Problem $1.$

Given: A wooden beam is to span a distance of $12$ feet and carry a distributed load of $100l\frac{b}{f}t.$ Assume the end constraints on the beam serve to act as simply supported.

The beam is a nominal $210($actual dimensions $9\mathrm{.}25$ inches $1\mathrm{.}5$ inches, and is a select structural grade timber with an allowable extreme fiber bending stress of $1500$ psi $.$

Find: What is the Factor of Safety against bending failure under the prescribed load?

Steps:

Find the reactions for the beam

Draw the shear and bending moment diagram, and determine the maximum moment that must be resisted.

Determine the extreme fiber bending stress due to the maximum bending moment factual $=M\frac{c}{\text{I}}$

Determine the $F{S}_{\text{b}\text{e}\text{n}\text{d}\text{i}\text{n}\text{g}}=\frac{f_{\text{a}\text{l}\text{l}\text{o}\text{w}\text{a}\text{b}\text{l}\text{e}}}{f_{\text{a}\text{c}\text{t}\text{u}\text{a}\text{l}}}$