91Ó°ÊÓ

The spreader beam \(A B\) is used to slowly lift the 3000 -lb pipe that is centrally located on the straps at \(C\) and \(D .\) If the beam is a \(\mathrm{W} 12 \times 45,\) determine if it can safely support the load. The allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=12 \mathrm{ksi}.\)

The simply supported beam is made of timber that has an allowable bending stress of \(\sigma_{\text {allow }}=1.20 \mathrm{ksi}\) and an allowable shear stress of \(\tau_{\text {allow }}=100\) psi. Determine its smallest dimensions to the nearest \(\frac{1}{8}\) in. if it is rectangular and has a height-to- width ratio of 1.5.

The joists of a floor in a warehouse are to be selected using square timber beams made of oak. If each beam is to be designed to carry \(90 \mathrm{lb} / \mathrm{ft}\) over a simply supported span of \(25 \mathrm{ft},\) determine the dimension \(a\) of its square cross section to the nearest \(\frac{1}{4}\) in. The allowable bending stress is \(\sigma_{\text {allow }}=4.5 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=125\) psi.

The beam is made from a plate that has a constant thickness \(b\). If it is simply supported and carries a uniform load \(w,\) determine the variation of its depth as a function of \(x\) so that it maintains a constant maximum bending stress \(\sigma_{\text {allow }}\) throughout its length.

Determine the variation in the depth \(d\) of a cantilevered beam that supports a concentrated force \(\mathbf{P}\) at its end so that it has a constant maximum bending stress \(\sigma_{\text {allow }}\) throughout its length. The beam has a constant width \(b_{0}.\)