The state of stress shown occurs in a machine

Determine the modulus of resilience for each of the following metals: (a) Stainless steel AISI 302 (annealed): E 5 190 GPa sY 5 260 MPa (b) Stainless steel 2014-T6 AISI 302 (cold-rolled): E 5 190 GPa sY 5 520 MPa (c) Malleable cast iron: E 5 165 GPa sY 5 230 MPa

Determine the modulus of resilience for each of the following alloys: (a) Titanium: E 5 16.5 3 106 psi sY 5 120 ksi (b) Magnesium: E 5 6.5 3 106 psi sY 5 29 ksi (c) Cupronickel (annealed) E 5 20 3 106 psi sY 5 16 ksi

Determine the modulus of resilience for each of the following grades of structural steel: (a) ASTM A709 Grade 50: sY 5 50 ksi (b) ASTM A913 Grade 65: sY 5 65 ksi (c) ASTM A709 Grade 100: sY 5 100 ksi

Determine the modulus of resilience for each of the following aluminum alloys: (a) 1100-H14: E 5 70 GPa sY 5 55 MPa (b) 2014-T6 E 5 72 GPa: sY 5 220 MPa (c) 6061-T6 E 5 69 GPa: sY 5 150 MPa

The stress-strain diagram shown has been drawn from data obtained during a tensile test of an aluminum alloy. Using E 5 72 GPa, determine (a) the modulus of resilience of the alloy, (b) the modulus of toughness of the alloy.

The stress-strain diagram shown has been drawn from data obtained during a tensile test of a specimen of structural steel. Using E 5 29 3 106 psi, determine (a) the modulus of resilience of the steel, (b) the modulus of toughness of the steel

The load-deformation diagram shown has been drawn from data obtained during a tensile test of a 0.875-in.-diameter rod of an aluminum alloy. Knowing that the deformation was measured using a 15-in. gage length, determine (a) the modulus of resilience of the alloy, (b) the modulus of toughness of the alloy.

The load-deformation diagram shown has been drawn from data obtained during a tensile test of structural steel. Knowing that the cross-sectional area of the specimen is 250 mm2 and that the deformation was measured using a 500-mm gage length, determine (a) the modulus of resilience of the steel, (b) the modulus of toughness of the steel.

Using E 5 29 3 106 psi, determine (a) the strain energy of the steel rod ABC when P 5 8 kips, (b) the corresponding strain energy density in portions AB and BC of the rod.

Using E 5 200 GPa, determine (a) the strain energy of the steel rod ABC when P 5 25 kN, (b) the corresponding strain-energy density in portions AB and BC of the rod.

A 30-in. length of aluminum pipe of cross-sectional area 1.85 in2 is welded to a fixed support A and to a rigid cap B. The steel rod EF, of 0.75-in. diameter, is welded to cap B. Knowing that the modulus of elasticity is 29 3 106 psi for the steel and 10.6 3 106 psi for the aluminum, determine (a) the total strain energy of the system when P 5 8 kips, (b) the corresponding strain-energy density of the pipe CD and in the rod EF.

Rod AB is made of a steel for which the yield strength is sY 5 450 MPa and E 5 200 GPa; rod BC is made of an aluminum alloy for which sY 5 280 MPa and E 5 73 GPa. Determine the maximum strain energy that can be acquired by the composite rod ABC without causing any permanent deformations.

A single 6-mm-diameter steel pin B is used to connect the steel strip DE to two aluminum strips, each of 20-mm width and 5-mm thickness. The modulus of elasticity is 200 GPa for the steel and 70 GPa for the aluminum. Knowing that for the pin at B the allowable shearing stress is tall 5 85 MPa, determine, for the loading shown, the maximum strain energy that can be acquired by the assembled strips.

Rod BC is made of a steel for which the yield strength is sY 5 300 MPa and the modulus of elasticity is E 5 200 GPa. Knowing that a strain energy of 10 J must be acquired by the rod when the axial load P is applied, determine the diameter of the rod for which the factor of safety with respect to permanent deformation is six.

The assembly ABC is made of a steel for which E 5 200 GPa and sY 5 320 MPa. Knowing that a strain energy of 5 J must be acquired by the assembly as the axial load P is applied, determine the factor of safety with respect to permanent deformation when (a) x 5 300 mm, (b) x 5 600 mm.

Using E 5 10.6 3 106 psi, determine by approximate means the maximum strain energy that can be acquired by the aluminum rod shown if the allowable normal stress is sall 5 22 ksi.

Show by integration that the strain energy of the tapered rod AB is U 5 1 4 P2L EAmin where Amin is the cross-sectional area at end B.

In the truss shown, all members are made of the same material and have the uniform cross-sectional area indicated. Determine the strain energy of the truss when the load P is applied.

"In the truss shown, all members are made of the same material and have the uniform cross-sectional area indicated. Determine the strain energy of the truss when the load P is applied."

"In the truss shown, all members are made of the same material and have the uniform cross-sectional area indicated. Determine the strain energy of the truss when the load P is applied."

"In the truss shown, all members are made of the same material and have the uniform cross-sectional area indicated. Determine the strain energy of the truss when the load P is applied."

Each member of the truss shown is made of steel and has the Problems 713 cross-sectional area shown. Using E 5 29 3 106 psi, determine the strain energy of the truss for the loading shown.

Each member of the truss shown is made of aluminum and has the cross-sectional area shown. Using E 5 72 GPa, determine the strain energy of the truss for the loading shown.

Taking into account only the effect of normal stresses, determine the strain energy of the prismatic beam AB for the loading shown.

Taking into account only the effect of normal stresses, determine the strain energy of the prismatic beam AB for the loading shown.

Taking into account only the effect of normal stresses, determine the strain energy of the prismatic beam AB for the loading shown.

Taking into account only the effect of normal stresses, determine the strain energy of the prismatic beam AB for the loading shown.

Using E 5 200 GPa, determine the strain energy due to bending for the steel beam and loading shown. (Ignore the effect of shearing stresses.)

Using E 5 200 GPa, determine the strain energy due to bending for the steel beam and loading shown. (Ignore the effect of shearing stresses.)

Using E 5 29 3 106 psi, determine the strain energy due to bending for the steel beam and loading shown. (Ignore the effect of shearing stresses.)

Using E 5 29 3 106 psi, determine the strain energy due to bending for the steel beam and loading shown. (Ignore the effect of shearing stresses.)

tion, show that for the given loading the maximum value of the strain-energy density in the beam is umax 5 15 U V where U is the strain energy of the beam and V is its volume.

The ship at A has just started to drill for oil on the ocean floor at a depth of 5000 ft. The steel drill pipe has an outer diameter of 8 in. and a uniform wall thickness of 0.5 in. Knowing that the top of the drill pipe rotates through two complete revolutions before the drill bit at B starts to operate and using G 5 11.2 3 106 psi, determine the maximum strain energy acquired by the drill pipe.

Rod AC is made of aluminum and is subjected to a torque T applied at C. Knowing that G 5 73 GPa and that portion BC of the rod is hollow and has an inner diameter of 16 mm, determine the strain energy of the rod for a maximum shearing stress of 120 MPa.

Show by integration that the strain energy in the tapered rod AB is U 5 7 48 T 2L GJmin where Jmin is the polar moment of inertia of the rod at end B.

The state of stress shown occurs in a machine component made Problems 715 of a grade of steel for which sY 5 65 ksi. Using the maximumdistortion- energy criterion, determine the factor of safety associated with the yield strength when (a) sy 5 116 ksi, (b) sy 5 216 ksi.

The state of stress shown occurs in a machine component made of a grade of steel for which sY 5 65 ksi. Using the maximumdistortion- energy criterion, determine the range of values of sy for which the factor of safety associated with the yield strength is equal to or larger than 2.2.

The state of stress shown occurs in a machine component made of a brass for which sY 5 160 MPa. Using the maximum-distortionenergy criterion, determine the range of values of sz for which yield does not occur.

The state of stress shown occurs in a machine component made of a brass for which sY 5 160 MPa. Using the maximum-distortionenergy criterion, determine whether yield occurs when (a) sz 5 145 MPa, (b) sz 5 245 MPa.

Determine the strain energy of the prismatic beam AB, taking into account the effect of both normal and shearing stresses.

A vibration isolation support is made by bonding a rod A, of radius R1, and a tube B, of inner radius R2, to a hollow rubber cylinder. Denoting by G the modulus of rigidity of the rubber, determine the strain energy of the hollow rubber cylinder for the loading shown.

The cylindrical block E has a speed v0 5 16 ft/s when it strikes squarely the yoke BD that is attached to the 78 -in.-diameter rods AB and CD. Knowing that the rods are made of a steel for which sY 5 50 ksi and E 5 29 3 106 psi, determine the weight of block E for which the factor of safety is five with respect to permanent deformation of the rods.

The 18-lb cylindrical block E has a horizontal velocity v0 when it strikes squarely the yoke BD that is attached to the 78 -in.-diameter rods AB and CD. Knowing that the rods are made of a steel for which sY 5 50 ksi and E 5 29 3 106 psi, determine the maximum allowable speed v0 if the rods are not to be permanently deformed

Collar D is released from rest in the position shown and is stopped by a small plate attached at end C of the vertical rod ABC. Determine the mass of the collar for which the maximum normal stress in portion BC is 125 MPa.

Solve Prob. 11.44, assuming that both portions of rod ABC are made of aluminum.

The 48-kg collar G is released from rest in the position shown and is stopped by plate BDF that is attached to the 20-mm-diameter steel rod CD and to the 15-mm-diameter steel rods AB and EF. Knowing that for the grade of steel used sall 5 180 MPa and E 5 200 GPa, determine the largest allowable distance h.

Solve Prob. 11.46, assuming that the 20-mm-diameter steel rod CD is replaced by a 20-mm-diameter rod made of an aluminum alloy for which sall 5 150 MPa and E 5 75 GPa.

The steel beam AB is struck squarely at its midpoint C by a 45-kg block moving horizontally with a speed v0 5 2 m/s. Using E 5 200 GPa, determine (a) the equivalent static load, (b) the maximum normal stress in the beam, (c) the maximum deflection of the midpoint C of the beam.

Solve Prob. 11.48, assuming that the W150 3 13.5 rolled-steel beam is rotated by 908 about its longitudinal axis so that its web is vertical.

A 25-lb block C moving horizontally with at velocity v0 hits the post AB squarely as shown. Using E 5 29 3 106 psi, determine the largest speed v0 for which the maximum normal stress in the pipe does not exceed 18 ksi.

Solve Prob. 11.50, assuming that the post AB has been rotated 908 about its longitudinal axis

The 2-kg block D is dropped from the position shown onto the end of a 16-mm-diameter rod. Knowing that E 5 200 GPa, determine (a) the maximum deflection of end A, (b) the maximum bending moment in the rod, (c) the maximum normal stress in the rod.

The 2-kg block D is dropped from the position shown onto the end of a 16-mm-diameter rod. Knowing that E 5 200 GPa, determine (a) the maximum deflection of end A, (b) the maximum bending moment in the rod, (c) the maximum normal stress in the rod.

The 45-lb block D is dropped from a height h 5 0.6 ft onto the steel beam AB. Knowing that E 5 29 3 106 psi, determine (a) the maximum deflection at point E, (b) the maximum normal stress in the beam.

Solve Prob. 11.54, assuming that a W4 3 13 rolled-steel shape is used for beam AB.

A block of weight W is dropped from a height h onto the horizontal beam AB and hits it at point D. (a) Show that the maximum deflection ym at point D can be expressed as ym 5 ysta1 1 B 1 1 2h yst b where yst represents the deflection at D caused by a static load W applied at that point and where the quantity in parenthesis is referred to as the impact factor. (b) Compute the impact factor for the beam and the impact of Prob. 11.52.

A block of weight W is dropped from a height h onto the horizontal beam AB and hits point D. (a) Denoting by ym the exact value of the maximum deflection at D and by y9m the value obtained by neglecting the effect of this deflection on the change in potential energy of the block, show that the absolute value of the relative error is (y9m 2 ym)yym, never exceeding y9my2h. (b) Check the result obtained in part a by solving part a of Prob. 11.52 without taking ym into account when determining the change in potential energy of the load, and comparing the answer obtained in this way with the exact answer to that problem.

Using the method of work and energy, determine the deflection at point D caused by the load P.

Using the method of work and energy, determine the deflection at point D caused by the load P.

Using the method of work and energy, determine the slope at point D caused by the couple M0.

Using the method of work and energy, determine the slope at point D caused by the couple M0.

Using the method of work and energy, determine the deflection at point C caused by the load P.

Using the method of work and energy, determine the deflection at point C caused by the load P.

Using the method of work and energy, determine the slope at point A caused by the couple M0.

Using the method of work and energy, determine the slope at point D caused by the couple M0.

Torques of the same magnitude T are applied to the steel shafts AB and CD. Using the method of work and energy, determine the length L of the hollow portion of shaft CD for which the angle of twist at C is equal to 1.25 times the angle of twist at A.

The 20-mm diameter steel rod BC is attached to the lever AB and to the fixed support C. The uniform steel lever is 10 mm thick and 30 mm deep. Using the method of work and energy, determine the deflection of point A when L 5 600 mm. Use E 5 200 GPa and G 5 77.2 GPa.

The 20-mm diameter steel rod BC is attached to the lever AB and to the fixed support C. The uniform steel lever is 10 mm thick and 30 mm deep. Using the method of work and energy, determine the length L of the rod BC for which the deflection at point A is 40 mm. Use E 5 200 GPa and G 5 77.2 GPa.

Two solid steel shafts are connected by the gears shown. Using the method of work and energy, determine the angle through which end D rotates when T 5 820 N ? m. Use G 5 77.2 GPa.

The thin-walled hollow cylindrical member AB has a noncircular Problems 731 cross section of nonuniform thickness. Using the expression given in Eq. (3.53) of Sec. 3.13, and the expression for the strain-energy density given in Eq. (11.19), show that the angle of twist of member AB is f 5 TL 4A 2G C ds t where ds is an element of the center line of the wall cross section and A is the area enclosed by that center line.

Each member of the truss shown has a uniform cross-sectional area A. Using the method of work and energy, determine the vertical deflection of the point of application of the load P.

Each member of the truss shown is made of steel and has a crosssectional area of 400 mm2. Using E 5 200 GPa, determine the deflection of point D caused by the 16-kN load.

Each member of the truss shown is made of steel and has a crosssectional area of 5 in2. Using E 5 29 3 106 psi, determine the vertical deflection of point B caused by the 20-kip load.

Each member of the truss shown is made of steel and has a uniform cross-sectional area of 5 in2. Using E 5 29 3 106 psi, determine the vertical deflection of joint C caused by the application of the 15-kip load.

Each member of the truss shown is made of steel; the crosssectional area of member BC is 800 mm2 and for all other members the cross-sectional area is 400 mm2. Using E 5 200 GPa, determine the deflection of point D caused by the 60-kN load.

The steel rod BC has a 24-mm diameter and the steel cable ABDCA has a 12-mm diameter. Using E 5 200 GPa, determine the deflection of joint D caused by the 12-kN load.

Using the information in Appendix D, compute the work of the loads as they are applied to the beam (a) if the load P is applied first, (b) if the couple M is applied first.

Using the information in Appendix D, compute the work of the loads as they are applied to the beam (a) if the load P is applied first, (b) if the couple M is applied first.

Using the information in Appendix D, compute the work of the loads as they are applied to the beam (a) if the load P is applied first, (b) if the couple M is applied first.

For the beam and loading shown, (a) compute the work of the loads as they are applied successively to the beam, using the information provided in Appendix D, (b) compute the strain energy of the beam by the method of Sec. 11.4 and show that it is equal to the work obtained in part a.

For the beam and loading shown, (a) compute the work of the loads as they are applied successively to the beam, using the information provided in Appendix D, (b) compute the strain energy of the beam by the method of Sec. 11.4 and show that it is equal to the work obtained in part a.

For the beam and loading shown, (a) compute the work of the loads as they are applied successively to the beam, using the information provided in Appendix D, (b) compute the strain energy of the beam by the method of Sec. 11.4 and show that it is equal to the work obtained in part a.

For the prismatic beam shown, determine the deflection of point D.

For the prismatic beam shown, determine the deflection of point D.

or the prismatic beam shown, determine the slope at point D.

or the prismatic beam shown, determine the slope at point D.

For the prismatic beam shown, determine the deflection at point D.

For the prismatic beam shown, determine the deflection at point D.

For the prismatic beam shown, determine the slope at point D.

For the prismatic beam shown, determine the slope at point D.

For the beam and loading shown, determine the slope at end A. Use E 5 200 GPa.

For the beam and loading shown, determine the slope at end C. Use E 5 29 3 106 psi.

For the beam and loading shown, determine the deflection at end C. Use E 5 29 3 106 psi.

For the beam and loading shown, determine the deflection at point D. Use E 5 200 GPa.

For the beam and loading shown, determine the deflection at point B. Use E 5 200 GPa.

For the beam and loading shown, determine the

deflection at point B. Use E 5 200 GPa.

For the beam and loading shown, determine the slope at end A. Use E 5 29 3 106 psi.

For the truss and loading shown, determine the horizontal and vertical deflection of joint C.

For the truss and loading shown, determine the Problems 747 horizontal and vertical deflection of joint C.

Each member of the truss shown is made of steel and has a cross-sectional area of 500mm2. Using E 5 200 GPa, determine the deflection indicated.Vertical deflection of joint B

Each member of the truss shown is made of steel and has a cross-sectional area of 500mm2. Using E 5 200 GPa, determine the deflection indicated.Horizontal deflection of joint B.

Each member of the truss shown is made of steel and has the cross-sectional area shown. Using E 5 29 3 106 psi, determine the deflection indicated. Vertical deflection of joint C.

Each member of the truss shown is made of steel and has the cross-sectional area shown. Using E 5 29 3 106 psi, determine the deflection indicated. Horizontal deflection of joint C.

Two rods AB and BC of the same flexural rigidity EI are welded together at B. For the loading shown, determine (a) the deflection of point C, (b) the slope of member BC at point C.

A uniform rod of flexural rigidity EI is bent and loaded as shown. Determine (a) the horizontal deflection of point D, (b) the slope at point D.

A uniform rod of flexural rigidity EI is bent and loaded as shown. Determine (a) the vertical deflection of point D, (b) the slope of BC at point C.

A uniform rod of flexural rigidity EI is bent and loaded as shown. Determine (a) the vertical deflection of point A, (b) the horizontal deflection of point A

For the beam and loading shown and using Castiglianos theorem, determine (a) the horizontal deflection of point B, (b) the vertical deflection of point B.

For the uniform rod and loading shown and using Castiglianos theorem, determine the deflection of point B.

Determine the reaction at the roller support and draw the bending-moment diagram for the beam and loading shown

Determine the reaction at the roller support and draw the bending-moment diagram for the beam and loading shown

Determine the reaction at the roller support and draw the bending-moment diagram for the beam and loading shown

Determine the reaction at the roller support and draw the bending-moment diagram for the beam and loading shown

For the uniform beam and loading shown, determine the reaction at each support.

Determine the reaction at the roller support and draw the b ending moment diagram for the beam and loading shown.

Three members of the same material and same cross-sectional area are used to support the loading P. Determine the force in member BC.

Three members of the same material and same cross-sectional area are used to support the loading P. Determine the force in member BC.

Three members of the same material and same cross-sectional area are used to support the loading P. Determine the force in member BC.

Three members of the same material and same cross-sectional area are used to support the loading P. Determine the force in member BC.

Knowing that the eight members of the indeterminate truss shown have the same uniform cross-sectional area, determine the force in member AB.

Knowing that the eight members of the indeterminate truss shown have the same uniform cross-sectional area, determine the force in member AB.

Rods AB and BC are made of a steel for which the yield strength is sY 5 300 MPa and the modulus of elasticity is E 5 200 GPa. Determine the maximum strain energy that can be acquired by the assembly without causing permanent deformation when the length a of rod AB is (a) 2 m, (b) 4 m

Assuming that the prismatic beam AB has a rectangular cross section, show that for the given loading the maximum value of the strain-energy density in the beam is umax 5 45 8 U V where U is the strain energy of the beam and V is its volume.

A 5-kg collar D moves along the uniform rod AB and has a speed v0 5 6 m/s when it strikes a small plate attached to end A of the rod. Using E 5 200 GPa and knowing that the allowable stress in the rod is 250 MPa, determine the smallest diameter that can be used for the rod.

A 160-lb diver jumps from a height of 20 in. onto end C of a diving board having the uniform cross section shown. Assuming that the divers legs remain rigid and using E 5 1.8 3 106 psi, determine (a) the maximum deflection at point C, (b) the maximum normal stress in the board, (c) the equivalent static load.

A block of weight W is placed in contact with a beam at some given point D and released. Show that the resulting maximum deflection at point D is twice as large as the deflection due to a static load W applied at D.

The 12-mm-diameter steel rod ABC has been bent into the shape Review Problems 755 shown. Knowing that E 5 200 GPa and G 5 77.2 GPa, determine the deflection of end C caused by the 150-N force.

Two steel shafts, each of 0.75-in diameter, are connected by the gears shown. Knowing that G 5 11.2 3 106 psi and that shaft DF is fixed at F, determine the angle through which end A rotates when a 750-lb ? in. torque is applied at A. (Ignore the strain energy due to the bending of the shafts.)

Each member of the truss shown is made of steel and has a uniform cross-sectional area of 3 in2. Using E 5 29 3 106 psi, determine the vertical deflection of joint A caused by the application of the 24-kip load.

A disk of radius a has been welded to end B of the solid steel shaft AB. A cable is then wrapped around the disk and a vertical force P is applied to end C of the cable. Knowing that the radius of the shaft is r and neglecting the deformations of the disk and of the cable, show that the deflection of point C caused by the application of P is

Three rods, each of the same flexural rigidity EI, are welded to form the frame ABCD. For the loading shown, determine the angle formed by the frame at point D.

The steel bar ABC has a square cross section of side 0.75 in. and is subjected to a 50-lb load P. Using E 5 29 3 106 psi for rod BD and the bar, determine the deflection of point C.

For the uniform beam and loading shown, determine the reaction at each support.