Calculating Required Section Modulus of a Simply Supported Beam

What is the required section modulus of a simply supported beam supporting a point load at its center?

Understanding the Calculation Process

A simply supported beam supports a point load of 12 kips acting at the center of its span, with an allowable bending stress of 33 ksi, and a span of 20 ft. The required section modulus can be calculated using the formula.

Formula for Section Modulus:

Z = I / y

Formula for Maximum Bending Moment:

M = PL / 4

Formula for Bending Stress:

σ = Mc / I

By substituting the given values and following the calculations, the required section modulus is determined to be approximately equal to 3.64 in³.