Questions and Answers of Mechanics Of Materials

The device serves as a compact torsion spring. It is made of A-36 steel and consists of a solid inner shaft CB which is surrounded by and attached to a tube AB using a rigid ring at B. The ring at A
The A-36 steel assembly consists of a tube having an outer radius of 1 in. and a wall thickness of 0.125 in. Using a rigid plate at B, it is connected to the solid 1-in.-diameter shaft AB. Determine
The hydrofoil boat has an A992 steel propeller shaft that is 100 ft long. It is connected to an in-line diesel engine that delivers a maximum power of 2500 hp and causes the shaft to rotate at 1700
The motor delivers 40 hp to the 304 stainless-steel shaft while it rotates at 20 Hz. The shaft is supported on smooth bearings at A and B, which allow free rotation of the shaft. The gears C and D
The motor delivers 40 hp to the 304 stainless-steel solid shaft while it rotates at 20 Hz. The shaft has a diameter of 1.5 in. and is supported on smooth bearings at A and B, which allow free
The tapered shaft has a length L and a radius r at end A and 2r at end B. If it is fixed at end B and is subjected to a torque T, determine the angle of twist of end A. The shear modulus is G. T A 2r
The shaft is made of A-36 steel, has a diameter of 80 mm, and is fixed at B while A is loose and can rotate 0.005 rad before becoming fixed. When the torques are applied to C and D, determine the
The shaft is made of A-36 steel and has a diameter of 80 mm.It is fixed at B and the support at A has a torsional stiffness of k = 0.5 MN ⋅ m/rad. If it is subjected to the gear torques shown,
The A-36 steel shaft is made from two segments: AC has a diameter of 0.5 in. and CB has a diameter of 1 in. If the shaft is fixed at its ends A and B and subjected to a uniform distributed torque of
A portion of the A-36 steel shaft is subjected to a linearly distributed torsional loading. If the shaft has the dimensions shown, determine the reactions at the fixed supports A and C. Segment AB
The shaft is made of bronze C86100 and has an elliptical cross section. If it is subjected to the torsional loading shown, determine the maximum shear stress within regions AB and BC, and the angle
The shaft is made of red brass C83400 and has an elliptical cross section. If the allowable shear stress is τallow = 20 MPa, and the relative angle of twist is limited to 2.50°, determine the
Segments AB and BC of the shaft have circular and square cross sections, respectively. If end A is subjected to a torque of T = 2 kN ⋅ m,, determine the absolute maximum shear stress developed in
Segments AB and BC of the shaft have circular and square cross sections, respectively. The shaft is made from A-36 steel with an allowable shear stress of τallow = 75 MPa, and an angle of twist at
The square shaft is used at the end of a drive cable in order to register the rotation of the cable on a gauge. If it has the dimensions shown and is subjected to a torque of 8 N⋅ m, determine the
The steel shaft is 12 in. long and is screwed tightly into the wall using a wrench. Determine the largest couple forces F that can be applied to the shaft without causing the steel to yield. Take τy
The steel shaft is 12 in. long and is screwed tightly into the wall using a wrench. Determine the maximum shear stress in the shaft and the amount of displacement that each couple force undergoes if
The tube is subjected to a torque of 750 N ⋅ m. Determine the average shear stress in the tube at points A and B. The mean dimensions are shown. 6 mm 100 mm 4 mm 750 N-m 4 mm 60 mm. 6 mm B
The mean dimensions of the cross section of an airplane fuselage are shown. If the fuselage is made of 2014-T6 aluminum alloy having allowable shear stress of τallow = 18 ksi, and it is subjected to
The mean dimensions of the cross section of an airplane fuselage are shown. If the fuselage is made from 2014-T6 aluminum alloy having allowable shear stress of Tallow 18 ksi, and the angle of twist
The tube is 5 mm thick and has the mean dimensions shown. Determine the average shear stress at points A and B if the tube is subjected to a torque of T = 500 N ⋅ m. Show the shear stress on volume
The steel used for the stepped shaft has an allowable shear stress of τallow = 8 MPa. If the radius at the transition between the cross sections is r = 2.25 mm, determine the maximum torque T that
The transition at the cross sections of the stepped shaft has a radius of 2.8 mm. Determine the maximum shear stress developed in the shaft. 20 mm B 50 mm 40 N-m 100 Nm 60 N-m
The stepped shaft is to be designed to rotate at 600 rpm while transmitting 60 kW of power. Is this possible if the allowable shear stress is τallow = 60 MPa and the radius at the transition on the
The built-up shaft is designed to rotate at 720 rpm. If the radius at the transition on the shaft is r = 7.5 mm, and the allowable shear stress for the material is τallow = 60 MPa, determine the
The shaft is made from a strain-hardening material as shown. If the shaft is subjected to a maximum shear strain of 0.0048 rad, determine the torque applied to the shaft. 2 in.- T
The tubular shaft is made of a strain-hardening material having the τ-γ diagram as shown. Determine the torque T that must be applied to the shaft so that the maximum shear strain is 0.01 rad. T
The tube is made of elastic perfectly plastic material, which has the τ-γ diagrams shown. Determine the torque T that just causes the inner surface of the shaft to yield. Also, find the residual
The shaft is made from a strain-hardening material having a τ-γ diagram as shown. Determine the torque T that must be applied to the shaft in order to create an elastic core in the shaft having a
The tapered shaft is made from 2014-T6 aluminum alloy, and has a radius which can be described by the equation r = 0.02(1 + x 3/2) m, where x is in meters. Determine the angle of twist of its end A
The assembly consists of an A36 steel rod CB and 2014-T6 aluminum rod BA, each having a diameter of 20 mm. If the rod is subjected to the axial loadings at A and at the coupling B, determine the
The assembly consists of two 12-mm-diameter A992 steel rods AB and CD, a 20-mm-diameter 6061-T6 aluminum rod EF, and a rigid bar AEC. If P = 20 kN, determine the displacement of end F of rod EF. 600
The assembly consists of two 12-mm-diameter A992 steel rods AB and CD, a 20-mm-diameter 6061-T6 aluminum rod EF, and a rigid bar AEC. If the horizontal displacement of end F of rod EF is 0.024 mm,
The linkage is made of two pin-connected A-36 steel members, each having a cross-sectional area of 1.5 in2 . If a vertical force of P = 50 kip is applied to joint A, determine the vertical
The linkage is made of two pin-connected A-36 steel members, each having a cross-sectional area of 1.5 in2 .Determine the magnitude of the force P needed to displace point A 0.025 in. downward. 2 ft
The rigid bar is supported by the pin-connected rod CB that has a cross-sectional area of 500 mm2 and is made of A-36 steel. Determine the vertical displacement of the bar at B when the load is
19. The load of 800 lb is supported by the four 304 stainless steel wires that are connected to the rigid members AB and DC. Determine the angle of tilt of each member after the load is applied. The
The assembly consists of three titanium (Ti-6A1-4V) rods and a rigid bar AC. The cross-sectional area of each rod is given in the figure. If a force of 6 kip is applied to the ring F, determine the
The bar has a length L and cross-sectional area A. Determine its elongation due to the force P and its own weight. The material has a specific weight (weight volume ) and a modulus of elasticity E.
Solve Prob. 4–26 when the load P acts vertically downward at C.Data from Prob. 4–26The truss consists of three members, each made from A-36 steel and having a cross-sectional area of 0.75 in2.
The rod has a slight taper and length L. It is suspended from the ceiling and supports a load P at its end. Show that the displacement of its end due to this load is Neglect the weight of the
Determine the relative displacement of one end of the tapered plate with respect to the other end when it is subjected to an axial load P. -d- d di P h
The 304 stainless steel post A has a diameter of d = 2 in. and is surrounded by a red brass C83400 tube B. Both rest on the rigid surface. If a force of 5 kip is applied to the rigid cap, determine
The 304 stainless steel post A is surrounded by a red brass C83400 tube B. If a force of 5 kip is applied to the rigid cap, determine the required diameter d of the steel post so that the load is
The composite bar consists of a 20-mm-diameter A-36 steel segment AB and 50-mm-diameter red brass C83400 end segments DA and CB. Determine the average normal stress in each segment due to the applied
The composite bar consists of a 20-mm-diameter A-36 steel segment AB and 50-mm-diameter red brass C83400 end segments DA and CB. Determine the displacement of A with respect to B due to the applied
The A-36 steel column, having a cross-sectional area of 18 in2 , is encased in high-strength concrete as shown. If an axial force of 60 kip is applied to the column, determine the average compressive
The A-36 steel column is encased in high-strength concrete as shown. If an axial force of 60 kip is applied to the column, determine the required area of the steel so that the force is shared equally
The two pipes are made of the same material and are connected as shown. If the cross-sectional area of BC is A and that of CD is 2A, determine the reactions at B and D when a force P is applied at
Two A-36 steel wires are used to support the 650-lb engine. Originally, AB is 32 in. long and A′ B′ is 32.008 in. long. Determine the force supported by each wire when the engine is suspended
The rigid member is held in the position shown by three A-36 steel tie rods. Each rod has a diameter of 20 mm. Determine the forces in the rods if a turnbuckle on rods AB and CD undergoes one and a
Two identical rods AB and CD each have a length L and diameter d, and are used to support the rigid beam, which is pinned at E. If a vertical force P is applied to the beam, determine the normal
Two identical rods AB and CD each have a length L and diameter d, and are used to support the rigid beam, which is pinned at E. If a vertical force P is applied to the beam, determine the angle of
The press consists of two rigid heads that are held together by the two A-36 steel 1/2 -in.-diameter rods. A 6061-T6 solid aluminum cylinder is placed in the press and the screw is adjusted so that
The press consists of two rigid heads that are held together by the two A-36 steel 1/2 -in.-diameter rods. A 6061-T6 solid aluminum cylinder is placed in the press and the screw is adjusted so that
The assembly consists of two 2014-T6 aluminum rods CD and EF of diameter 20 mm, an A992 steel rod AB of diameter 30 mm, and a rigid G. If the supports at A, D, and F are rigid, determine the average
Rod AB has a diameter d and fits snugly between the rigid supports at A and B when it is unloaded. The modulus of elasticity is E. Determine the support reactions at A and B if the rod is subjected
If the 1.5-in.-diameter supporting rods are made from 2014-T6 aluminum, determine the average normal stress developed in each rod when P = 80 kip. D 4 ft 3 ft C A P 3 ft B
If the supporting rods of equal diameter are made from 2014-T6 aluminum, determine the required diameter to the nearest 1/16 in. of each rod when P = 80 kip. The allowable normal stress of the
The center post B of the assembly has an original length of 124.7 mm, whereas posts A and C have a length of 125 mm. If the caps on the top and bottom can be considered rigid, determine the average
The distributed loading is supported by the three suspender bars. AB and EF are made of aluminum and CD is made of steel. If each bar has a cross-sectional area of 450 mm2, determine the maximum
The horizontal beam is assumed to be rigid and supports the distributed load shown. Determine the vertical reactions at the supports. Each support consists of a wooden post having a diameter of 120
The horizontal beam is assumed to be rigid and supports the distributed load shown. Determine the angle of tilt of the beam after the load is applied. Each support consists of a wooden post having a
If the assembly fits snugly between two rigid supports A and C when the temperature is at T1 , determine the normal stress developed in both segments when the temperature rises to T2. Both solid
If the assembly fits snugly between the two supports A and C when the temperature is T1 , determine the normal stress developed in both segments when the temperature rises to T2. Both segments are
A 6-ft-long steam pipe is made of A-36 steel with σy = 40 ksi. It is connected directly to two turbines A and B as shown. The pipe has an outer diameter of 4 in. and a wall thickness of 0.25 in. The
The three bars are made of A-36 steel and form a pin-connected truss. If the truss is constructed when T1 = 50°F, determine the force in each bar when T2 = 110°F. Each bar has a cross-sectional
The three bars are made of A-36 steel and form a pinconnected truss. If the truss is constructed when T1 = 50°F, determine the vertical displacement of joint A when T2 = 150°F. Each bar has a
Three bars, each made of different materials, are connected together and placed between two walls when the temperature is T1 = 12°C. Determine the force exerted on the (rigid) supports when the
The A-36 steel rod has a diameter of 50 mm and is lightly attached to the rigid supports at A and B when T1 = 80°C. If the temperature becomes T2 = 20°C and an axial force of P = 200 kN is applied
The A-36 steel rod has a diameter of 50 mm and is lightly attached to the rigid supports at A and B when T1 = 50°C.Determine the force P that must be applied to the collar at its midpoint so that,
The 50-mm-diameter cylinder is made from Am 1004-T61 magnesium and is placed in the clamp when the temperature is T1= 20C. If the 304-stainless-steel carriage bolts of the clamp each have a diameter
The 50-mm-diameter cylinder is made from Am 1004-T61 magnesium and is placed in the clamp when the temperature is T1 = 15°C. If the two 304-stainless-steel carriage bolts of the clamp each have a
The rigid block has a weight of 80 kip and is to be supported by posts A and B, which are made of A-36 steel, and the post C, which is made of C83400 red brass. If all the posts have the same
Determine the maximum axial force P that can be applied so as not to exceed an allowable tensile stress ofσ allow = 200 MPa. P 40 mm 40 mm 120 mm 30 mm += 22 mm P
Determine the maximum axial force P that can be applied to the bar. The allowable stress is σ allow = 21 ksi. P 1.875 in. 0.125 in. 1.25 in. 0.75 in. r = 0.25 in. P
Determine the maximum axial force P that can be applied to the plate. The allowable stress is σ allow = 36 ksi. P 0.5 in. 0.54 in. P 0.45 in. 4.5 in. 3 in, 0.45 in.
Two steel wires, each having a cross-sectional area of 2 mm2 are tied to a ring at C, and then stretched and tied between the two pins A and B. The initial tension in the wires is 50 N. If a
The wire BC has a diameter of 0.125 in. and the material has the stress–strain diagram shown. Determine the vertical displacement of the handle at D if the pull at the grip is slowly increased and
The 10-mm-diameter shank of the steel bolt has a bronze sleeve bonded to it. The outer diameter of this sleeve is 20 mm. If the yield stress for the steel is (σy)st = 640 MPa, and for the bronze
The 10-mm-diameter shank of the steel bolt has a bronze sleeve bonded to it. The outer diameter of this sleeve is 20 mm. If the yield stress for the steel is (σy)st = 640 MPa, and for the bronze
The rigid beam is supported by a pin at A and two steel wires, each having a diameter of 4 mm. If the yield stress for the wires is σy = 530 MPa, and Est = 200 GPa, determine the intensity of the
The rigid beam is supported by a pin at A and two steel wires, each having a diameter of 4 mm. If the yield stress for the wires is σy = 530 MPa, and Est = 200 GPa, determine (a) the intensity of
The 2-in.-diameter bar is fixed connected at its ends and supports the axial load P. If the material is elastic perfectly plastic as shown by the stress–strain diagram, determine the smallest load
Determine the resultant internal loading on the cross section through point C of the pliers. There is a pin at A, and the jaws at B are smooth. 20 N -120 mm- 40 mm 15 mm- 80 mm 30 20 N B
Determine the resultant internal loading on the cross section through point D of the pliers. There is a pin at A, and the jaws at B are smooth. 20 N -120 mm- 40 mm 15 mm- 80 mm 30 20 N D B
Determine the resultant internal normal force acting on the cross section through point A in each column. In (a), segment BC weighs 180 lb ft and segment CD weighs 250 lb ft. In(b), the column has a
The sky hook is used to support the cable of a scaffold over the side of a building. If it consists of a smooth rod that contacts the parapet of a wall at points A, B, and C, determine the normal
The curved rod has a radius r and is fixed to the wall at B.Determine the resultant internal loadings acting on the cross section at point A which is located at an angle from the horizontal. B P
The pipe assembly is subjected to a force of 600 N at B. Determine the resultant internal loading acting on the cross section at point C. 150 mm 150 mm 400 mm 2 B 60 30 A 500 mm 600 N
If the drill bit jams when the handle of the hand drill is subjected to the forces shown, determine the resultant internal loadings acting on the cross section of the drill bit at A. Z F-30 lb 9 in.
A 175-lb woman stands on a vinyl floor wearing stiletto highheel shoes. If the heel has the dimensions shown, determine the average normal stress she exerts on the floor and compare it with the
The specimen failed in a tension test at an angle of 52° when the axial load was 19.80 kip. If the diameter of the specimen is 0.5 in., determine the average normal and average shear stress acting
The built-up shaft consists of a pipe AB and solid rod BC.The pipe has an inner diameter of 25 mm and outer diameter of 30 mm. The rod has a diameter of 15 mm. Determine the average normal stress at
The 150-kg bucket is suspended from end E of the frame. Determine the avarage normal stress in the 6-mm diameter wire CF and the 15-mm diameter short struct BD. 0.6 m 30 1.2 m 0.6 m 0.6 m D B A E
The 150-kg bucket is suspended from end E of the frame. If the diameters of the pins at A and D are 6 mm and 10 mm, respectively, determine the average shear stress developed in these pins. Each pin
If the pedestal is subjected to a compressive force of 500 lb, specify the x and y coordinates for the location of point P(x, y), where the load must be applied on the cross section, so that the
The beam is supported by a pin at B and a short link AC.Determine the average shear stress developed in the pins at A, B, and C. All pins are in double shear as shown, and each has a diameter of 30
During a tension test, the wooden specimen is subjected to an average normal stress of 2 ksi. Determine the axial force P applied to the specimen. Also, find the average shear stress developed along
When the hand is holding the 5-lb stone, the humerus H, assumed to be smooth, exerts normal forces FC and FA on the radius C and ulna A, respectively, as shown. If the smallest cross-sectional area

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