Solved: The axle of an automobile is acted upon by the

For the given state of stress, determine the normal and shearing stresses exerted on the oblique face of the shaded triangular element shown. Use a method of analysis based on the equilibrium of that element, as was done in the derivations of Sec. 7.2

For the given state of stress, determine the normal and shearing stresses exerted on the oblique face of the shaded triangular element shown. Use a method of analysis based on the equilibrium of that element, as was done in the derivations of Sec. 7.2

For the given state of stress, determine the normal and shearing stresses exerted on the oblique face of the shaded triangular element shown. Use a method of analysis based on the equilibrium of that element, as was done in the derivations of Sec. 7.2

For the given state of stress, determine the normal and shearing stresses exerted on the oblique face of the shaded triangular element shown. Use a method of analysis based on the equilibrium of that element, as was done in the derivations of Sec. 7.2

For the given state of stress, determine (a) the principal planes, (b) the principal stresses

For the given state of stress, determine (a) the principal planes, (b) the principal stresses

For the given state of stress, determine (a) the principal planes, (b) the principal stresses

For the given state of stress, determine (a) the principal planes, (b) the principal stresses

For the given state of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the corresponding normal stress.

For the given state of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the corresponding normal stress.

For the given state of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the corresponding normal stress.

For the given state of stress, determine (a) the orientation of the planes of maximum in-plane shearing stress, (b) the maximum in-plane shearing stress, (c) the corresponding normal stress.

For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) 258 clockwise, (b) 108 counterclockwise.

For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) 258 clockwise, (b) 108 counterclockwise.

For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) 258 clockwise, (b) 108 counterclockwise.

For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) 258 clockwise, (b) 108 counterclockwise.

The grain of a wooden member forms an angle of 158 with the vertical. For the state of stress shown, determine (a) the in-plane shearing stress parallel to the grain, (b) the normal stress perpendicular to the grain.

The grain of a wooden member forms an angle of 158 with the vertical. For the state of stress shown, determine (a) the in-plane shearing stress parallel to the grain, (b) the normal stress perpendicular to the grain.

A steel pipe of 12-in. outer diameter is fabricated from 14 -in.-thick plate by welding along a helix that forms an angle of 22.58 with a plane perpendicular to the axis of the pipe. Knowing that a 40-kip axial force P and an 80-kip ? in. torque T, each directed as shown, are applied to the pipe, determine s and t in directions, respectively, normal and tangential to the weld.

Two members of uniform cross section 50 3 80 mm are glued together along plane a-a that forms an angle of 258 with the horizontal. Knowing that the allowable stresses for the glued joint are s 5 800 kPa and t 5 600 kPa, determine the largest centric load P that can be applied.

Two steel plates of uniform cross section 10 3 80 mm are welded together as shown. Knowing that centric 100-kN forces are applied to the welded plates and that b 5 258, determine (a) the in-plane shearing stress parallel to the weld, (b) the normal stress perpendicular to the weld.

Two steel plates of uniform cross section 10 3 80 mm are welded together as shown. Knowing that centric 100-kN forces are applied to the welded plates and that the in-plane shearing stress parallel to the weld is 30 MPa, determine (a) the angle b, (b) the corresponding normal stress perpendicular to the weld.

A 400-lb vertical force is applied at D to a gear attached to the solid 1-in. diameter shaft AB. Determine the principal stresses and the maximum shearing stress at point H located as shown on top of the shaft.

A mechanic uses a crowfoot wrench to loosen a bolt at E. Knowing that the mechanic applies a vertical 24-lb force at A, determine the principal stresses and the maximum shearing stress at point H located as shown on top of the 34 -in. diameter shaft.

The steel pipe AB has a 102-mm outer diameter and a 6-mm wall thickness. Knowing that arm CD is rigidly attached to the pipe, determine the principal stresses and the maximum shearing stress at point K.

The axle of an automobile is acted upon by the forces and couple shown. Knowing that the diameter of the solid axle is 32 mm, determine (a) the principal planes and principal stresses at point H located on top of the axle, (b) the maximum shearing stress at the same point.

For the state of plane stress shown, determine (a) the largest value of txy for which the maximum in-plane shearing stress is equal to or less than 12 ksi, (b) the corresponding principal stresses.

For the state of plane stress shown, determine the largest value of sy for which the maximum in-plane shearing stress is equal to or less than 75 MPa.

Determine the range of values of sx for which the maximum inplane shearing stress is equal to or less than 10 ksi.

For the state of plane stress shown, determine (a) the value of txy for which the in-plane shearing stress parallel to the weld is zero, (b) the corresponding principal stresses.

Solve Probs. 7.5 and 7.9, using Mohrs circle

Solve Probs. 7.7 and 7.11, using Mohrs circle.

Solve Prob. 7.10, using Mohrs circle.

Solve Prob. 7.12, using Mohrs circle.

Solve Prob. 7.13, using Mohrs circle.

Solve Prob. 7.14, using Mohrs circle.

Solve Prob. 7.15, using Mohrs circle.

Solve Prob. 7.16, using Mohrs circle.

Solve Prob. 7.17, using Mohrs circle.

Solve Prob. 7.18, using Mohrs circle.

Solve Prob. 7.19, using Mohrs circle

Solve Prob. 7.20, using Mohrs circle.

Solve Prob. 7.21, using Mohrs circle.

Solve Prob. 7.22, using Mohrs circle.

Solve Prob. 7.23, using Mohrs circle.

Solve Prob. 7.24, using Mohrs circle.

Solve Prob. 7.25, using Mohrs circle

Solve Prob. 7.26, using Mohrs circle.

Solve Prob. 7.27, using Mohrs circle.

Solve Prob. 7.28, using Mohrs circle.

Solve Prob. 7.29, using Mohrs circle.

Solve Prob. 7.30, using Mohrs circle.

Solve Prob. 7.30, using Mohrs circle and assuming that the weld forms an angle of 608 with the horizontal.

Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown.

Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown.

Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown.

Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown.

For the state of stress shown, determine the range of values of u for which the magnitude of the shearing stress tx9y9 is equal to or less than 8 ksi.

For the state of stress shown, determine the range of values of u for which the normal stress sx9 is equal to or less than 50 MPa.

For the state of stress shown, determine the range of values of u for which the normal stress sx9 is equal to or less than 100 MPa.

For the element shown, determine the range of values of txy for which the maximum tensile stress is equal to or less than 60 MPa.

For the element shown, determine the range of values of txy for which the maximum in-plane shearing stress is equal to or less than 150 MPa.

For the state of stress shown it is known that the normal and shearing stresses are directed as shown and that sx 5 14 ksi, sy 5 9 ksi, and smin 5 5 ksi. Determine (a) the orientation of the principal planes, (b) the principal stress smax, (c) the maximum in-plane shearing stress.

The Mohrs circle shown corresponds to the state of stress given in Fig. 7.5a and b. Noting that sx9 5 OC 1 (CX9) cos (2up 2 2u) and that tx9y9 5 (CX9) sin (2up 2 2u), derive the expressions for sx9 and tx9y9 given in Eqs. (7.5) and (7.6), respectively. [Hint: Use sin (A 1 B) 5 sin A cos B 1 cos A sin B and cos (A 1 B) 5 cos A cos B 2 sin A sin B.]

(a) Prove that the expression sx9sy9 2 t2 x9y9, where sx9, sy9, and tx9y9 are components of the stress along the rectangular axes x9 and y9, is independent of the orientation of these axes. Also, show that the given expression represents the square of the tangent drawn from the origin of the coordinates to Mohrs circle. (b) Using the invariance property established in part a, express the shearing stress txy in terms of sx, sy, and the principal stresses smax and smin.

For the state of plane stress shown, determine the maximum shearing stress when (a) sx 5 6 ksi and sy 5 18 ksi, (b) sx 5 14 ksi and sy 5 2 ksi. (Hint: Consider both in-plane and out-of-plane shearing stresses.)

For the state of plane stress shown, determine the maximum shearing stress when (a) sx 5 0 and sy 5 12 ksi, (b) sx 5 21 ksi and sy 5 9 ksi. (Hint: Consider both in-plane and out-of-plane shearing stresses.)

For the state of stress shown, determine the maximum shearing stress when (a) sy 5 40 MPa, (b) sy 5 120 MPa. (Hint: Consider both in-plane and out-of-plane shearing stresses.)

For the state of stress shown, determine the maximum shearing stress when (a) sy 5 20 MPa, (b) sy 5 140 MPa. (Hint: Consider both in-plane and out-of-plane shearing stresses.)

For the state of stress shown, determine the maximum shearing stress when (a) sz 5 14 ksi, (b) sz 5 24 ksi, (c) sz 5 0.

For the state of stress shown, determine the maximum shearing stress when (a) sz 5 14 ksi, (b) sz 5 24 ksi, (c) sz 5 0.

For the state of stress shown, determine the maximum shearing stress when (a) sz 5 0, (b) sz 5 145 MPa, (c) sz 5 245 MPa.

For the state of stress shown, determine the maximum shearing stress when (a) sz 5 0, (b) sz 5 145 MPa, (c) sz 5 245 MPa.

For the state of stress shown, determine two values of sy for which the maximum shearing stress is 10 ksi.

For the state of stress shown, determine two values of sy for which the maximum shearing stress is 73 MPa.

For the state of stress shown, determine the value of txy for which the maximum shearing stress is (a) 10 ksi, (b) 8.25 ksi.

For the state of stress shown, determine the value of txy for which the maximum shearing stress is (a) 60 MPa, (b) 78 MPa

For the state of stress shown, determine two values of sy for which the maximum shearing stress is 80 MPa

For the state of stress shown, determine the range of values of txz for which the maximum shearing stress is equal to or less than 60 MPa

For the state of stress of Prob. 7.69, determine (a) the value of sy for which the maximum shearing stress is as small as possible, (b) the corresponding value of the shearing stress.

The state of plane stress shown occurs in a machine component made of a steel with sY 5 325 MPa. Using the maximum-distortionenergy criterion, determine whether yield will occur when (a) s0 5 200 MPa, (b) s0 5 240 MPa, (c) s0 5 280 MPa. If yield does not occur, determine the corresponding factor of safety.

Solve Prob. 7.81, using the maximum-shearing-stress criterion.

The state of plane stress shown occurs in a machine component made of a steel with sY 5 45 ksi. Using the maximum-distortionenergy criterion, determine whether yield will occur when (a) txy 5 9 ksi, (b) txy 5 18 ksi, (c) txy 5 20 ksi. If yield does not occur, determine the corresponding factor of safety.

Solve Prob. 7.83, using the maximum-shearing-stress criterion.

The 36-mm-diameter shaft is made of a grade of steel with a 250-MPa tensile yield stress. Using the maximum-shearing-stress criterion, determine the magnitude of the torque T for which yield occurs when P 5 200 kN.

Solve Prob. 7.85, using the maximum-distortion-energy criterion.

The 1.75-in.-diameter shaft AB is made of a grade of steel for which the yield strength is sY 5 36 ksi. Using the maximum-shearingstress criterion, determine the magnitude of the force P for which yield occurs when T 5 15 kip ? in.

Solve Prob. 7.87, using the maximum-distortion-energy criterion

aluminum casting. Knowing that for the aluminum alloy used sUT 5 80 MPa and sUC 5 200 MPa and using Mohrs criterion, determine whether rupture of the casting will occur.

aluminum casting. Knowing that for the aluminum alloy used sUT 5 80 MPa and sUC 5 200 MPa and using Mohrs criterion, determine whether rupture of the casting will occur.

The state of plane stress shown is expected to occur in an aluminum casting. Knowing that for the aluminum alloy used sUT 5 10 ksi and sUC 5 30 ksi and using Mohrs criterion, determine whether rupture of the casting will occur.

The state of plane stress shown is expected to occur in an aluminum casting. Knowing that for the aluminum alloy used sUT 5 10 ksi and sUC 5 30 ksi and using Mohrs criterion, determine whether rupture of the casting will occur.

The state of plane stress shown will occur at a critical point in an aluminum casting that is made of an alloy for which sUT 5 10 ksi and sUC 5 25 ksi. Using Mohrs criterion, determine the shearing stress t0 for which failure should be expected.

The state of plane stress shown will occur at a critical point in a pipe made of an aluminum alloy for which sUT 5 75 MPa and sUC 5 150 MPa. Using Mohrs criterion, determine the shearing stress t0 for which failure should be expected.

The cast-aluminum rod shown is made of an alloy for which sUT 5 60 MPa and sUC 5 120 MPa. Using Mohrs criterion, determine the magnitude of the torque T for which failure should be expected.

The cast-aluminum rod shown is made of an alloy for which sUT 5 70 MPa and sUC 5 175 MPa. Knowing that the magnitude T of the applied torques is slowly increased and using Mohrs criterion, determine the shearing stress t0 that should be expected at rupture.

A machine component is made of a grade of cast iron for which sUT 5 8 ksi and sUC 5 20 ksi. For each of the states of stress shown, and using Mohrs criterion, determine the normal stress s0 at which rupture of the component should be expected.

A spherical gas container made of steel has a 5-m outer diameter and a wall thickness of 6 mm. Knowing that the internal pressure is 350 kPa, determine the maximum normal stress and the maximum shearing stress in the container.

The maximum gage pressure is known to be 8 MPa in a spherical steel pressure vessel having a 250-mm outer diameter and a 6-mm wall thickness. Knowing that the ultimate stress in the steel used is sU 5 400 MPa, determine the factor of safety with respect to tensile failure.

A basketball has a 9.5-in. outer diameter and a 0.125-in. wall thickness. Determine the normal stress in the wall when the basketball is inflated to a 9-psi gage pressure.

A spherical pressure vessel of 900-mm outer diameter is to be fabricated from a steel having an ultimate stress sU 5 400 MPa. Knowing that a factor of safety of 4.0 is desired and that the gage pressure can reach 3.5 MPa, determine the smallest wall thickness that should be used.

A spherical pressure vessel has an outer diameter of 10 ft and a wall thickness of 0.5 in. Knowing that for the steel used sall 5 12 ksi, E 5 29 3 106 psi, and n 5 0.29, determine (a) the allowable gage pressure, (b) the corresponding increase in the diameter of the vessel.

A spherical gas container having an outer diameter of 5 m and a wall thickness of 22 mm is made of steel for which E 5 200 GPa and n 5 0.29. Knowing that the gage pressure in the container is increased from zero to 1.7 MPa, determine (a) the maximum normal stress in the container, (b) the corresponding increase in the diameter of the container.

A steel penstock has a 750-mm outer diameter, a 12-mm wall thickness, and connects a reservoir at A with a generating station at B. Knowing that the density of water is 1000 kg/m3, determine the maximum normal stress and the maximum shearing stress in the penstock under static conditions.

A steel penstock has a 750-mm outer diameter and connects a reservoir at A with a generating station at B. Knowing that the density of water is 1000 kg/m3 and that the allowable normal stress in the steel is 85 MPa, determine the smallest thickness that can be used for the penstock.

The bulk storage tank shown in Photo 7.3 has an outer diameter of 3.3 m and a wall thickness of 18 mm. At a time when the internal pressure of the tank is 1.5 MPa, determine the maximum normal stress and the maximum shearing stress in the tank.

Determine the largest internal pressure that can be applied to a Problems 483 cylindrical tank of 5.5-ft outer diameter and 58 -in. wall thickness if the ultimate normal stress of the steel used is 65 ksi and a factor of safety of 5.0 is desired.

A cylindrical storage tank contains liquefied propane under a pressure of 1.5 MPa at a temperature of 388C. Knowing that the tank has an outer diameter of 320 mm and a wall thickness of 3 mm, determine the maximum normal stress and the maximum shearing stress in the tank.

The unpressurized cylindrical storage tank shown has a 3 16-in. wall thickness and is made of steel having a 60-ksi ultimate strength in tension. Determine the maximum height h to which it can be filled with water if a factor of safety of 4.0 is desired. (Specific weight of water 5 62.4 lb/ft3.)

For the storage tank of Prob. 7.109, determine the maximum normal stress and the maximum shearing stress in the cylindrical wall when the tank is filled to capacity (h 5 48 ft).

A standard-weight steel pipe of 12-in. nominal diameter carries water under a pressure of 400 psi. (a) Knowing that the outside diameter is 12.75 in. and the wall thickness is 0.375 in., determine the maximum tensile stress in the pipe. (b) Solve part a, assuming an extra-strong pipe is used, of 12.75-in. outside diameter and 0.5-in. wall thickness.

The pressure tank shown has a 8-mm wall thickness and butt-welded seams forming an angle b 5 208 with a transverse plane. For a gage pressure of 600 kPa, determine, (a) the normal stress perpendicular to the weld, (b) the shearing stress parallel to the weld.

For the tank of Prob. 7.112, determine the largest allowable gage pressure, knowing that the allowable normal stress perpendicular to the weld is 120 MPa and the allowable shearing stress parallel to the weld is 80 MPa.

For the tank of Prob. 7.112, determine the range of values of b that can be used if the shearing stress parallel to the weld is not to exceed 12 MPa when the gage pressure is 600 kPa.

The steel pressure tank shown has a 750-mm inner diameter and a 9-mm wall thickness. Knowing that the butt-welded seams form an angle b 5 508 with the longitudinal axis of the tank and that the gage pressure in the tank is 1.5 MPa, determine, (a) the normal stress perpendicular to the weld, (b) the shearing stress parallel to the weld.

The pressurized tank shown was fabricated by welding strips of plate along a helix forming an angle b with a transverse plane. Determine the largest value of b that can be used if the normal stress perpendicular to the weld is not to be larger than 85 percent of the maximum stress in the tank.

The cylindrical portion of the compressed-air tank shown is fabricated of 0.25-in.-thick plate welded along a helix forming an angle b 5 308 with the horizontal. Knowing that the allowable stress normal to the weld is 10.5 ksi, determine the largest gage pressure that can be used in the tank.

For the compressed-air tank of Prob. 7.117, determine the gage pressure that will cause a shearing stress parallel to the weld of 4 ksi.

Square plates, each of 0.5-in. thickness, can be bent and welded together in either of the two ways shown to form the cylindrical portion of a compressed-air tank. Knowing that the allowable normal stress perpendicular to the weld is 12 ksi, determine the largest allowable gage pressure in each case

The compressed-air tank AB has an inner diameter of 450 mm and a uniform wall thickness of 6 mm. Knowing that the gage pressure inside the tank is 1.2 MPa, determine the maximum normal stress and the maximum in-plane shearing stress at point a on the top of the tank.

For the compressed-air tank and loading of Prob. 7.120, determine the maximum normal stress and the maximum in-plane shearing stress at point b on the top of the tank.

The compressed-air tank AB has a 250-mm outside diameter and Problems 485 an 8-mm wall thickness. It is fitted with a collar by which a 40-kN force P is applied at B in the horizontal direction. Knowing that the gage pressure inside the tank is 5 MPa, determine the maximum normal stress and the maximum shearing stress at point K.

In Prob. 7.122, determine the maximum normal stress and the maximum shearing stress at point L.

ness is fabricated from a 4-ft section of spirally-welded pipe AB and is equipped with two rigid end plates. The gage pressure inside the vessel is 300 psi and 10-kip centric axial forces P and P9 are applied to the end plates. Determine (a) the normal stress perpendicular to the weld, (b) the shearing stress parallel to the weld

Solve Prob. 7.124, assuming that the magnitude P of the two forces is increased to 30 kips.

A brass ring of 5-in. outer diameter and 0.25-in. thickness fits exactly inside a steel ring of 5-in. inner diameter and 0.125-in. thickness when the temperature of both rings is 508F. Knowing that the temperature of both rings is then raised to 1258F, determine (a) the tensile stress in the steel ring, (b) the corresponding pressure exerted by the brass ring on the steel ring.

Solve Prob. 7.126, assuming that the brass ring is 0.125 in. thick and the steel ring is 0.25 in. thick.

For the given state of plane strain, use the method of Sec. 7.10 to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

For the given state of plane strain, use the method of Sec. 7.10 to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

For the given state of plane strain, use the method of Sec. 7.10 to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

For the given state of plane strain, use the method of Sec. 7.10 to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

For the given state of plane strain, use Mohrs circle to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

For the given state of plane strain, use Mohrs circle to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

For the given state of plane strain, use Mohrs circle to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

For the given state of plane strain, use Mohrs circle to determine the state of plane strain associated with axes x9 and y9 rotated through the given angle u.

The following state of strain has been measured on the surface of a thin plate. Knowing that the surface of the plate is unstressed, determine (a) the direction and magnitude of the principal strains, (b) the maximum in-plane shearing strain, (c) the maximum shearing strain. (Use n 5 13 )

The following state of strain has been measured on the surface of a thin plate. Knowing that the surface of the plate is unstressed, determine (a) the direction and magnitude of the principal strains, (b) the maximum in-plane shearing strain, (c) the maximum shearing strain. (Use n 5 13 )

The following state of strain has been measured on the surface of a thin plate. Knowing that the surface of the plate is unstressed, determine (a) the direction and magnitude of the principal strains, (b) the maximum in-plane shearing strain, (c) the maximum shearing strain. (Use n 5 13 )The following state of strain has been measured on the surface of a thin plate. Knowing that the surface of the plate is unstressed, determine (a) the direction and magnitude of the principal strains, (b) the maximum in-plane shearing strain, (c) the maximum shearing strain. (Use n 5 13 )

"The following state of strain has been measured on the surface of a thin plate. Knowing that the surface of the plate is unstressed, determine (a) the direction and magnitude of the principal strains, (b) the maximum in-plane shearing strain, (c) the maximum shearing strain. (Use n 5 13 )The following state of strain has been measured on the surface of a thin plate. Knowing that the surface of the plate is unstressed, determine (a) the direction and magnitude of the principal strains, (b) the maximum in-plane shearing strain, (c) the maximum shearing strain. (Use n 5 13 )"

For the given state of plane strain, use Mohrs circle to determine(a) the orientation and magnitude of the principal strains, (b) the maximum in-plane strain, (c) the maximum shearing strain.

For the given state of plane strain, use Mohrs circle to determine(a) the orientation and magnitude of the principal strains, (b) the maximum in-plane strain, (c) the maximum shearing strain.

For the given state of plane strain, use Mohrs circle to determine(a) the orientation and magnitude of the principal strains, (b) the maximum in-plane strain, (c) the maximum shearing strain.

For the given state of plane strain, use Mohrs circle to determine(a) the orientation and magnitude of the principal strains, (b) the maximum in-plane strain, (c) the maximum shearing strain.

Determine the strain Px knowing that the following strains have been determined by use of the rosette shown:

The strains determined by the use of the rosette shown during the Problems 499 test of a machine element are Determine (a) the in-plane principal strains, (b) the in-plane maximum shearing strain.

The rosette shown has been used to determine the following strains at a point on the surface of a crane hook: P1 5 1420 3 1026 in./in. P2 5 245 3 1026 in./in. P4 5 1165 3 1026 in./in. (a) What should be the reading of gage 3? (b) Determine the principal strains and the maximum in-plane shearing strain.

The strains determined by the use of the rosette attached as shown during the test of a machine element are P1 5 293.1 3 1026 in./in. P2 5 1385 3 1026 in./in. P3 5 1210 3 1026 in./in. Determine (a) the orientation and magnitude of the principal strains in the plane of the rosette, (b) the maximum in-plane shearing strain.

Using a 458 rosette, the strains P1, P2, and P3 have been determined at a given point. Using Mohrs circle, show that the principal strains are: Pmax, min 5 1 2 1P1 1 P32 6 1 22 c 1P1 2 P222 1 1P2 2 P322 d 1/2 (Hint: The shaded triangles are congruent.)

Show that the sum of the three strain measurements made with a 608 rosette is independent of the orientation of the rosette and equal to P1 1 P2 1 P3 5 3Pavg where Pavg is the abscissa of the center of the corresponding Mohrs circle.

A single strain gage is cemented to a solid 4-in.-diameter steel shaft at an angle b 5 258 with a line parallel to the axis of the shaft. Knowing that G 5 11.5 3 106 psi, determine the torque T indicated by a gage reading of 300 3 1026 in./in.

Solve Prob. 7.150, assuming that the gage forms an angle b 5 358 with a line parallel to the axis of the shaft.

A single strain gage forming an angle b 5 188 with a horizontal plane is used to determine the gage pressure in the cylindrical steel tank shown. The cylindrical wall of the tank is 6-mm thick, has a 600-mm inside diameter, and is made of a steel with E 5 200 GPa and n 5 0.30. Determine the pressure in the tank indicated by a strain gage reading of 280m.

Solve Prob. 7.152, assuming that the gage forms an angle b 5 358 with a horizontal plane.

The given state of plane stress is known to exist on the surface of a machine component. Knowing that E 5 200 GPa and G 5 77.2 GPa, determine the direction and magnitude of the three principal strains (a) by determining the corresponding state of strain [use Eq. (2.43) and Eq. (2.38)] and then using Mohrs circle for strain, (b) by using Mohrs circle for stress to determine the principal planes and principal stresses and then determining the corresponding strains.

The following state of strain has been determined on the surface of a cast-iron machine part: Px 5 2720m Py 5 2400m gxy 5 1660m Knowing that E 5 69 GPa and G 5 28 GPa, determine the principal planes and principal stresses (a) by determining the corresponding state of plane stress [use Eq. (2.36), Eq. (2.43), and the first two equations of Prob. 2.72] and then using Mohrs circle for stress, (b) by using Mohrs circle for strain to determine the orientation and magnitude of the principal strains and then determine the corresponding stresses.

A centric axial force P and a horizontal force Qx are both applied at point C of the rectangular bar shown. A 458 strain rosette on the surface of the bar at point A indicates the following strains: P1 5 260 3 1026 in./in. P2 5 1240 3 1026 in./in. P3 5 1200 3 1026 in./in. Knowing that E 5 29 3 106 psi and n 5 0.30, determine the magnitudes of P and Qx.

Solve Prob. 7.156, assuming that the rosette at point A indicates the following strains: P1 5 230 3 1026 in./in. P2 5 1250 3 1026 in./in. P3 5 1100 3 1026 in./in.

Two wooden members of 80 3 120-mm uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that b 5 228 and that the maximum allowable stresses in the joint are, respectively, 400 kPa in tension (perpendicular to the splice) and 600 kPa in shear (parallel to the splice), determine the largest centric load P that can be applied

Two wooden members of 80 3 120-mm uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that b 5 258 and that centric loads of magnitude P 5 10 kN are applied to the members as shown, determine (a) the in-plane shearing stress parallel to the splice, (b) the normal stress perpendicular to the splice.

The centric force P is applied to a short post as shown. Knowing that the stresses on plane a-a are s 5 215 ksi and t 5 5 ksi, determine (a) the angle b that plane a-a forms with the horizontal, (b) the maximum compressive stress in the post.

Determine the principal planes and the principal stresses for the state of plane stress resulting from the superposition of the two states of stress shown.

For the state of stress shown, determine the maximum shearing stress when (a) sz 5 124 MPa, (b) sz 5 224 MPa, (c) sz 5 0.

For the state of stress shown, determine the maximum shear

The state of plane stress shown occurs in a machine component made of a steel with sY 5 30 ksi. Using the maximum-distortionenergy criterion, determine whether yield will occur when (a) txy 5 6 ksi, (b) txy 5 12 ksi, (c) txy 5 14 ksi. If yield does not occur, determine the corresponding factor of safety.

A torque of magnitude T 5 12 kN ? m is applied to the end of a tank containing compressed air under a pressure of 8 MPa. Knowing that the tank has a 180-mm inner diameter and a 12-mm wall thickness, determine the maximum normal stress and the maximum shearing stress in the tank.

The tank shown has a 180-mm inner diameter and a 12-mm wall thickness. Knowing that the tank contains compressed air under a pressure of 8 MPa, determine the magnitude T of the applied torque for which the maximum normal stress is 75 MPa.

The brass pipe AD is fitted with a jacket used to apply a hydrostatic pressure of 500 psi to portion BC of the pipe. Knowing that the pressure inside the pipe is 100 psi, determine the maximum normal stress in the pipe.

For the assembly of Prob. 7.167, determine the normal stress in the jacket (a) in a direction perpendicular to the longitudinal axis of the jacket, (b) in a direction parallel to that axis.

Determine the largest in-plane normal strain, knowing that the following strains have been obtained by the use of the rosette shown: P1 5 250 3 1026 in./in. P2 5 1360 3 1026 in./in. P3 5 1315 3 1026 in./in.