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cluded that, in general, this curve 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: El = Eiln/3.5. In accordance with the assumed end conditions, a Cm 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 t/3 eccentricity (f'm=2,320 psi). As previously noted, this curve is probably accurate or slightly conservative for eccentricities greater than t/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/3 eccentricity 10-ft wall strength exceeded the average prism strength. At the t/3 and t/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

t/6 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 slenderness 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 1/3 was assumed to equal the average flexura! strength of prisms, loaded at a t/3 eccentricity.

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The allowable compressive stress under axial loading is reduced for slenderness effects, using a reduction factor of [1 (h/40t3]. The allowable short-wall axial stress is 0.2f'm for unreinforced masonry and 0.225f'm for reinforced masonry. Allowable flexural compressive stresses are 0.3f'm and 0.33f'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/3, reinforced walls may be designed on the basis of an uncracked section.

These design recommendations consider wall enderness; however, the h/t ratio does not take into count the properties of the cross section, and erefore does not differentiate between solid and llow sections. Other variables associated with enderness effects and not considered in these -sign equations are end fixity effects (effective ngth),3 the effect of the manner in which the ember is loaded (the shape of the moment diagram d the resultant deflection curve), and the relationip between the strength and the modulus of asticity of the masonry.

A short-wall interaction curve can be developed ing the recommended interaction equation, eq (5), e allowable axial and flexural stresses, and the her requirements contained in the NCMA stanrd as mentioned previously.

Figure 7.1 shows interaction curves of allowable -rtical loads and moments, computed for the 6-in inforced masonry walls by the NCMA standard. asonry strength ƒ'm was taken as the average axial mpressive strength of the 6-in three-block prisms sted in the investigation reported herein. The shed curve (A) was computed without any slenerness reduction and represents short-wall capaci. The solid curves labeled B and C were computed r the 10- and 16-ft walls, respectively. The dashed dial lines represent the load eccentricities. ed in the tests. The intersection points of these dial lines with the interaction curves represent the lowable vertical loads at these eccentricities. Note at the upper, linear part of the interaction curves, nich represents capacities of uncracked sections, extended in each case by a dotted line to the t/3

1 Some general consideration is given in NCMA Standard to ntilever members and members subject to sidesway.

TABLE 7.1

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eccentricity. These dotted lines correspond to the provision that walls may be designed for uncracked sections up to the t/3 eccentricity. Curve C, which corresponds to an h/t ratio of 34, is actually an extrapolation of the NCMA standard which limits the h/t ratio for load bearing reinforced walls to 30. The NCMA equation could not be used to develop an interaction curve for the 20-ft walls, since the equation for slenderness reduction goes to 0 at an h/t 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 ulti

Comparison of Allowable Loads by NCMA Standard with
Average Ultimate Load Capacities of 6-in

Reinforced Walls

Case 1

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Case 2 Computed Ultimate

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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 correspond 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 10ft 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 appears 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 increase 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 standard, the walls can actually support a greater ultimate moment than at any lower vertical load. For eccentric 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 reinforcement. 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 t/6, and particularly for large eccentricities, the margin of safety against an increase in horizontal live loads is substantially smaller than that provided against an increase in vertical live loads. Thus, it may be concluded that reinforced walls, designed in accordance with present practice have a greater and more

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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 t/4 eccentricity. Thus the 13 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 ultimate moment capacity which was based on the flexural compressive prism strength at the t/3 eccen tricity. Curves C and D are extrapolations of the NCMA standard, which limits the maximum h/t 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 particu lar 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 t/3 eccentricity. It is

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portant to note, that for unreinforced walls built solid units, which can be designed on the basis of cracked section, these margins of safety may drop en lower and approach unity. Thus, while margins safety against an increase of vertical loads are ther high, the margins against an increase in rizontal loads may be extremely small.

The allowable vertical loads and moments shown figures 7.1 and 7.2 and listed in tables 7.1 and 7.2

ere based on the average axial compressive

rengths of the prisms as determined by tests. For e 6-in prisms, f'm was 1890 psi and for the 8-in -isms, f'm was 1700 psi. If f'm values are not deterined by tests, the NCMA standard permits f'm alues to be assumed on the basis of the unit rengths. For the 6-in and 8-in hollow concrete ock used in this investigation which had strengths 4080 psi and 4230 psi (net area), respectively, the ssumed values of f'm permitted are 2017 psi and 047 psi. Based on this investigation, the assumed alues of f'm permitted in the NCMA standard are bout 7 percent too high for the 6-in prisms and bout 20 percent too high for the 8-in prisms. Acordingly, if these assumed values of f'm were used the comparisons given in tables 7.1 and 7.2, the argins of safety would be smaller than the values eported.

Three important conclusions may be drawn from his discussion:

(1) Present NCMA design criteria provide a large margin of safety with respect to vertical loads. This argin of safety is necessary, since present design rocedures do not account for all the variables that ffect wall capacity.

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

acts on the wall, 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 discrepancies 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 scaling" which is presently applied to develop allowable 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 ultimate 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 life of a building should be taken into account.

(3) Based on the prism strengths obtained in this investigation, the assumed values of axial compres

sive strength f'm 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 increases 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 axially loaded prisms.

(4) The capacity of short and slender concrete masonry walls can be predicted with reasonable accuracy 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 includes additional design variables not presently considered 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 i acknowledged.

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

James W. Raines was the Laboratory Technicia in charge of instrumentation.

Frank A. Rankin and Jessie C. Hairston, Labore tory 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.

John E. Breen, Professor of Civil Engineering at the University of Texas, critically reviewed the report and participated in the analysis of test results

10. References

[1] National Building Code of Canada, Ottawa, Canada (195 [2] National Concrete Masonry Association, Specification fi the Design and Construction of Load-Bearing Concre Masonry, Arlington, Virginia (1968).

[3] Sampling and Testing Concrete Masonry Units. AS C140-65T (1965).

[4] Mortar for Unit Masonry, ASTM C270-68 (1968). [5] Mortar and Grout for Reinforced Masonry, ASTM C4766 (1963).

[6] Dickey, W. L., Reinforced Brick Masonry, Modern Masonr Conference, Washington, D.C., September 19-20. 19% Building Research Institute, National Academy Sciences-National Research Council, Publication **

(1956).

[7] Deformed Billet-Steel Bars for Concrete Reinforceme ASTM A615-68 (1968).

[8] Yokel, F. Y., Mathey, R. G., and Dikkers, R. D., Strength fl Masonry Walls under Compressive and Transverse Loads. National Bureau of Standards, Building Science Series 34 (in preparation).

[9] MacGregor, J. G., Breen, J. E., and Pfrang, E. O., Design Slender Concrete Columns, Journal of the Americ Concrete Institute, Vol. 67, No. 1, pp. 6-28 (1970). [10] Structural Clay Products Institute, Recommended Practice for Engineered Brick Masonry, McLean, Virginia (196

U.S. GOVERNMENT PRINTING OFFICE: 1970 0-404-45

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