The shaft is supported by journal bearings at A and B that

The beam is made of timber that has an allowable bending stress of \(\sigma_{\text {allow }}=6.5 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=500 \mathrm{kPa}\). Determine its dimensions if it is to be rectangular and have a height-to-width ratio of 1.25. Assume the beam rests on smooth supports.

Determine the minimum width of the beam to the nearest \(\frac{1}{4} \text { in }\). that will safely support the loading of P = 8 kip. The allowable bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=15 \mathrm{ksi}\).

Solve Prob. 11–2 if P = 10 kip. Determine the minimum width of the beam to the nearest \(\frac{1}{4} \text { in }\). that will safely support the loading of P = 8 kip. The allowable bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=15 \mathrm{ksi}\).

The brick wall exerts a uniform distributed load of 1.20 kip/ft on the beam. If the allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=12 \mathrm{ksi}\), select the lightest wide-flange section with the shortest depth from Appendix B that will safely support the load. If there are several choices of equal weight, choose the one with the shortest height.

Select the lightest-weight wide-flange beam from Appendix B that will safely support the machine loading shown. The allowable bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=14 \mathrm{ksi}\).

The spreader beam AB 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 W12 X 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 \(\tau_{\text {allow }}=12 \mathrm{ksi}\).

Select the lightest-weight wide-flange beam with the shortest depth from Appendix B that will safely support the loading shown. The allowable bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress of \(\tau_{\text {allow }}=14 \mathrm{ksi}\).

Select the lightest-weight wide-flange beam from Appendix B that will safely support the loading shown. The allowable bending stress \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress of \(\tau_{\text {allow }}=14 \mathrm{ksi}\).

Select the lightest W360 wide-flange beam from Appendix B that can safely support the loading. The beam has an allowable normal stress of \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=80 \mathrm{MPa}\). Assume there is a pin at A and a roller support at B.

Investigate if the W250 X 58 beam can safely support the loading. The beam has an allowable normal stress of \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=80 \mathrm{MPa}\). Assume there is a pin at A and a roller support at B.

The beam is constructed from two boards. If each nail can support a shear force of 200 lb, determine the maximum spacing of the nails, \(s, s^{\prime}, \text { and } s^{\prime \prime}\), to the nearest \(\frac{1}{8}\) inch for regions AB, BC, and CD, respectively.

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 lb/ft over a simply supported span of 25 ft, determine the dimension a of its square cross section to the nearest \(\frac{1}{4} \text { in }\). The allowable bending stress is \(\sigma_{\text {allow }}=4.5 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=125 \mathrm{psi}\).

The timber beam has a width of 6 in. Determine its height h so that it simultaneously reaches its allowable bending stress \(\sigma_{\text {allow }}=1.50 \mathrm{ksi}\) and an allowable shear stress of \(\tau_{\text {allow }}=50 \mathrm{psi}\). Also, what is the maximum load P that the beam can then support?

The beam is constructed from four boards. If each nail can support a shear force of 300 lb, determine the maximum spacing of the nails, \(s, s^{\prime} \text { and } s^{\prime \prime}\), for regions AB, BC, and CD, respectively.

The beam is constructed from two boards. If each nail can support a shear force of 200 lb, determine the maximum spacing of the nails, \(s, s^{\prime} \text { and } s^{\prime \prime}\), to the nearest \(\frac{1}{8} \text { in }\). for regions AB, BC, and CD, respectively.

If the cable is subjected to a maximum force of P = 50 kN, select the lightest W310 wide-flange beam that can safely support the load. The beam has an allowable normal stress of \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=85 \mathrm{MPa}\).

If the W360 X 45 wide-flange beam has an allowable normal stress of \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=85 \mathrm{MPa}\), determine the maximum cable force P that can safely be supported by the beam.

If P = 800 lb, determine the minimum dimension a of the beam’s cross section to the nearest \(\frac{1}{8} \text { in }\). to safely support the load. The wood has an allowable normal stress of \(\sigma_{\text {allow }}=1.5 \mathrm{ksi}\) and an allowable shear stress of \(\tau_{\text {allow }}=150 \mathrm{ksi}\).

If a = 3 in. and the wood has an allowable normal stress of \(\sigma_{\text {allow }}=1.5 \mathrm{ksi}\), and an allowable shear stress of \(\tau_{\text {allow }}=150 \mathrm{psi}\), determine the maximum allowable value of P that can act on the beam.

The beam is constructed from three plastic strips. If the glue can support a shear stress of \(\tau_{\text {allow }}=8 \mathrm{kPa}\), determine the largest magnitude of the loads P that the beam can support.

If the allowable bending stress is \(\sigma_{\text {allow }}=6 \mathrm{MPa}\), and the glue can support a shear stress of \(\tau_{\text {allow }}=8 \mathrm{kPa}\), determine the largest magnitude of the loads P that can be applied to the beam.

The beam is made of Douglas fir having an allowable bending stress of \(\sigma_{\text {allow }}=1.1 \mathrm{ksi}\) and an allowable shear stress of \(\tau_{\text {allow }}=0.70 \mathrm{ksi}\). Determine the width b if the height h = 2b.

Select the lightest-weight wide-flange beam from Appendix B that will safely support the loading. The allowable bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=14 \mathrm{ksi}\).

Draw the shear and moment diagrams for the shaft, and determine its required diameter to the nearest \(\frac{1}{8} \text { in }\). if \(\sigma_{\text {allow }}=30 \mathrm{ksi}\) and \tau_{\text {allow }}=15 \mathrm{ksi}. The journal bearings at A and C exert only vertical reactions on the shaft. Take P = 6 kip.

Draw the shear and moment diagrams for the shaft, and determine its required diameter to the nearest \(\frac{1}{4} \text { in }\). if \(\sigma_{\text {allow }}=30 \mathrm{ksi}\) and \tau_{\text {allow }}=15 \mathrm{ksi}. The journal bearings at A and C exert only vertical reactions on the shaft. Take P = 12 kip.

Select the lightest-weight wide-flange beam from Appendix B that will safely support the loading. The allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=12 \mathrm{ksi}\).

Draw the shear and moment diagrams for the W14 X 22 wide-flange beam and check if the beam will safely support the loading. The allowable bending stress is \(\sigma_{\text {allow }}=30 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=15 \mathrm{ksi}\).

Select the lightest-weight W16 wide-flange beam from Appendix B that will safely support the loading. The allowable bending stress is \(\sigma_{\text {allow }}=30 \mathrm{ksi}\) and the allowable shear stress \(\tau_{\text {allow }}=15 \mathrm{ksi}\).

The beam is to be used to support the machine, which exerts the forces of 6 kip and 8 kip. If the maximum bending stress is not to exceed \(\sigma_{\text {allow }}=22 \mathrm{ksi}\), the required width b of the flanges.

The steel beam has an allowable bending stress \(\sigma_{\text {allow }}=140 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=90 \mathrm{MPa}\). Determine the maximum load that can safely be supported.

Determine the variation in the width w as a function of x for the cantilevered beam that supports a concentrated force P at its end so that it has a maximum bending stress \(\sigma_{\text {allow }}\) throughout its length. The beam has a constant thickness t.

The tapered beam supports a uniform distributed load w. If it is made from a plate and has a constant width b, determine the absolute maximum bending stress in the beam.

The tapered beam supports the concentrated force P at its center. Determine the absolute maximum bending stress in the beam. The reactions at the supports are vertical.

The beam is made from a plate that has a constant thickness b. If it is simply supported and carries the distributed loading shown, determine the variation of its depth h 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 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 \(b_{0}\).

Determine the variation of the radius r of the cantilevered beam that supports the uniform distributed load so that it has a constant maximum bending stress \(\sigma_{\text {max}}\) throughout its length.

The tapered beam supports a uniform distributed load w. If it is made from a plate that has a constant width \(b_{0}\), determine the absolute maximum bending stress in the beam.

Determine the variation in the width b as a function of x for the cantilevered beam that supports a uniform distributed load along its centerline so that it has the same maximum bending stress \(\sigma_{\text {allow }}\) throughout its length. The beam has a constant depth t.

The tubular shaft has an inner diameter of 15 mm. Determine to the nearest millimeter its minimum outer diameter if it is subjected to the gear loading. The bearings at A and B exert force components only in the y and z directions on the shaft. Use an allowable shear stress of \(\sigma_{\text {allow }}=70 \mathrm{MPa}\), and base the design on the maximum shear stress theory of failure.

Determine to the nearest millimeter the minimum diameter of the solid shaft if it is subjected to the gear loading. The bearings at A and B exert force components only in the y and z directions on the shaft. Base the design on the maximum distortion energy theory of failure with \(\sigma_{\text {allow }}=150 \mathrm{MPa}\).

The 50-mm-diameter shaft is supported by journal bearings at A and B. If the pulleys C and D are subjected to the loadings shown, determine the absolute maximum bending stress in the shaft.

The pulleys fixed to the shaft are loaded as shown. If the journal bearings at A and B exert only horizontal and vertical forces on the shaft, determine the required diameter of the shaft to the nearest \(\frac{1}{8} \text { in }\). using the maximum shear stress theory of failure, \(\tau_{\text {allow }}=12 \mathrm{ksi}\).

The pulleys fixed to the shaft are loaded as shown. If the journal bearings at A and B exert only horizontal and vertical forces on the shaft, determine the required diameter of the shaft to the nearest \(\frac{1}{8} \text { in }\). Use the maximum distortion energy theory of failure, \(\tau_{\text {allow }}=12 \mathrm{ksi}\).

The two pulleys fixed to the shaft are loaded as shown. If the journal bearings at A and B exert only vertical forces on the shaft, determine the required diameter of the shaft to the nearest \(\frac{1}{8} \text { in }\). using the maximum distortion energy theory. \(\tau_{\text {allow }}=67 \mathrm{ksi}\).

The shaft is supported by journal bearings at A and B that exert force components only in the x and z directions. If the allowable normal stress for the shaft is \(\sigma_{\text {allow }}=15 \mathrm{ksi}\), determine the smallest diameter of the shaft to the nearest \(\frac{1}{8} \text { in }\). Use the maximum distortion energy theory of failure.

The shaft is supported by journal bearings at A and B that exert force components only in the x and z directions. Determine the smallest diameter of the shaft to the nearest \(\frac{1}{8} \text { in }\). Use the maximum shear stress theory of failure with \(\tau_{\text {allow }}=6 \mathrm{ksi}\).