April 1973).

[17] Yokel, F. Y., Dikkers, R. D., Strength of Load Bearing

Masonry Walls, Journal of the Structural Division, Proceedings of the American Society of Civil Engineers

(May 1971).

[18] Leonhardt, F., Walther, R., Versuche an Wandartigen

Tragern mil Unterschiedhcher Belastung, Lagerung und Bewehrung mit Schlussfolgerungen, Wilhelm Ernst &

Sohn, Berlin (1966).

[19] Yokel, F: Y., Dikkers, R. D., Fattal, S. G., Closure on

Strength of Load Bearing Masonry Wcdls, Journal of the Structural Division, Proceedings of the American Society

of Civil Engineers (May 1973).

[20] Hilsdorf, H. K., Investigation into the Failure Mechanism

of Brick Masonry Loaded in Axial Compression, Inter- national Conference on Masonry Structural Systems,

University of Texas, Austin (1967).

[21] American Concrete Institute, Committee 531, Concrete masonry structures — design and construction, J. Am.

Conor. Inst. 67, Nos. 5 and 6 (1970).

[22] Uniform Building Code, International Conference of Building Officials, Whittier, California (1973).

[23] Standard Method of Test for Flexural Bond Strength of Masonry, ASTM E 518-74 (1974).

57
(
NBS-1 14A <REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. fuhlic;ation ok ri;por r no. NBS-BSS 73

2, Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Structural Performance of Masonry Walls Under

Compression and Flexure

5. Publication Date June 1976

6, Performing Organization Code

7. AUTHOR(S)

S. G. Fattal and L. E. Cattaneo

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4615130

11. Contract/Grant No.

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Brick Institute of America, McLean, Va. 22101

National Bureau of Standards, Washington, D. C. 20234

National Concrete Masonry Assoc., Arlington, Va. The Departments of the Army, the Navy and the Air Force,

Washington, D. C.

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Library of Congress Catalog Card Number: 75-619305

16. ABSTRACT (A 200-word or less factual summary of most significarjt information. If document includes a significant bibliography or literature survey, mention it here.)

Ninety-five prisms and fifty-six walls of brick, concrete block and composite

brick and block masonry construction were tested under various combinations of

compressive and transverse loads. Constitutive relations for masonry are developed from test results. By using rational analysis it is shown that

prism strength can be predicted on the basis of linear behavior at failure.

It is also shown that wall strength can be predicted on the basis of prism

strength when an appropriate allowance is made for the effect of wall slenderness

on sectional capacity.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) -Q^^^y.. buckling; Composite walls; Compressive strength;

concrete block; constitutive relations; flexural strength; masonry; masonry walls;

mortar; slenderness ratio; standards; stiffness; structural stability; walls.

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