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BUILDING SCIENCE SERIES 33

National

Bureau

of

[Standards

Compressive Strength

of Slender Concrete

lasonry Walls
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UNITED STATES DEPARTMENT OF COMMERCE • Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Compressive Strength of Slender Concrete

Masonry Walls

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

Building Research Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

Building Science Series 33

Nat. Bur. Stand. (U.S.), Bldg. Sci. Set. 33, 32 pages (Dec. 1970)

COD EN; BSSNB

Issued December 1970

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catalog No. Cl3.29/2:33), Price 40 cents
^^mHAl BUREAU OF STANDARDS

SEP 1 2 1971

The contents of this report are not to be used for advertising or promotional purposes. Citation of proprietary products does not constitute an official endorsement or approval by the National Bureau

of Standards for use of such commercial products.

Library of Congress Catalog Card Number: 72-609407
Contents Page

List of Symbols iv SI Conversion Units iv Abstract 1

1. Introduction and Objective 1

2. Scope 1 3. Test Specimens 2

4. Test Procedure and Instrumentation 6

5. Test Results 8

6. Interpretation of Results 14

7. Discussion of Present Design Procedures 24

8. Conclusions and Recommendations 28

9. Acknowledgment 28

10. References 28

III
List of Symbols

a Flexural compressive strength coefficient kh

af'm Flexural compressive strength of masonry

Cm Moment correction coefficient M

e Eccentricity relative to centroid of section Mi E Modulus of elasticity M2

El Initial tangent modulus of elasticity n Em Modulus of elasticity of masonry

Eg Modulus of elasticity of steel P

Et Tangent modulus of elasticity at failure fa Computed axial compressive stress P0 Fa Allowable axial compressive stress fm Computed flexural compressive stress P'

Fm Allowable flexural compressive stress fm Axial compressive strength of masonry P^^

determined from axial prism test h Unsupported height of wall

/ Moment of inertia of section

In Moment of inertia based on uncracked net

section i k Reduction coefficient to account for end §

fixity

Unsupported height of wall reduced for entj

fixity

Maximum moment acting on the wall

Larger end moment acting on the wall

Smaller end moment acting on the wall

Stiffness ratio of reinforcing steel tc masonry

Applied vertical compressive load (or re- action to that load)

Cross-sectional axial compressive loa(

capacity

Resultant compressive force acting on cross section

Critical load for stability — induced compression failure computed on the basis ol a modified EI, accounting for section

cracking and reduced stiffness at maximum stress. Thickness of wall

Transverse deflection

SI Conversion Units

In view of present accepted practice in this country in this technological area, common U.S. units of measurement have been used throughout this paper. In recognition of the position of the USA as a signatory

to the General Conference on Weights and Measures, which gave official status to the metric SI systems of units in 1960, we assist readers interested in making use of the coherent system of SI units, by giving con- version factors applicable to U.S. units used in this paper.

IS'

Length

1 in = 0.0254* meter

1 ft = 0.3048* meter

Area

1 in2 = 6.4516* X lO'^ meter^

1 ft2 = 0.09290 meter2

Force

1 lb (lbf) = 4.448 newton

1 kip = 4448 newton

Pressure, Stress

1 psi = 6895 newton/meter^

1 ksi = 6.895 X 10^ newton/meter^

Mass/Volume

1 Ib/ft^ (lbm/ft3)= 16.02 kilogram/meter3

Moment

1 kip-in = 113.0 newton-meter

*Exartly

IV
Compressive Strength of Slender Concrete Masonry Walls

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

Sixty reinforced and unreinforced concrete masonry walls of different slenderness ratios were

tested to failure under vertical loads applied axially and at various eccentricities. Prism specimens,

made of similar masonry units and mortars, were also tested under the same loading conditions. Analysis of test results indicates that wall strength can be conservatively predicted by evaluating cross-sectional wall capacity on the basis of prism strength and reducing the capacity for slenderness effects by

evaluating the added moments attributable to wall deflection. Test results were also compared with al- lowable loads computed in accordance with the current NCMA standard.

Key words: Buckling; compressive strength: concrete block walls: elastic stability; flexural strength: masonry walls: reinforced concrete masonry walls; slenderness effect; structural stability.

1. Introduction and Objective

At the present time only a limited amount of ex- perimental data is available on the compressive

strength of slender concrete masonry walls. Present

design practice accounts for slenderness effects by

stress correction factors [1]' or empirical equations

[2]. The designer has no rational method by which

he can evaluate slenderness effects, and important

parameters such as cross-sectional properties, end

support conditions, and the relationship between

compressive strength and elastic properties of the

masonry are not taken into consideration.

The objectives of this investigation were to deter- mine and analyze the effects of wall slenderness and

load eccentricity on the strength of slender concrete masonry walls. This analysis was intended to represent a step in the development of rational

design methods for masonry walls subjected to axial and eccentric vertical loads.

2. Scope

Two wall systems representing reinforced and un- reinforced masonry construction were tested:

1. 6-in reinforced concrete masonry walls.

2. 8-in unreinforced concrete masonry walls.

"This work was performed with the aid of a financial grant from

the National Concrete Masonry Association (NCMA).

' Figures in brackets indicate literature references listed in section 10.

For each of these wall systems specimens were con- structed which were 4-ft wide and approximately 10,

16, and 20-ft high.^ These walls were tested to destruction under vertical loads which were applied

axially and at eccentricities of i, i and i of the wall

thickness.

For each combination of wall height and load ec- centricity, two companion specimens were tested. One of these specimens was instrumented to measure horizontal deflections and wall shortening

under vertical loads. All of these specimens were

tested at an approximate age often days. In addition,

two 10-ft high and two 20-ft high walls of each wall

system were tested axially at an age of more than 28

days to determine the strength increase with an additional curing period.

Following construction, four of the unreinforced

walls were found to have undersized block and in- creased joint thicknesses as a consequence. These

specimens were tested, and an additional four

specimens with correct joint size were added to pro- vide unbiased data. As indicated in table 2.1, a total of 28 reinforced walls and 32 unreinforced walls were tested. An investigation of masonry prism strength under

eccentric compressive loads was also conducted by

subjecting 8-in and 6-in masonry prisms to the same

loading conditions that were used for the full scale

' Hereafter in this report heights of walls are referred to as 10 ft, 16 ft and 20 ft. However, actual wall heights were 9 ft-3 f in, 15 ft11 tin and 19 ft-3 1 in.

1
TABLE 2.1 Scope and Number of Walls Tested Corner Block Lintel Block

Wall System

Wall Height

ft 0

Load

t/6

Eccentricity

t/4 t/3

Number

of Walls Tested

6-in 10 4 2 2 2 10

reinforced 16 2 2 2 2 8

20 4 2 2 2 10

8- in 10 6 4 2 2 14

unreinforced 16 2 2 2 2 8

20 4 2 2 2 10

Total number of walls tested 60

walls. Two-block high as well as three-block high

prisms were tested in order to determine the effect of prism height on the prism strength.

The investigation was completed by an analysis of

results which is presented in section 6 of this report,

and a discussion of present design practice which is included in section 7.

3. Test Specimens

3.1. Materials

3.1.1. Masonry Units

Concrete masonry units used in the construction

of test specimens were 8 X 8 X 16-in two-core hollow

block, which were used in the unreinforced walls,

and 6 X 8 X 16-in two-core hollow block which were

used in the reinforced walls. The units were made of a blend of light and nor- mal weight aggregate (cinder and limestone) and were autoclaved. Cementitious material was portland cement and siHca flour. The specified compressive strength of the units, based on net cross-sectional area, was 3.000 psi. Actual average compres6 X 8 X 16-in Masonry Units

TABLE 3.1

8 X 8 X 16 -In Masonry Units

Figure 3.1. Masonry units.

sive strength of the units tested was 4230 psi and

4080 psi for the 8-in and the 6-in units, respectively.

The masonry units used are illustrated in figure

3.1. Dimensions and properties of the masonry units

which were determined in accordance with ASTM

standard C140-65T [3] are recorded in table 3.1.

3.1.2. Mortar

The mortar used in all wall panels was type S mortar, in accordance with the proportion specifications

a/ Dimensions and Properties of Concrete Masonry Units—

Unit Width Height Length Minimum

Thickness

in

Gross AreaNet

Area Compressive

Strength

Oven

Dry Weight

Concrete

Weight

Water Absorption

in in in Face

Shell Web in2 %

Gross Area

psi

Net Area

psi lb Ib/ft^ Ib/ft^

8-in block7 5/8 7 5/8 15 19/32 1 5/16 1 118.90 52.33 2213 4230 29.71 108.20 11.32

6-in 5 5/8 7 5/8 15 5/8 1 1 87.89 55.89 2280 4080 22.78 105.09 12.21 block

a/ Values given in the table represent the average results from tests or measurements of 5 units.

2
of ASTM C270 [4] . Type I portland cement, masonry cement and sand were proportioned 1/2:1:4 by

volume. The sand was bank run siliceous aggregate

from White Marsh. Maryland, with a fineness modulus of 1.73. Forty-one sets of 2-in mortar cubes were made

during the fabrication of the wall panels. The mortar

cubes were made and stored under the same conditions as the wall panels. In general, the mortar cubes were tested at approximately the same age as the

corresponding walls. However, some of the rein- forced concrete masonry wall panels took 6 days to fabricate because of waiting time for two grouting

operations and weekend delays. The age of tested

mortar cubes, therefore, ranged from 7 to 53 days.

Mortar cube strength averaged 1180 psi. Individual

mortar cube tests are hsted in table 3.2. As indicated

in the table, the cube strengths ranged from 700 to 1768 psi. However, 30 of the 41 sets of cubes had

compressive strengths within 300 psi of the average

value.

Since many batches of mortar were used in the

construction of a wall panel and many of the walls

took up to 6 days to fabricate, the mortar strength

varied in different elevations of the wall. The

average mortar strength was 1180 psi.

3.1.3. Grout

The grout used in the reinforced concrete masonry wall panels was a coarse grout in accordance with

ASTM C476 [5]. The grout mix had the following

proportions by weight:

Type I Portland Cement 47 lb Sand 120 lb Gravel 80 lb Water 40 lb

Proportions of portland cement, sand and gravel by

volume were 1:3:2. The bank-run sand and gravel were siliceous ag- gregates. The sand had a fineness modulus of 1.73. The gravel had a maximum size of f in.

TABLE 3.2 Compressive Strength of Mortar Cubes

Average

Date of Date of Compressive

No. Test Fabrication Test Age Strength

days psi

1 6/27 7/15 18 758

2 6/28 7/15 17 1166

3 7/1 7/15 14 1282

4 8/26 9/10 15 1271

5 7/3 7/23 20 950

6 7/5 7/23 18 1250

7 7/8 7/23 15 1006

8 7/9 7/23 14 1125

9 7/11 7/29 18 862

10 7/10 7/29 19 1768

11 7/12 7/29 17 1317

12 7/16 8/14 29 1139

13 7/16 8/14 29 1000

14 7/30 8/20 21 1309

15 7/31 8/20 20 1125

16 8/2 8/20 18 1500

17 8/6 8/20 14 1340

18 8/8 8/21 13 1175

19 7/9 7/18 9 1123 20 7/1 7/16 15 1244

21 7/2 7/16 14 1286

22 10/7 11/4 28 1628

23 10/7 10/14 7 967

24 9/20 10/2 12 1651 25 9/6 9/26 20 1438

26 9/10 9/26 16 915

27 9/13 9/27 14 1050 28 9/16 9/27 11 1414

29 9/17 9/27 10 1187 30 8/22 9/18 27 700

31 8/27 9/18 22 1267

32 8/29 9/18 20 736

33 9/3 9/18 15 1428

34 7/19 9/10 53 1208

35 7/22 9/10 50 1033

36 7/24 9/10 48 1149

37 7/26 9/10 46 1386

38 8/14 9/10 27 794

39 9/18 9/30 12 1354

40 9/18 9/30 12 1356

41 9/19 9/30 11 769 Average 1180

3
TABLE 3.3 Compressive Strength of Grout Cylinders

No. Test

Date of

Fabrication

Date of TestAge

days

Wall Designation

Compressive

Panel Strength

No. psi

1 7/24 9/9 47 20-R-O 20-R-O

1 2476

2

2 7/26 9/9 45 20-R-O 20-R-O

1 2264

2

3 7/10 7/23 13 16-R-T4

16-R-T4

5 1910

6

4 7/15 7/26 11 16-R-T4

16-R-T4

5 2009

6

5 8/2 8/17 15 16-R-T3 16-R-T3

7 2193

8

6 7/10 7/18 8 16-R-T6 16-R-T6

3 1857

4

7 8/19-8/30 9/27 28-39 2228

8 8/19-8/30 9/27 28-39 2900

9 8/19-8/30 9/27 28-39 2387

10 8/19-8/30 9/27 28-39 2546

11 9/6 9/27 21 20-R-T4

on D TA

7 2449

QO

Average 2290

Eleven 6 X 12-in gi out cylinders were made during

the fabrication of the reinforced masonry walls, and

cured under similar conditions as the walls. The

compressive strengths ranged from 1857 psi to 2900

psi and averaged 2290 psi when tested at ages from

8 to 47 days. Individual test results are tabulated in table 3.3. It was observed that in general the

strengths increased with an increase in age of the

grout cylinder. The cylinders tested at the least age. 8 days, gave the lowest compressive strength. Since

the test results indicated that the majority of the

cylinders, a total of 8, had compressive strengths

within 300 psi of the average value, the average

value of compressive strength can be assumed to be

a representative value for all the grout cyHnders.

It has been observed [6] that because of the

water absorption by the masonry units, grout within

the walls achieves a significantly higher strength

than the same grout when cured as cylinders. It may

therefore be assumed that the grout within the walls

had a compressive strength higher than the 2290 psi

cylinder strength.

3.1.4. Steel Reinforcement

Vertical and horizontal steel in the reinforced wall

panels consisted of ASTM A615 [7] No. 5 deformed

bars with a minimum specified yield strength of 60,000 psi.

3.2. Construction of Specimens '•

(I 3.2.1. General ( The wall panels and prisms were built and cured i in the laboratory at approximately 73 °F and 50 per- cent relative humidity. Wall panels were constructed in pairs between wooden guides to assure ; proper alignment and plumbness. Joint thickness was controlled at | in by horizontal lines at 16-in in- tervals which correspond to the height of two blocks

and two joints. This method led to oversized joints in

^ four unreinforced panels, where block which were

undersized in height were used.

3

3.2.2. 6-in Reinforced Walls '

3 Wall panels were constructed in three nominal n sizes: 4 X 10-ft, 4 X 16-ft and 4 X 20-ft. Walls were ( built of the 6 X 8 X 16-in concrete block which were j laid in running bond. j A wall cross section is shown in figure 3.2(a). Face- ji shell bedding was used for the horizontal and verti- J cal mortar joints, and mortar was also placed on the p cross webs around the cores which were to be '

grouted. The mortar joint thickness was I in. One / No. 5 bar was gi'outed into each of the two outside j cores of the wall as shown in figure 3.2(a). Vertical t bars in the 16- and the 20-ft walls were spliced near | 4
- # 5 Bof

c—3/8" Mortar Joint

1^

(a ) Typical Horizontal Section

-Top of Won

e

<7) —

" — aw — r

T

*5 Bors

-Bottom of Bond Beam

Bottom of Bond Beam —

—Top of 1st Lift in 16 and 20 ft Walls

—— m A

#5 Bors

± 4V

A B

lO-fi Won 8' -8"

i6-fi Won 7'-4" 8'-7r

20- ft Wall 9'-4" 9' -llf" —Bottom of Bond Beam

(b) Reinforcement Detoils

Figure 3.2. 6-in reinforced walls.

jmidheight over a length of 30 bar diameters (19 in).

I Horizontal reinforcement consisting of one No. 5 .deformed bar was installed in each bond beam as

I shown in figure 3.2(b). These bars were grouted into

i6 X 8 X 16-in hntel block laid horizontally. The 10-ft 'walls had bond beams at the top and bottom course.

I whereas the 16- and 20-ft walls had an additional

bond beam at midheight. The actual cross-sectional

dimensions of the walls were 47 f in by 5 f in; actual

I panel heights were 9 ft - 3 1 in, 15 ft - 11 f in, and 19

|ft-3|in. Present design practice [2] specifies an area of

I steel not less than 0.0013 times the cross-sectional

! area of the wall in one direction and not less than

0.0007 in the other direction. The area of vertical

steel used in the reinforced walls of this investigaition was equal to 0.0023 times the cross-sectional

area. The area of principal reinforcement was. therefore, about twice the minimum area required. The

I area of horizontal reinforcement varied from 0.0007

times the cross-sectional area for the 20-ft walls to 0.001 times the cross-sectional area for the 10-ft

j walls. The reinforced walls were constructed in the fol- lowing manner: The first course of each wall consisted of three whole hntel units (see fig. 3.1) which

were laid on a full mortar bed on a plastic sheet

placed on the laboratory floor. These units formed a

horizontal trough into which the horizontal reinforcement could be grouted. A strip of painted 2.5 Ib/yddiamond-mesh metal lath was placed over the top of these lintel units in the middle 32-in of the wall to contain the grout. Wall construction was then con- tinued to the bottom of the next bond beam course. After completion of every three courses of block,

mortar protrusions were removed from the two end

cores by a 2-ft long stick, to keep these cores clean

for grouting. Clean-out holes were provided at each

end of the bond beam. Sand was placed at the bot- tom of the vertical cores to be grouted to facilitate removal of the mortar droppings. Before grouting,

the end cores and the bond beam were inspected

and cleaned by compressed air. Horizontal and vertical reinforcement bars were

then placed and tied together, to prevent dislocation

of the bars during grouting. Prior to grouting, the

clean-out holes were covered by boards.

Walls were at least 16 hours old before grouting. In the first few walls, grout was consolidated by

rodding. Subsequently, a vibrator was used to insure

filling of voids, particularly in the bond beams. Grout was poured to within one inch from the top of the lift and reconsolidated after 30 minutes to remove air voids caused by water absorption by the masonry

units. The grout in the first lift was permitted to set overnight before construction of the second half of

the wall was started. The second half of the 16-ft walls contained two bond beams which had only two

lintel blocks. At the outer end of these beams regular

half-block were used. Openings were cut into these

half-block to accommodate the horizontal bar and to provide cleanout holes at mid height. In the 20-ft walls all bond beams were built of three whole lintel block. The upper bond beam of the 10-ft walls also consisted of three whole lintel units. The 10-ft walls were constructed in one hft. Two lifts were used in the 16- and 20-ft walls.

3.2.3. 8-in Unreinforced Walls

Wall panels, as in the case of the reinforced walls, were constructed in nominal sizes of 4X 10 ft, 4 X 16

ft and 4 X 20 ft. buih in running bond with 8 X 8 X 16-

in masonry units. Face shell bedding was used for the horizontal and vertical joints and additional mortar was placed on the cross webs at the two wall

ends. Mortar-joint thickness was f in. Actual cross- sectional dimensions of the walls were 47 f in X 7 f

in. Actual wall heights were 9 ft - 3 f in. 15 ft - 11 f in and 19 ft -31 in.

404-485 O - 70 - 2 5
Figure 3.3. 20-ft high 8-in unreinforced wall panel.

The first course was constructed from three whole

masonry units. Each alternate course contained two

half-block at the wall ends. Kerf block were used as

half-block, and corner block were used where whole

units were required at the wall ends (refer to fig. 3.1). A typical 20-ft high wall panel is shown in figure 3.3.

3.2.4. Prism Specimens

Prism specimens were built in stacked bond (one

block wide) using the 8 X 8 X 16-in block and the 6 X

8 X 16-in block. Mortar was applied in face shell bedding as in the walls with |-in thick mortar joints.

Three-block high as well as two-block high

specimens were constructed.

Prisms were built at random during construction

of the walls, using the same mortar batches, and

Figure 4.1. Loading system and frame.

cured under the same conditions as the walls. Befon

testing, prisms were capped with high-strengtl!

plaster.

! 4. Test Procedure and | Instrumentation

Wall panels were tested in a steel frame with an adjustable top cross-beam that could be raised oi lowered to accommodate the various wall heights.

Eight 30-ton capacity hydraulic rams were attached

to the cross-beam. Figure 4.1 shows the loading

system and the frame with a 20-ft wall in place.

Figure 4.2 shows a diagram of the test setup. At

the base a 1-in thick steel plate was cemented to the

laboratory floor by high-strength plaster. The wall

panel was set on top of this plate on another bed of high-strength plaster. When the wall was set, carei was taken to assure wall plumbness and alignment.:

Another 1-in thick steel plate was cemented to the

top of the wall, to prevent wall failure by stress concentration. A 4 i-in diameter steel half-round was set on this steel plate with the flat side toward the wall.j

The load was applied to the curved top of this steeli half-round through a 4-in thick steel plate which

6
Figure 4.2. Test setup.

I transmitted the load from the eight symmetricallylocated hydraulic rams. The loading head is shown

in figure 4.3. The test setup described above was

designed to prevent rotation at the base of the wall,

! while permitting free rotation at the top. Sidesway of

I the top of the wall was minimized by tying the loadji ing frame to the laboratory wall at a height of 23 ft

j above the floor level. Great care was taken to position the wall and the steel half-round precisely in

j order to apply the load at the desired eccentricity.

Wall instrumentation is also illustrated schematij cally in figure 4.2. Aluminum tubes of 2-in diameter

' were attached to the sides of the walls. At the upper

: end these tubes had a pinned connection to the wall

i and at the lower end they were attached to a guide

which kept the tubes in line with the centerline of

the wall but permitted them to slide downwards as

the wall contracted under the load. For the first four

16-ft reinforced wall specimens, aluminum tubing of

1-in diameter was used. It was observed, however,

that this tubing tended to deflect slightly, and 2-in diameter tubes were used in subsequent tests. All instruments for the measurement of deflections were attached to these aluminum tubes.

Horizontal deflections and wall shortenings were measured by linear variable differential transformers

(LVDT's), capable of reading 0.0001 in. Instrument

readings were electronically scanned at every 20 kip

increment of vertical load and recorded in digital

form. These data were manually key punched onto

cards and automatically reduced, analyzed and

Figure 4.3. Loading head.

plotted by computer. Computer output consisted of

tabulated test results and plotted load-deflection curves. Instruments were installed to measure wall shortening and horizontal deflections at i-height. midheight and f-height of the wall. The instruments were installed symmetrically at both wall ends.

One 10-ft unreinforced wall was also instrumented

over a 24-in gage length on each wall face to deter- mine the modulus of elasticity of the masonry.

Tests were carried out in duplicate for the same

wall height and eccentricity. The first of the two

walls tested was not instrumented and only failure load was recorded. The second specimen was instru- mented, but the instrumentation was removed at about § of the failure load of the first specimen.

Deflection readings at wall failure are therefore not

available. This procedure was adopted to protect the

instrumentation from damage by explosive wall

failures. The walls were moved from the fabrication area to the test frame by a fork lift truck. Before moving, the

walls were carefully braced to prevent damage to the

specimen. A wall being moved by the fork lift truck

is shown in figure 4.4.

7
Prism specimens were tested in the same manner

as the wall panels. The prisms were set in highstrength plaster on a steel plate. A 1-in steel plate was set in plaster on top of the prisms, and load was

applied'by a 4i-in steel half-round. Three-block high, as well as two-block high prisms were tested in duplicate for each load eccentricity.

5. Test Results

5.1. 6-in Reinforced Walls

Results of tests on the 6-in reinforced walls are presented in table 5.1 and plotted in figure 5.1. Loaddeflection curves for these walls are shown in figures

5.2 through 5.4. The curves show horizontal deflecTABLE 5.1 Summary of 6-in Wall Test Results

Wall Specimen Age Eccentricity Ultimate Load Designation No. days in kip

10-R-O 1 30-32 0 0 354 8 10-R-O 2 29-31 0 0 328 0 10-R-O 3 n-12 0 0 361 8 10-R-O 4 14-15 0 0 369 4 10-R-T6 , 5 15-16 t/6 0.94 296 2 10-R-T5^' 6 15-16 t/6 0.94 263 4 10-R-T4 7 14-18 t/4 1.41 247 3 10-R-T4 8 14-18 t/4 1.41 236 6 10-R-T3 9 14-15 t/3 1.88 189 8 10-R-T3 10 14-15 t/3 1.88 185 5

16-R-O 1 10-16 0 0 274 7 16-R-O 2 11-17 0 0 281 2 16-R-T6 3 7-13 t/6 0.94 212 9 16-R-T6 4 11-17 t/6 0.94 201 6 16-R-T4 5 8-14 t/4 1.41 170 4 16-R-T4 6 9-15 t/4 1.41 190 9 16-R-T3 7 7-9 t/3 1 .88 146 8 16-R-T3 8 8-10 t/3 1.88 153 2

20-R-O 1 45-49 0 0 343 2 20-R-O 2 45-49 0 0 331 7 20-R-O. , 5 12-18 0 0 253 8 20-R-O^' 6 7-13 0 0 184 4 20-R-T6 3 19-21 t/6 0.94 198 4 20-R-T6 4 19-21 t/6 0.94 202 0 20-R-T4 7 8-19 t/4 1.41 119 4 20-R-T4 8 9-20 t/4 1.41 129 0 20-R-T3 9 9-13 t/3 1.88 73 5 20-R-T3 10 10-14 t/3 1.88 83 9

- Bottom lintel block cracked during fabrication. - Wall had a broken block on one end of the 8th course from the top.

8
400

160

10 16 20 mLL HEIGHT, ft

Figure 5.1. Failure loads for 6-in reinforced walls.

»/t» 1/6

0 005 0 10 0.15 HORIZONTAL DEFLECTION, in

120

< 80

-e/t= 1/6

0 0.05 0.10 0.15 0.20 HORIZONTAL DEFLECTION , in

Figure 5.3. Load-deflection curves for 16-ft reinforced walls.

0 10 0.15 0.20 0.25 HORIZONTAL DEFLECTION, in

Figure 5.2. Load-deflection curves for lO-ft reinforced walls.

Figure 5.4. Load-deflection curves for 20-ft reinforced walls.

tions at f height of the walls which are the largest

measured deflections.

Figure 5.5 shows typical wall failures. A log of aU

recorded individual failures is presented in table 5.2. The 10-ft high walls with small eccentricity of load

failed by vertical splitting and compression. The

walls subjected to the largest eccentricity of load

failed by crushing in the top 3 courses.

All of the 16-ft high walls failed along a horizontal

joint, approximately i the wall height from the top of

the wall. These waUs developed large deflections

prior to failure.

9
Axiolly Loaded 10- ft Panel Eccentrically Loaded 16- ft Panel

Figure 5.5. Typical failures of 6-in reinforced walls.

The 20-ft high walls also failed at horizontal joints,

approximately i of the wall height from the top of the

wall. Deflections of the 20-ft walls were considerably

larger than in the 16-ft walls. At eccentricities of

and tJS, the walls deflected excessively and tended

to sHp out of the loading system. These walls

recovered after load removal and exhibited only

small residual deflections. Most walls crushed at a

horizontal joint 6 to 7 courses below the top of the

wall.

10
TABLE 5.2 Failures of 6-i"n Reinforced Walls

Wall Specimen Age Description of Failure Designation No. days

10-R-O 1 30-32 Split down one side of one face about 1 unit from end. Failure occurred when top l/4h came out. 10-R-T4 7 14-18 Top failed. 1D-R-T4 8 14-18 Failure in top 3 courses. 10-R-T3 9 14-15 Failure in top 2 courses.

16-R-O 1 10-16 Wall broke along horiz. joint l/4h from top. 16-R-O 2 11-17 Wall broke along horiz. joint l/4h from top. 16-R-T6 3 7-13 Wall broke along horiz. joint l/4h from top. 16-R-T6 4 11-17 Wall broke along horiz. joint l/4h + from top. 16-R-T4 5 8-14 Wall broke along horiz. joint between 4th & 5th course

from top, compressive failure in 5th course. 16-R-T4 6 9-15 Wall broke along horiz. joint between 5th & 6th course

from top. 16-R-T3 8 8-10 Failed at 6th course from top.

20-R-O 1 45-49 Crushing of 7th course from top. 20-R-O 5 12-18 Failure occurred in the 7th & 8th courses from the top. A large vertical crack developed at 214 kip in the instrumented part of the test. Crack extended from 18th

to 24th course. There was no top reinforcement on west

side of wal 1

20-R-T6 3 19-21 Crushing between 6th & 7th courses from the top on the compression side of wall. 20-R-T6 4 19-21 Crushing between 6th & 7th courses from the top on the compression side of wall. There was a slight bend in the wall about the top of the 15th course from the bottom. 20-R-T4 7 8-19 Wall slipped out of loading system with no apparent

sign of failure. 20-R-T4 8 9-20 Wall deflected considerably about 2 courses above bond

beam (mid height) then slipped away from loading system. After failure had little residual deflection. 20-R-T3 9 9-13 Failure occurred by excessive bending at bottom of 7th course from the top. 20-R-T3 10 10-14 Large deflection prior to failure with greatest deflection 7th course from the top.

11
TABLE 5.3 Sumnary of 8-in Wall Test Results

Wall Specimen

Designation No. Agedays Eccentricity

in

Ultimate

Load

kip

10-N-O 1 33-36 0 0 232 3 10-N-O , 2 35-33 0 0 231 7 in w 0^' J If;

I 0- IP1 o u u 1 /u /I 10-N-(F-' 4 18-20 0 0 159 7 10.N-T6^/ ^' 5 15 t/6 1 27 172 6 10-N-T&2.' 6 18 t/6 1 27 166 1 10-N-T4. 7 13-16 t/4 1 91 203 2 10-N-T4^' 8 15-18 t/4 1 91 217 2 10-N-T3 9 13 t/3 2 54 198 4 10-N-T3 10 16 U/ 0 54 C\J 1 nu

10-N-O 13 10-11 0 0 278 7 10-N-O 14 11-12 0 0 225 2 10-N-T6 11 12 t/6 1 27 157 4 10-N-T6 12 13 t/6 1 27 196 8

I 6-N-O ] n nu

co 16-N-O 2 14-18 0 0 273 5 16-N-T6 3 14-15 t/6 1 27 199 7 16-N-T6 5 8-10 t/6 1 27 181 7

1 D-IN- 1 4 Z/ H 1 Ql 1 7c; 5

0 16-N-T4 6 11-13 t/4 1 91 172 0

1 D-IX- 1 J

7/ in 11 i- / 'i 1/ 0

o

C

1 Afi 1

1 16-N-T3 8 11-12 t/3 2 54 169 4

20-N-O 1 39-44 0 0 233 5 20-N-O 2 39-44 0 0 249 2 cc

n

U

A

u 20-N-O 6 12-13 0 0 208 1 20-N-T6 4 22 t/5 1 27 188 7 20-N-T5 5 12-13 t/6 1 27 180 2 20-N-T4 7 14-15 t/4 1 91 143 0 20-N-T4 8 14-15 t/4 1 91 143 0 20-N-T3 9 8-10 t/3 2 54 148 1 20-N-T3 10 8-10 t/3 2 54 150 5

a/ Walls had some mortar joints of thickness in excess of

3/8 in.

'aj Wall was damaged by the yoke used in transporting it.

5.2. 8-in Unreinforced Walls

The wall test results are summarized in table 5.3 and plotted in figure 5.6. Figures 5.7 through 5.9 show load-deflection curves for the deflections at |

height of the 8-in walls. Wall failures are shown in figure 5.10. A log of all recorded individual failures is shown in table 5.4. The 10-ft high walls failed in a manner resembling

the failure of three-block high prisms. Axially loaded

walls developed vertical cracks with final failure oc- curring by crushing between the second and fourth course from the top or bottom end of the wall at both

wall faces. Eccentrically loaded walls failed between

the top and the fourth course from the top by compressive failure on one wall face at a mortar joint, ex- cept for one wall loaded at an eccentricity of i/6 which failed near its base.

The 16-ft high walls generally failed along a horizontal joint at approximately I of their height.

One axiaUy loaded wall and one wall loaded at an ec- centricity of f/6 failed by compression near the

second course from the bottom of the wall. Most 20-ft high walls also failed along a horizontal

joint at approximately | of their height. One axiaUy

loaded wall and one with a load eccentricity of f/6 failed by crushing of the mortar joint three courses from the bottom.

12
300

200

<o

<o

£ 100 I- >

e=0

Eccentricities

e =0

o e =t/6

A e =t/4 A e =t/3

10 16 20

WALL HEIGHT , f

J—

0.05 QIO 015 0.20 HORIZONTAL DEFLECTION , in

Figure 5.8. Load-deflection curves for 16-ft unreinforced walls.

Figure 5.6. Failure loads for 8-in unreinforced walls.

HORIZONTAL DEFLECTION , in

Figure 5.7. Load-deflection curves for 10-ft unreinforced walls.

13
Figure 5.10. Typical failures of 8-in unreinforced walls.

5.3. Prisms

Test results on eccentrically loaded 2-block high

and 3-block high prisms made of 6-in and 8-in block

are given in tables 5.5 and 5.6, respectively. These

tables note the age, as well as the date of fabrication

of prisms. This is noted since the strength of prisms

fabricated on certain dates sometimes deviated markedly from the generally observed trend.

6. Interpretation of Results

6.1. Stress-Strain Relationships

Stress-strain relationships, measured on unreinforced as well as reinforced walls, are shown in figure 6.1. Curve A shows a stress-strain curve computed from the longitudinal deformation of an axially

loaded 16-ft unreinforced wall (specimen 2). This is

the only case where deflections were measured to the point of ultimate load. In all other cases instru- mentation was removed prior to failure. Curves B

and C are stress-strain curves for axially loaded 10-ft unreinforced walls, computed from the average of

measurements of 4 linear variable differential trans- formers having a gage length of 24 in, which were specially installed for that purpose. (Curve B is for specimen 14 and curve C for specimen 4.) Curve C

was obtained from one of the specimens with excessive joint thickness and may therefore represent a

wall of lower than normal strength. The ultimate

compressive strength of the specimens from which

curves B and C were derived is also shown in the

figure. Stress was computed on the basis of the

average net area, determined in accordance with

ASTM Standard C140-65T.

There is good agreement between the three

curves. In general, the measured stress-strain

14
TABLE 5.4 Failures of 8-in Unreinforced Walls

Wall Specimen

Age Description of Failure Designation No. days

10--N -0 1 33- 36 Wall split through center vertically to bottom

l/4h where it broke down and out to bottom

corners. Typical compression failure of block.

10--N -0 2 35- 38 Compression failure in 2nd course from bottom.

10--N -0 3 16- 18 Vertical splitting and cracking in the shape of

an inverted V at top l/4h point of wall.

10--N.-T4 7 13- 16 Bending with subsequent compression failure in mortar joint at yoke location (top of 9th course).

10--N'-T3 9 13 Bending in the wall, compressive failure in the mortar joint on inside of bend and sudden rupture.

10--N.-T3 10 16 Bending and subsequent failure at the mortar

joint between 3rd and 4th courses from the top.

10--N--T6 11 1

Splitting of 1st and 2nd courses from the bottom.

16-N--0 1 11- 15 Wall broke about l/4h from top along a horizontal joint and blew out of frame.

16-N--0 2 14- 18 Compression failure in 2nd course from bottom,

wall broke up and fell straight down.

16-N--T6 3 14- 15 Compression failure in 1st and 2nd courses from bottom, wall broke along horizontal joint l/4h from bottom.

16-N--T6 5 8- 10 Wall broke along horizontal joint between l/3h and l/4h from the top.

16-•N--T4 4 14- 15 Wall broke along horizontal joint l/4h from the

top.

16-N--T4 6 11- 13 Failure originated at 2nd course from top and wall

fell sideways.

16-N--T3 8 11- 12 Failed at 6th joint from top.

20--N--0 1 39- 44 Failure 5th course from the top - 2/3 way through

test vertical cracking in 2nd and 3rd courses

from bottom.

20-N--0 3 22 Failed near the top.

20-N--0 5 12- 13 Crushing about 3rd course from the bottom.

on -N--T5 4 22 Failure occurred 5th course from top along horizontal joint.

20- -T6 5 12- 13 Failure in mortar joint 3rd course from the bottom.

20-.^.-T4 7 14- 15 Failure occurred l/4h from top, very little deflection was visible prior to failure.

20- -T4 8 14- 15 Failure occurred about l/5h from the top.

20--N -T3 9 8- 10 Failure occurred near 7th course from the top.

20--N -T3 10 8- 10 Spalling at 2nd course from top. Failure at 6th course from top.

15
TABLE 5.5 Summary of 6-in Prism Test Results

Prism Designation

Height Eccentricity Eccentricity

in 6-2-0

6-2-0

6-2-0

6-2-0 6-2-0

6-2-0

6-2-0 6-2-T6

6-2-T6 6-2-T4

6-2-T4

6-2-T4

6-2-T3

6-2-T3 6-2-T3

Average Date Maximum Maximum of

^9e Load Load Construction

days kip kip 2-block

2-block

2-block 2-block

2-block

2-block

2-block

2-block

2-block

2-block

2-block

2-block 2-block

2-block

2-block

00

00

0

0

0t/6

t/6 t/4

t/4 t/4

t/3 t/3

t/3

000

0

0

0

00.94

0.94

1.41

1 .41 1.41 1.88 1.88

1 .88

3128

13

9n

1111

9

9

910

11

9

7

9 6-3-0

6-3-0

6-3-0

6-3-0

6-3-0

6-3-0

6-3-0 6-3-T6 6-3-T6 6-3-T4

6-3-T4

6-3-T4

6-3-T3

6-3-T3

3-block

3-block

3-block 3-block

3-block

3-block 3-block

3-block

3-block

3-block

3-block

3-block

3-block 3-block

77.4 93.0

80.6

81.2

69.6 76.4

74.5

74.0

72.6 76.0

112.0 67.4 63.8

84.2

83.0

85.2

76.5

73.3

85.1

77.0

0

0

0

0

0

0

0t/6 t/6 t/4

t/4 t/4 t/3

t/3

7/11 7/16

7/31 7/9 9/15

9/15

9/15

7/31 8/6 8/12 9/3

9/15

8/6 9/6 8/12

00

0

0

0'0

00.94

0.94

1.41

1.41

1.41 1.88

1.88

2929

14

9

9n

11

9

11

7

9

7

82.3

87.6

81.3

58.7 90.4

77.6 89.5

61.0

62.5

72.6 63.0

109.2 78.6

85.0

84.9

79.5

61.

81.6

81.8

7/11 7/16

7/31 7/9 8/12 9/15

9/15

8/6

8/6 8/12

9/15

9/6 8/12

9/6

curves can be approximated by a straight line. Curve

A, which is the only curve that covers stress-strain

relations to the point of failure, was derived from a specimen of higher-than-average strength. This curve therefore covers a range of stresses not nor- mally developed by a typical specimen.

The following values of moduli of elasticity were

experimentally derived for the unreinforced walls:

Initial modulus of elasticity, Ei = 1.4 X lO^ psi.

Approximate final tangent modulus of elasticity

at the stress level of most wall failures, Et =

0.4 X 106

Curve D in figure 6.1 shows stress-strain relation- ships for an axially loaded reinforced 10-ft wall. In

this case, stresses were determined on the basis of

the transformed section shown in figure 6.2. This

transformed section was developed using a "net"

cross-sectional area for the block which is based on

minimum face-shell and web thicknesses, the area

of the grout and a transformed steel area based on an 'V' of 29 assuming that the average modulus of

elasticity of masonry is approximately 1 X 10^ psi and that of steel is 29 X lO^ psi. It can be seen from

a comparison of curve D with curves A, B and C that the area transformation which conservatively as- sumed equal stiffness for grout and masonry and

also was based on minimum, rather than average,

net area of masonry probably resuhed in overestimating the stresses in the masonry.

The value of the initial modulus of elasticity

derived from curve D is 2.8 X IQe psi. A tangent

modulus at failure could not be obtained since in- strumentation was removed before the masonry

developed its uhimate strength. Note that the stress- strain curve is essentially linear up to a stress of

about 80 percent of the failure stress. A linear stress- strain relationship probably approximates the stress distribution up to failure reasonably well.

16
TABLE 5.6 Sumnary of 8-in Prism Test Results

Average Date Maximum Maximum of Prism Height Eccentricity Eccentricity Age Load Load Construction

Designation in days kip kip

8-2-0 2-block 0 0 28 109 5 108 5 7/17 8-2-0 2-block 0 0 28 107 5 7/18 8-2-0 2-block 0 0 14 77 0 7/1 3-2-0 2-block 0 0 13 87 6 7/2

8-2-0 2-block 0 0 12 75 2 84 6 7/31 8-2-0 2-block 0 0 12 71 0 7/31 8-2-0 2-block 0 0 11 112 0 9/15 8-2-T6 2-blcck t/6 1.27 15 82 6 77 3 7/2 8-2-T6 2-block t/5 1 .27 12 72 0 7/17 8-2-T4 2-block t/4 1.91 13 69 3 7/18 8-2-T4 2-block t/4 1.91 13 71 0 75 0 7/18 8-2-T4 2-block t/4 1.91 9 84 6 8/12 8-2-T3 2-block t/3 2.54 11 72 0 9/15 8-2-T3 2-block t/3 2.54 8 60 6 71 4 7/29 8-2-T3 2-block t/3 2.54 19 58 5 8/6 8-2-T3 2-block t/3 2.54 9 94 6 8/12

8-3-0 3-block 0 0 28 78.3 7/18 8-3-0 3-block 0 0 31 101.0 89.0 7/17 3-3-0 3-block 0 0 29 87.6 7/17 8-3-0 3-block 0 0 14 87.8 7/1 8-3-0 3-block 0 0 13 89.2 96.4 7/2 8-3-0 3-block 0 0 11 117.0 9/15

8-3-0 3-block 0 0 11 91.5 9/15

8-3-T6 3-block t/6 1.27 14 64.7 7/17 8-3-T6 3-block t/6 1.27 11 62.6 65.0 7/18 8-3-T6 3-block t/6 1.27 15 67.8 8-3-T4 3-block t/4 1.91 13 56.9 7/18 8-3-T4 3-block t/4 1.91 13 58.2 60.1 7/18 8-3-T4 3-block t/4 1.91 9 65.2 8/12 8-3-T3 3-block t/3 2.54 15 53.4 7/29 8-3-T3 3-block t/3 2.54 14 48.3 57.7 7/30 8-3-T3 3-block t/3 2.54 9 71.6 8/12

0 001

MASONRY:

STEEL; FOR steel: FOR GROUT

X lO^psi £5=29 X lO^psi

En

n= 1

= 29

TRANSFORMED AREAS MASONRY : 128 GROUT 46

steel: 17 TOTAL 191 in^

STRAIN

Figure 6.1. Stress-strain curves. Figure 6.2. Assumed transformed area for reinforced masonry

wall.

17
MOMENT, kIp-in

Figure 6.3. 6-in hollow block prisms under eccentric loading.

6.2. Cross-Sectional Capacity

In order to study the capacity of slender walls, it

is first necessary to consider the strength of short

wall sections. Figure 6.3 shows a plot of the failure loads of eccentrically loaded three-block high 6-in prisms. Loads were applied axially and at eccentricities of f/6, and tl3. Note that even though there is considerable difference between individual test points at the same eccentricity, no trend can be observed for the failure load to decrease with increasing eccentricity. Similar behavior has been observed

elsewhere for solid sections of concrete as weU as clay-masonry [8]. It is apparent that flexural compressive strength of masonry increases significantly

with increasing strain gradients.

The 6-in block of which prisms were tested were

used in the construction of the reinforced masonry

walls. However, these walls also contained grout and

steel, and the section capacity of a reinforced wall

wiU depend on the strength and relative stiffness of

all the component materials. The correlation

between prism strength and wall strength is discussed below.

The average axial compressive prism strength

computed from the 6-in prism tests, based on minimum net area, is 1890 psi. This stress, multiplied by the transformed area shown in figure 6.2 (191 in^), results in a computed axial failure load of

361 kip. This should be compared with the average

336-kip failure load for the 10-ft axiaUy loaded rein- forced walls. Thus the 10-ft walls developed approximately the predicted ultimate axial strength. This is a good correlation, considering the difference

between individual test points.

It is somewhat more difficult to compare flexural compressive strength, since at each eccentricity the

6-in prisms developed different flexural compressive

strength, with an apparent increase in strength with [ increasing strain gradients. Average flexural com- j pressive strengths developed at an eccentricity of «/3

| by the 6-in prisms and by the 10-ft reinforced walls j respectively, are compared below. The transformed J section in figure 6.2 was used to compute stresses in { the reinforced walls. The following stresses were j computed: ,

Average flexural strength of 6-in prisms, at tj3

"

eccentricity: 4,400 psi; Average flexural

| strength of 10-ft walls, at tl3 eccentricity:

2,900 psi. «

Stresses were computed for a hnear stress dis- , tribution. While the 6-in prisms developed flexural i compressive strength which exceeded the strength .i under axial loading by as much as 130 percent, the j strength increase in the case of the wall was only 50

percent. Thus, there is good correlation between

wall strength and prism strength under axial loading, \ while under eccentric loading the prisms developed

higher flexural compressive strength than the walls.

, The question arises whether the strength of the 10-ft ( wall was reduced by slenderness effects. The failure f mode of these walls indicates that they failed near s the top. where the eccentric load was applied. It will « be explained later that this type of failure is an indi- j, cation that slenderness had no significant effect on

wall strength. The discrepancy between flexural strength of prisms and walls is probably caused by

composite action of the wall rather than by slen- , derness effects. \ Figure 6.4 shows the failure loads of the 10-ft high ; reinforced walls, plotted against applied moments i

MOMENT, kip-in

Figure 6.4. Short-wall interaction-curve and test results for

10-ft high reinforced masonry walls.

18
(load X eccentricity). Test points for individual

specimens are numbered in accordance with table

5.1. If it is assumed that the strength of the 10-ft walls was not appreciably affected by slenderness,

this plot also represents the cross-sectional capacity

of these walls. The solid curve shown in the figure is a theoretical interaction curve for the section capacity of this wall. Moments were computed on the as- sumption that at failure plane sections remain plane

and that the stress distribution was approximately

linear. The transformed section in figure 6.2 was

used in the computations. The yield strength of the

steel, /'s, was taken as 60,000 psi, and /'m, the compressive strength of masonry, was computed from

the average prism strength under axial load as 1890

psi. Additional information pertaining to the

development of theoretical interaction curves is contained in reference [8]

It can be seen by comparing the actual test results with the intersection points of the solid interaction curve with the dashed sloping hues representing the

various load eccentricities of the tests, that moment

capacities are very conservatively predicted.

Another interaction curve has been computed, using

the average flexural compressive strength of 2,900

psi, developed by the walls at the maximum test ec- centricity of f/3. This curve is shown by the dashed

line in figure 6.4. Note that this curve agrees with actual test results only at the f/3 eccentricity. At

smaller eccentricities the curve overestimates wall

strength, and it is apparent by the way the curve

diverges from the test results that flexural strength

increased with increasing eccentricity. If this observation is extrapolated to eccentricities greater than

t/3, it may be deduced that the curve is conservative

for eccentricities greater than f/3, but overestimates

moment capacities for eccentricities smaller than

f/3. If we define flexural strength as a/'m, where a is

f'^ in Compression- 1,700 psi Apporent af'm 'n Flenuro (Maiimuni);2,320psi

< 50 -

100 MOMENT, kip-in

a function of load eccentricity (or strain gradients),

then for the test results of the reinforced walls at f/3 eccentricity a — 1.5. Figure 6.5 shows a plot of the failure loads of

three-block high 8-in prisms subjected to axial and

eccentric vertical loads. Again an interaction curve was computed on the basis of average axial compressive strength, /',„ = 1700 psi. This curve is represented by the soHd curve in figure 6.5. It can be seen that moment capacities are very conservatively

predicted by this curve. Another interaction curve

has been developed on the basis of the average flexural compressive strength at the f/3 eccentricity and

is shown in the figure by the dashed curve. As in the case of the reinforced walls this curve diverges from

the trend of the test results at smaller eccentricities,

indicating that "a" is a function of strain gradients.

Again it may be deduced that the dashed curve is probably conservative for load eccentricities greater

than f/3, while overestimating capacities for smaller

load eccentricity. In this case af'm at the f/3 eccentricity is 2,320 psi and a — 1.37. A comparison of prism strength with 10-ft wall

panel strength is shown in figure 6.6. The interaction curves for a = 1 and a = 1.37, developed from the

prism data, are also plotted in the figure. Note that

at the larger eccentricities average wall strength ex- ceeded prism strength, while under axial loading and

at the tl6 eccentricity, wall strength tended to be

somewhat lower than prism strength. A comparison

of all the eccentric wall tests seems to show no

noticeable effect of the magnitude of load eccentricity on failure load. However, there is considerable

scatter in experimental results at axial load and at the tl6 eccentricity. In general there appears to be

no trend for the section capacity to decrease at this

400

O PRISM TEST A 10 ft PANEL TEST

ZOO -

200 400

MO^E^IT, kip-in

Figure 6.5. 8-in hollow block prisms under eccentric loading.

Figure 6.6. Comparison of prism strength and 10-ft panel

strength for unreinforced walls.

19
wall height. The interaction curve developed on the

basis of axial strength is, in general, conservative for eccentric loads, although one wall test each at axial

load and at t/G eccentricity falls below the predicted

strength. This scatter appears to be caused primarily

by strength variations between individual test specimens.

6.3. Slenderness Effects

6.3.1. General

Slenderness effects are illustrated in figure 6.7 which shows the free body diagram of the upper part

of a wall, subject to a vertical load P applied at its top at an eccentricity e. The free body is in equilibrium when force P is resisted at the bottom of the free body by the resultant colinear force P' . If the wall

deflected at the bottom of the free body by an amount 8 relative to the line of action of the vertical force, the resisting moment acting at the base of the

free body will be P(e + 8), and thus, the external

moment acting at the top of the wall will be magnified

by the amount P • 8.

It has been shown [9] that for the case of rein- forced concrete columns the maximum moment can be approximately computed by the following equation:

this case) and

M^Pe Cr. Pe (1) 1-

Pcr where C,„ is a correction factor, relating different

moment distributions to the basic case of a pin

ended column acted upon by a vertical load at equal

eccentricities at the top and the bottom, {Cm = 1 for

e S

Per

tt'-EI ikh

(2)

is the axial load that will cause stability-induced

compression failure. "A" in the term kh is a "length

coefficient," by which height is adjusted to equivalent height, accounting for end support conditions. In the case of masonry walls a similar mechanism

will cause a decrease in wall strength with increasing wall slenderness. Inspection of the wall failure descriptions in tables 5.2 and 5.4 reveals a general

trend for the more slender walls to fail in flexure

along a horizontal joint in the vicinity of the point of maximum deflection, while shorter walls tended to

fail near the top where the eccentricity of the applied

load relative to the undeflected wall is greatest.

However, the magnitude of this moment magnifier

effect in the case of masonry walls depends on

several parameters:

(1) End Fixity: The flat ended condition of these

tests appears to resemble fixed ended conditions at the base of the wall. However, previous experience

with similar conditions in brick walls [10] indicates,

that while the effect of eccentrically appHed loads can be approximately predicted by eq (1) for pin

ended conditions (even in the case of double curvature), wall strength was overestimated when it was assumed that flat ended walls similar to those in this investigation are fixed ended. Assumptions made

with respect to end conditions are discussed in the

following section.

(2) Stiffness: The stiffness EI, in the case of masonry, is subject to change with the magnitude

and distribution of stresses that act on the cross section. Both E and / depend on the moment distribution at failure; E decreases with increasing stresses, as can be seen in curve A in figure 6.1 while /

decreases with section cracking. Since greater

deflections and smaller failure loads are associated

with greater eccentricities and slenderness, more

section cracking takes place with a corresponding

decrease in stiffness. It has been shown for concrete columns [9] that slenderness effects can be approximately predicted by using an "equivalent £"/":

EIEjln

2.5

(3)

Figure 6.7. Slenderness effects.

where

£", = Initial tangent modulus of elasticity,

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

20
However, this equation is valid only in a range of loads and eccentricities where section cracking is not very significant.

For the case of brick masonry, slenderness effects have been approximately predicted [8] by the fol- lowing equation:

£/ = (0.2+^)^ 0.7

where Po = Short wall axial load capacity deter- mined on the basis of prism strength, or for low

vertical loads:

EI = EJn

In the interpretation of test results of this in- vestigation eq (3) was used for the reinforced walls,

assuming that reinforced masonry and reinforced concrete have similar properties. For unreinforced

walls the reduction was based on the observation

that the initial tangent modulus of elasticity equals

about 3.5 times the modulus of elasticity at failure. Thus the "equivalent EI" was taken as:

EI

EJn

3.5

(4)

kh=0.8h

Figure 6.9. Assumed conditions of base fixity.

great stiffness of these walls and the relatively minor

amount of rotation associated with a significant loss

in end stiffness are probably contributing factors to the loss of end fixity. The 16- and 20-ft walls show a much more pronounced effect of end fixity. Average

conditions of base fixity which were assumed for the

16- and 20-ft walls are illustrated in figure 6.9. These

conditions correspond to the following end moments:

6.3.2. 6-in Reinforced Walls

(1) End fixity: End conditions are related to the

shape of deflection curves. Figure 6.8 shows measured deflection curves for the 10-, 16-, and 20-ft reinforced walls. The curves for the 10-ft walls seem

to indicate that *here was only a minor amount of end fixity in spite of the flat-ended condition. The

-02"

h= 10' P= 120 kip h= 16'

P-- 60kip

h = 20' P- 40 kip

Figure 6.8. Typical deflection curves for eccentrically loaded

reinforced walls.

Mi = Pe M2 = -l/4Pe

M2//kfi = -l/4

In accordance with reference [9] , this condition

would correspond to the following values of Cm and

k:

C;„ = 0.6 + 0.4 (-1/4) =0.5

A -0.8

These assumed end conditions are conservative with

respect to the 16- and 20-ft walls.

(2) Slenderness effects: Figure 6.10 shows the test results of all the reinforced walls. Apphed end mo- ments (Pe) are plotted against vertical load. It is evident that the strength of the 16- and 20-ft walls was considerably reduced by slenderness effects. The solid curve (Curve A) in figure 6.10 is the

short-wall interaction curve for the section capacity

of these walls, developed on the basis of the average

axial strength of the 6-in prisms which was discussed

in section 6.2. As noted previously, this curve is very

conservative with respect to moment capacity. From

this curve, interaction curves for slender walls can

21
E 200

10 WALLS

16' WALLS 20 WALLS

THEORETICAL INTERACTION CURVES

A : h =0,L = IO' B : h = 16'

C h = 20'

-L

400 600 MOMENT, kip-in

Figure 6.10. Comparison of test results on 6-in reinforced walls with theoretical interaction, cun^es based on axial prism

strength

.

be developed by reducing the moment at each level of P by the moment magnifier equation. Such

reduced interaction curves were developed, using a Cm value of 0.5, a A value of 0.8, and an EI value of

Eilnl2.5. For the 10-ft high walls no slenderness effects are predicted by the moment magnifier equation. Thus

the solid curve for section capacity is also the in- teraction curve for the 10-ft walls. Curve B is the

reduced interaction curve for the 16-ft walls. Comparison of this curve with the test results of the 16-ft walls shows that the axial load, which is the critical load for stabiUty-induced compression failures, was

accurately predicted. Capacities under eccentric

vertical loads are conservatively predicted.

Curve C (fig. 6.10) is the computed interaction curve for the 20-ft walls. This curve closely predicts

the axial strength of one of the 20-ft walls. The other

wall developed significantly higher strength. This is probably attributable to the fact that this wall had a longer than average curing period. (This wall was

tested at an age of 12-18 days, compared with the 7- 13 day age of the lower strength wall.) The two 20-ft walls tested at i/6 eccentricity both developed

strength considerably in excess of the predicted

strength and developed strengths similar to that of

the 16-ft walls. These walls also had a longer than

average curing period (19-21 days). At the i/4 eccentricity the predicted strength is close to the observed

strength. At the tl3 eccentricity wall strength is overestimated by the theory. At that eccentricity, in accordance with the failure description in table 5.2,

the 20-ft walls developed a stabihty failure, where

very large increments of deflection were associated

with relatively minor increase in axial load. These

two walls represent an extreme condition {hit — 41,

ejt = i) which is outside the range presently con- sidered in the design of slender masonry walls. At

this extreme condition, wall stiffness EI is con- siderably reduced by section cracking. The expression Eilnl2.5 is an average stiffness reduction and

does not consider the variable of progressive section

cracking which is a function of P/Pq- When this ex- pression was developed it was recognized that it is valid over a range of values of P/Po, sufficient to cover all practical design cases. The extreme case of

failure at a very low value of P/Po is outside the

range of the expression.

It may be concluded that except for the extreme

case of 20-ft walls loaded at i/3 eccentricity the

theoretical interaction curves are conservative.

It has been noted in section 6.2 that the interaction curve based on axial compressive prism

strength is very conservative and that flexural compressive strength increases with increasing strain gradients. The dashed curve shown in figure 6.4 was

developed on the basis of the flexural strength at the

eccentricity of tj3 and is probably accurate or conservative for eccentricities greater than t/S. Reduced

interaction curves, developed from this curve should

therefore accurately predict the test results for values of P below the failure load for short walls at the tl3 eccentricity.

Figure 6.11 shows reduced theoretical interaction curves developed from this section capacity curve

(curve A), together with the test results. Note that there is excellent correlation between Curve B, the

theoretical interaction curve for 16-ft walls, and the

test results. The solid portion of curve B, as well as the point at axial load are computed by theory. The

0 WALLS a 16' WALLS O 20' WALLS

THEORETICAL INTERACTION CURVES

400 MOMENT, kip-in 600

Figure 6.11. Comparison of test results on 6-in reinforced walls with theoretical interaction curves based onflexural compressive

strength.

22
lighter dashed portion is a straight-line interpolation

between the computed axial capacity and the range

covered by the solid curve, which is computed.

Curve C, which was computed for the 20-ft walls

shows good correlation with waU tests at the i/4 ec- centricity and with one wall test at axial load. The

other walls tested at axial load and the walls tested

at tl6 eccentricity were stronger and the walls at the

f/3 eccentricity failed at a lower load than the pre- dicted load, as previously discussed. On the whole,

the trend of the test results, as well as actual failure loads are in good agreement with the theoretical predictions.

6.3.3. 8-in Unreinforced Walls

(1) End fixity: Figure 6.12 shows measured deflection curves for the 8-in walls. Again it appears that the 10-ft walls developed only minor end restraint,

while 16- and 20-ft walls developed partial end fixity. The "negative" deflections measured in the 16-ft walls were probably caused by deformation of the

aluminum pipes on which the LVDT's were

mounted. In all other tests larger diameter pipe was

used. Again it is assumed that base-fixity conditions were in accordance with figure 6.9.

(2) Slenderness effects: Test results of the 8-in wall panels are plotted in figure 6.13. Under axial load the two 20-ft walls and the two 16-ft walls failed

at different load levels, and the average failure load

of the 16-ft walls was considerably higher than that

of the 20-ft walls. The 10-ft walls, however, showed

a considerable discrepancy in failure load. One of

these walls developed a failure load close to that of

the 16-ft walls, and the other failed at a lower load.

Two of the prisms failed at loads similar to the

failure loads of the 16-ft walls and one prism

developed greater strength than all other specimens.

There appears to be a polarization of test results of

the 16- and the 20-ft walls. The strength of the 10-ft walls and the prism strengths are such that no

statistically significant effect of wall height on

strength can be derived for walls up to the height of

16 ft. At the tl6 eccentricity all the wall and prism tests except for one 10-ft wall test are concentrated

between the failure loads of 166 to 200 kip. There ap- pears to be no noticeable correlation between waU

height and strength within the range of wall heights

tested. At the i/4 and tji eccentricities there is a definite

polarization in accordance with wall heights. However, this observation is not supported by the prism

strengths. At the t/4 eccentricity prism tests have an

average similar to the average of all wall tests, and

at the tl3 eccentricity there is a considerable varia- tion in prism strength with a scatter over the entite

range of wall strengths. Since at the maximum ec- centricity any test will be close to the failure en- velope of the section capacity, test results may be

very sensitive to the precision of the positioning of

applied loads. The possibility therefore, can not be

ruled out that the polarization of these test results may be coincidental and that the spread of the

results may represent normal strength variations

due to material strength, workmanship and precision

of load application.

The solid curve in figure 6.13 (Curve A) is the

short-wall interaction curve developed on the basis

of the average axial strength of the 8-in prisms. This

curve was discussed in section 6.2 and it was conh = 10'

P = 80 kip

h = 20

P= 40 kip

Figure 6.12. Typical deflection curves for eccentrically load

unreinforced walls.

A 10-FT WALLS a 16-FT WALLS

O 20-FT WALLS

PRISM STRENGTH x 3

,o1» THEORETICAL INTERACTION CURVES A;h=0,h=IO'

: h = 16'

C h =20'

400 MOMENT, kip-in

Figure 6.13. Comparison of test results on 8-in unreinforced

walls with theoretical interaction curves based on axial prism

strength.

23
i lO-FT WALLS

16 -FT WALLS

O 20 -FT WALLS

-» PRISM STRENGTH « 3

< 200

THEORETICAL INTERACTION CURVES

A h =0, h = 10' B h = 16'

, C h = 20' J I I \ L

200 400 MOMENT, kip-in

Figure 6.14. Comparison of test results on 8-in unreinforced

walls with theoretical interaction curves based on flexural compressive strength.

eluded that, in general, this eurve is conservative

with respect to eccentric loads. Curves B and C are reduced interaction curves for the 16- and 20-ft walls, respectively. These curves were developed

from Curve A by the moment magnifier method,

using the stiffness reduction derived for unreinforced masonry: EI = EJnl^-^. In accordance with

the assumed end conditions, a C,,, factor of 0.5 was

used, together with a k factor of 0.8. Note that, in all cases, these reduced interaction curves are conservative. Figure 6.14 shows reduced interaction curves which were developed from a short-wall interaction curve that is based on the average prism strength at the i/3 eccentricity (/'„, = 2,320 psi). As previously

noted, this curve is probably accurate or slightly conservative for eccentricities greater than i/3. These

reduced interaction curves should be less conservative than the curves shown in figure 6.13 and should

predict the ultimate strength of the walls more closely. In figure 6.14, Curve A is the short-wall interaction curve. Curve B is for 16-ft walls and Curve C is for 20-ft walls. The solid portions of these curves were computed by theory. The lighter dashed lines are straight-line interpolations between the end

point of the computed curves and the computed

axial loads. The reduced curves, thus computed, are

slightly conservative. This may be because of the

fact that at the t/S eccentricity 10-ft wall strength ex- ceeded the average prism strength. At the i/3 and ^/4 eccentricities, the order of magnitude of observed

slenderness effects is in good agreement with the

magnitude of computed slenderness effects. This

agreement also occurs with respect to the 16- and

20-ft walls under axial loads. In all these cases the

reduced interaction curves are conservative. At the

tl6 eccentricity the wall tests show no correlation

between length and ultimate load, however, the

reduced curves are conservative with respect to the

16- and 20-ft walls.

It may be concluded from the discussion of figures

6.13 and 6.14, that the strength of slender walls was

conservatively predicted by the moment magnifier

method, when it was assumed that the flexural compressive strength of the masonry equals the average

axial prism strength. The order of magnitude of slen- derness effect, as well as the strength of slender

walls were approximately predicted by the moment

magnifier method, when the flexural compressive

strength of masonry at load eccentricities greater

than tJS was assumed to equal the average flexural strength of prisms, loaded at a f/3 eccentricity.

7. Discussion of Present Design

Procedures

The latest recommended design procedures for eccentrically loaded slender concrete masonry walls are presented in the 1968 NCMA standard [2]. This

standard requires that members subject to eccentric

loads be proportioned such that:

1

;

i

i

I

fa_iJni_ ^ ^ Fa Fm^

(5)

where:

fa

Fa

f>n F„,

Computed axial compressive stress equal

to the total vertical load divided by the

net area. Compressive stress permitted by the stan- dard for axial loading,

Computed flexural stress, Flexural compressive stress permitted by

the standard.

The allowable compressive stress under axial loading is reduced for slenderness effects, using a . reduction factor of [1 — (A/40fp]. The allowable

short -wall axial stress is 0.2/' m for unreinforced

masonry and 0.225/' m for reinforced masonry. Al- lowable flexural compressive stresses are 0.3/' m and

0.33/' m for unreinforced and reinforced masonry,

respectively. The standard does not permit tensile stresses in unreinforced masonry walls built with

hollow units, thus limiting load eccentricity to the ' edge of the kern. For solid unreinforced masonry

and for reinforced masonry cracked sections are per- mitted. It is also stated in the standard, that up to a

load eccentricity of t/S, reinforced walls may be " designed on the basis of an uncracked section.

24
These design recommendations consider wall

slenderness; however, the hit ratio does not take into account the properties of the cross section, and

therefore does not differentiate between solid and

hollow sections. Other variables associated with

slenderness effects and not considered in these

design equations are end fixity effects (effective

length),^ the effect of the manner in which the

member is loaded (the shape of the moment diagram

and the resultant deflection curve), and the relation- ship between the strength and the modulus of

elasticity of the masonry.

A short-wall interaction curve can be developed

using the recommended interaction equation, eq (5), the allowable axial and flexural stresses, and the

other requirements contained in the NCMA stan- dard as mentioned previously.

Figure 7.1 shows interaction curves of allowable

vertical loads and moments, computed for the 6-in reinforced masonry walls by the NCMA standard.

Masonry strength /',„ was taken as the average axial compressive strength of the 6-in three-block prisms

tested in the investigation reported herein. The

dashed curve (A) was computed without any slen-

! derness reduction and represents short-wall capacij ty. The solid curves labeled B and C were computed

j for the 10- and 16-ft walls, respectively. The dashed

I radial Unes represent the load eccentricities

used in the tests. The intersection points of these

I radial lines with the interaction curves represent the

allowable vertical loads at these eccentricities. Note

that the upper, linear part of the interaction curves, which represents capacities of uncracked sections,

is extended in each case by a dotted Une to the f/3

100

e = '/•» e= 1/3

A - SHORT- WALL CAPACITY

B - lO-FT WALLS

C - 16-FT WALLS

ULTIMATE MOMENT

CAPACITY ^

I L. 20 40 60 80 100 120 140 MOMENT, kip -in

3 Some general consideration is given in NCMA Standard to cantilever members and members subject to sidesway.

Figure 7.1. Allowable loads on 6-in reinforced walls (NCMA

1968).

eccentricity. These dotted lines correspond to the

provision that walls may be designed for uncracked

sections up to the tj3 eccentricity. Curve C, which

corresponds to an a/t ratio of 34, is actually an ex- trapolation of the NCMA standard which limits the

hit ratio for load bearing reinforced walls to 30. The

NCMA equation could not be used to develop an in- teraction curve for the 20-ft walls, since the equation

for slenderness reduction goes to 0 at an hit ratio of

40.Computed allowable loads for the 6-in reinforced

walls and average ultimate strengths of the test specimens are compared in table 7.1. Margins of

safety were computed in two ways: The ratio of

average ultimate loads to allowable loads was computed for specific load eccentricities, and the ratio of ultimate moments to allowable moments was computed for specific levels of vertical loads. The first case pertaining to a constant load eccentricity involves a radial "scaling down" of the ultiTABLE 7.1 Comparison of Allowable Loads by NCMA Standard with Average Ultimate Load Capacities of 6-in Reinforced Walls

Wall Length

ft

e/t Case 1 Case 2 Allowable Average Margin of Vertical Ultimate Safety

Load Vertical Load /Ultimate Load \ Capacity ^Allowable Loady

kip kip

Allowable Computed Ultimate Margin of Moment Moment at Safety Allowable /ultimate Moment

Vertical Load ^Allowable Momenty kip- in kip- in

10

0

1/6 1/4

1/3

63 365 5.8

43 280 6.5

38 ^, 242 6.4

29(33)-' 188 6.5(5.7)

0 210

40 175 4.4

52 165 3.2 54(62) 148 2.7(2.4)

16

01/6 1/4

1/3

28 278 9.9

24 207 8.6 21(22) 181 8.6

18(20) 150 8.3(7.5)

0 147

23 140 6.1

30 135 4.5

34(38) 129 3.8(3.4)

— Numbers in parentheses are computed on the basis of an uncracked section.

25
mate interaction diagram along the lines of constant

eccentricity. This scaling down indicates the margins of safety against an increase in vertical loads,

acting at the same eccentricity. In a building, a load

increase without a change in eccentricity would cor- respond approximately to an increase in occupancy

load above the design load level. The margins of

safety for this case are given in table 7.1. For the 10-

ft walls they vary from 5.7 to 6.5. For the 16-ft walls

the margins of the safety vary from 7.5 to 9.9. It ap- pears that these margins of safety are quite high for short walls, and, for the end conditions applied in this investigation, they increase for increasing wall

slenderness.

The second case, which pertains to a constant vertical load, while increasing the moment acting on the

wall, corresponds to a horizontal scaling down of the

ultimate interaction diagram. In a building, this case

of constant vertical load would correspond to an in- crease in horizontal live loads (wind loads) without

a corresponding increase in vertical live loads. The

margins of safety for this second case are also presented in table 7.1. It is important to note, that within the limit of vertical loads presently permitted

in design, ultimate moments increase with vertical loads. At the maximum permitted vertical load, at which no moment is permitted in the NCMA stan- dard, the walls can actually support a greater ulti- mate moment than at any lower vertical load. For ec- centric loads the margins of safety vary from 2.4 to 4.4 for the 10-ft walls and from 3.4 to 6.1 for the 16-ft walls. It is apparent that the safety margins decrease

with increasing load eccentricity. It can also be observed that the safety margins are greater for the more slender walls. The ultimate moment capacity is shown by a dashed line in figure 7.1. It appears that much of the

margin of safety is due to the high ultimate moment

at no vertical load which is attributable to the rein- forcement. Since the specimens in this investigation

had about twice the minimum required reinforcement, it may be concluded that for walls with

minimum reinforcement, margins of safety may have

been smaller. When margins of safety for Case 1 are compared with those given for Case 2, it is apparent

that for eccentricities greater than tl6, and particularly for large eccentricities, the margin of safety

against an increase in horizontal live loads is substantially smaller than that provided against an in- crease in vertical live loads. Thus, it may be con- cluded that reinforced walls, designed in accordance

with present practice have a greater and more

uniform margin of safety with respect to vertical live loads than the margin provided with respect to horizontal live loads. Figure 7.2 shows interaction diagrams for allowa-j ble vertical loads and moments, computed by the

A- SHORT-WALL CAPACITY B- 10-FT WALLS

C - 16-FT WALLS

D - 20- FT WALLS

60 80 MOMENT, kip-in

Figure 7.2. Allowable toads on 8-in unreinforced walls (NCMA,

1968). NCMA standard for the 8-in unreinforced masonry

walls. Curve A is the short-wall interaction curve, and curves B, C, and D are for the 10-, 16- and

the 20-ft walls, respectively. Note that the interaction curves are cut off at the kern eccentricity, which is slightly larger than the ?/4 eccentricity. Thus the i/3 eccentricity falls outside the curves, since it is not permitted under this standard. The dashed line to the right of the curves is the computed short-wall ul- timate moment capacity which was based on the

flexural compressive prism strength at the tjZ eccentricity. Curves C and D are extrapolations of the

NCMA standard, which limits the maximum hjt ratio

to 20 for unreinforced load-bearing walls. Computed allowable loads for the 8-in unreinforced walls are compared in table 7.2 with the

average ultimate strengths achieved by the test specimens. Margins of the safety against an increase

in vertical loads applied at the same eccentricity

(Case 1), vary from 4.4 to 6.4 for the 10-ft walls, from

5.8 to 6.2 for the 16-ft walls, and from 6.0 to 7.1 for the 20-ft walls. In general it appears, for the particular end and loading conditions used in this investigation, that these margins of safety are quite uniform

and on the high side. Safety margins against an increase in moments at the same vertical load (Case 2) are also given in table

7.2. As in the case of the 6-in reinforced walls, these

margins of safety decrease with increasing eccentricity, dropping to 1.75 at the ^/3 eccentricity. It is

26
TABLE 7.2 Comparison of Allowable Loads by NCMA Standard with Average Ultimate Load Capacities of 8-in Unreinforced Walls

Case 1 Case 2 Wall Length

ft

e/t Allowable Average Margin of Vertical Ultimate Safety Load Vertical Load /Ultimate Load \

Capacity I Allowable Load)

kip kip ^

'

Allowable Computed Ultimate Margin of Moment Moment at Safety Allowable /Ultimate Moment ^ Vertical Load I Allowable Moment

kip- in kip- in

10

01/6 1/4

57 252 4.4

39 177 4.5

33 210 6.4

0 144

50 122 2.4

63 no 1.75

16

01/6 1/443 268 6.2

33 191 5.8

30 1 74 5.8

0 129 42 108 2.6

57 100 1.75

20

01/6

1/4

32 202 6.3

26 184 7.1 24 143 6.0

0 105

33 88 2.7

46 80 1 . 75

i important to note, that for unreinforced walls built

iof solid units, which can be designed on the basis of

a cracked section, these margins of safety may drop

: even lower and approach unity. Thus, while margins

Iof safety against an increase of vertical loads are

rather high, the margins against an increase in horizontal loads may be extremely small. The allowable vertical loads and moments shown

in figures 7.1 and 7.2 and listed in tables 7.1 and 7.2 were based on the average axial compressive

strengths of the prisms as determined by tests. For

the 6-in prisms,/'TM was 1890 psi 'and for the 8-in prisms, /'m was 1700 psi. If/ m values are not deter- mined by tests, the NCMA standard permits fm

values to be assumed on the basis of the unit

strengths. For the 6-in and 8-in hollow concrete

block used in this investigation which had strengths

of 4080 psi and 4230 psi (net area), respectively, the

assumed values of /',„ permitted are 2017 psi and

2047 psi. Based on this investigation, the assumed

values of fm permitted in the NCMA standard are about 7 percent too high for the 6-in prisms and

about 20 percent too high for the 8-in prisms. Accordingly, if these assumed values of/'m were used

in the comparisons given in tables 7.1 and 7.2, the

margins of safety would be smaller than the values

reported.

Three important conclusions may be drawn from

this discussion:

(1) Present NCMA design criteria provide a large

margin of safety with respect to vertical loads. This

margin of safety is necessary, since present design

procedures do not account for all the variables that

affect wall capacity.

The most important variables not accounted for are end fixity, the shape of the moment diagram that

acts on the waU, cross-sectional characteristics, and

the modulus of elasticity of the masonry. In the past,

it may not have been justified to account for all these

variables, since design standards also contained

rather restrictive requirements relating to allowable

stresses, lateral support and minimum thicknesses

of masonry bearing walls. However, with the increasing use of masonry load-bearing walls in multi-story

construction, it is no longer justified to disregard

these variables and compensate for the resulting dis- crepancies by excessive margins of safety.

The close prediction of experimental results in this investigation by the moment magnifier method

indicates that the introduction of a rational design

method which considers additional variables is practical.

(2) The margin of safety provided by present

design practice against an increase in moment,

without a corresponding increase in vertical load, is in some cases extremely small. On the other hand,

at maximum allowable vertical load, no moment is permitted, although it appears that at that load the

wall actually develops the highest ultimate moment

capacity. It appears that the philosophy of "radial

scaUng" which is presently applied to develop al- lowable wall capacities on the basis of ultimate

capacities leads to excessive margins of safety in some cases, while in other cases the margins of safety are extremely slim. The philosophy behind the scaling down of ulti- mate loads in order to arrive at reasonable design

loads should be reexamined, and all possible load

combinations that may act on masonry walls during

the hfe of a building should be taken into account.

(3) Based on the prism strengths obtained in this investigation, the assumed values of axial compres27
sive strength /',„ permitted for hollow concrete units

in present design criteria are too high and should be

reexamined.

8. Conclusions and

Recommendations

8.1. Conclusions Related to Tests Results

The following conclusions can be derived from the

interpretation of the test results:

(1) Theoretical interaction curves for the capacity

of short concrete masonry walls, computed on the

basis of compressive strength developed by masonry

prisms under axial loading, closely predict axial compressive load capacity and conservatively predict moment capacity.

(2) Flexural compressive strength of masonry in- creases with increasing strain gradients (increasing

load eccentricity).

(3) Slender concrete masonry wall capacity can

be conservatively predicted by the moment magnifier method, when short-wall capacity is based on

compressive strength of axiaUy loaded prisms.

(4) The capacity of short and slender concrete masonry walls can be predicted with reasonable ac- curacy when the increase in flexural compressive

strength with increasing strain gradients is taken

into account.

8.2. Conclusions Related to Present Design

Practice

The following conclusions can be derived from the

review of present design practice:

(1) Present design criteria [2] provide a large

margin of safety with respect to vertical loads on

load bearing concrete masonry walls but the margin

of safety provided against an increase in moment,

without an increase in vertical loads, is not uniform

and in some cases extremely small.

(2) Introduction of a rational design procedure

such as the moment magnifier method which in- cludes additional design variables not presently con- sidered is feasible and also desirable in the interest of both safety and economy.

(3) Assumed values of masonry compressive

strength permitted in present design criteria are too high for hollow unit construction.

9. Acknowledgment

The contribution of the following persons is acknowledged.

William C. Euler was the Masonry Contractor in charge of the construction of specimens.

James W. Raines was the Laboratory Technician

in charge of instrumentation.

Frank A. Rankin and Jessie C. Hairston, Laboratory Technicians, were in charge of the preparation!

of the specimens for testing.

Henry T. Toennies and Kevin D. Callahan from

the National Concrete Masonry Association assisted

in the planning of the research program.

Edward O. Pfrang, Chief of the Structures Section, participated in the conception and planning of the program, and made many contributions to this

'

report.

j John E. Breen, Professor of Civil Engineering at the University of Texas, critically reviewed the re-

port and participated in the analysis of test results.

10. References

[1] National Building Code of Canada, Ottawa, Canada (1965)

[2] National Concrete Masonry Association. Specification for the Design and Construction of Load-Bearing Concrete Masonry, Arlington, Virginia (1968). !

[3) Sampling and Testing Concrete Masonry Units, ASTiM

C140-65T (1965).

{ [4] Mortar for Unit Masonry, ASTM C270-68 (1968).

j [5] Mortar and Grout for Reinforced Masonry, ASTM C476-6^

(1963). !

[6] Dickey, W. L.. Reinforced Brick Masonry, Modern Masonr)|

Conference, Washington, D.C., September 19-20. 1956;^ Building Research Institute, National Academy of! Sciences-National Research Council, Publication 466

(1956). [7] Deformed Billet-Steel Bars for Concrete Reinforcement,

ASTM A615-68 (1968). [8] Yokel, F. Y., Mathey, R. G., and Dikkers, R. D., Strength of Masonry Walls under Compressive and Transverse

Loads. National Bureau of Standards, Building Science

Series 34 (in preparation).

[9] MacCregor, J. G., Breen, J. E., and Pfrang, E. O., Design of Slender Concrete Columns, Journal of the American

Concrete Institute, Vol. 67, No. 1, pp. 6-28 (1970). [10] Structural Clay Products Institute, Recommended Practice | for Engineered Brick Masonry, McLean, Virginia (1969).

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