894

COMPRESSlVE STRESS DISTRIBUTION OF GROUTED HOLLOW BRICK MASONRY

JEFFREY M. YOUNG Structural Engineer

CH2M HILL 7201 NW 11th PL

Gainesville, FL 32607, USA

and

ABSTRACT

RUSSELL H. BROWN Professor and Head

Civil Engineering Department Clemson University

Clemson, SC 29634-0911, USA

Presently masonry design codes in the United States are based on the principIe of working stress designo To date little research has been done in the area of uI timate strength design of masonry. An experimental project was performed to determine the compressive stress distribution of grouted hollow clay masonry under strain gradient.

A total of thirty tests was performed on grouted hollow clay masonry prisms. The experimental variables of the project included unit width, unit strength and neutral axis location. Fifteen prisms were subjected to in-plane loading under strain gradient, and fifteen prisms were subjected to concentric loading for determination of standard prism compressive strength, fIm' Servo controlled actuators imposed the neutral axis at a location controlled by a displacement transducer, and load was gradually increased to failure. A data acquisition board and computer automatically recorded data from load cells, displacement transducers, and apressure transducer . Using the recorded test data and basic equations of mechanics, the properties of the Whitney stress block, which is popularly used in ultimate strength design of reinforced concrete, were determined for grouted hollow clay masonry.

NOTATION AND DEFINITIONS

a Depth of equivalent rectangular stress block b Thickness of member (3.5, 5.5 or 7.5 in.) C Resultant compressive force c = Distance from neutral axis to extreme compressive fiber eA Eccentricity of in-plane hydraulic jack load f- = Extreme fiber flexural stress

c f'c = Axial compressive strength of concrete fIm = Axial compressive strength of masonry fo = Average stress on are a in compressio~

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k1k3 = Ratio of average stress on area in compression to axial prism strength

kl Ratio of average stress on area in compression to extreme fiber flexural stress

k2 Ratio of distance from extreme compressive fiber to resultant compressive force to distance from extreme compressive fiber to neutra I axis

k3 = Ratio of extreme fiber flexural stress to axial prism strength  = Offset of the prism away from center of testing machine PI = Compression machine load PA = Hydraulic jack load Maxim~~ stress = Largest value of stress Ultimate stress = Value of stress at ultimate strain Peak strain = Value of strain at maximum stress Ultimate strain = Value of strain selected to be the maximum amount of

allowable strain

INTRODUCTION

Until the start of this decade, little research had been done in the USA to develop ultimate strength design of masonry. Although concrete design has been performed mainly by the principIe of ultimate strength design for several years, masonry design has been performed by the principIe of working stress designo In order to develop a design procedure for masonry based on ultimate strength design, certa in properties of the masonry must be known. The properties, k1k3 and k2 are the same properties that are used in the well-known Whitney stress block, developed by C.S. Whitney in 1942 [1], that serves as the foundation of ultimate strength design of concrete.

Thirty tests were performed on grouted brick prisms which varied in thickness and brick strength. Half of the prisms were loaded simultaneously with a compression load and an eccentric load by means of a closed-Ioop servo controlled system. The eccentric load was applied in order to produce in-plane bending on these running bond prisms. The remaining fifteen tests involved concentric compression loading on stack bond prism. The displacements used to determine strain and to control the loading apparatus were measured by displacement transducers. AlI loads and displacements were automatically recorded onto computer diskettes by means of a personal computer and a data acquisition board which monitored the electronic signals of the loading apparatus and the displacement transducers. The recorded loads and displacements were used to calculate the values of klk3' k2 and strain.

TEST PROGRAM

MateriaIs Three different sizes and strengths of brick were used in testing. The only dimension that varied was the wall thickness. The actual unit height and length were 3.5 in. and 15.625 in. respectively, while the thickness dirnensions were 3.5 in., 5 . 5 in., and 7.5 in. A cross section of a typical brick is shown in the top of Fig. 1. Type "s" rnortar rnixed in accordance with the proportion method of ASTM C270-82, Specification for Mortar for Unit Masonry [2] was used in the construction of alI specimens and was mixed on site. Grout which met the ASTM Standard Specification for Grout for Masonry (ASTM C476-83) [3] was obtained from a local concrete batch planto Sika Grout Aid® (Type 2), manufactured by the Sika

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Corporation, was added in liquid form to improve workability and reduce shrinkage.

Test Specimens The prisms for in-plane testing, which involved bending and compression loads, were constructed of brick laid in running bond with faceshell bedding. The prisms constructed for twenty eight day compressive strength testing, which involved compression loads, were constructed of brick laid in stack bond. The approximate dimensions of each prism varied according to the brick thickness. AlI prisms were approximately 22. 875 inches high (6 courses), 15.625 inches wide (one unit or two half units) and 3.5, 5 . 5 or 7.5 inches thick.

Each prism was allowed to cure for a mlnlmum of two days before grout was added. The grout was added to the two side cells, or the left and right hollow cells, of the prism. After being grouted the prisms were allowed to cure for a minimum of twenty eight days before being tested. After approximately one week the prisms were capped with the gypsum capping compound, Hydrostone®.

Neutral Axis Location The neutral axis, as shown in Figure 1, coincided with the short edge of the prisms opposite the compression face for alI in-plane tests . This location of the neutral axis occurred whe n ~ = t.

NEUTRAL .-.xIS RXTRBMB CatPRBSSION

7 FACE

D~D'/

STRAIN VARIATION

Figure 1. Neutral Axis Location and Strain Variation for In-plane Testing

Loading Apparatus A 600,000 pound universal compression machine manufactured by Forney Incorporated was the centerpiece of the testing equipment. The Forney machine was modified to enable the application of eccentric as well as concentric loads. For in-plane testing a 50 kip jack applied the eccentric load while a 20 kip jack kept 1ltlhe upper platen leveI in the

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out-of-plane direction. The neutral axis was maintained at the desired location by requiring zero displacement of a displacement transducer mounted directly to the prism. A schematic of the in-plane loading system is shown in Figure 2. The offset of the prism ~, was necessary to ensure that the capacity of the in-plane jack was not exceeded during the performance of a testo

Ne utral­Axis­Controlling Transduccr

Tqmsducer Extent ion Rod

Compression Load. P 1

r- k2ê

c ::E klk) fIm bc

~I

Actuator Load, P A

Figure 2. Schematic of Loading Apparatus In-plane Testing

A 50 kip load cell was used to monitor the load applied by the in-plane jack while a 20 kip load cell was used to monitor the load applied by the out-of-plane jack. The amount of load which needed to be applied by the jacks in order to maintain the desired location of the neutral axis was determined by a closed-Ioop control system. The control system automatically increased or decreased the amount of jack load for the duration of a test based on the signal of the transducer controlling the neutral axis. The amount of load being applied by the jacks and the displacements were automatically recorded by a data acquisition system.

Control System A closed-Ioop control system was used to achieve the previously described loading conditions. A servo controller was used to monitor the output of three linear variable differential transformers (LVDTs), or displacement transducers. The servo controller responded to the electrical output of the LVDTs and either increased or decreased the amount of fluid pressure available to the hydraulic jacks which in turn increased or decreased the amount of load being applied to the prism.

Two LVDTs controlled the out-of-plane jacks which prevented the upper platen from bending in the out-of-plane direction. A third LVDT was mounted directly on the prism at the desired location of the neutral axis.

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Two more LVDTs were mounted at the compression face to measure displacement and thereby calculate extreme fiber strain.

TEST RESULTS AND DATA ANALYSrS

Derivation of klk3 loading conditions formula for klk3 is

and k2 : and issued derived by C -Pl - Pa Pl + Pa

Figure 2 depicts a prism under in-plane in the derivation of klk3 and k2' The

summing forces in the vertical direction: l:Fy = O

, C klk3fmb~ P1 + P

a;

therefore, klk3 (P1 + Pa)

The formula for k2 is deriv~d l:Mp = O = C (0.5c

1

If b~. m by summing

6. - ki) 0.5~ - 6. - k ~ = P e I C'

2 a a '

moments about Pl: P e

a a

therefore, k 2 0.5 - 6./~ - P e IC~ a a

Properties of the Compressive Stress Block

(1)

(2)

Values of klk3: The shape of the regression curves of klk3 versus extreme fiber strain in Figure 3 is similar to those of earlier researchers. A study of the mean value of klk3 at maximum load in Table 1 for the various prism types reveals a pattern: prisms with higher axial strengths have lower values of klk3 than prisms with lower axial strength, which agrees with Matthys' findings. This pattern is true for a11 cases except the case of the 4 in. medium strength prisms .

A comparison of the 4 in., 6 in., and 8 in. thick medium strength prisms at maximum stress indicates that prism width is not a major factor in the value of klk3' The 4 in. prisms have the lowest value of k1k3, but the 6 in. and 8 in. prisms have practically the same value of klk3 '

Values of klk3 and k2 at different extreme fiber strain leveIs are given in Tables 2 and 3, respectively. Based on the information in Tables 1, 2 and 3, a strain of 0.0030 could safely be chosen as ultimate strain for alI of the prism classes except the 4 in. prisms . With extreme fiber strain equal to 0.0030, the mean value of k1k3 is 0.7421 with a coefficient of variation of 8.7%.

A strain of 0.0025 could safely be chosen as ultimate strain for the 4 in. wide prisms. lf 0.0025 is taken as ultimate strain for the 4 in. prisms, the value of klk3 is 0.5531 with a coefficient of variation of 7.4%. rf 0.0025 is taken as ultimate strain for alI 5 prism classes, the overall value of klk3 is 0.6443 with a coefficient of variation of 11.9% .

Values of k2: The regression plot of k2 versus extreme fiber strain shown in Figure 3 has the same general shape as plots of k2 produced by earlier researchers such as Matthys. Matthys found that the greater the brick strength the greater the value of k2, but this research found just the opposite. A comparison of the mean values of k2 at maximum load for the 6 in. wide prisms listed in Table 1 indicates that k2 decreases with an increase in brick strength. AIso, a comparison of the mean values of k2 at various leveIs of strain in Table 3 gives the same results - the

•

Figure 3.

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1.0

o o

o

o

0 .6 o ~ C

DO w ~kJ D

O

D D O

D O O

O D

c B

0.2 O O

0 .0 'r-~~~T"'""'"~~...,,~~~-.,-~~~.,-r~~~T'"""'~~-rrr

0.000 0.001 0.002 0.003 0,004 0.005 0.006

EXTREME FIBER STRAIN (IN/IN)

k1k3 and k2 Versus Extreme Fiber Strain for 6 in Medium Strength Prisms and In-plane Testing

higher the brick strength the lower the value of k2. similar pattern. Hognestad found that the value decreased with an increase in f'c .

Concrete exhibits a of k2 for concrete

As with the values of k1k3' a review of the data in Tables 1, 2, and 3 gives strong support to selecting an ultimate strain of 0.0030 -for a11 prism classes except the 4 in . wide prisms. Four of the five prism classes have strain values which meet or exceed 0.0030. The values of k2 for those prism types with an ultimate value of strain of 0.0030 is 0.3721 with a coefficient of variation of 4.1%. A value of ultimate strain of 0.0025 could be used for the 4 in. prisms and would give a mean value of k2 of 0.3890 with a coefficient of variation of 8 . 3%. If a strain value of 0.0025 is selected for every class of prisms, the value of k2 is 0 . 3732 with a coefficient of variation of 5.0% .

Equivalent Rectangular Stress Block As Whitney and others have done for concrete, an equivalent stress block can be developed for masonry using the calculated valu~s of k1k3 and k2. The depth of the equivalent stress block, a, equals 2k2c and the stress

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value of the equiva~ent stress block equals fc. The depth of the stress block must equal 2k2c in order for the centroid of the stess block to coincide with the centroid of the nonuniform stress distribution as required. With a stress block depth of 2k2~,_the resultant compressive force, C, is located at a depth of a/2, or k2c, of the equivalent stress block which coincides with the location of C for the nonuniform stress distribution. The value of f- is determined by setting C for the nonuniform stress distributÚm equal to C for the rectangular stress distribution as follows:

C parabolic klk3f'mb~

k1k3f'mb~

k1k3f 'm

C rectangular, f-ab

c '

f~2k2~b,

f~2k2'

TABLE 1 VALUES OF k1k3' k2' AND EXTREME FIBER STRAIN AT MAXIMUM STRESS FOR

IN-PLANE TESTING

Prisrn Width, Strength and Replication

4 in Mediurn 1 2 3

Mean CV%

6 in Low 1 2 3

Mean CV%

6 in Medium 1 2 3

Mean CV%

6 in High 1 2 3

Mean CV%

8 in Mediurn 1 2 3

Mean CV%

Extreme Fiber Flexural Stress

fc (ksi)

2.226 2.123 2.325 2.325

11.5

2.925 3.358 3.311 3.198 7.4

2.739 3.443 3.902 3.361

17.4

3.583 3.325 3.490 3.466 3.8

3.591 3.279 4.358 3.743

14.8

*Denotes instrumentation problern.

Mean f rn

(ksi)

3.87 3.87 3.87

3.63 3.63 3.63

3.96 3.96 3.96

4.52 4.52 4.52

4.37 4.37 4.37

k1k3

0.5275 0.6037 0.6494 0.5935

10.4

0.7662 0.8721 0.8592 0.8325 6.9

0.7225 0.8160 0.9380 0.8255

13.1

0.7928 0.7772 0.7336 0.7679 4.0

0.7941 0.7469 0 . 9193 0.8201

10.9

k2

0.3618 0.4004 0.4327 0.3983 8.9

0.4155 0.4038 0.4166 0.4120 1.7

0.3798 0.4149 0.3934 0.3960 4.5

0.4166 0.3796 0.3640 0.3867 7.0

0.4227 0.4204 0.3763 0.4065 6.4

Peak Extreme Fiber Strain

0.0027 0.0029 0.0029 0.0028 4.1

0.0050 0.0043 0.0044 0.0046 8.2

0.0028 0.0037 0.0037 0.0034

15.3

0.0033 0.0038 0.0034 0.0035 7.6

0.0034 0.0024* 0.0033 0.0034 2.1

Value not included in calculations . •

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TABLE 2 VALUES DF k1k3 AT VARIOUS STRAIN LEVELS FOR IN-PLANE TESTING

Prism Width, Strain (inLin) Strength and Replica tions 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040

4 in Medium 1 0.2809 0.3730 0.4557 0.5071 2 0.2628 0.3504 0.4894 0.5675 3 0.3485 0.4552 0.5252 0.5847

Mean 0.2974 0.3929 0.4901 0.5531 CV% 15.2 14.0 7.1 7.4

6 in Low 1 0.2868 0.3909 0.4791 0.5645 0.6379 0.7090 0.7480 2 0.3566 0.4603 0.5556 0.6467 0.7219 0.7985 0.8618 3 0.2933 0.4005 0.5020 0.5931 0.6829 0.7537 0.8289

Mean 0.3122 0.4172 0.5122 0.6014 0.6809 0.7532 0.8116 CV% 12.4 0.9 7.7 6.9 6.2 5.9 7.5

6 in Medium 1 0.3005 0.4485 0.5892 0.6834 2 0.3417 0.4643 0.5673 0.6491 0.7118 0.7817 3 0.4163 0.5395 0.6432 0.7385 0.8160 0.9084

Mean 0.3528 0.4841 0.5999 0.6903 0.7639 0.8451 CV% 16.6 10.0 6.5 6.5 9.6 10.6

6 in High 1 0.3559 0.4835 0.5777 0.7139 0.7637 2 0.2506 0.3787 0.4893 0 . 5801 0.6641 0.7305 3 0.2910 0.4026 0.5004 0.5904 0.6724

Mean 0.2992 0.4216 0.5225 0.6281 0.7001 CV% 17.8 13.0 9.2 11.9 7.9

8 in Medium 1 0.4140 0.5207 0.6135 0.6942 0.7607 2 0 . 4246 0.5388 0.6155 3 0.5061 0.6147 0.7123 0.8032 0.8859

Mean 0.4482 0.5581 0.6471 0.7487 0.8233 CV% 11.2 8.9 8.7 10.3 10.8

Mean 0.3420 0.4548 0.5544 0.6443 0.7421

CV% 18.6 14.7 12.0 11.9 8.7

f: = k1k3f m / 2k2 ·

The values of a and f- at ultimiate strain for each class of prisms are presented in Table 4 ãlong with the values of k1k3, k2 and fIm.

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TABLE 3 VALUES OF k2 AT VARIOUS STRAIN LEVELS FOR IN-PLANE TESTING

Prism Width, Strain {in[in} Strength and Replications 0.0010 0 . 0015 0 . 0020 0.0025 0.0030 0 . 0035 0 . 0040

4 in Medium 1 0.3925 0.3728 0.3611 0.3571 2 0.3645 0 . 4032 0.3891 0 . 3882 3 0.4347 0.4114 0.4029 0 . 4217

Mean 0.3972 0.3958 0.3844 0 . 3890 CV% 8.9 5.1 5 . 5 8 . 3

6 in Low 1 0.3789 0.3738 0.3718 0 . 3760 0.3822 0.3898 0.4297 2 0.4346 0.4113 0.3980 0 . 3904 0.3868 0.3861 0 . 3967 3 0.3866 0.3805 0 . 3753 0.3731 0.3744 0.3779 0 . 3882

Mean 0.4000 0.4885 0.3817 0.3798 0.3811 0.3846 0.4049 CV% 7.5 5.1 3 . 7 2 . 4 1.6 1.6 5.4

6 in Medium 1 0.3748 0.3455 0.3397 0 .3463 2 0.3459 0.3439 0.3458 0.3521 0.3578 0.3923 3 0.3999 0.3780 0 . 3702 0 . 3696 0 . 3726 0 . 3869

Mean 0.37 35 0.3558 0 . 3519 0.3560 0.3562 0.3896 CV% 7 . 2 5.4 4 . 6 3.4 2.9 1.0

6 in High 1 0.3888 0 . 3778 0.3715 0.3944 0.3949 2 0.2657 0 . 2902 0 . 3055 0.3174 0 . 3285 0 . 3529 3 0.3678 0.3533 0.3445 0 . 3406 0 . 3386

Mean 0.3408 0.3404 0.3405 0 . 3508 0 . 3540 CV% 19.3 13.3. 9.7 11. 3 10.1

8 in Medium 1 0 .4195 0 . 4010 0 . 3921 0.3890 0.3922 2 0.4449 0 . 4217 0.4107 3 0 . 4430 0.4166 0.4004 0.3895 0 . 3839

Mean 0.4358 0.4131 0.4011 0.3893 0.3881 CV% 3 . 2 2.6 2.3 0 . 0 1.5

Mean 0.3895 0 . 3787 0 .3 719 0.3732 0.3721

CV% 9.0 7.9 6 . 7 5.0 4 . 1

Load-Deformation Relationships Concentric Loading: Table 5 provides stress values of the different prism

types at various strain leveIs . The data in this table indicates that at any given leveI of strain, the higher the brick strength the greater the leveI of stress . This occurrence is expected since the more dense the material the greater the amount of loasi that is required to produce

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TABLE 4 EQUIVALENT RECTANGULAR STRESS BLOCK VALUES FOR IN-PLANE TESTING

Extreme prism Width Fiber k1k3 k2 2k2 f a f-m c and Strength Strain (psi) (in) (psi)

4 in Medium 0.0025 0.5531 0.3890 0.7780 3870 12.16 2752

6 in Low 0.0030 0.6809 0 . 3811 0.7622 3630 11. 91 3243

6 in Medium 0.0030 0.7639 0.3652 0.7304 3960 11. 41 4142

6 in High 0.0030 0.7701 0.3540 0.7080 4520 11. 06 4470

8 in Medium 0.0030 0.8233 0.3881 0.7762 4370 12.13 4635

deformation. A comparison of strain leveIs in materiaIs with different densities will reveal that the less dense the material the greater the amount of strain for any leveI of stress.

For prisms of the same strength but different in size, test results indicate that at maximum stress the greater the brick width the larger the amount of strain. Table 5 indicates that at any given leveI of strain, except one, the 8 in. prisms are subjected to the largest amount of stress, followed by the 4 in. prisms and then the 6 in. prisms.

In-Plane Loading: The mean values of strain at maximum stress in Table 1 indicate that, like the concentric testing, the higher the brick strength the lower the amount of strain. Df the 6 inch brick the low strength has the greater strain followed by the medium strength and finally the high strength brick.

A comparison of test data revealed that at maximum stress the strain values of prisms loaded in bending and compression are greater than the strain values of prisms loaded in compression only. These resul ts agree with the findings of Hognestad [4] and agree in part with the findings of Matthys [5]. Figure 5 is a graphical comparison of extreme fiber flexural stress and axial stress versus strain for prisms loaded in bending and compression and compression only.

SUMMARY ANO CONCLUSIONS

An experimental project was performed to determine the compressive stress distribution of grouted hollow clay masonry under strain gradient. Brick masonry prisms were tested concentrically with a compression machine, hydraulic jacks, and a closed-loop servo controller. Bending was applied in-plane. Based on the test data the properties of the compressive stress block, klk3 and k2' and load-deformation characteristics were determined.

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TABLE 5 STRESS VALUES (psi) AT VARIOUS STRAIN LEVELS FOR CONCENTRIC TESTING

Prism Width, Strain (inLin) Strength and Replication 0.0010 0.0015 0.0020 0 . 0025 0.0030

4 in Medium 1 2275 2933 2967 2 2320 3230 3 2610 3430 3925 4520

Mean 2402 3198 3446 4520 CV% 7.6 7 . 8 19 . 7

6 in Low 1 2325 2970 3490 3885 4105 2 1895 2550 3100 3005 3 1733 2460

Mean 1984 2660 3295 3445 CV% 15.4 10 . 2 8.4 18 . 1

6 in Medium 1 1895 2690 3933 2 2300 2880 3305 3520 3 2390 2950 3575

Mean 2195 2840 3604 3520 CV% 12.0 4 . 7 8.7

6 in High 1 2640 3780 4305 2 1800 2580 3905 4005 3410 3 2875 3780 4510 4875

Mean 2378 3380 4240 4440 3410 CV% 22.8 20.5 7.3 13.9

8 in Medium 1 2500 3200 3795 4275 4325 2 2840 3695 4320 3 2700 3520 4360

Mean 2680 3427 4158 CV% 6.4 7.3 7.6

The following conclusions and observations were drawn from the results obtained in this project:

1. An equivalent rectangular stress block for masonry can be developed. The shape of the stress block is such that the resultant

compressive force occurs at mid-depth and coincides with the location of the resultant force for the nonuniform stress distribution; also, its magnitude is equal to that of the nonuniform distribution.

2. Based on the test data, it can be stated that at maximum streSS

the strain of prisms in compression is less than the extreme fib~r strain of prisms in flexure; also, the stress of prisms ~n compression is greater than the extreme fiber stress of prisms ~n flexure .

41

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3. A strain of 0.0030 is recommended for use as ultimate strain of the 6 in. and 8 in. prisms. For an ultimate strain of 0.0030 the value of k1k3 and k2 for grouted hollow brick masonry under strain gradient is 0.7421 and 0.3721, respectively. A strain of 0 . 0025 is recommended for use as ultimate strain of the 4 in. prisms and has a value of k1k3 and k2 of 0.5531 and 0.3890, respective1y.

REFERENCES

1. Whitney, C. S . , "Plastic Theory of Reinforced Concrete Design, " Transitions, American Society of Civil Engineers, Vol. 107, 1942, pp. 251-326.

2. "Standard Specification for Mortar and Unit Masonry," American Society for Testing and MateriaIs, ASTM C270 - 82, Philadelphia, Pa.

3 . "Standard Specification for Grout for Masonry," American Society for Testing and MateriaIs, ASTM C476 - 83, Philadelphia, Pa.

4. Hognestad, E ., Hanson, N. W. , and McHenry, D., "Concrete Stress Distribution in Ultimate Strength Design," Journal of the American Concrete Institute, Vol. 27, No. 4, December 1955.

5. Matthys, J.H., and Chanprichar, B., "Ultimate Strength Flexural Theory for Reinforced Brick Masonry," Masonry: Research, Application, and Problems, ASTM STP 871, J.C . Grogran and J.T. Conway, eds., American Society for Testing and MateriaIs, Philadelphia, Pa., 1985, pp. 38-66.