Foundation, Concrete and Earthquake Engineering

### STUDY ON STRENGTH OF CONCRETE USING VARIOUS COARSE AGGREGATES, PART-7

In which σ = stress in the fiber farthest from the neutral axis, psi

M = bending moment at the section, lb-in.

I = moment of inertia of the cross section, in.

c = distance from neutral axis to farthest fiber, in.

Since the assumptions on which the flexure formula are based do not hold true at high stresses approaching failure, modulus of rupture is a fictitious value; however, it is convenient for purposes of evaluation and is commonly used. The modulus of rupture ranges from 11 to 23 percent of the compressive strength. The use of rough-textured or angular aggregates results in relatively high flexural strength as compared to compressive strength.

An approximate relationship between flexural and compressive strength is
f¢c X (R/K)2

in which  f¢c = compressive strength, psi

R = modulus of rupture, psi

K = a constant, usually between 8 and 10

3.4 Shear strength

The following formula is adopted for the shear strength of concrete–

SS = VQ/(Ib)  In which,

SS = Strength in psi

V = Vertical shear obtained from SFD. Shear strength Calculation for Beam Section
Q = Static moment about the neutral axis of the shaded area   I = Moment of inertia.

b = Width of the beam.