Mechanics of Materials 9th. Edition by Gere, James Monroe; Goodno, Barry J. | 9781337093354 | 1337093351

Mechanics of Materials

8 SOLVED PROBLEMS

148 SOLVED PROBLEMS

Question: 8.1

A compressed-air tank having an inner diameter of 5.5 m and a wall thickness of 45 mm is formed by welding two steel hemispheres (Fig. 8-5).(a) If the allowable tensile stress in the steel is 93 MPa, what is the maximum permissible air pressure pa in the tank?(b) If the allowable shear stress in ...

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(a) Allowable pressure based upon the tensile stre...

Question: 3.11

A prismatic bar AB, fixed at one end and free at the other, is loaded by a distributed torque of constant intensity t per unit distance along the axis of the bar (Fig. 3-42). (a) Derive a formula for the strain energy of the bar. (b) Evaluate the strain energy of a hollow shaft used for drilling ...

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(a) Strain energy of the bar. The first step in th...

Question: 3.10

A solid circular bar AB of length L is fixed at one end and free at the other (Fig. 3-41). Three different loading conditions are to be considered: (a) torque Ta acting at the free end; (b) torque Tb acting at the midpoint of the bar; and (c) torques Ta and Tb acting simultaneously. For each case ...

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(a) Torque

T_{a}

acting at the free...

Question: 3.3

A hollow shaft and a solid shaft constructed of the same material have the same length and the same outer radius R (Fig. 3-13). The inner radius of the hollow shaft is 0.6R. (a) Assuming that both shafts are subjected to the same torque, compare their shear stresses, angles of twist, and weights. ...

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(a) Comparison or shear stresses. The maximum shea...

Question: 3.2

A steel shaft is to be manufactured either as a solid circular bar or as a circular tube (Fig. 3-12). The shaft is required to transmit a torque of 1200 N⋅m without exceeding an allowable shear stress of 40 MPa nor an allowable rate of twist of 0.75°/m. (The shear modulus of elasticity of the steel ...

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(a) Solid shaft. The required diameter

d_{...

Question: 3.7

A motor driving a solid circular steel shaft transmits 30 kW to a gear at B (Fig. 3-34). The allowable shear stress in the steel is 42 MPa. (a) What is the required diameter d of the shaft if it is operated at 500 rpm? (b) What is the required diameter d if it is operated at 3000 rpm? ...

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(a) Motor operating at 500 rpm. Knowing the horsep...

Question: 8.2

A cylindrical pressure vessel is constructed from a long, narrow steel plate by wrapping the plate around a mandrel and then welding along the edges of the plate to make a helical joint (Fig.8-9). The helical weld makes an angle α = 55° with the longitudinal axis. The vessel has inner radius ...

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Use a four-step problem-solving approach. Combine ...

Question: 9.6

A cantilever beam AB supports a uniform load of intensity q acting over part of the span and a concentrated load P acting at the free end (Fig. 9-18a). Determine the deflection δB and angle of rotation θB at end B of the beam (Fig. 9-18b). Note: The beam has length L and constant flexural rigidity ...

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Use a four-step problem-solving approach. 1. Conce...

Question: 6.7

A channel section UPN 220 is subjected to a bending moment M = 2 kN·m oriented at an angle θ = 10° to the z axis (Fig. 6-30).Calculate the bending stresses σA and σB at points A and B, respectively, and determine the position of the neutral axis. ...

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Use a four-step problem-solving approach. Combine ...

Question: 11.5

A steel wide-flange column of a HE 320A shape (Fig. 11-29a) is pin-supported at the ends and has a length of 7.5 m. The column supports a centrally applied load P1 = 1800 kN and an eccentrically applied load P2 = 200 kN (Fig. 11-29b). Bending takes place about axis 1–1 of the cross section, and the ...

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Use a four-step problem-solving approach. Part (a)...

Question: 6.8

A Z-section is subjected to bending moment M = 3 kN·m at an angle θ = -20° to the z axis, as shown in Fig. 6-32. Find the normal stresses at A, B, D, and E (σA, σB, σD ,and σE , respectively) and also find the position of the neutral axis. Compare the results obtained from use of the neutral axis. ...

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Use a four-step problem-solving approach. Combine ...

Question: 10.7

The two-span beam ABC in Fig. 10-22 has a pin support at A, a roller support at B, and either a roller (Fig. 10-22) or elastic spring support (Fig. 10-23) (spring constant k) at C. The beam has a height of h and is subjected to a temperature differential with temperature T1 on its upper surface and ...

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Use a four-step problem-solving approach. Part (a)...

Question: 9.19

An overhanging beam ABC of height h has a pin support at A and a roller support at B.The beam is heated to a temperature T1 on the top and T2 on the bottom (see Fig. 9-47). Determine the equation of the deflection curve of the beam, and the deflection δC at end C. ...

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Use a four-step problem-solving approach. Combine ...

Question: 9.12

A simple beam ADB supports a concentrated load P acting at the position shown in Fig. 9-26. Determine the angle of rotation θA at support A and the deflection δD under the load P. Note: The beam has a length L and constant flexural rigidity EI. ...

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Use a four-step problem-solving approach. 1. Conce...

Question: 9.11

Find the angle of rotation θB and deflection δB at the free end B of a cantilever beam ACB supporting a uniform load of intensity q acting over the right-hand half of the beam (Fig. 9-25). Note: The beam has a length L and constant flexural rigidity EI. ...

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Use a four-step problem-solving approach. 1. Conce...

Question: 9.10

Determine the angle of rotation θB and deflection δB at the free end B of a cantilever beam AB supporting a concentrated load P Fig. 9-24). Note: The beam has a length L and constant flexural rigidity EI. ...

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Use a four-step problem-solving approach. 1. Conce...

Question: 9.8

A compound beam ABC has a roller support at A, an internal hinge (that is, moment release) at B, and a fixed support at C (Fig. 9-20a). Segment AB has a length of a and segment BC has a length of b. A concentrated load P acts at a distance 2a/3 from support A, and a uniform load of intensity q acts ...

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Use a four-step problem-solving approach. 1. Conce...

Question: 9.7

A cantilever beam AB with a uniform load of intensity q acting on the right-hand half of the beam is shown in Fig. 9-19a. Obtain formulas for the deflection δB and angle of rotation θB at the free end (Fig. 9-19c). Note: The beam has length L and constant flexural rigidity EI. ...

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Use a four-step problem-solving approach. 1. Conce...