steel I-beam

[logistic_guy]

A very long \(\displaystyle \text{S}127 \times 15\) steel I-beam, \(\displaystyle 0.127\)-\(\displaystyle \text{m}\) deep, resting on a foundation for which \(\displaystyle k = 1.4 \ \text{MPa}\), is subjected to a concentrated load at midlength. The flange is \(\displaystyle 0.0762\)-\(\displaystyle \text{m}\) wide, and the cross-sectional moment of inertia is \(\displaystyle 5.04 \times 10^{-6} \ \text{m}^4\). What is the maximum load that can be applied to the beam without causing the elastic limit to be exceeded? Assume that \(\displaystyle E = 200 \ \text{GPa}\) and \(\displaystyle \sigma_{yp} = 210 \ \text{MPa}\).

 

[logistic_guy]

To warm up the audience, we write the relation between moment and load.

\(\displaystyle M = -\frac{P}{4\beta}f_3(\beta_x)\)