Solved: Determine the largest internal pressure that can be applied to a cylindrical

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. 14.2.

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. 14.2.

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. 14.2.

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. 14.2.

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) \(25^{\circ}\) clockwise, (b) \(10^{\circ}\) counterclockwise.

For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) \(25^{\circ}\) clockwise, (b) \(10^{\circ}\) counterclockwise.

For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) \(25^{\circ}\) clockwise, (b) \(10^{\circ}\) counterclockwise.

For the given state of stress, determine the normal and shearing stresses after the element shown has been rotated through (a) \(25^{\circ}\) clockwise, (b) \(10^{\circ}\) counterclockwise.

The grain of a wooden member forms an angle of \(15^{\circ}\) 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 \(15^{\circ}\) 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.

Two plates of uniform cross section \(10 \times 80 \ \mathrm{mm}\) 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 \(\beta\), (b) the corresponding normal stress perpendicular to the weld.

The centric force P is applied to a short post as shown. Knowing that the stresses on plane a-a are \(\sigma=-15 \mathrm{ksi}\) and \(\boldsymbol{\tau}=5 \mathrm{ksi}\), determine (a) the angle \(\beta\) that plane a-a forms with the horizontal, (b) the maximum compressive stress in the post.

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 \(\frac{3} {4}-\mathrm{in.}\) 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 H.

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.

Solve Probs. 14.5 and 14.9, using Mohr’s circle.

Solve Probs. 14.6 and 14.10, using Mohr’s circle.

Solve Prob. 14.11, using Mohr’s circle.

Solve Prob. 14.12, using Mohr’s circle.

Solve Prob. 14.13, using Mohr’s circle.

Solve Prob. 14.14, using Mohr’s circle

Solve Prob. 14.15, using Mohr’s circle.

Solve Prob. 14.16, using Mohr’s circle.

Solve Prob. 14.17, using Mohr’s circle.

Solve Prob. 14.18, using Mohr’s circle.

Solve Prob. 14.19, using Mohr’s circle.

Solve Prob. 14.20, using Mohr’s circle.

Solve Prob. 14.21, using Mohr’s circle.

Solve Prob. 14.22, using Mohr’s circle.

Solve Prob. 14.23, using Mohr’s circle.

Solve Prob. 14.24, using Mohr’s circle.

For the state of plane stress shown, use Mohr’s circle to determine (a) the largest value of \(\tau_{xy}\) 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, use Mohr’s circle to determine the largest value of \(\sigma_y\) for which the maximum in-plane shearing stress is equal to or less than 75 MPa.

For the state of plane stress shown, use Mohr’s circle to determine (a) the value of \(\tau_{xy}\) for which the in-plane shearing stress parallel to the weld is zero, (b) the corresponding principal stresses.

Solve Prob. 14.43 assuming that the weld forms an angle of \(60^{\circ}\) 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.

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

A spherical gas container made of steel has an 18-ft outer diameter and a wall thickness of \(\frac{3}{8} \ \mathrm{in}\). Knowing that the internal pressure is 60 psi, determine the maximum normal 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 \(\sigma_\mathrm{U} = 400 \ \mathrm{MPa}\), determine the factor of safety with respect to tensile failure.

A spherical gas container having an outer diameter of 15 ft and a wall thickness of 0.90 in. is made of a steel for which \(E = 29 \times 10^6 \ \mathrm{psi}\) and \(\nu = 0.29\). Knowing that the gage pressure in the container is increased from zero to 250 psi, determine (a) the maximum normal stress in the container, (b) the increase in the diameter of the container.

A spherical pressure vessel has an outer diameter of 3 m and a wall thickness of 12 mm. Knowing that for the steel used \(\sigma_\mathrm{all} = 80 \ \mathrm{MPa}, E = 200 \ \mathrm{GPa}\), and \(\nu = 0.29\), determine (a) the allowable gage pressure, (b) the corresponding increase in the diameter of the vessel.

A spherical pressure vessel of 750-mm outer diameter is to be fabricated from a steel having an ultimate stress \(\sigma_\mathrm{U} = 400 \ \mathrm{MPa}\). Knowing that a factor of safety of 4.0 is desired and that the gage pressure can reach 4.2 MPa, determine the smallest wall thickness that should be used.

When filled to capacity, the unpressurized storage tank shown contains water to a height of 15.5 m above its base. Knowing that the lower portion of the tank has a wall thickness of 16 mm, determine the maximum normal stress in the tank. (Density of \(\mathrm{water} = 1000 \ \mathrm{kg/m}^3\).)

Determine the largest internal pressure that can be applied to a cylindrical tank of 1.75-m outer diameter and 16-mm wall thickness if the ultimate normal stress of the steel used is 450 MPa and a factor of safety of 5.0 is desired.

The storage tank shown contains liquefied propane under a pressure of 210 psi at a temperature of \(100^{\circ} \mathrm{F}\). Knowing that the tank has an outer diameter of 12.6 in. and a wall thickness of 0.11 in., determine the maximum normal stress in the tank.

The bulk storage tank shown in Photo 14.3 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 in the tank.

A steel penstock has a 36-in. outer diameter and a 0.5-in. wall thickness, and connects a reservoir at A with a generating station at B. Knowing that the specific weight of water is \(62.4 \ \mathrm{lb/ft}^3\), determine the maximum normal stress in the penstock under static conditions.

A steel penstock has a 36-in. outer diameter and connects a reservoir at A with a generating station at B. Knowing that the specific weight of water is \(62.4 \ \mathrm{lb/ft}^3\) and that the allowable normal stress in the steel is 12.5 ksi, determine the smallest wall thickness that can be used for the penstock.

The cylindrical portion of the compressed air tank shown is fabricated of 6-mm-thick plate welded along a helix forming an angle \(\beta = 30^{\circ}\) with the horizontal. Knowing that the allowable stress normal to the weld is 75 MPa, determine the largest gage pressure that can be used in the tank.

The cylindrical portion of the compressed air tank shown is fabricated of 6-mm-thick plate welded along a helix forming an angle \(\beta = 30^{\circ}\) with the horizontal. Determine the gage pressure that will cause a shearing stress parallel to the weld of 30 MPa.

The pressure tank shown has a \(\frac{3}{8}-\mathrm{in.}\) wall thickness and butt welded seams forming an angle \(\beta = 20^{\circ}\) with a transverse plane. For a gage pressure of 85 psi, determine (a) the normal stress perpendicular to the weld, (b) the shearing stress parallel to the weld.

The pressure tank shown has a \(\frac{3}{8}-\mathrm{in.}\) wall thickness and butt welded seams forming an angle \(\beta = 25^{\circ}\) with a transverse plane. Determine the largest allowable gage pressure knowing that the allowable normal stress perpendicular to the weld is 18 ksi and the allowable shearing stress parallel to the weld is 10 ksi.

The pipe shown was fabricated by welding strips of plate along a helix forming an angle \(\beta\) with a transverse plane. Determine the largest value of \(\beta\) 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 pipe.

The pipe shown has an outer diameter of 600 mm and was fabricated by welding strips of 10-mm-thick plate along a helix forming an angle \(\beta = 25^{\circ}\) with a transverse plane. Knowing that the ultimate normal stress perpendicular to the weld is 450 MPa and that a factor of safety of 6.0 is desired, determine the largest allowable gage pressure that can be used.

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. 14.67, determine the maximum normal stress and the maximum in-plane shearing stress at point b on the top of the tank.

A pressure vessel of 10-in. inner diameter and 0.25-in. wall thickness 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 \(\mathbf{P}\) and \(\mathbf{P}^{\prime}\) 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. 14.69 assuming that the magnitude of P of the two forces is increased to 30 kips.

The cylindrical tank AB has an 8-in. inner diameter and a 0.32-in. wall thickness. Knowing that the pressure inside the tank is 600 psi, determine the maximum normal stress and the maximum in-plane shearing stress at point K.

Solve Prob. 14.71 assuming that the 9-kip force applied at point D is directed vertically downward.

Two members of uniform cross section \(50 \times 80 \ \mathrm{mm}\) are glued together along plane a-a that forms an angle of \(25^{\circ}\) with the horizontal. Knowing that the allowable stresses for the glued joint are \(\sigma = 800 \ \mathrm{kPa}\) and \(\tau = 600 \ \mathrm{kPa}\), determine the largest axial load \(\mathbf{P}\) that can be applied.

Determine the largest internal pressure that can be applied to a cylindrical tank of 5.5-ft outer diameter and \(\frac{5}{8}-\mathrm{in.}\) 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 spherical pressure tank has a 1.2-m outer diameter and a uniform wall thickness of 10 mm. Knowing that the gage pressure is 1.25 MPa in the tank, determine the maximum normal stress. (Use E = 200 GPa and \(\nu = 0.30\).)

For a state of plane stress it is known that the normal and shearing stresses are directed as shown and that \(\sigma_x = 5 \ \mathrm{ksi}, \sigma_y = 12 \ \mathrm{ksi}\), and \(\sigma_\mathrm{max} 18 \ \mathrm{ksi}\). Determine (a) the orientation of the principal planes, (b) the maximum in-plane shearing stress.

For the state of plane stress shown, determine (a) the principal planes, (b) the principal stresses, (c) the maximum shearing stress.

The grain of a wooden member forms an angle of \(15^{\circ}\) with the vertical. For the state of plane stress shown, determine (a) the in-plane shearing stress parallel to the grain, (b) the normal stress perpendicular to the grain.

A cylindrical steel pressure tank has a 26-in. inner diameter and a 603 uniform \(\frac{1}{4}-\mathrm{in.}\) wall thickness. Knowing that the ultimate stress of the steel used is 65 ksi, determine the maximum allowable gage pressure if a factor of safety of 5.0 must be maintained.

Two wooden members of \(80 \times 120\)-mm uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that \(\beta=22^{\circ}\) 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 \(\mathbf{P}\) that can be applied.

Two wooden members of \(80 \times 120\)-mm uniform rectangular cross section are joined by the simple glued scarf splice shown. Knowing that \(\beta=25^{\circ}\) and that the centric loads of magnitude P = 10 kN are applied to the member as shown, determine (a) the in-plane shearing stress parallel to the splice, (b) the normal stress perpendicular to the splice.

The axle of an automobile is acted upon by the forces and couple shown. Knowing that the diameter of the solid axle is 1.25 in., 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.

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 the 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.

A torque of magnitude \(T = 12 \ \mathrm{kN} \cdot \mathrm{m}\) 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 in-plane shearing stress in the tank.