Solved: The beam is constructed from three boards.

If the wide-flange beam is subjected to a shear of V = 20 kN, determine the shear stress on the web at A. Indicate the shear-stress components on a volume element located at this point.

If the wide-flange beam is subjected to a shear of V = 20 kN, determine the maximum shear stress in the beam.

If the wide-flange beam is subjected to a shear of V = 20 kN, determine the shear force resisted by the web of the beam.

If the beam is subjected to a shear of V = 30 kN, determine the web’s shear stress at A and B. Indicate the shear-stress components on a volume element located at these points. Set w = 200 mm. Show that the neutral axis is located at \(\bar{y}=0.2433 \mathrm{~m}\) from the bottom and \(I=0.5382\left(10^{-3}\right) \mathrm{m}^{4}\).

If the wide-flange beam is subjected to a shear of V = 30 kN, determine the maximum shear stress in the beam. Set w = 300 mm.

The wood beam has an allowable shear stress of \(\tau_{\text {allow }}=7 \mathrm{MPa}\). Determine the maximum shear force V that can be applied to the cross section.

The shaft is supported by a thrust bearing at A and a journal bearing at B. If P = 20 kN, determine the absolute maximum shear stress in the shaft.

The shaft is supported by a thrust bearing at A and a journal bearing at B. If the shaft is made from a material having an allowable shear stress of \(\tau_{\text {allow }}=75 \mathrm{MPa}\), determine the maximum value for P.

Determine the largest shear force V that the member can sustain if the allowable shear stress is \(\tau_{\text {allow }}=8 \mathrm{ksi}\).

If the applied shear force V = 18 kip, determine the maximum shear stress in the member.

The overhang beam is subjected to the uniform distributed load having an intensity of w = 50 kN/m. Determine the maximum shear stress in the beam.

The beam is made from a polymer and is subjected to a shear of V = 7 kip. Determine the maximum shear stress in the beam and plot the shear-stress distribution over the cross section. Report the values of the shear stress every 0.5 in. of beam depth.

Determine the maximum shear stress in the strut if it is subjected to a shear force of V = 20 kN.

Determine the maximum shear force V that the strut can support if the allowable shear stress for the material is \(\tau_{\text {allow }}=40 \mathrm{MPa}\).

Sketch the intensity of the shear-stress distribution acting over the beam’s cross-sectional area, and determine the resultant shear force acting on the segment AB. The shear force acting at the section is V = 35 kip. Show that \(I_{N A}=872.49 \mathrm{in}^{4}\).

Plot the shear-stress distribution over the cross section of a rod that has a radius c. By what factor is the maximum shear stress greater than the average shear stress acting over the cross section?

If the beam is subjected to a shear of V = 15 kN, determine the web’s shear stress at A and B. Indicate the shear-stress components on a volume element located at these points. Set w = 125 mm. Show that the neutral axis is located at \(\bar{y}=0.1747 \mathrm{~m}\) from the bottom and \(I_{N A}=0.2182\left(10^{-3}\right) \mathrm{m}^{4}\).

If the wide-flange beam is subjected to a shear of V = 30 kN, determine the maximum shear stress in the beam. Set w = 200 mm.

If the wide-flange beam is subjected to a shear of V = 30 kN, determine the shear force resisted by the web of the beam. Set w = 200 mm.

Determine the length of the cantilevered beam so that the maximum bending stress in the beam is equivalent to the maximum shear stress.

If the beam is made from wood having an allowable shear stress \(\tau_{\text {allow }}=400 \mathrm{psi}\), determine the maximum magnitude of P. Set d = 4 in.

Determine the largest intensity w of the distributed load that the member can support if the allowable shear stress is \(\tau_{\text {allow }}=800 \mathrm{psi}\). The supports at A and B are smooth.

If w = 800 lb/ft, determine the absolute maximum shear stress in the beam. The supports at A and B are smooth.

Determine the shear stress at point B on the web of the cantilevered strut at section a–a.

Determine the maximum shear stress acting at section a–a of the cantilevered strut.

Railroad ties must be designed to resist large shear loadings. If the tie is subjected to the 34-kip rail loadings and an assumed uniformly distributed ground reaction, determine the intensity w for equilibrium, and calculate the maximum shear stress in the tie at section a–a, which is located just to the left of the rail.

The beam is slit longitudinally along both sides. If it is subjected to a shear of V = 250 kN, compare the maximum shear stress in the beam before and after the cuts were made.

The beam is to be cut longitudinally along both sides as shown. If it is made from a material having an allowable shear stress of \(\tau_{\text {allow }}=75 \mathrm{MPa}\), determine the maximum allowable shear force V that can be applied before and after the cut is made.

The composite beam is constructed from wood and reinforced with a steel strap. Use the method of Sec. 6.6 and calculate the maximum shear stress in the beam when it is subjected to a shear of V = 50 kN. Take \(E_{\mathrm{st}}=200 \mathrm{GPa}\), \(E_{\mathrm{w}}=15 \mathrm{GPa}\).

The beam has a rectangular cross section and is subjected to a load P that is just large enough to develop a fully plastic moment \(M_{p}=P L\) at the fixed support. If the material is elastic perfectly plastic, then at a distance x < L the moment M = Px creates a region of plastic yielding with an associated elastic core having a height \(2^{\prime}\). This situation has been described by Eq. 6–30 and the moment M is distributed over the cross section as shown in Fig. 6–48e. Prove that the maximum shear stress in the beam is given by \(\tau_{\max }=\frac{3}{2}\left(P / A^{\prime}\right)\), where \(A^{\prime}=2 y^{\prime} b\), the cross-sectional area of the elastic core.

The beam in Fig. 6–48f is subjected to a fully plastic moment \(\mathbf{M}_{p}\). Prove that the longitudinal and transverse shear stresses in the beam are zero. Hint: Consider an element of the beam shown in Fig. 7–4d.

The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in. If each nail can support a 400-lb shear force, determine the maximum shear force V that can be applied to the beam.

The beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in. If a shear force of V = 900 lb is applied to the boards, determine the shear force resisted by each nail.

The beam is constructed from three boards. If it is subjected to a shear of V = 5 kip, determine the maximum allowable spacing s of the nails used to hold the top and bottom flanges to the web. Each nail can support a shear force of 500 lb.

The beam is constructed from three boards. Determine the maximum shear V that it can support if the allowable shear stress for the wood is \(\tau_{\text {allow }}=400 \mathrm{psi}\). What is the maximum allowable spacing s of the nails if each nail can resist a shear force of 400 lb?

The double T-beam is fabricated by welding the three plates together as shown. Determine the shear stress in the weld necessary to support a shear force of V = 80 kN.

The double T-beam is fabricated by welding the three plates together as shown. If the weld can resist a shear stress \(\tau_{\text {allow }}=90 \mathrm{MPa}\), determine the maximum shear V that can be applied to the beam.

The beam is constructed from three boards. Determine the maximum loads P that it can support if the allowable shear stress for the wood is \(\tau_{\text {allow }}=400 \mathrm{psi}\). What is the maximum allowable spacing s of the nails used to hold the top and bottom flanges to the web if each nail can resist a shear force of 400 lb?

A beam is constructed from three boards bolted together as shown. Determine the shear force in each bolt if the bolts are spaced s = 250 mm apart and the shear is V = 35 kN.

The simply supported beam is built up from three boards by nailing them together as shown. The wood has an allowable shear stress of \(\tau_{\text {allow }}=15 \mathrm{MPa}\), and an allowable bending stress of \(\sigma_{\text {allow }}=9 \mathrm{MPa}\). The nails are spaced at s = 75 mm, and each has a shear strength of 1.5 kN. Determine the maximum allowable force P that can be applied to the beam.

The simply supported beam is built up from three boards by nailing them together as shown. If P = 12 kN, determine the maximum allowable spacing s of the nails to support that load, if each nail can resist a shear force of 1.5 kN.

The T-beam is constructed as shown. If each nail can support a shear force of 950 lb, determine the maximum shear force V that the beam can support and the corresponding maximum nail spacing s to the nearest \(\frac{1}{8} \text { in }\). The allowable shear stress for the wood is \(\tau_{\text {allow }}=450 \mathrm{psi}\).

The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If each nail can resist a shear force of 50 lb, determine the largest force P that can be applied to the beam without causing failure of the nails.

The box beam is constructed from four boards that are fastened together using nails spaced along the beam every 2 in. If a force P = 2 kip is applied to the beam, determine the shear force resisted by each nail at A and B.

The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the distributed load has a maximum intensity of \(w_{0}=3 \mathrm{kip} / \mathrm{ft}\), determine the maximum shear stress resisted by the glue.

The member consists of two plastic channel strips 0.5 in. thick, glued together at A and B. If the glue can support an allowable shear stress of \(\tau_{\text {allow }}=600 \mathrm{psi}\), determine the maximum intensity \(w_{0}\) of the triangular distributed loading that can be applied to the member based on the strength of the glue.

The beam is made from four boards nailed together as shown. If the nails can each support a shear force of 100 lb., determine their required spacing \(s^{\prime}\) and s if the beam is subjected to a shear of V = 700 lb.

The beam is made from three polystyrene strips that are glued together as shown. If the glue has a shear strength of 80 kPa, determine the maximum load P that can be applied without causing the glue to lose its bond.

The timber T-beam is subjected to a load consisting of n concentrated forces, \(P_{n}\). If the allowable shear \(V_{\text {nail }}\) for each of the nails is known, write a computer program that will specify the nail spacing between each load. Show an application of the program using the values L = 15 ft, \(a_{1}=4 \mathrm{ft}, P_{1}=600 \mathrm{lb}, a_{2}=8 \mathrm{ft}, P_{2}=1500 \mathrm{lb}, b_{1}=1.5 \mathrm{in}\)., \(h_{1}=10 \text { in., } b_{2}=8 \text { in., } h_{2}=1 \text { in., and } V_{\text {nail }}=200 \mathrm{lb}\).

A shear force of V = 300 kN is applied to the box girder. Determine the shear flow at points A and B.

A shear force of V = 450 kN is applied to the box girder. Determine the shear flow at points C and D.

A shear force of V = 18 kN is applied to the box girder. Determine the shear flow at points A and B.

A shear force of V = 18 kN is applied to the box girder. Determine the shear flow at point C.

The aluminum strut is 10 mm thick and has the cross section shown. If it is subjected to a shear of V = 150 N, determine the shear flow at points A and B.

The aluminum strut is 10 mm thick and has the cross section shown. If it is subjected to a shear of V = 150 N, determine the maximum shear flow in the strut.

The beam is subjected to a shear force of V = 50 kip. Determine the shear flow at points A and B.

The beam is subjected to a shear force of V = 50 kip. Determine the maximum shear flow in the cross section.

The H-beam is subjected to a shear of V = 80 kN. Determine the shear flow at point A.

The H-beam is subjected to a shear of V = 80 kN. Sketch the shear-stress distribution acting along one of its side segments. Indicate all peak values.

The built-up beam is formed by welding together the thin plates of thickness 5 mm. Determine the location of the shear center O.

The assembly is subjected to a vertical shear of V = 7 kip. Determine the shear flow at points A and B and the maximum shear flow in the cross section.

The box girder is subjected to a shear of V = 15 kN. Determine the shear flow at point B and the maximum shear flow in the girder’s web AB.

Determine the location e of the shear center, point O, for the thin-walled member having a slit along its section.

Determine the location e of the shear center, point O, for the thin-walled member. The member segments have the same thickness t.

The beam supports a vertical shear of V = 7 kip. Determine the resultant force in segment AB of the beam.

The stiffened beam is constructed from plates having a thickness of 0.25 in. If it is subjected to a shear of V = 8 kip, determine the shear-flow distribution in segments AB and CD. What is the resultant shear supported by these segments? Also, sketch how the shear flow passes through the cross section. The vertical dimensions are measured to the centerline of each horizontal segment.

The pipe is subjected to a shear force of V = 8 kip. Determine the shear flow in the pipe at points A and B.

Determine the location e of the shear center, point O, for the thin-walled member. The member segments have the same thickness t.

A thin plate of thickness t is bent to form the beam having the cross section shown. Determine the location of the shear center O.

Determine the location e of the shear center, point O, for the tube having a slit along its length.