Masonry Magazine October 1975 Page. 12
DETERMINATION OF MODULUS OF ELASTICITY, Em
In many instances, it is desirable or necessary to know the modulus of elasticity, Em, of the masonry being used. The modulus of elasticity of the masonry can be determined by instrumentation of the specimens to be tested for the determination of ultimate compressive strength. General practice for obtaining the strain of masonry in compression requires the installation of strain gages on compressive prisms. These strain gages, having equal gage lengths, are installed on each end of the prism along the neutral axis of the section (see Fig. 4). It is necessary in the case of multiple wythe wall constructions and/or multiple wythes of dissimilar materials to determine the neutral axis prior to loading as the load should also be applied at the neutral axis. The gage lengths should be as long as practicable. Dial strain gages during test should be read at predetermined load levels up to approximately 75 to 80 percent of the anticipated ultimate load and then removed to prevent damage to the gages at specimen failure. The strain in the masonry is determined by averaging the strain gage readings and dividing by the gage lengths as given by the formula:
y = (AV₁ + AV₂) / 2g
where:
Y = strain, average over entire section, in./in. (cm/cm)
AV₁ = dial reading gage No. 1, in. (cm)
AV₂ = dial reading gage No. 2, in. (cm)
g = vertical gage length, in. (cm)
Once the strains at the various load levels, determined by formula (5) are obtained and stresses are calculated, a stress-strain curve for the specimen should be plotted (see Fig. 5). There are several methods of determining the modulus of elasticity from the stress-strain curve. The most common for masonry are the initial tangent modulus and secant modulus methods. The modulus of elasticity is the slope of the tangent or the secant of the curve. The secant modulus is most commonly used for masonry and is easier to determine. The two points selected on the stress-strain curve are generally at 0 psi (kgf/cm²) and 250 psi (17.57 kgf/cm²) stress levels and the modulus is calculated as follows:
Em = (fmo + fm250) / (Yo + Y250) = (0 + 250) / (Yo + 7250)
where:
Em = secant modulus of elasticity, psi (kgf/cm²)
fo = 0 psi (kgf/cm²) stress
fm250 = 250 psi (17.57 kgf/cm²) stress
Yo = strain at 0 psi stress, in./in. (cm/cm)
¥250 = strain at 250 psi stress, in./in. (cm/cm)
In addition to the determination of the modulus of elasticity by actual tests, the modulus may be based upon f'm of the compressive prism tests stated as a function of f'm. (See Tables 3 and 4 of the design standard.)
DETERMINATION OF f'v AND E, (v AND G)
There are two methods of test provided in ASTM standards for the determination of the shear strength of