Questions and Answers of Mechanics of Materials

If the box wrench is subjected to the 50 lb force, determine the principal stresses and maximum in-plane shear stress at point A on the cross section of the wrench at section a€“a. specify
Determine the principal stress at point D, which is located just to the left of the 10-kN force. 10 kN ,100 mm D30 -1m+1m: |B 2 m 300 mm 100 mm 100 mm
Determine the normal and shear stresses at point D that act perpendicular and parallel, respectively, to the grains. The grains at this point make an angle of 30° with the horizontal as shown.
The cylindrical pressure vessel has an inner radius of 1.25 m and a wall thickness of 15 mm. It is made from steel plates that are welded along the 45° seam. Determine the normal and shear stress
A spherical pressure vessel has an inner radius of 5 ft and a wall thickness of 0.5 in. Draw Mohr’s circle for the state of stress at a point on the vessel and explain the significance of the
The pedal crank for a bicycle has the cross section shown. If it is fixed to the gear at B and does not rotate while subjected to a force of 75 lb, determine the principal stresses on the cross
The rotor shaft of the helicopter is subjected to the tensile force and torque shown when the rotor blades provide the lifting force to suspend the helicopter at midair. If the shaft has a diameter
The frame supports the triangular distributed load shown. Determine the normal and shear stresses at point E that act perpendicular and parallel, respectively, to the grains. The grains at this point
The frame supports the triangular distributed load shown. Determine the normal and shear stresses at point D that act perpendicular and parallel, respectively, to the grains. The grains at this point
The thin-walled pipe has an inner diameter of 0.5 in. and a thickness of 0.025 in. If it is subjected to an internal pressure of 500 psi and the axial tension and torsional loadings shown, determine
Determine the principal stresses, the maximum in-plane shear stress, and average normal stress. Specify the orientation of the element in each case. 20 MPa 80 MPa 30 MPa
The post is fixed supported at its base and a horizontal force is applied at its end as shown, determine (a) the maximum in-plane shear stress developed at A and (b) the principal stresses at A. K3
The grains of wood in the board make an angle of 20° with the horizontal as shown. Determine the normal and shear stresses that act perpendicular and parallel to the grains if the board is
Draw Mohr€™s circle that describes each of the following states of stress. 2 ksi 800 psi 60 MPa 8 ksi 800 psi (a) (b) (c)
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 10 ksi 8 ksi 15 ksi
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. A 200 MPa 100 MPa - 150 MPa
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 50 MPa 30 MPa
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 20 MPa 100 MPa 40 MPa
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 30 ksi 9 ksi
Draw Mohr€™s circle that describes each of the following states of stress. 200 psi 3 ksi 100 psi (a) (b)
Draw Mohr€™s circle that describes each of the following states of stress. 2 ksi | 600 psi 20 MPa 800 psi (a) (b) (c)
Determine the equivalent state of stress if an element is oriented 60° clockwise from the element shown. 65 ksi
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 12 ksi 20 ksi 10 ksi
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress. Specify the orientation of the element in each case. 80 MPa 60 MPa
Mohr’s circle for the state of stress is shown in Fig. 9–17a. Show that finding the coordinates of point P (sx′, tx′y′) on the circle gives the same value as the stress transformation Eqs.
Solve Prob. 9€“16 using Mohr€™s circle.Data from 9-16 50 MPa 15 MPa
Solve Prob. 9€“15 using Mohr€™s circle.Data from 9-15 60 MPa 30 MPa 45 MPa
Solve Prob. 9€“11 using Mohr€™s circleData from 9-11Determine the equivalent state of stress on an element at the same point oriented 60° clockwise with respect to the element
Solve Prob. 9€“6 using Mohr€™s circle.Data from 9-6Determine the stress components acting on the inclined plane AB. B 8 ksi 5 ksi 40° 3 ksi
Solve Prob. 9€“3 using Mohr€™s circle.Data from 9-3Determine the stress components acting on the inclined plane AB. A 400 psi - 650 psi 60°
Solve Prob. 9€“2 using Mohr€™s circle.Data from 9-2 65 MPa A. /30 20 MPa
Solve Prob. 9€“42 for point B.Data from 9-42The box beam is subjected to the 26-kN force that is applied at the center of its width, 75 mm from each side. Determine the principal stresses
The box beam is subjected to the 26-kN force that is applied at the center of its width, 75 mm from each side. Determine the principal stresses at point A and show the results in an element located
Solve Prob. 9€“40 for point B located on the web at the top of the bottom flange. 50 kN B. -1 m- 3 m 12 mm 10 mm- 250 mm 12 mm 200 mm
The wide-flange beam is subjected to the 50-kN force. Determine the principal stresses in the beam at point A located on the web at the bottom of the upper flange. Although it is not very accurate,
Solve Prob. 9€“38 for point B, which is located on the outer surface of the pipe. 12 in. 60 lb 30 12 in. B. У х
The steel pipe has an inner diameter of 2.75 in. and an outer diameter of 3 in. If it is fixed at C and subjected to the horizontal 60-lb force acting on the handle of the pipe wrench at its end,
The shaft has a diameter d and is subjected to the loadings shown. Determine the principal stresses and the maximum in-plane shear stress at point A. The bearings only support vertical
The internal loadings at a cross section through the 6-in. diameter drive shaft of a turbine consist of an axial force of 2500 lb, a bending moment of 800 lb · ft, and a torsional moment of
The internal loadings at a cross section through the 6-in. diameter drive shaft of a turbine consist of an axial force of 2500 lb, a bending moment of 800 lb · ft, and a torsional moment of
Determine the principal stresses in the cantilevered beam at points A and B 30 mm- 40 mm- Bz 800 mm 120 mfm 1200 mm 150 mm 15 kN
The 2-in.-diameter drive shaft AB on the helicopter is subjected to an axial tension of 10 000 lb and a torque of 300 lb · ft. Determine the principal stresses and the maximum in-plane shear
Solve Prob. 9€“31 for the normal stress acting perpendicular to the seam. 40° 200 N 200 N 100 mm
A paper tube is formed by rolling a cardboard strip in a spiral and then gluing the edges together as shown. Determine the shear stress acting along the seam, which is at 50° from the horizontal,
The beam has a rectangular cross section and is subjected to the loadings shown. Determine the principal stresses at point A and point B, which are located just to the left of the 20-kN load. Show
The bell crank is pinned at A and supported by a short link BC. If it is subjected to the force of 80 N, determine the principal stresses at (a) point D and (b) point E. The crank is constructed from
A rod has a circular cross section with a diameter of 2 in. It is subjected to a torque of 12 kip · in. and a bending moment M. The greater principal stress at the point of maximum flexural
Solve Prob. 9€“25 for point C. 20 mm 200 mm 20 mm 20 mm iB 100 mm 10 kN-m 80 kN 60 kN 500 N-m
Solve Prob. 9€“25 for point B. 20 mm 200 mm 20 mm 20 mm iB 100 mm 10 kN-m 80 kN 60 kN 500 N-m
The internal loadings at a section of the beam are shown. Determine the in-plane principal stresses at point A. Also compute the maximum in-plane shear stress at this point. 20 mm 200 mm - 20 mm
The wood beam is subjected to a load of 12 kN. If grains of wood in the beam at point A make an angle of 25° with the horizontal as shown, determine the normal and shear stress that act
The grains of wood in the board make an angle of 20° with the horizontal as shown. Determine the normal and shear stress that act perpendicular and parallel to the grains if the board is
The state of stress at a point in a member is shown on the element. Determine the stress components acting on the plane AB. 50 MPa 28 MPa 30 100 MPa
The stress acting on two planes at a point is indicated. Determine the shear stress on plane a€“a and the principal stresses at the point. 80 ksi 90° 45 60 ksi i 60°
The stress along two planes at a point is indicated. Determine the normal stresses on plane b€“b and the principal stresses.
Determine the equivalent state of stress on an element at the same point which represents (a) the principal stress, and (b) the maximum in-plane shear stress and the associated average normal stress.
A point on a thin plate is subjected to the two stress components. Determine the resultant state of stress represented on the element oriented as shown on the right. 60 MPa 85 MPa 45° 30° 85 MPa
Determine the equivalent state of stress on an element at the same point which represents (a) the principal stress, and (b) the maximum in-plane shear stress and the associated average normal stress.
Determine the equivalent state of stress on an element at the point which represents (a) the principal stresses and (b) the maximum in-plane shear stress and the associated average normal stress.
The state of stress at a point is shown on the element. Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation
Determine (a) the principal stresses and (b) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case. 200 MPa 100 MPa 300 MPa
Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 50 MPa A 100 MPa 60° B
Determine the equivalent state of stress on an element at the same point oriented 60° counterclockwise with respect to the element shown. Sketch the results on the element. 100 MPa 75 MPa 150 MPa
Determine the equivalent state of stress on an element at the same point oriented 60° clockwise with respect to the element shown. Sketch the results on the element. 100 MPa 75 MPa 150 MPa
Solve Prob. 9€“9 using the stress transformation equation developed in Sec. 9.2. 80 MPa 30 MPa 30 40 MPa
Determine the stress components acting on the plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 80 MPa 30 MPa 30 40 MPa
Solve Prob. 9€“7 using the stress transformation equations developed in Sec. 9.2. 60 MPa 80 MPa 50° 40 MPa
Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 60 MPa 80 MPa 50 40 MPa B.
Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 8 ksi 5 ksi 40° 3 ksi
Determine the normal stress and shear stress acting on the inclined plane AB. Solve the problem using the stress transformation equations. Show the results on the sectional element. 15 ksi
Determine the normal stress and shear stress acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 15 ksi в 60° 5 ksi
Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. A 400 psi 650 psi 60°
Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium described in Sec. 9.1. 65 MPa 30 B 20 MPa
Prove that the sum of the normal stresses σx + σy = σx′ + σy′ is constant. See Figs. 9–2a and 9–2b.
The screw of the clamp exerts a compressive force of 500 lb on the wood blocks. Sketch the stress distribution along section a€“a of the clamp. The cross section is rectangular, 0.75 in. by
The joint is subjected to the force system shown. Sketch the normal-stress distribution acting over section a€“a if the member has a rectangular cross section of width 0.5 in. and thickness
The joint is subjected to the force system shown. Determine the state of stress at points A and B, and sketch the results on differential elements located at these points. The member has a
The rib-joint pliers are used to grip the smooth pipe C. If the force of 100 N is applied to the handles, determine the state of stress at points A and B on the cross section of the jaw at section
The beam in Fig. 6–48f is subjected to a fully plastic moment MP. Prove that the longitudinal and transverse shear stresses in the beam are zero. Hint: Consider an element of the beam shown in Fig.
The 1/2-in.-diameter bolt hook is subjected to the load of F = 150 lb. Determine the stress components at point B on the shank. Show the result on a volume element located at this point. 1.5 in. A
The block is subjected to the eccentric load shown. Determine the normal stress developed at points A and B. Neglect the weight of the block. 100 mm 150 kN 150 mm
The block is subjected to the eccentric load shown. Sketch the normal-stress distribution acting over the cross section at section a€“a. Neglect the weight of the block. 100 mm 150 kN 150 mm
The spreader bar is used to lift the 2000-lb tank. Determine the state of stress at points A and B, and indicate the results on a differential volume element. E l in. 1 in. 0.5 ft 1.5 ft. 30 30
The drill is jammed in the wall and is subjected to the torque and force shown. Determine the state of stress at point A on the cross section of the drill bit at section a€“a. 400 mm a 20
The drill is jammed in the wall and is subjected to the torque and force shown. Determine the state of stress at point B on the cross section of the drill bit at section a€“a. 400 mm a 20
The frame supports the distributed load shown. Determine the state of stress acting at point D. Show the results on a differential element at this point. 4 kN/m 20 mm 60 mm BA 20 mm D. 50 mm |-1.5
The frame supports the distributed load shown. Determine the state of stress acting at point E. Show the results on a differential element at this point. 4 kN/m 20 mm 60 mm BA 20 mm D. 50 mm -3 m
The rod has a diameter of 40 mm. If it is subjected to the force system shown, determine the stress components that act at point A, and show the results on a volume element located at this point. 100
Solve Prob. 8€“40 for point B. 100 mm 300 mm в 100 N-m 1500 N 800 N 600 N
The beveled gear is subjected to the loads shown. Determine the stress components acting on the shaft at point A, and show the results on a volume element located at this point. The shaft has a
The beveled gear is subjected to the loads shown. Determine the stress components acting on the shaft at point B, and show the results on a volume element located at this point. The shaft has a
Determine the normal stress developed at points A and B. Neglect the weight of the block. 6 kip 3 in. 12 kip 6 in.: D. B.
Sketch the normal-stress distribution acting over the cross section at section a€“a. Neglect the weight of the block. 6 kip -3 in. 12 kip 6 in. D. B.
The man has a mass of 100 kg and center of mass at G. If he holds himself in the position shown, determine the maximum tensile and compressive stress developed in the curved bar at section
The solid rod is subjected to the loading shown. Determine the state of stress at point A, and show the results on a differential volume element located at this point. 200 mm 200 mm 20 kN 'B 100 kN
The solid rod is subjected to the loading shown. Determine the state of stress at point B, and show the results on a differential volume element located at this point. 200 mm 200 mm 20 kN 'B 100 kN
The solid rod is subjected to the loading shown. Determine the state of stress at point C, and show the results on a differential volume element located at this point. 200 mm 200 mm 20 kN 'B 100 kN
The post has a circular cross section of radius c. Determine the maximum radius e at which the load P can be applied so that no part of the post experiences a tensile stress. Neglect the weight of
The post having the dimensions shown is subjected to the load P. Specify the region to which this load can be applied without causing tensile stress at points A, B, C, and D. х те.
The vertebra of the spinal column can support a maximum compressive stress of Ïƒmax, before undergoing a compression fracture. Determine the smallest force P that can be applied to a

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