ML17300A530

Factors Influencing Deflections in Grouted Hollow Unit Concrete Masonry Walls.

ML17300A530
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Site:	Palo Verde
Issue date:	09/18/1986
From:	ATKINSON-NOLAND & ASSOCIATES
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ML17300A525	List: ML17300A524 ML17300A530 ML17300A532
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Text

Enclosure 2 FACTORS INFLUENCING GEFLEt:TIGNS !N

-GBGUTED -HGLLGMt UN!T CONCRETE MMDNRY 'lNALLS 86o92q0y0~

" 8~09 PDR ADOCK 05000528, PDR Atkinson-Noland 5 Associates

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Sept. l8, l986 FACTORS INFLUENCING DERLECTlONS XN GROUTED HOLLOW UNIT CONCRETE MASONRY WALLS

i. PREFACE This report presents the results of a brief survey on the modulus of rupture and modulus of elasticity of grouted hollow concrete unit masonry. These material properties are significant parameters in assessing the out-of-plane stiffness and deflections of the twelve-inch concrete masonry walls in the PVNGS facility near Pheonix, Arizona.

While many documents were reviewed in the course of this study~

the data obtained are not exhaustive. Additional data exists which could not be obtained in the time available.

The observations herein are based upon the data examined.

While additional data could influence specific numerical values, dramatic changes in basic relationships would not be expected.

0 Xi. TABLE OF CONTENTS PREFACE ii. TABZE OF CONTENTS

1.0 INTRODUCTION

2.0 DISCUSSION AND ANALYSIS OF THE ZOAD-DEFORMATION BEHAVIOR QF SLENDER CONCRETE MASONRY WALLS PER THE UNIFORM BUIZDING CODE 3.0 DISCUSSION OF THE MODUZUS OF RUPTURE OF CONCRETE PER THE ACI 318-83 CONCRETE CODE 4.0 ADDITIONAL PERTINENT DATA ON THE MODULUS OF RUPTURE 39 5.0 OBSERVATIONS 50

6.0 REFERENCES

52 7.0 APPENDIX UNIFORM BUILDING CODE, SECTION 2411 55

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1.0 INTRODUCTION

This report presents the results of a short'tudy of out-of-plane deflections in grouted hollow unit concrete masonry. At-tention was focused on grouted masonry; ungrouted masonry was not emphasized, and clay brick masonry was not considered at all be-cause it is felt'that information from tests performed on these materials is not relevant to grouted concrete masonry.

Specifically, this document reports on the basis for code specified procedures for calculating deflections. In the Uniform Building Code (Ref. 1), deflections for slender masonry walls are covered in section 2411(b) as a part of the design method for re-inforced masonry slender walls (section 2411, Ref. 1). The prov-isions of this section were developed from a single experimental research project, the resuits of which are summarized iu Test ~Re ort on Slender Walls (Ref 3). Accordingly, a'ignificant portion of this report (section 2) concentrates on the data and conclusions presented in Ref. 3. In particular, the origin of code specified values for the modulus of rupture for concrete masonry was invest-igated. The sensitivity of deflection calculations to the assumed values of modulus of rupture, modulus of eJasticity, and moment of inertia was also investigated.

Following the analysis of the Slender Hall Test Report in section 2.0, the basis for the value of the modulus of rupture for concrete given in the ACI code (4), is discussed in section 3.0.

Other pertinent research data and test results related to the mod-ulus of rupture of concrete masonry are collected and summarized in section 4.0. Some observations are presented in section 5.0.

Jimitgd bibliography folJaws in section 6. 0.=

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2.0 DISCUSSION AND ANALYSIS OP THE LOAD-DEFORMATZON BEHAVIOR CONCRETE MASONRY WALLS PER THE UNIFORM BUILDING CODE Ol'LENDER

. The method for calculating the mid-height deflection of a simply supported masonry wall subjected to out-of-plane lateral loads is covered in the UBC in section 2411 (b) as part of the design method for reinforced masonry slender walls. UBC section 2411(b) is reproduced in full in Appendix A. In this section of this report, basic parameters of the UBC deflection calculation and their associated assumptions will be discussed. In section 2.1. the deflection calculations in the UBC are outlined, followed by a description of the Slender Wall Test Program (Ref. 3) from which they are derived. In section 2.2, some detailed results of the Slender Wall Tests (Ref. 3) are presented and analysed in order to clarify the origin of code specified values for modulus of rupture.

section 2.3 provides further analysis of the Slender Wall Tests assuming a modified effective section. In section 2.4, load-defor-mat>on curves are calculated per UBC (section 2411(b) ), and compared to the original test data from the Slender Wall Tests. The sensi-tivity of these calculations to assumed values of modulus of rupture and modulus of elasticity are also discussed. ZinaJZy, in section 2.5, ACI and UBC methods of calculating the cracked load-deformation behavior of reinforced masonry walls are compared.

2.1 Basis for UBC Provisions for Calculation of Deflections in Slender Masonry Walls According to the UBC, the midheight deflection of a reinforced masonry slender wall is computed by the following formula:

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5MPr (forM,(Mo) ........:.....:...'...........(11-12) 48<Ay '

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6, M,P> M<<) h2

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48E 48 r 4 (f rN<<< hfs N).........(11-13)

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>VHERE:

h = heightof the wall.

N, = service moment at the midheight of the panel, including Pd, effects.

E~f = 1000f':

= gross, cracked moment of inertia of the wall cross section.

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N = cracking moment strength of the masonry wall.

N= nominal moment strength of the masonry wall.

The equation numbers used are from the 1985 UBC (Ref. 2). The cracking moment strength of the wall is determined by the formula:

N<<= Sf, .(1 1-14)

AVHERE.

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S = section modulus.

f, = modulus of rupture For concrete and masonry, the modulus of rupture, f,, is defined by Park and Pauley (Ref. 8) as:

fr ~ K ~ m where f' m

K Ultimate co~pressive masonry stress Value used to relate f (2-1) to f' m The UBC lists in section 2411 (b) values for "K" for several types of masonry construction. For concret'e masonry units, "K" is given as 2.5. The basis for this value is discussed in section 2.2. For concrete, the UBC has adopted the ACI 318-83 Building Code (Ref. 4) value for "K" of 7.5. The basis for the concrete value is reported in section 3 of this document.

The "Commentary'o ChaPter 24 of the Uniform Building Code, 1985" published by the Masonry Society (Ref. 2) gives back~und

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information on the masonry chapter of the UBC. It states'that the values foz "K" given in the UBC (and, indeed, the entire UBC. rein-forced masonry slender wall section, 2411) are based upon tests from a comprehensive 1982 reinforced slender wal3. test program sponsored by the American Concrete Institute (ACI') and the Structural Engineers Association of Southern California (SEASC) (Ref- 3) ~

In the Slender Wall Test Program reported in Ref. 3, thirty 24 foot tall concrete, concrete masonry, and brick masonry walls of various thicknesses were tested. The walls were laterally 3.oaded by an airbag as well as vertically by an eccentric and relatively moderate dead load. Some test results are shown in Table 2.1. For, concrete masonry, three tests were performed on each of three wall thicknesses (nominally 6, 8, and 10 inches). The load-def3.ection curves for each thickness of concrete masonry wall are plotted in Figs. 2.1 through 2.3, and the averages of the three curves for each.

thickness are plotted together in Fig. 2.4. The averaged load-deflection results from the four different thicknesses of conczete panels are given in Fig. 2.5.

2.2 Analysis of Slender Wall Test Results (Ref. 3)

In order to understand the basis for the design recommendations made by the S3,ender Wall Report (Ref. 3) (subsequently accepted by the UBC (Ref. 1)), it is important to determine what and. why ceztain assumptions (for example, material properties) and conclusions (for example, "K" = 2.5 for concrete masonry) were made.

In addition to the Slender Hall Test Report, the original test data for the entiz'e Test Program of Ref. 3 were obtained to det-ermine the basis for the information and conclusions of that Report

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I 4 I (Ref. 32). An analysis of these data is described in detail below.

.The results of the analysis are summarized in Tables 2.3 through 2.5: An explanation of each column in Tables 2.3 through 2.5 of this document is given in notes following each table 2.2.1 Compressive Strength and Elastic Modulus of Masonry Zn the Slender Wall Test Program (Ref. 3), prisms were built for each wall thickness and tested at the age of 28 days. In addition, at the end of the program, prisms were cut from the test walls and tested'at an age of over one year. The results of these two sets of prism tests are reported on page 2-3 of the Report. ,'aS There was some discrepency between the results of the two tests, and hence some difficulty in selecting values of f'm and E to use in this analysis.

According to the original test data (Ref. 32), the results reported on page 2-3 of Ref. 3 were obtained from three prism tests for each wall thickness made at 28 days. The reported elastic tangent modulus was measured during one prism test of each wall type. The elastic modulus was calculated by the authors of Slender Wall Test Report (Reft 3) as the slope between two subjectively selected points just above the origin on the stress-strain curve. After one year, one prism was cut from each wall and compressive strength and stiffness data was taken. This data is reported in Fig. 2-4 of Ref. 3, however t'e data shows greater scatter than Pig ~ '2-4 implies. Refering to the original test data (Ref 32), the results of each prism test are collected and reported in Table 2.2. The prism test results appear to be inconclusive as to the actual material properties of the walls tested in the ACI-

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TAELE 2.1 (Ref. 3)

SLENDER WALLS TEST RESULTS Wall Thick-ness, f'r Vert.

Lat.

Load Defi.

at Max.

Lat.

No. and TYpe t,

in. Ps3.

h/t Ratio Load, plf at psfY f Yield, Defi.,

in. in.

Date Tested 9.63 2460 30 320 94 5.3 17.1 3- 9-81 9.63 2460 30 860 82 5.5 8.0 2-25-81 9.63 2460 30 860 73 6.3 19.0 2-18-81 7.63 2595 38 860 75 6.5 11.2 3-10-81 CMU 5 7.63 2395 38 860 75 7.5 10.3 3-12-81 6 7.63 2595 38 320 71 5.8 14.S 4-21-81 5.63 3185 51.2 320 46 9.0 17.7 4-22-81 5.63 3185 51.2 320 38 15 9 4-30-81 5.63 3185 51.2 320 46 9.8 11.0 5- 1-81 10 9.6 3060 30.3 320 94 15.6 4-20-81 11 9.6 3060 30.3 320 89 9.3 16.8 4-17-81 12 9.6 3oeo 30.3 320 74 9.0 14.6 5-11-81 Br 13 7.50 3440 38.4 320 40 12.0 19.6 5- 8-81 14 7.50 3440 38.4 320 54 14.0 15.9 5- 7-81 15 7.50 3440 38.4 320 66 10.5 14.8 5>> 6-81 16 5.50 6243 52.4 320 57 8.0 19.3 4-15-81 iiBr 17 5.50 6243 52.4 320 48 8.2 18.2 4-16-81 18 5.50 6243 52.4 320 55 7.9 11.1 5- 4-81.

19 9.50 4000 30.3 320 87 7.3 9.9 5-14-81 20 9.50 4000 30.3 320 83 5.3 7.0 5-12-81 2I 9.50 4QOO 3Q.3 320 83 7.5 12 3 4-27-81 22 7.25 4000 39.7 320 57 5.4 12.2 4-28-81 23 7.25 4000 39.7 320 52 7.4 11.8 4-29-81 24 7.25 4000 39.7 seo 57 7.6 11.8 4-14-81 Con 25 5.75 4000 52.4 860 51 8.1 13.2 3-14-81 26 5.75 4000 52.4 860 42 7.2 11.1 3-18-81 27 5.75 4QOO 52.4 ~ 320 42 8.5 12.4 3-23-81 28 4.75 4000 60.6 320 32 11.6 13. 0 5- 5-81 29 4.75 4000 60.6 320 34 12:6 . 19.2 5-15-81 30 4.75 4oaa eo.e 320 34 13.1 15.2 5-14-81 Note: CMU = Concrete MasonrY Unit; Br = Two-WYthe Brick HBr = Hollow Brick; Con = Concrete

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PANE

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PANE 8 1 2 3 4 5 6 7 8 9 18 ll 12 13 14 1S 16 17 18 19 Deflection in.

Pig. 2.1 Load Deflection Curves, 10" Concrete Block Masonry (Ref. 3) 118 98 48 38 PANEL 8 DA C 28 PANEL 8 8 .1 2 3 4 S 6 7 B 9 18 31 12 g3 Deflection in.

pi 2 2 Load Deflection Curves, 8" Concrete Block masonry (Ref. 3)

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PANEL f 7 PANEL 8 8 PANEL 8 9 8 1 2 3 4 5 6 7 8 9 18 11 12 13 14 15 16 17 1S Deflection in.

Fip 2 ~ 3 goad - Deflection Curves, 6" Concrete Block Masonry /Red e ~ 3) 118 Panels 1, 2, 3 Panels 4, 5, 6

. 78 LW 0 88 Panels 7, 8, 9 For h/t values, see 'Table 5-l

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2 3 4 5 8 y 8 18 ll 12 13 14 15 18 1 Deflection in.

Fig. 2 4 Deflection at Mid-Height: 6", 8", 10" Concrete (Ref. 3)

Block Masonry 10

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9 ~ Panels 19, 20, 21 u 88 W

Panels 22, 23, 24 o'0 Ol 48 Panels 25, 26, 27 M

~ 38 P anels 28, 29; 30 For h/t values, see Table 5-1 8 1 2 3 4 5 8 7 8 8 18 ll 12 13 14 1S 18 17 18 DEFLECTION IN in.

Deflection in Inches at Hid-Height: Concrete Pane>s ~

(Ref. 3)

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TABI.E 2.2 PRISM TESTING DATA REF. 32 FIEK,D BUIK,T PRISMS (28 day) WAK K CUT PRISMS (1 year)

Comp. Elastic Comp. Comp. plastic Strength Modulus Strength Strength Hodulus Hall Type (psi) (x 10~ ) (uncorrected) (corrected)( ) (x 10 )

6" CMO 3045 N.A. NBA. 2.49 3115 4600 5290 N.A. ~

3395 1.59 3382 3890 1.82 AVERAGE (3185) (3990) (4590) (2.16) 8" CMU 2535 4409 4365 2.03 2490 3914 3405. 1.29 2760 1.72 4098 3935 1. 03 AVERAGE (2595) (4140) (3900) 10" CMU 2270 4460 4330 1.75 2530 4805 4325 1.75 2570 3828 3560 1.28 AVERAGE (2460) (4365) (4070) (1.59)

NOTES:

(1) This table is an accumulation of information from the original test data.

(2) The elastic modulus was calculated by the authors of Reference 3 as the slope between two subjectively selected points just above the origin on  !

the stress-strain curve.

(3) The corrected prism strengths were obtained by multiplying the uncorrected prism strengths by the appropriate h/t correction factors as per 1979 UBC.

Both uncorrected and corrected values were presented in ref. 32, and are duplicated here for clarity.

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TABZE 2.3 REINFORCED CONCRETE MASONRY WAZL PANEZ DATA (Reft 3)

(1)

Wall f'ateral (2)

Test load at (3) (4)

Defi. at Cracking (5) fr (6)

It K(l Cracking Moment (from test) from Type (pei) Cracking (in.) (lb-in) (psi) Test 6" CMV 3185 B. 7~sf 0.7 8748 138 2.5 8" CMU 2595 26 psf 0.5 24876 214 4.2 10" CMU 2460 42 psf 0.3 38580 208 4.2 (1) The compressive strength of the actual masonry used in the test program (Ref. 3).

(2) The lateral load at initial cracking as calculated from cracking information given on Page 6-3 of Ref. 3 and yielding information given in Table 5-1 of Ref. 3.

(3) The deflection at cracking used to calculate the cracking moment in 'Col. (4). This value was read from Figs. 2.1 through 2.3 (Ref. 3).

(4) The initial cracking moment at mid-height was calculated including P - Q effects as outlined in Ref. 3 (page 7-16).

(5) The modulus of rupture from the tests as calculated by UBC 'Eqn. 11-14 (See page 5 of this report).

(6) The value "K" as defined hy Eqn. 2.1 of this report as calculated from test data.

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a TABLE 2.4 REINFORCED TILT-UP CONCRETE WALL PANEL DATA (Ref. 3)

(7) (8) (9) (10) (11) (12)

WalI Thickness fc'ateral Test load at Defi. at Cracking Cracking Moment fz (from test)

II II rom K

(in. ) (,p ai ) Cracking (in.) (lb-in) (psi) Test'.9 4.75 4000 20 psf 0.35 18340 371 5.75 4000 31 psf 0.40 29590 33? 5.3 7.25 4000 39 psf 0.45 35470 447 7.0 9.50 4000 76 psf 0.20 66970 406 6.4 (7) The compressive strength of the actual concrete used in the test program (Ref. 3).

(8) The lateral load at initial cracking as calculated =rom cracking information given on Page 6-4 of Ref. 3 and yielding information given in Table 5-1 of Ref. 3.

(9) The deflection at cracking used to calculate the cracking moment in Col. (8). This value was read. from Pig. 2.5 (Ref. 3).

(10) The initial cracking moment at mid-height was calc'lated.

including P -L effects as outlined ia Ref. 3 (page Z-DG).

(11) The modulus of rupture from the tests as calculated by UBC Eqn. 11-14 (See page 5 of this report').

(12) The value "K" as defined by Eqn. 2.1 of this report as calculated from test data.

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TABLE 2.5 REINFORCED CONCRETE MASONRY WALL PANEZ DATA (with tensile face shell removed)

(13) ( 14.) (15)

Depth w/o Wall one face shell-(in) fr II K II Type (psi )

6" CMU 4. 375 228 4.0 8" CMU 6.375 306 6.0 10II CMU 8.125 292 5.9 (13) The thickness of the concrete masonry wall assuming one face shell has been removed. (Fig. 2-6)

(14) The modulus of rupture calculated assuming the cracking moment was resisted by the one face shell in compression and the grout core.

(15) The value for "K"- using the modulus of rupture calculated in Col. (14).

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SEASC test program (Ref. 3), particularly with regard to the elastic modulus. For lack of better information, the compressive strength of the walls was taken to be the average of the 28 day tests in accordance with the UBC (Ref. 1). These are the values listed in Column 1 of Table 2.3.

2.2.2 Cracking Load and Cracking Moment The Report (Ref. 3) states (in the section in which the con-crete block wall results are discussed on page 6-3) that "cracked performance ffor the 10, 8, and 6 inch walls] started at approxi-mateZy 508, 35K, and 20'f the yield, respectively". Test values for the lateral load on the walls at yielding are given in Table 2.1 of this report (reprinted from Ref. 3). The cracking load. was obtained by taking the specified percentage of the reported yield load, and is reported for each thickness of wall in Column 2 of Table 2.3.

The deflection at cracking can be read directly from the av-eraged load-deformation plot (Fig. 2.4). With this information and the lateral load at cracking (Column 2 of Table 2.3), the cracking moment, including P 5 ef fects, can be calculated using Equation Xl-7 from the UBC reprinted below:

wh>

+ PON

+ (P'N + P..) ~............,(i l-7)

EVEEERE:

w factored distributed lateral load.

h = height of the wall between points of support.

Il'N factored weight of the wall tributary to the section under consideration.

N horizont d dcf lection at mitlhcight under factored load; P5 c ffccts shall be included in deflection calculation.

factored load from tributary floor or roof loads.

eccentricity of P, ....

axial load at midhcight of wall, tncluding tributary wall weight 16

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The cracking moments calculated from the slender wall tests of Ref.

for each concrete masonry wall thickness are shown in Column 4 of Table 2.3.

2.2.3 Modulus of Rupture ("K" values)

The values for the modulus of rupture and the resulting value for "K" are not given explicitly in the Slender Wal3. Test Report (Ref. 3), however, they can be derived from the text and from the load-deformation p3.ots given in the Report. The modulus of rupture is calcu3.ated using Equation (11-14) of this document and the "K" va3ue is calculated using equation 2.1. These values are given in Columns 5 and 6 of Table 2.3 respectively.

The method used to obtain values for "K" and the modulus of rupture for the concrete masonry walls of'ef. 3 was also used to ana3.yze the reinforced concrete tilt-up panel test results given in that reference. (See Table 2.1) Twelve pane3.s with four different thicknesses were tested. All had the same amount of reinforcing, and thus different steel ratios. Averaged load-deformation results F

are given im Pig. 2.5. Values for "K" were calculated as for con-crete masonry, and the results are summarized 'in Table 2.4. Jn case, the "K" value fell short of the ACI (Ref. 4) recommended value of 7.5.

The relationship of the compressive strength of masonry to its modulus of rupture (Equation 2.1 of this document) was probably mode3,led for simplicity after a similar relationship for concrete as presented in the ACl code (Ref. 4). However, the masonry relation-ship between modulus of rupture and compressive streng& does not appear to be based on any reported statistical correlation between 17

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the two ProPerties. Even the original ACI equation (9-g) after which it is modeled is based on a very poor correlation, as will be seen in section 3 of this xeport. Apparently, a closer look at the "K" value is warranted.

2.3 Analysis of Slender Wall Tests (Ref. 3) Assuming the Face Shells Have no Tensile Strength In some codes (Refs. 1 and 32), the tensile strength of an reinforced masonry wall is assumed to be zero. In this spirit, the Slender Walls of Ref. 3 were again analyzed as described above assuming the face shells of the concrete masonry units carry no tensile stresses. Basica3,1y, the modulus of rupt'ure is recalculated .

based on the section properties of a wa)1 without one face shell as shown in Fig. 2.6. The assumption is made with this analysis that, before the wall section is fully cracked, the tensile force required to resist bending is provided primarily by the grout. The modulus of rupture and "K" values resulting from this analysis is summarized in Table 2.5.

She values Ior ~ ~dulm wf ~ture resultiag from %he anal-ysis of the concrete masonry assuming the face shells resist no tension are given in Col. 14. These values are similar to tensile strength values reported in the literature for grout. (The compres-sive strength of the grout used in the slender wall test program of Ref. 3 was 3106 psi. Ref. 18 reports the tensile strength of grout is about 9X of its compressive strength, while Ref. 23 reports 8@,)

The values for "K" resulting from the analysis of the concrete masonry using modified section properties (given in Col. l5 of Table 2.6) are more aligned with values from t'e concrete walls. This is illustrated in Pig. 2.7 which plots the relationship of the "K" 18

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Reinforced Concrete Hasonry Shaded area considered in Mall (only unit shown) calculation of moment of inertia Area of tensile face shell neglected Picure 2.6

'CaldulaGon 'of"&omen&. of Tnertia Neglecting Pace Shell in Tension 19

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RELATIONSHIP BETWEEN EFFECTIVE

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.walls used in the slender wall test (Ref. 3). The "K" value-wall thickness relation for concrete masonry based on the gross area is also given in Fig. 2.7 along with an extrapolated value for 12 inch concrete masonry.

2.4 Comparison of UBC Slender Hall Zoad-Deformation Predictions to the Tests.%rom Which They Were Derived Except for the "K" value calculated for the 6", concrete masonry walls, "K" values calculated from the Test data (Ref. 3) are higher than the value recommended by the UBC. This is because the UBC recommended "K" value for concrete masonry of 2.5 was derived solely l'

from the three 6" concrete masonry wall tests of Ref. 3. Thicker walls (with proportionately more grout) were not included. Figure 2.8 shows analytical load-deformation curves for K = 2 and K = 3 superimposed upon the 6" concrete masonry wall:test data,.from Ref.

3. It is not clear from the text of Ref. 3 or the original test data (Ref. 32) which values for the compressive strength or the elastic modulus were used in the development of the curves in Fig.

2.8. It is apparent, after graphical interperataion, that the value of modulus of elasticity used in Fig. 2.8 was approximatel'y equal to the test value from the wall-cut prisms (2160 ksi).

Since the material properties used in the development of the curves in Fig. 2.8 are not clearly defined, and the results obtained from 28 day tests in Ref. 3 were dissimilar to those obtained from prisms cut from the walls themselves, particularly the values for the. elastic modulus, the influence of these properties on the load-

~ ~ ~y I

deformation curves of Ref.'-'3 (and thusly the slender masonry 'wall

• - 'I I , ~

design equations of the UBC) was investigated.

I To develop the predicted load-deformation curves shown in Fig.

<<l 2.8; an iterative procedure must be used, because, when P -A effects 21

~ ~ I W

l l

I 0

40 PAN L7 PANEL 8 0 Phyla.L 9 fr 3 Jf' ~I fr 2 Jf' g

--D 0

~E' I 20 Q,Q <<+

D~ ~ q S ~

0 0

0 10 PAf'0 0

l 0

3 4 MIVlEIQIT 0 klZCTICH, IN.

FiLure 2.8 Calculated Load-Deflection Relations for 6" Concrete Masonry (Ref. 3) 22

I h

l l

1 t

1 Ql 0

are included, the moment and resulting deflection are irzterdepen-dent. This procedure- is outlined in sectj.on 7.4.3 of the s3.ender wall test report (Ref. 3). A short computer program was written'o perform this iterative procedure. Material properties required to calculate the load-deformation are the elastic modulus and the compressive strength of the masonry (required to calcu3ate the modu3us of rupture per Equation 2-1 of this report.). The modulus of rupture (as represented by the "K" value) influences the point of cracking on the load-deformation curve. (The point of cracking is the knee in the loadMeformation curve just after the inital elastic portion.) If the modulus of rupture (or the value for "K") in-creases, the 3.oad required to crack the wall wiII increase. The elastic modulus affects the slope of the load-deformation curve both before and after cracking. Zf the e3.astic modulus increases, both the initial elastic load-deformation slope and the cracked slope

'will be stiffer.

Tn Fig. 2.9, the predicted load-deformation curve for 6" con-crete masonry wal3s are plotted using the value der %e elastic modulus obtained in the 28-day prism test (See Table 2.2 of thj.s report) and K = -2.5. The value for the cracked moment of inertia was taken from Table 7-2 of Ref. 3 Agreement is quite good. Pigs.

2.10 and 2.11 show the predicted load-deformation results for 8" and 10" concrete masonry, respectively, using the same material prop-erties specified above. Also included are the test results from the Slender Hall Test Program (Ref. 3). 'he UBC prescribed "K" values t

are too low to accurately predict the point of cracking for the 8" and 10" concrete masonry wa13.s. Prom the calculations of Table 2.3, a more reasonab3e "X" value far both the 8" and 10" walls wou3d be 23

I 0

I I

"t CO~PARISON OF UBC CALCULATED LOAD-DEFLECTION CURVE TO THE DATA FROM hVICH IT WAS DERIVED 80 (6" Concrete Hasonry) 70 60 PANEL 7 0 PANEL 8 0 PANEL 9 E = 1590 ksi 40 f.m = 3185 psi K = 2.5 Icr 17 in" 30 20 oX 0 X 0

10 0 0

I 0 4 MIDHEIQ(T DEFLECTION (incl)es)

Fi ure 2.9 24

)

I 0

90 COMPARISON OF UBC CALCULATED LOAD-DEFLECTION CUR%'E TO THE DATA FRO~f WHICH IT WAS DERIVED (8" Concrete Hasonry) 80 70 40 X PANEL 4 20 0 PANEL 5 a IANEL 6 1720 ksi 10 = 2595 III psi includes)

K 2 05 Icr = 43 in" 0

0 2 3 4 HIDllE'1CllT DEFLECTION (

Figure 2.10

)

l 0

90 X CO.IPARISON OF UBC CALCULATED LOAD-DEFLECTION CURVES TO THE DATA FRO~I NiICII IT WAS DERIVED (10" Concrete Hasonry) 80 X 0

70 60 X

.50 Q:

c V.

M40 f

X E = 2,170 ksi f = 2460 psi K = 2.5 30 p Icr ~ 100 in4 X PANEL 1 20 0 PANEL 2 0 PANEL 3 10 0

0 2 3 4 5 HIDHEICIIT DEFLECTION (inches)

i IL I

J t

j 0

4:2. For the 10" wall, the elastic modulus obtained from the 28 day prism tests is much higher than the modulus measured from the wal3, cut prisms. The curve shown in Figure 2.11. is based on the elastic modulus from the 28-day prism tests, and the resulting load-deformation curve .under estimates the measured deflections in the 10" Slender Hall tests. (See also section 2.4.2 and Fig. 2.15.)

2.4.1 Effect of the Modulus of Rupture on the Predicted Load-Deformation Curves The value of <he modulus of rupture controls the 3,oad which can be sustained before cracking occurs. The influence of the modulus of rupture (as represented in Eqn. 2.1 of this report by the value "K") is illustrated in Figure 2.12 in which a 68K increase in the "K" values resulted in a 68K increase in the load required to crack the wall, The slope of the load-deformation curve, both before and after cracking, is not dependent on the value of "K".

2.4.2 Effect of the Elastic Modulus on the Predicted Load-Deformation Curves To determine the influence that the assumption for the elastic modulus has on the predicted load-deformation response of slender masonry walls per the UBC, the elastic modulus was varied while a3.l other parameters were held constant. The resulting load-deforma-tion plots for 6", 8", and 10" concrete masonry are plotted in Figs.

2.13 through 2.15 respectively. Zt wou3.d appear from these figures that the average wall cut prism elastic modulus va3ues predict the load-deformation behavior of the walls more accurately than the 28 day prism values.

One could also conclude from this test data that the UBC rela-tionship stating that the elastic modulus is 1000 times the compres-s )

sive strength of the masonry provides an upper bound for the 27

I I

I

90 CO~PARISON OF PREDICTED LOAD-DEFLECTION CURVES FOR DI FEPZNT VALUES OF "K" (10" Concrete Masonry) 80 70

=.,5O

/

/x Crack Point for K = 4.2

=40 lx Jo K=4.2 K= 2.5 Crack Poiac for K=25 X PANFL 1 20 0 0 PANEL PANEL 3 E = 2,1i0 ksi fz = 2460 psi 10 Icr = 100 in4 0

3 4 MIDHEIGHT DEFLECTION (inches)

I l

l I

1

)

I f

90 COk!PARISON OF PREDICTED LOAD-DEFLECTION CURVES FOR DIFFERENT VALUES OF ELASTIC 1'iODULUS (6" Concrete Hasonry) 80 70 E = 500 ksi E ~ 1500 ksi

~~ ~ ~ ~~ E > 2500 ksi 60 AN!'.I. 7

~50 0 PANEL 8 a  !'ANEL 9 K = 2.5 f = 3185 psi Icr = 17 in4 X o 30 Xa p

~ e

'a X 0 20 0

,g X

~

0' ~0 10 0 I I 0 3 4 5

".IIDHFIOHT DEFLECTION (inches)

Fi".ure 2.13 29

f

)

1

)

1 l

f f

90 COHPARISON OF PREDICTED LOAD-DEFLECTION CURVES

'FOR DIFFERENT VALUES OF ELASTIC HODULUS (8" Concrete Hasonry) 80 D/

70 r

60 D

y I p p

I ,I xp X PANLL 4 p PANEL 5 0 PANEL 6 io

I j

K-4 ~

fm = 2595 psi E r E =

500 1500 ksi ksi Icr =43 in" E = 2500 ksi 0

0 3 4 HIDE/EIC)lT DEFLECTION ( inches)

Fieure 2.14 30

I I

l l

0 I

J I

0

~ ~

I 90 X CO~PARISON OF PREDICTED LOAD-DEFLECTION CURVES FOR DIFFERENT VALUES OF ELi&TIC !10DULUS (10" Concrete Masonry) 80 I 0

/

70 60 'D

/

/

QO / X

/X r

-"40 X

b E = 500 ksi I

I E = 1500 ksi 30 g g

X PANEL 1 0 PANEL 2 PANEL 3 K = 4 '

10 fn = 2460 psi Icr = 100 in4 0

3 4 HIDHEIGHT DEFLECTION (inches) 31

I r" 4 I

l I

f

measured value of elastic modulus. A report from Atkinson and Kingsley (Ref. 33) reported data from twenty compression tests on grouted concrete masonry. For prism'ompressive strengths ranging from 3037 psi to 4084 psi, the ratio of the elastic modulus to the compressive strength varied from 502 to 646. It should be pointed out, however that the elastic modulus as calculated from a stress-strain curve is highly sensitive to the method by which it is calc-ulated. The elastic modulus values were calculated by Atkinson and Kingsley as a secant modulus to 50@ of the compressive strength.

Values for the elastic modulus calculated as an initial tangent modulus can be much higher.

2.5 Comparison of ACX and UBC Methods of Calculating the Cracked Zoad-Deformation Behavior For purposes of calculating deflections, both the ACI and UBC codes call for using the gross area of a concrete or masonry wall when calculating the uncracked moment of inertia. After the wall has cracked, the method for calculating the wall deflection of each code differs. Figures 2.16 and 2 '7 illustrate the effect of each method on t'e theoretical code-calculated load deflection curves for 6" and 10" concrete masonry walls. The experimental values from the Slender Wall Test Program (Ref. 3) are also included for comparison.

The UBC states in section 2411 (b) 4 that after cracking, the moment of inertia immediately changes from the uncracked to the cracked value. This results in a bilinear. load-deflection curve for the walls as seen in Figures 2.16 and 2.17.

The ACX code (Ref. 4) uses Eqn. 9-7 (shown below) to calculate an effective moment of inertia which replaces the elastic moment of inertia in the deflection calculation.

32

1 0

0

40 PA'KL 7 Q PANEL 8 CO>PARISON OF UBC AND ACI METHOD C3 PANEL 9 OF CALCULATING CRACKED DEFLECTION E 1590 ksi (6" Concrete Hasonry) 30 l fm ~ 3185 psi 2.5 ~

Q Icr 17 in.

ACL

~

7 0 0 a

~o ~llHC o

LO 0

~ ~

~ ~ Behavior for a completely cracked section with f = 0.

r 0

HID HEIGHT DEFLECTION (in)

J I

90 X COMPARISON OF UBC AND ACI METHOD OF CALCULATING CRACKED DEFLECTION (10" Concrete Masonry) 80 70 Xg

/

0 IJBC r

60

~50 x~

0 Behavior for a completely ~

cracked section with X PANEL 1 20 0 PANEL 2' PANEL 3 E ~ 700 ksi '0 fm = 2170 psi 4.2 X Icr 100 in".

0 0 3 4 5 MIDHEIGHT DEFLECTION (inches)

Fi ure 2.17 34

I l

ft J

5 J I

This results in a gradual transition from the uncracked to the cracked value as seen in Figure 2.16 and 2.17. As the moment gets much larger than the cracked moment, the load-deflection curve asymptotically approaches the line, (shown as a dotted line in Figures 2.16 and 2.17), representing the behavior of a wall with no tensile strength, (fz = 0).

For deflections in the range of usual engineering interest, it .

appears that both methods provide reasonably accurate predictions of the load-deformation data reported in the Slender Hall Test Report.

35

qt j

0

3.0 DISCUSSION OP THE MODULUS OP RUPTURE OR CONCRETE PER TBE ACI 318-83 CONCRETE CODE In section 9.5.2.3 of the ACI code (4), equation 9-9 gives a value for the modulus of rupture of normal weight concrete for use dn calculating deflections in nonprestressed one-way construction.

Equation 9-9 states:

f, = 7.5 ~f'c (f'c in psi)

Other values are given for lightweight concrete Whi3e the modulus of ruptu e of concrete is not a function of compressive strength i~

alone, the value in Equation 9-9 is widely accepted for purposes of design (5,6,7,8,9,10).

Several different values of this equation using different K values have been suggested. Most appear to be based on the data of Branson. Branson (6), (citing references 12 and 13}, recommends the following equation for f , which includes the concrete weight, w:

f, = 0.55 Iw f'c (w in pcf, f'c in psi)

For normal weight concrete, (w=145 pcf}, this gives:

f, = ) 5S ~f'

. ( f

' in ps i ) (Eq. 3.2)

The value of K = 7.84 results in values of f 4R-5g greater equation 9-9 (in which K = 7.5). Figures 3.1, 3.2, and 3.3f (from ref. 6), compare Equation 3.2 to results of 332 tests on various weight concretes (11). In Figure 3.3, the data scatter is considerable, and the correlation to equation 3.2 is very poor. For example, from Figure 3.2, only 27% of the test data fell within +-

10% of the computed resul. ts using equation 3. 2. Note al.so <hat Equation 3.2 represents a mean value, and not a Sower bound of test results.

It is relevant to note that the K values listed in Table 2.2, 36

l f

l00 Percentage of data agtceing within a X '~ d<aerepancy 70 or 60 SO Probability of fr by Eos. l I-2) <o l 1-5) agreemen< within 233 data points g X '~ discrepancy 40 I, by Eq fl-7) 332 data p<s.

fe by E<t, (I-l3)- 274 da< ~ p<s, a IO e 20 13 140 a 50 X 5 discrepancy between corn.

pu<ed and cape<<men<a< rcsul<s.

as show'n m Frg. I-2 for X + 20'l Ct<r vcs showing the probabihty of agreement with ex pcrimemal data invo)ring dilferent weigh< conc<

lor calculated results of/'. /and E,.

Fi< ure 3.1 Tabu)a<ed values from Fig. I-3 showing the probability of kgreemen< <<i<h eaperi-rnen<al Jat ~ involving dilferent <<eight conercte. fur calculated results of f;, fand E, Pctcentagc of data agreeing within g X 'iscrepancy or Probability of agreement within + X% discrepancy iX, f,'y Eqs. (I.2) to f, by Eq. (I.7) E, by Eq. II-l3)

-274 data pts.

discrepancy (I.S)-253 data pts. -332 data pts.

k I0% 62" 27"lo 62%

93% 6l 83%

97% 950 r g 40% I 00% 94%

I 00% 98%

IOO;,'ic ure 3. 2 X

~ aa 600

~+ ~

~ gk k

~

a, t' aa a La.

~ Qaa ~ a a

aa'a 8 500 4< 'fi ~

Ia1

~ 84 ~

!aa a'a

~ aaa ~ Eo. I )-7)

Q i Nor,-wt

~ ht<<-<-w<

200 300 400 5<X< 600 ~ 700 500 Eapcritnent ~I /,. psi Figure 3.3 37

l J

l f,,'

I I

J I

column 16 (of this report) for concrete walls vary from 4.9 to 5.8.

These are signi icantly lower than the value K=7.5 recommended by the ACI 31S-S". code (4).

38

/

~

4 1,

1

' l I

4.0 ADDITIONAL PERTINENT DATA ON MODULUS OF RUPTURE 4.1 NCMA The "Specification for the Design and Construction of Load-Bearing Concrete Masonry" (14), published by the National Concrete Masonry Association, specifies, in section 3.3.2, values for the

.allowable tension in flemxre for concrete masonry. For tension normal to the bedjoints and type M or S mortar, the allowable stress for hollow unit masonry is 23 psi, and for grouted or solid masonry, 39 psi. The derivation of these values is traced in Reference 15.

Tables 4.1 and 4.2, reprinted from Reference 15, show the pertinent test data. Test specimens were uniformly loaded walls tested in accordance with ASTM E 72.

The design values for grouted masonry were not obtained from tests on grouted walls, but from tests on six composite walls com-posed of 4-inch concrete bricks and 4-inch hollow blocks (Table 4.1) . The .gross area af Me ~alla was greater Chan 75K solid, so the walls were designated as solid masonry. Furthermore, it is I

assumed that solid and grouted masonry have identical behavior, a point that has been disputed by Hamid (18). The reported mean value of modulus of rupture was 157 psi (based on the gross area), and a factor of safety of 4 was applied. to obtain the design value of 39 psio The design values for hollow unit masonry were obtained from the 2Z tests, from three sources, shown in Tab3.e 4.2. The mean modulus of rupture for types M and S mortar (14 specimens) was 93 psi on the net area. Applying a factor of safety of 4 gives the allowable value of 23 psi.

39

I 1

I t'

I

~ ~

TABLE 4r 11LEXURAL STREYGTII> VERTICAL Sl'A'2 CO>XCR TE IIASO'AR: L'ALLS PROD TESTS hT X>'C.'8, L>KBORATORY Wall

~Hodulus of Ruoture Net I fa>;. Net Ho=tar AST.'I Noninal Uniform Section Gross Bedded lor tar Thickness Load ifodulus Area, Area, Type- in. ps>.C in 3/ft ps i i ps i Honouythe Halls of lfolloM Unit" H 8 85.15 80.97 61.74 88.73 H 8 ~ -' 87.10 80.97 63.15 90.76 H 91.00 80.97 65.97 94 82 H 8 103.35 80 97 7I> .93 107.69 S 8 62.40 80.97 45. 2Ii 69.47 S 8 72.15 80. 97 52.31 75.18 S 12 183.3 1GIi . 6Ii 57 11 i 93 94 S 12 161.2 164.64 50.22 82.62 Composite balls of Concrete Brick E Hollolr C!IU,'

I 8 22/. r 3 103.8? 161.16 180 67~

S 8 219.7 103.82 159.29 178.55 S 8 187.2 78.16 135.72 202 09 I S 8 228r8 103.82 165 '8 1S5.95 S 8 218 r Ii 78.16 158.34 235.77 S 8 223. 6 78.16 162.11 2Iil.3S S 12 171.6 3.39. 83 D3 46 3.03 55 S 12 150.8 139.83 46.98 .'1.00 S 12 156. 0 139.83 Ii8. GO 94.14 S 12 213.2 139 '3 66.42 128.66 Cavity I alls I

I S 10 98.8 50.36 158r62 165.55  !

S 10 156.0 50.36 250. I,I, 261.38 .

S 10 SS. Ii 4i8.16 141.91 S 10 119.6 50. 36> 192.0l "OO.I 0:.

S 10 50. 36 183.GG 191.GS 10 109.2 4S.16 175.30 191.32 S

(4-.4-4) lIi5. 6 50.36 233 '3 2.I 3 9I>

S S

12 12 (Ii-Ii-li) lIi5.G 50.3G 233 '3 'l' ~ r ~

I J>> 135.2 77 80 127-38 14>G. 63 ~

S 1>> (G 2-I> )

(6-2-Ii) 119.6 77.Cn 11" 68> ) 29.70 rcn>; ire'>cnts.

.'nrtar tv~c f>y proportion Air >:

r r l+CQ i>(>t )melo> Cif~ ill r: OH:i:.loca> O.'a% ' 4a 40

T

(

I l

l f

TABLE 4.2 PLE>:UPAL STRENGTH SIYGLE liYTHE HALLS OF 110LL01? UKITS-U?iIFOP2f LOAD VERTICAL SPAY l'for c r T)'pe I Proporcion iifoJulus of Rupture ASTif C 270 psi, Net Area Reference H 110 17 lf 108 NCVUX lf 102 17 lf 97 17 ~

lf 95. NVfA S 94 hCl  %

91 llCL"UX lf 89 l:C'f.%

l? 88 16 S 84 17 S 83 l'ClfA S 81 1.7 S 75 hC~Lh, S 69 KC1 67 16 N

N 16 S 60 17 N 58 16 45 16 0 60 17 0 41 16 0 36 16 36 16-0 0 33 16 0 32 16 0 30 17 0 27 16 41

ai Mf 1

l lq{'

4.2 UNIPORM BUILDING CODE (1)

Section 2406(c) 4. specifies allowable tensile stresses for wal3s in flexure. Por tension normal to bed joints and concrete units, the allowable stress is 40 psi for so3.id units and 25 psi for hollow units. The Commentary to Chapter 24 of the Uniform Bui3.ding Code (2) contains an extensive discussion of factors affecting tensi3.e bond strength in masonry, (including mortar propor.ions, mortar air content, unit initial rate of absorption, unit moisture content, joint geometry, mortar joint thickness, workmanship, and curing conditions), however, there is no discussion of the origin of the given allowable values. No specific data is cited, and no safety factors are given. The commentary includes, without comment, the allowable values given in Reference 14 for concrete un'ts, (discussed in section 4.1 above), and the values provided in Ref-erence %9 for solid clay units.

4. 3 ACI 531-79 The ACI Code for reinforced concrete masonry (21) also spec-.

ifies al3.owable values for masonry in tension. The allowable stres-ses are for both axial tension and tension in flexure, and they are related to mortar strength. Ror tension normal to bed joints, the allowable stresses are 0.5 ~m~ (maximum 25 psi) for hollow unit masonry, and 1.0 Ijme (maximum 40 gsi) for solid or groused masonry.

m is the specified 28-day minimum required compressive strength of mortar per ASTM C 270, ysi.

ACI 531-?9 states that stresses can be increased by 1.33 for earthquake design.

49

,h l

I"

%C C

l l

4.4 CMI STANDARD 301-76 The 1976 CMI Standard allows 0 psi for the tensile strength of masonry.

4.5 AUSTRALIAN STANDARD CA47-1 9 69 The Australian Standard allows 10 psi for tensile stress normal to bed joints.

4.6 DRYSDALE, HAMID, AND TONEPF, 1983 (20)

Drysdale et. al. discuss allowable tensile stresses in masonry in ref erence (20) . The authors find the allowable tensile stresses in North American codes (21,26) to be unjustified and unconservative based on test data on small scale specimens (18,24,25). They also point out, however, that "tests on full scale walls clearly indicate that, at least where walls are supported on more than two edges, capacities ezceed by a considerable amount the predictions using strengths from small wall specimens and elastic analysis".

authors state the difficulty of identifying trends in the research data and the allowable stresses reported in the codes due to the large scatter in most data, (coeficients of variation within groups of apparently identical specimens are often on the order of 0.30).

They do acknowledge, however, that "grouted blockwork has been shown to have very much improved tensile strength. normal to the bed joints" (18,28,29). As a result, "for a safety factor of 2.0 be-tween the characteristic strength -... and the allowable stress, the allowable stresses for grouted blockwork would be conservative Table 4.6.1 is included from Reference 20 for reference. Note 43

BLOCK COMPRESSIVE STRENGTH (MPo)

IO l5 20 25 2.25 0

G. FLEXURAL TENS ION 2.0 NORMAL TO BED JOINTS III z ~ rt eetle<<I Sot I ~ er trot \ o I O ~ <<tel r I1 C'.re<<trO ftrt llI I I e I.75 O 0 ~ ree ~I I I trr'l~

tsI 0 ol I I I ~ ~ t ~

ffI 0 Io AAH1 O It ~ eH1 ol I I )r ~ t ~

I I.50 I4 eeee ~ I I I I ~ rt ~

Io lit S,t: ere<< ol I I ttst ~

0 E 0 0

O 1.25 <<roe r I t Il t ~ St r

I hA<<o <<rtASII

~ Atl<<I<<

ttrt IAAOIAI

~

Z I.O <<Atlr'I<< lerllr I ISI II: tl"11 l. Ht ~

Ht

~ I 07fl D drWI I So'.

Isf V'4

~~ 050- ~

~

Ar e~ II A ISI Alt d A IS as sol.Io a>>oil.ow

~ 0,25 AS S 1IO 8 IIOLLOW 05 I.O I 5 2.0 2.5 30 3,5 I.O 0.5 5.0 BLOCK TRANSVERSE STREIIGTH (MPo)

Figure 4. 6. 1 DATA AND ALLOMAlll,F S'fRFSSFS FOR FI,FxunAL Tl:.NSTON NOIIHAL To zslr.

BED JOTNl'S

I I

f t

that the data for grouted masonry falls above the data for ungrouted concrete masonry.

4.7 MILLER, NUNN, HEGEMIER, 1978 (Ref. 30)

Reference (30) reports the results of a study on the effect of various grouting strategies on the strength and elastic moduli of concrete masonry. Modulus oX rupture tests were not performed; however, some prisms were tested in direct tension normal to the bed joint in addition to standard compression tests of prisms. Por concrete, the split cylinder tensile strength usually ranges from 50% to 75K of the modulus of rupture (8), so it is likely that direct tension tests would represent a lower bound of modulus of rupture values for grouted masonry. Results of the compression and tension tests are reprinted in'tables 4.7.1 and 4.7.2. ("Pie3,d practice" prisms were built using standard constuction site proc-edures, and "controlled slump" prisms were built in carefully con-trolled laboratory conditions.) If, as is the ~ractice with ghe modulus of rupture, the tensile strength is related to Lt f'm by the equation f, = K ~f'm these results yield a mean K factor of 2.3 for the "field practice" prisms, and 2.5 for the "controlled slump" prisms.

4.8 DRYSDALE AND HAMIDr 1984 (Ref. 18)

Drysdale and Hamid report on an experimental study of effect of grauting on the Xlexura3. tensile strength of concrete block masonry in Ref. 18. Their results are summarized in table 4.8 1. The tests directly relating to grouted concrete masonry are shaded. Three different strengths of grout were used, however.,

45

I g

l J

i l

07 j

I

fable 4.7.1 Tidble 4.7.2 Compressive Strength of 4-Course Field Practice Prisms Compressive Strength of 4-Course Controlled Slump Prisms I

STD VI IIII STD STD VIBR ADM ADM VIBR STD ADM ADht VIER I .

I)48 2274 2I8I Zoot 2140 2!2) 1685 2)59 1449 1102 2140 17) 5 2584 2426 Z)50 2282 1398 2089 2324 Failure Stree ~ IC 2079 2241 1574 2595 2173 Failure Stress I (pall 207 2 1735 2746 1887 24)4 2)08 2 I 48 C

I ps ll- 1490 2358 2450 2468 1928 16) 4 2544 tTlean 1984 2171 1673 2566 mean 1524 2316 2323 22!5 I 6o. 4 69. 2 std. dev, ZIZ 142

~ td. devo 176 96 173

[

I I 1 Tensile Strength of 3-Course Tensile Strength of 3-Course Controlled Slump Prisms Field Practice Prisms STD STD VIBR ADht ADM VIBR I STD STD VIBR ADM ADht VtQR 74. 9 99. 8 91. 8 160. 0

69. 7 I I 'I, 2 116.

91.

3 8 I

92. 5 lo. 7 94.

98. 6 8

Failure Stress I

)pall 82,1 105. 0 119. 7 9). 8 114. 8, 81. I

92. 4

70. 4 150. 0 161. 0

'178. 6 Failure Stre ~ s 1 t I I I. 2 127. 3 118. 3 116. )

lo. 4 88. 2 l)3. 4 Ips II 84. 3 113. 0 I 143. Z

95. 4

69. 9 89. 9 95. 8 107. 4 lo7. I mean 89. 3 107. 7 los. s I I 2. I 9). 5

~ t* dev. 20. 9 16. 3 10. 9 19. 3 mean 95. 7 114. 6 83. 9 I 62. 4 stdt deva 14. 5 17. 9 10. 4 11.9  !

l I

f l

e Il I

4 FlZXURAL TEHS ION TEST n UI.TS Flerural Tensile Str ergth a Hor tar j(ornal to Bed Joints Parallel to Bed Joints Block Crout Stiength Croup Type Type (Nina )

No ~ of I't (X/nn2 ) V d

(S) Ho. of I'H/re tp 2

) V d

(S)

Tests Te sts 1

1 HOMAL 16. 5 5 o- 43 62 37. 8 1.00 18.4

~ 2 HORXAL CH '17. 4 7 1. 40 203 6 1,71 11 2 16.8.'.36 3 HORXAL G( 16.1 6 197 12 3' HOR'IAL GS 16. 7 6 67 242 9.T 5 HOLA L CH 17. 8 5 0.77 112 6.0 o SOLlD - 18 ~ 0.88 98 2'1.4 1. 25 8.1 a', Stresses are based on nini~n I'ace shell area for +groused specinens and on gross area for grouted specie!ns

4) Only centr al cell grou.ed in tuo and a hal I'lccw iong uai1 (5 c i is) c) Based on nininus face shell area d) Coefficient oi'ariation 47

0 l

f l

'r's 0

within the range of commonly used grout, the compressive strength of the grout was found to have a minima3. effect on the modulus of rupture. They found that grouting concrete masonry causes a 233%

increase in flexural tensile strength over hollow concrete masonry.

Grouted concrete masonry gave an average tensile strength of at least 197 psi. No prism strength va3ues were given making ca1c-ulation of "K" impossible. The flexural capacities of their as-semblages were greater than predicted when superimposing tensi3.e bond strength and grout tensile strength. An analysis in which failure was controlled by the extreme fiber of grout'n3y slight1y underestimated strength, however, the analysis showed sensitivity :o "subjective assumptions".

4.9 DRYSDAZE AND HAMID, 1982 (Ref. 29)

In Ref. 29, Drysdale and Hamid report on the in-plane tensile strength of concrete masonry. Tensile strength was measured usin-splitting tension tests of masonry assembleges. (Note that for concrete splitting tensile strength is usually 50% to 75@ of modulus of rupture, (Ref. 8)). Results are summarized in, Table 4.9.1 with shaded values relating specifically to grouted concret Grouting was found to have a profound effect on the ten- 'asonry.

sile strength normal to the bed joint.

48

I 1

I

Table 4.9.1 CAN, ), ClV, ENG, VOI., 9. INN2

~ y Summhry of split(inn test results 5plltt tnt Tensile 5trendth pere))e) to 8ed Joints f Nerve) to hrd Jatnts Series dtock Type Crovt No, No. of f (4) (nye) f V(l) aa. of f (nya) fn (Nyel Ytt)

Type (Npe )

Spe" teens spe Inens 0.55 ""- 0.2n 0.59 23 ~ 3 (O.a9) rs) 2 CN 5 O.NS O.hd IT ~ 0 1 90 we. N8 CN (e) 0.15 3

Hollov 4 CN 3 0 90 20. 5 0.14 10. 3 CS 12. I 3 O.ya 2.9 3 0.30 0.5a 5. ~

751 solid CN 2 I. nd 1 a,t 8 I90 we. Nd 5 O. 99 0.99  ! O.yn 0.10 I~ e 100l sc'0 3 0.52 I S2 3,1 3 0.21 CD 61 Te.\

(O.ne) (d)

Hollov

'10 CN II O.cy 15 ~ 9 1 Odd 8.2 2 0.73 2.1e 190 are, 58 ('I 18) (

~

)

Hol1ov IP 1 I In 9.T 3 0SS 1,60 N.d n

(0.89) ( )

~

I~ CN a O.hd 13.2 2 I.OT I 0.22 0.6e 0.20 0.58 190 we, IIollov 0.63 ISrh OTT 0.62',0 16 CN 3 IT Ian wo Iasllov NN

~

a... ~ j.....

18 2a0 me Ho I I ov NN a '- rr ';.. O.TO 2 0.6I I~ ) for grovt and oloca prorwrt1 ~ a ~ see Teolae 1 oad (4) oaaed on feat one)i tnlcoaeas aalacent to tne central veo.

(4) posed an dross cree for ~ II apeetoeos. I ~ ) vopey Iwed Jotnta.

(c) ~ aaed on ~ INI%% fec ~ anal I tNI ~ aneeo ( f3 otooo Twtwn.

49

(

l 4

a+

e

5.0 OBSERVATIONS The data and information presented herin were compiled in a very short time and cannot be considered an exhaustive treatment of the subject. A problem encountered was a general lack of standard-ization of the data reported. Por example, the use of different symbols or teqms to identify the same physical quantity. Also differences in experimental procedure may qualify some of the re-suits. Further investigation would be required to resolve some of these issues.

No experimental values for modulus of rupture were found for 12-inch (nominal) grouted concrete block masonry. Based primarily on the results of the slender wall program (3):

1) it appears that K values in f X = K /f'm increases with thickness,

2) it appears that K values for grouted concrete block masonry, assuming zero tensile'strength of the mortar bed joint, are of the same order as the K values for concrete panels,

3) it appears that the K values for concrete panels are less than the value of 7.5 given by ACI 318-83 (4), and

4) it appears that K value of 2.5 for concrete masonry is a lower bound. K = 2.5 was derived from 6" wall tests only, and the Slender Ha3.3, tests seem to indicate that the value of K increases with wall thickness.

The effect of the value of masonry elastic modulus on out-of-plane deflection calculaions is significant. Por this reason, care must be taken .in assuming elastic modulus values based on 50

I f

01

~E li 0

compressive strength data. Specific information on the numerical value of the elastic modulus (E) for masonry is difficult to derive from the literature, since no convention has been consistently followed in the definition of E for nonlinear material behavior.

This difficulty, combined with the inherent variability of masonry material properties, makes the prediction of E values difficult.

The UBC recommends taking the value of E as 1000 f'm. Test data, using measured values of compressive strength and elastic modulus, indicates that this may be an upper bound on masonry stiffness rather than a mean value'. Assuming a lower ratio of E/f 'm may be appropriate. Average measured values of elastic modulus for grouted hollow concrete masonry prisms (Refs. 3,30,33) range from 1500 ksi to 2600 ksi.

Different techniques for calculating the moment of inertia after initial cracking can also affect deflection calculations. The ACI technique for calculating an effective moment of inertia results in a slightly stiffer section, and thus smaller deflections, than if the section is assummed to be completely cracked as per the UBC.

Both techniques provide a reasonable prediction of out-of-plane deflections within the range of engineering interest, based on data from the Slender Wall Test Report (Ref. 3). (Both ACI and UBC deflection calculations shown in Figures 2.16 and 2.17 were based on measured modulus of rupture values: f = 138 psi for 6" masonry, f r r 208 psi in 10" wall)

Further time and effort would be required to fully document existing data on the modulus of e2asticity and the modulus of rupture for grouted-hollow"unit concrete masonry.'ata exists in 51

l various places which would require time to acquire. Because of different methods used by the various researchers to present and analyze data, time and effort would be required to convert all data to a common form for analysis.

It is apparent, however, based upon the experience of this study and the experience of Atkinson-Noland and Associates in many previous masonry studies, that it would be very difficult to base precise conclusions regarding the values of the modulus of rupture and the modulus of elasticity for a specific wall or walls upon data in the literature. Present standards and methods for determining material properties, fabrication of specimens, and recording data are not sufficiently uniform to support precise comparisons of results, however, they may be satisfactory at this time to establish design values. It is the authors'pinion that values required for analysis of specific masonry are best obtained by tests of samples of the specific masonry or of samples built to replicate the specific masonry.

5la

]

I i'

0

6-0 REFERENCES Uniform Building Code, 1985 edition, Enternation Conference of Building Officials, pp. 170-171.

2. The Masonry Society, "Commentary to Chapter 24 of the Uniform Building-Code, 1985". p.77, 1986.

3. Task Committee on Slender Walls, "fest Report on Slender Walls". American Concrete Institute, ACI-SEASC, 1982.

American Concrete Institute, "ACI 318-83, Building Code Requirements for Reinforced Concrete". Detroit, Michigan, 1983.

American Concrete Institute, "ACI 318R-83, Commentary on Building Code Requirements for Reinforced Concrete". Detroit, Michigan, 1983.

Branson, D.E., "Deformation of Concrete Structures". McGraw Hill Book Company, New York, new York, 1977, p.546.

7. American Concrete Institute Committee 435, "Deflections of Reinforced Concrete Flexural Members". (ACI 435.2R-66), ACI Journal, Proceedings Vol.63, No.6, June 1986, pp.637-674.

8. Park, R. and Paulay, T., "Reinforced Concrete Strucures". John Wiley 6 Sons, New York, New York, 1975.

9 Winter, George and Nilson, Arthur H., "Design oX Concrete Structures". McGraw-Hill Book Company, St. Louis, Missouri, 1979.

10. Ferguson, Phil M., "Reinforced Concrete Fundamentals, Fourth Edition". John Wiley 9 Sons, New York, 1979.

Chen, C.I. and Branson, D.E., "Design Procedures for Predicting and Evaluating the Time-Dependent Deformation of Reinforced, Partially Prestressed and Fully Prestresssed Structures of Different Weight Concrete". Research Report, Civil Engineering Department, University of Iowa, Ames Iowa, August 1972.

12. Branson, D.E. and Kripanarayanan, K.M., "Loss of Prestress, Camber and Deflection of Non-Composite and Composite Prestressed, Concrete Structures". (four papers presented by D.E.B, on various aspects at the 6th Congress, Fhdhration Internationale de la Prhcontraimte,'rague, June 1970.; and at Design Seminars sponsored by the Prestressed Concrete Institute, Chicago, January 1971 and June 1971 and by the California Division of Highways and Ceramic Lightweight Aggregate Association, Sacramento, March 1971), pCX Journal Vol.16, pp.22-52, Sept.-Oct. 1971.

f 4

~"

i 0

13. Branson, D.E., "Compression Steel Effect on Long-Time Deflections, Proceedings, American Concrete Journal, Vol.68, No.8, pp.555-559, August 1971.

14. National Concrete Masonry Association, "Specification for the Design and Construction of Zoad-Bearing Concrete Masonry".

NCMA, Arl'ington, Virginia, 1979.

15. National Concrete Masonry Association, "Research Data and Discussion relating to 'Specification for the Design and Construction of Z,oadbearing Concrete Masonry'". NCMA, Arlington, Virginia, 1970.

16. Hedstrom, R.O., "Zoad Tests of Patterned Concrete Masonry Nails". Proceedings, American Concrete Institute, Vol.57,

p. 1265, 1961.

17. Copeland, R.E. and Saxes, E.L., "Tests of Structural Bond of Masonry Mortars to Concrete Block". Proceedings, American Concrete Institute, Vol.61, No.ll, November 2964.

18. Drysdale, R.G. and Hamid, A.A., "Effect of grouting on the Flexural Tensile Strength of Concrete Block Masonry".

submitted to the International Journal of Masonry Construc-tion.

19. Structural Clay Products Institute, "Recommended Practice for Engineered Brick Masonry". SCPI, McZ,ean, Virginia, Nov. 1969.

2D Drysdal+, R G. md Hamid, -A 4. md Zoneff 4 D, ~'Co'mments .on Block Masonry Design Code Provisions for Allowable Stresses" ~

Proceedings of the 3rd Canadian Masonry Symposium, Edmonton Canada, June 1983.

21. ACI Committee 531, "Building Code Requirements for Concrete Masonry Structures". ACI 531-79, Detroit, Michigan, 1978.

22. Colorado Masonry Institute Committee 301, "Standard 301-76 Building Code Requirements for Masonry Construction". CM1 Denver, Colorado, June 1976.

23. Standards Association of Australia, "Australian Standard CA47-1969 SAA Brickwork Code (Clay Bricks and Concrete Bricks)".

SAA, Australia, 1969.

24. Drysdale, R. G., and Hamid, A.A-, "Influence of Block properties on the Flexural Strength of Concrete Masonry". Seventh Austzalian Conference on the Mechanics of Structures and Matezials, University of Hestern Australia, May 1980.

25. Gaizns, D,A. and Scrivener, J.C., "Local Research into Concrete Masonry Subject to Lateral Loads", University of Melbourne, Australia-53

e 1

l" P,

e~'y

26. Canadian Standards Association. "Masonry Design and Construction for Buildings". Standard CAN3-S304-M78, Rexdale, Ontario, 1978.

27. Hegemier, G.A. and Endebrock, E., "Masonry Wall Failure Analysis in Nuclear Power Plants". Trans Science Corporation, La Jolla, California, March 1983.

28. Drysdale, R.G., and Hamid, A.A. and Heidegrecht, A.C., "Tensile Strength of Concrete Masonry". American Society of Civil Engineers, Journal of the Structural Division, Vol.105, No.ST?, July 1979, pp. 1261-1276.

29. Drysdale, Tt.G. and Hamid, A.A., "In-Plane Tensile Strength of Concrete Masonry". CJCE., Vol.9, No.3, 1982, pp. 413-421.

30. Miller, M.E. and Hegemier, G.A. and Nunn, R.O., "the Influence of Plaws, Compaction. and Admixture on the Strength and Elastic Moduli of Concrete Masonry".. University of California, San Diego Report ¹USCD/AMES/TR-78-2, San Diego, 19?8.

31. Drysdale, R.G. and Hamid, A.A., "Tension Pailure Criteria for plain-Concrete Masonry". American Society of Civil Engineers, Journal of Structural Engineering, Vol.110, No.2, Pebruary, 1984. ASCE, ISSN 0733-9445/84.

32. Original, unpublished data from the Slender Wall Test Program (Ref.3).

~cia and Concrete ~Masonr in Compression, report to the Nat'ional Science Poundation, Sept., 1985.

~ wa ~

r ~~ ~

7 0 APPENDIX MiIPORt BUILDING CODE - SECTION 24>]

Design, Reinforced Masonry Slender Wall 24 1 l. (a) General. In lieu of the procedure prescribed in Section 2409, the

'ec.

procedures set forth in this section, which consider's the slenderness of walls by representing effects of axial forces and deflection in calculation of moments, may exceed 0.04 f's be used when the vertical load stress at the location of maximum inoment does not computed by the following formula:

P~, + Pp~Q 04ff .(11-1)

Ag SVEEERE:

P, = load from tributary floor or roof area.

P = weight of the wall tributary to section under consideration.

f = ultimate compressive masonry stress as determined by Section 2406 (b).

The value off'~ shall not exceed 6000 psi. >.

A> = grossareaof wall:

(b) Slender IVall Design Procedure. l. h faximum and minimum reinforce-ment. The reinforcement shall not exceed the following ratios, p, of reinforce-ment area to gross masonry area:

-.f>> = 40ksl f>> = 60ksi Concrete B lock Masonry 0.0048 0.0032 Hollow Brick Masonry and

'wo-wythe Brick Masonry 0.0060 0.0040.

. Minimum reinforcement shall be provided in accordance with Section 2407 (h) 4 8 for all seismic areas when using this method of analysis.

~ I

2. Moment and deflection calculations. All moment and deflection calcula-tions in Section 2411 (b) are based on simple support conditions top and bottom.

Qthcr support and fixityconditions, mo)nents and dcflcctions shall be calculated using established principles of mechanics, 55

~ ~~ ~

1 0

l l

I I

f l

~P

~ gP 2411 UNIFORM BUILDINGCODE

. 3. Strength design. A. Load factors. Factored loads shall be based on:

U = 1.4 D + 1.7L, or ............ ~ ~ .. ~ ~ ~ ~ ........(11-2)

U = 0.75 (1.4D + 1.7L + 1.87 E), or .(11-3)

U = 0.75(1.4D + 1.7L+ 1.7IV), or........ .......,(11-4)

U = 0.9D + 1.43E, or: ~ ~ 0 ~ ~ 0 ~ O(1 I 5)

U = 0.9D +. 1.3)V . . ~ ....., ..(11-6)

WI1ERE:

D = dead loads, or related internal moments and forces.

E = load effects of carthquakc, or rclatcd internal mo>>ic>>ts and forces.

I. = live loads, or related internal moments and forces.

U = required strength to resist factored loads, orrelated internal moments and forces.

P = wind load, or related internal moments and forces.

B. Requtred moment. Required moment and axial force shall be determined at the midheight of the wall and shall be used for design. The moment strength, M, shall be at least equal to:

0

)v h>

= "

>~u + P,+ (P.+ P,) A.............(11-7) 8 2 IV11ERE:

factored distributed lateral load.

height of the wall between points of support.

factored weight of thc wall tributary to thc section under consideration.

ltoriro>>tal dcf lection nt micllicight under factored load; Ph effects shall be included in deflection calculation.

P Oll factored load from tributary floor or roof loads.

e eccentricity of P.

PN axial load at tnidhcigi>t of wall, including tributary wall weight.

P> P>.> + P~o ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ o(1 1 8)

C. Design strength. Design strength provided by the reinforced masonry wall cross section in terms of axial force and moment shall be computed as the nominal strength (see Section 2602, Definitions) multiplied by a strength reduction factor, f,m set forthinEormula (11-9).

, 168

~ ~ ~

J4 K

j 1

f

1985 EolTlON 241 0 WHERE:

M= nominal moment strength found for cross sections subjected to combined flexure and given axial load.

. The strength reduction factor for flexure, $ , shall be as follows:

Special Inspection Yes No Concrete Block and Hollow Brick (Designated 6-inch thickness or greater) and two-wythe brick masonry 0.8 0.5 Hollow Brick Masonry-(Designated 5-inch or less thickness) 0.6>> 0.4>>

>>EXCEPTION: $ = 0.8 for special inspection and b = 0.5 fornoncontinuous inspection when vert icalTeinforcing bars are held in position at the top, bottom and at intervals not farther apart than l 92 bar diameters.

D. Desigrt assumptions for nominal strength. Nominal strength of singly reinforced masonry wall cross sections to combined flexure and axial load shall be based on applicable conditions of equilibrium and compatibility of strains. Strain in reinforcement and masonry walls shall be assumed directly proportional to the distance from the neutral axis.

Maximum usable strain at extreme masonry compression fiber shall be as-sumed equal to 0.003.

Stress in reinforcement below specified yield strength fy for grade of reinforce-ment used shall be taken as E, times steel strain. For strains greater than that corresponding fo f>>, stress in reinforcement shall be considered independent of strain and equal to . f Tensile strength of masonry walls shall be neglected in fiexuralsalculations of strength, except when computing requirements for deflection.

Relationship between masonry compressive stress and masonry strain may be assumed to be rectangular as defined by the following:

(i) Masonry stress of 0.85 f'hall be assumed uniformly distributed over an equivalent compression zone bounded by edges of the cross section and a straight line located parallel to the neutral axis at a distance a = 0.85 c from the fiber of maximum compressive strain.

(ii) Distance c from fiber of maximum strain to the neutral axis shall be measured in a direction perpendicular to that axis.

4. Deflection design. The midheight deflection, Aunder service lateral and vertical loads (without load factors) shall be limited by the relation

'6,, = 0.007h..........:........;....(11-10)

EXCEPTION: For hollow brick masonry designated5 inches or less in thickness where vertical reinforcement bars are not held in position at the top, bottom and at intervals not farther apart than l92 bar diameters, use 5, = 0.005h.............,..........(11-11) 169

0 ~ y f

l 1

~

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2431 UNlFORM BUlLDINGCODE The midheight deflection shall be computed with the following formula:

SMfrs (forM, (Mo) . .(11-12) 48 Egr 5M,P2 5 (M,M) h2

+

48E lit g 4 Irl Cl' YVHERE:

= height of the wall.

M, = service momentat the midheight of the panel, including Pd, effects.

E~ = I000f'~.'

1<,I= gross, cracked moment of inertia of the wall cross section.

M = cracking moment strength of the masonry wall.

M= nominal moment strength of the masonry wall.

The cracking moment strength of the wall shall be determined from the formula:

Mar = Sfr ~ ~ ~

~ (l l 14)

AVHERE:

4 S = section modulus.

g = modulus of rupture shall be assumed as follows for calculating deflec-tton:

f,psi Concrete Masonry Units 2 5'p.si'i's Hollow Brick Units SVf .p 7wo-wythe Brick Walls 2.0~f'~ psi s ~

170

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