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.