A beam is made of a material that has a modulus of elasticity in compression different

If the beam is subjected to a bending moment of \(M= 20 \ \mathrm{kN} \cdot \mathrm{m}\) determine the maximum bending stress in the beam.

If the beam is subjected to a bending moment of \(M= 50 \ \mathrm{kN} \cdot \mathrm{m}\), sketch the bending stress distribution over the beam’s cross section.

If the beam is subjected to a bending moment of \(M= 50 \ \mathrm{kN} \cdot \mathrm{m}\) determine the maximum bending stress in the beam.

If the beam is subjected to a bending moment of \(M= 10 \ \mathrm{kN} \cdot \mathrm{m}\) determine the maximum bending stress in the beam.

If the beam is subjected to a bending moment of \(M= 5 \ \mathrm{kN} \cdot \mathrm{m}\) determine the bending stress developed at point A.

A member having the dimensions shown is used to resist an internal bending moment of \(M= 90 \ \mathrm{kN} \cdot \mathrm{m}\) Determine the maximum stress in the member if the moment is applied (a) about the z axis (as shown) (b) about the y axis. Sketch the stress distribution for each case.

Determine the moment M that will produce a maximum stress of 10 ksi on the cross section.

Determine the maximum tensile and compressive bending stress in the beam if it is subjected to a moment of \(M = 4 \ \mathrm{kip} \cdot \mathrm{ft}\).

The channel strut is used as a guide rail for a trolley. If the maximum moment in the strut is \(M= 30 \ \mathrm{N} \cdot \mathrm{m}\) determine the bending stress at points A, B, and C.

The channel strut is used as a guide rail for a trolley. If the allowable bending stress for the material is \(\sigma_{\text {allow }}=175 \mathrm{MPa}\) determine the maximum bending moment the strut will resist.

The beam is subjected to a moment \(\mathbf{M}\). Determine the percentage of this moment that is resisted by the stresses acting on both the top and bottom boards, A and B, of the beam.

Determine the moment \(\mathbf{M}\) that should be applied to the beam in order to create a compressive stress at point D of \(\sigma_D = 30 \ \mathrm{MPa}\). Also sketch the stress distribution acting over the cross section and compute the maximum stress developed in the beam.

The beam is made from three boards nailed together as shown. If the moment acting on the cross section is \(M = 600 \ \mathrm{N} \cdot \mathrm{m}\) determine the maximum bending stress in the beam. Sketch a three-dimensional view of the stress distribution acting over the cross section.

The beam is made from three boards nailed together as shown. If the moment acting on the cross section is \(M = 600 \ \mathrm{N} \cdot \mathrm{m}\), determine the resultant force the bending stress produces on the top board.

The aluminum strut has a cross-sectional area in the form of a cross. If it is subjected to the moment \(M = 8 \ \mathrm{kN} \cdot \mathrm{m}\), determine the bending stress acting at points A and B, and show the results acting on volume elements located at these points.

The aluminum strut has a cross-sectional area in the form of a cross. If it is subjected to the moment \(M = 8 \ \mathrm{kN} \cdot \mathrm{m}\), determine the maximum bending stress in the beam, and sketch a three-dimensional view of the stress distribution acting over the entire cross-sectional area.

If the beam is subjected to an internal moment of \(M = 100 \ \mathrm{kip} \cdot \mathrm{ft}\), determine the maximum tensile and compressive bending stress in the beam.

If the beam is made of material having an allowable tensile and compressive stress of \((\sigma_{\text{allow}})_t = 24 \ \mathrm{ksi}\) and \((\sigma_{\text{allow}})_c = 22 \ \mathrm{ksi}\) respectively, determine the maximum allowable internal moment \(\mathbf{M}\) that can be applied to the beam.

The beam is constructed from four boards as shown. If it is subjected to a moment of \(M_z=16 \ \mathrm{kip} \cdot \mathrm{ft}\), determine the stress at points A and B. Sketch a three-dimensional view of the stress distribution.

The beam is constructed from four boards as shown. If it is subjected to a moment of \(M_z=16 \ \mathrm{kip} \cdot \mathrm{ft}\), determine the resultant force the stress produces on the top board C.

A box beam is constructed from four pieces of wood, glued together as shown. If the moment acting on the cross section is \(10 \ \mathrm{kN} \cdot \mathrm{m}\), determine the stress at points A and B and show the results acting on volume elements located at these points.

Determine the dimension a of a beam having a square cross section in terms of the radius r of a beam with a circular cross section if both beams are subjected to the same internal moment which results in the same maximum bending stress.

The steel rod having a diameter of 1 in. is subjected to an internal moment of \(M=300 \ \mathrm{lb} \cdot \mathrm{ft}\). Determine the stress created at points A and B. Also, sketch a three-dimensional view of the stress distribution acting over the cross section.

If the moment acting on the cross section of the beam is \(M=4 \ \mathrm{kip} \cdot \mathrm{ft}\), determine the maximum bending stress in the beam. Sketch a three-dimensional view of the stress distribution acting over the cross section.

If \(M=4 \ \mathrm{kip} \cdot \mathrm{ft}\), determine the resultant force the bending stress produces on the top board A of the beam.

The rod is supported by smooth journal bearings at A and B that only exert vertical reactions on the shaft. If d = 90 mm, determine the absolute maximum bending stress in the beam, and sketch the stress distribution acting over the cross section.

The rod is supported by smooth journal bearings at A and B that only exert vertical reactions on the shaft. Determine its smallest diameter d if the allowable bending stress is \(\sigma_{\text{allow}} = 180 \ \mathrm{MPa}\).

Two designs for a beam are to be considered. Determine which one will support a moment of \(M=150 \ \mathrm{kN} \cdot \mathrm{m}\) with the least amount of bending stress. What is that stress?

The simply supported truss is subjected to the central distributed load. Neglect the effect of the diagonal lacing and determine the absolute maximum bending stress in the truss.The top member is a pipe having an outer diameter of 1 in. and thickness of \(\frac{3}{16} \mathrm{in.}\), and the bottom member is a solid rod having a diameter of \(\frac{1}{2} \ \mathrm{in}\).

The axle of the freight car is subjected to wheel loadings of 20 kip.If it is supported by two journal bearings at C and D, determine the maximum bending stress developed at the center of the axle, where the diameter is 5.5 in.

The steel beam has the cross-sectional area shown. Determine the largest intensity of distributed load \(w_0\) that it can support so that the maximum bending stress in the beam does not exceed \(\sigma_{\text {max}}=22 \ \mathrm{ksi}\).

The steel beam has the cross-sectional area shown. If \(w_0=0.5 \ \mathrm{kip} / \mathrm{ft}\), determine the maximum bending stress in the beam.

The boat has a weight of 2300 lb and a center of gravity at G. If it rests on the trailer at the smooth contact A and can be considered pinned at B, determine the absolute maximum bending stress developed in the main strut of the trailer. Consider the strut to be a box-beam having the dimensions shown and pinned at C.

The shaft is supported by a smooth thrust bearing at A and smooth journal bearing at D. If the shaft has the cross section shown, determine the absolute maximum bending stress in the shaft.

Determine the moment \(\mathbf{M}\) that must be applied to the beam in order to create a maximum stress of 80 MPa. Also sketch the stress distribution acting over the cross section.

The steel beam has the cross-sectional area shown. Determine the largest intensity of distributed load w that it can support so that the bending stress does not exceed \(\sigma_{\text{max}}=22 \ \mathrm{ksi}\).

The steel beam has the cross-sectional area shown. If w = 5 kip/ft, determine the absolute maximum bending stress in the beam.

If the beam ACB in Prob. 6–9 has a square cross section, 6 in. by 6 in., determine the absolute maximum bending stress in the beam.

If the crane boom ABC in Prob. 6–3 has a rectangular cross section with a base of 2.5 in., determine its required height h to the nearest \(\frac{1}{4} \mathrm{in.}\) if the allowable bending stress is \(\sigma_{\text{allow}} = 24 \ \mathrm{ksi}\).

If the reaction of the ballast on the railway tie can be assumed uniformly distributed over its length as shown, determine the maximum bending stress developed in the tie. The tie has the rectangular cross section with thickness t = 6 in.

The reaction of the ballast on the railway tie can be assumed uniformly distributed over its length as shown. If the wood has an allowable bending stress of \(\sigma_{\text{allow}}=1.5 \ \mathrm{ksi}\), determine the required minimum thickness t of the rectangular cross sectional area of the tie to the nearest \(\frac{1}{8} \mathrm{in}\).

Determine the absolute maximum bending stress in the tubular shaft if \(d_i=160 \ \mathrm{mm}\) and \(d_o=200 \ \mathrm{mm}\).

The tubular shaft is to have a cross section such that its inner diameter and outer diameter are related by \(d_i=0.8d_o\). Determine these required dimensions if the allowable bending stress is \(\sigma_{\text{allow}} = 155 \ \mathrm{MPa}\).

The wood beam has a rectangular cross section in the proportion shown. Determine its required dimension b if the allowable bending stress is \(\sigma_{\text{allow}} = 10 \ \mathrm{MPa}\).

Determine the absolute maximum bending stress in the 2-in.-diameter shaft which is subjected to the concentrated forces. The journal bearings at A and B only support vertical forces.

Determine the smallest allowable diameter of the shaft which is subjected to the concentrated forces. The journal bearings at A and B only support vertical forces. The allowable bending stress is \(\sigma_{\text{allow}} = 22 \ \mathrm{ksi}\).

If the beam has a square cross section of 9 in. on each side, determine the absolute maximum bending stress in the beam.

If the compound beam in Prob. 6–42 has a square cross section, determine its dimension a if the allowable bending stress is \(\sigma_{\text{allow}}=150 \ \mathrm{MPa}\).

If the beam in Prob. 6–28 has a rectangular cross section with a width b and a height h, determine the absolute maximum bending stress in the beam.

Determine the absolute maximum bending stress in the 80-mm-diameter shaft which is subjected to the concentrated forces. The journal bearings at A and B only support vertical forces.

Determine the smallest allowable diameter of the shaft which is subjected to the concentrated forces. The journal bearings at A and B only support vertical forces. The allowable bending stress is \(\sigma_{\text{allow}} = 150 \ \mathrm{MPa}\).

The man has a mass of 78 kg and stands motionless at the end of the diving board. If the board has the cross section shown, determine the maximum normal strain developed in the board. The modulus of elasticity for the material is E = 125 GPa. Assume A is a pin and B is a roller.

The two solid steel rods are bolted together along their length and support the loading shown. Assume the support at A is a pin and B is a roller. Determine the required diameter d of each of the rods if the allowable bending stress is \(\sigma_{\text{allow}}=130 \ \mathrm{MPa}\).

Solve Prob. 6–94 if the rods are rotated \(90^{\circ}\) so that both rods rest on the supports at A (pin) and B (roller).

The chair is supported by an arm that is hinged so it rotates about the vertical axis at A. If the load on the chair is 180 lb and the arm is a hollow tube section having the dimensions shown, determine the maximum bending stress at section a–a.

A portion of the femur can be modeled as a tube having an inner diameter of 0.375 in. and an outer diameter of 1.25 in. Determine the maximum elastic static force P that can be applied to its center. Assume the bone to be roller supported at its ends. The \(\sigma-\epsilon\) diagram for the bone mass is shown and is the same in tension as in compression.

If the beam in Prob. 6–18 has a rectangular cross section with a width of 8 in. and a height of 16 in., determine the absolute maximum bending stress in the beam.

If the beam has a square cross section of 6 in. on each side, determine the absolute maximum bending stress in the beam.

The steel beam has the cross-sectional area shown. Determine the largest intensity of the distributed load \(w_0\) that it can support so that the maximum bending stress in the beam does not exceed \(\sigma_{\text{allow}}=22 \ \mathrm{ksi}\).

The steel beam has the cross-sectional area shown. If \(w_0=2 \ \mathrm{kip/ft}\), determine the maximum bending stress in the beam.

The bolster or main supporting girder of a truck body is subjected to the uniform distributed load. Determine the bending stress at points A and B.

Determine the largest uniform distributed load w that can be supported so that the bending stress in the beam does not exceed \(\sigma_{\text{allow}}=5 \ \mathrm{MPa}\).

If w = 10 kN/m, determine the maximum bending stress in the beam. Sketch the stress distribution acting over the cross section.

If the allowable bending stress for the wood beam is \(\sigma_{\text{allow}}=150 \ \mathrm{psi}\), determine the required dimension b to the nearest \(\frac{1}{4} \mathrm{in.}\) of its cross section.Assume the support at A is a pin and B is a roller.

The wood beam has a rectangular cross section in the proportion shown. If b = 7.5 in., determine the absolute maximum bending stress in the beam.

A beam is made of a material that has a modulus of elasticity in compression different from that given for tension. Determine the location c of the neutral axis, and derive an expression for the maximum tensile stress in the beam having the dimensions shown if it is subjected to the bending moment \(\mathbf{M}\).

The beam has a rectangular cross section and is subjected to a bending moment \(\mathbf{M}\). If the material from which it is made has a different modulus of elasticity for tension and compression as shown, determine the location c of the neutral axis and the maximum compressive stress in the beam.