The beam is constructed from four plates and is subjected

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 T-beam is subjected to a vertical shear of V = 12 kip, determine the maximum shear stress in the beam. Also, compute the shear-stress jump at the flange web junction AB. Sketch the variation of the shear-stress intensity over the entire cross section.

If the T-beam is subjected to a vertical shear of V = 12 kip, determine the vertical shear force resisted by the flange.

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

The shaft is supported by a smooth thrust bearing at A and a smooth 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 developed in the beam.

The beam has a rectangular cross section and is made of wood having an allowable shear stress of \(\tau_{\text {allow }}=200 \ \mathrm{psi}\). Determine the maximum shear force V that can be developed in the cross section of the beam. Also, plot the shear-stress variation over the cross section.

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 \(\tau_{\text {allow }}=40 \ \mathrm{MPa}\).

The strut is subjected to a vertical shear of V = 130 kN. Plot the intensity of the shear-stress distribution acting over the cross-sectional area, and compute the resultant shear force developed in the vertical segment AB.

The steel rod has a radius of 1.25 in. If it is subjected to a shear of V = 5 kip, determine the maximum shear stress.

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.

The steel rod is subjected to a shear of 30 kip. Determine the maximum shear stress in the rod.

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 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.

Determine the maximum shear stress in the T-beam at the critical section where the internal shear force is maximum.

Determine the maximum shear stress in the T-beam at section C. Show the result on a volume element at this point.

The beam has a square cross section and is made of wood having an allowable shear stress of \(\tau_{\text {allow }}=1.4 \ \mathrm{ksi}\). If it is subjected to a shear of V = 1.5 kip, determine the smallest dimension a of its sides.

The beam is slit longitudinally along both sides as shown. If it is subjected to an internal shear of V = 250 kN, compare the maximum shear stress developed 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 internal shear force V that can be applied before and after the cut is made.

Write a computer program that can be used to determine the maximum shear stress in the beam that has the cross section shown, and is subjected to a specified constant distributed load w and concentrated force P . Show an application of the program using the values L = 4 m, a = 2 m, P = 1.5 kN, \(d_{1}=0, \quad d_{2}=2 \mathrm{~m}\), w = 400 N/m, \(t_{1}=15 \mathrm{~mm}, t_{2}=20 \mathrm{~mm}\), b = 50 mm, and h = 150 mm.

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-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 \(2 y^{\prime}\). 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 developed 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. 6–48 f 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 as shown in Fig. 7–4c .

The beam is constructed from two boards fastened together at the top and bottom with two rows of nails spaced every 6 in. If each nail can support a 500-Ib shear force, determine the maximum shear force V that can be applied to beam.

The beam is construced from two boards fastened together at the top and bottom with two rows of nails spaced every 6 in. If an internal shear force of V = 600 lb is applied to the boards, determine the shear force resisted by each nail.

The boards are glued together to form the built-up beam. If the wood has an allowable shear stress of \(\tau_{\text {allow }}=3 \ \mathrm{MPa}\), and the glue seam at B can withstand a maximum shear stress of 1.5 MPa, determine the maximum allowable internal shear D that can be developed in the beam.

The boards are glued together to form the built-up beam. If the wood has an allowable shear stress of \(\tau_{\text {allow }}=3 \ \mathrm{MPa}\), and the glue seam at D can withstand a maximum shear stress of 1.5 MPa, determine the maximum allowable shear V that can be developed in the beam.

Three identical boards are bolted together to form the built-up beam. Each bolt has a shear strength of 1.5 kip and the bolts are spaced at a distance of s = 6 in. If the wood has an allowable shear stress of \(\tau_{\text {allow }}=450 \ \mathrm{psi}\), determine the maximum allowable internal shear V that can act on the beam.

Three identical boards are bolted together to form the built-up beam. If the wood has an allowable shear stress of \(\tau_{\text {allow }}=450 \text { psi }\), determine the maximum allowable internal shear V that can act on the beam. Also, find the corresponding average shear stress in the \(\frac{3}{8} \text { in }\). diameter bolts which are spaced equally at s = 6 in.

The beam is subjected to a shear of V = 2 kN. Determine the average shear stress developed in each nail if the nails are spaced 75 mm apart on each side of the beam. Each nail has a diameter of 4 mm.

A beam is constructed from three boards bolted together as shown. Determine the shear force developed in each bolt if the bolts are spaced s = 250 mm apart and the applied 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 \(\tau_{\text {allow }}=1.5 \ \mathrm{MPa}\), 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 the nails can each 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 made from four pieces of plastic that are glued together as shown. If the glue has an allowable strength of \(400 \ \mathrm{lb} / \mathrm{in}^{2}\), determine the maximum shear the beam will support.

The box beam is made from four pieces of plastic that are glued together as shown. If V = 2 kip, determine the shear stress resisted by the seam at each of the glued joints.

A beam is constructed from four boards which are nailed together. If the nails are on both sides of the beam and each can resist a shear of 3 kN, determine the maximum load P that can be applied to the end of the beam.

The beam is subjected to a shear of V = 800 N. Determine the average shear stress developed in the nails along the sides A and B if the nails are spaced s = 100 mm apart. Each nail has a diameter of 2 mm.

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 symmetric box girder. Determine the shear flow at A and B.

A shear force of V = 18 kN is applied to the box girder. Determine the shear flow at 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 = 5 kip. Determine the shear flow at points A and B.

The beam is constructed from four plates and is subjected to a shear force of V = 5 kip. Determine the maximum shear flow in the cross section.

The channel is subjected to a shear of V = 75 kN. Determine the shear flow developed at point A.

The channel is subjected to a shear of V = 75 kN. Determine the maximum shear flow in the channel.

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.

Determine the shear-stress variation over the cross section of the thin-walled tube as a function of elevation y and show that \(\tau_{\max }=2 V / A\), where \(A=2 \pi r t\). Hint: Choose a differential area element \(d A=R t \ d \theta\). Using dQ = y dA, formulate Q for a circular section from \(\theta\) to \((\pi-\theta)\) and show that \(Q=2 R^{2} t \cos \theta\), where \(\theta=\sqrt{R^{2}-y^{2}} / R\).

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

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

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

The built-up beam is fabricated from the three thin plates having a thickness t. Determine the location of the shear center O.

Determine the location e of the shear center, point O, for the thin-walled member having the cross section shown. 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.

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 thin-walled member having the cross section shown.

The beam is fabricated from four boards nailed together as shown. Determine the shear force each nail along the sides C and the top D must resist if the nails are uniformly spaced at s = 3 in. The beam is subjected to a shear of V = 4.5 kip.

The T-beam is subjected to a shear of V = 150 kN. Determine the amount of this force that is supported by the web B.

The member is subject to a shear force of V = 2 kN. Determine the shear flow at points A, B, and C. The thickness of each thin-walled segment in 15 mm.

Determine the shear stress at points B and C on the web of the beam located at section a–a.

Determine the maximum shear stress acting at section a–a in the beam.