Solved: The steel bar AB has a rectangular cross section.

Determine the critical buckling load for the column. The material can be assumed rigid.

The column consists of a rigid member that is pinned at its bottom and attached to a spring at its top. If the spring is unstretched when the column is in the vertical position, determine the critical load that can be placed on the column.

The aircraft link is made from an A992 steel rod. Determine the smallest diameter of the rod, to the nearest \(\frac{1}{16} \text { in }\)., that will support the load of 4 kip without buckling. The ends are pin connected.

Rigid bars AB and BC are pin connected at B. If the spring at D has a stiffness k, determine the critical load \(P_{cr}\) that can be applied to the bars.

A 2014-T6 aluminum alloy column has a length of 6 m and is fixed at one end and pinned at the other. If the cross-sectional area has the dimensions shown, determine the critical load. \(\sigma_{Y}=250 \mathrm{MPa}\).

Solve Prob. 13–5 if the column is pinned at its top and bottom. A 2014-T6 aluminum alloy column has a length of 6 m and is fixed at one end and pinned at the other. If the cross-sectional area has the dimensions shown, determine the critical load. \(\sigma_{Y}=250 \mathrm{MPa}\).

The W12 X 50 is made of A992 steel and is used as a column that has a length of 20 ft. If its ends are assumed pin supported, and it is subjected to an axial load of 150 kip, determine the factor of safety with respect to buckling.

The W12 X 50 is made of A992 steel and is used as a column that has a length of 20 ft. If the ends of the column are fixed supported, can the column support the critical load without yielding?

A steel column has a length of 9 m and is fixed at both ends. If the cross-sectional area has the dimensions shown, determine the critical load. \(E_{\mathrm{st}}=200 \mathrm{GPa}, \nu_{\mathrm{st}}=0.3\), \(\sigma_{Y}=250 \mathrm{MPa}\).

A steel column has a length of 9 m and is pinned at its top and bottom. If the cross-sectional area has the dimensions shown, determine the critical load. \(E_{\mathrm{st}}=200 \mathrm{GPa}\), \(\sigma_{Y}=250 \mathrm{MPa}\).

The A992 steel angle has a cross-sectional area of \(A=2.48 \mathrm{in}^{2}\) and a radius of gyration about the x axis of \(r_{x}=1.26 \mathrm{in}\). and about the y axis of \(r_{y}=0.879 \mathrm{in}\). The smallest radius of gyration occurs about the a–a axis and is \(r_{a}=0.644 \mathrm{in}\). If the angle is to be used as a pin-connected 10-ft-long column, determine the largest axial load that can be applied through its centroid C without causing it to buckle.

The 50-mm-diameter C86100 bronze rod is fixed supported at A and has a gap of 2 mm from the wall at B. Determine the increase in temperature \(\Delta T\) that will cause the rod to buckle. Assume that the contact at B acts as a pin.

Determine the maximum load P the frame can support without buckling member AB. Assume that AB is made of steel and is pinned at its ends for y–y axis buckling and fixed at its ends for x–x axis buckling. \(E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=360 \mathrm{MPa}\).

The W8 X 67 wide-flange A-36 steel column can be assumed fixed at its base and pinned at its top. Determine the largest axial force P that can be applied without causing it to buckle.

Solve Prob. 13–14 if the column is assumed fixed at its bottom and free at its top. The W8 X 67 wide-flange A-36 steel column can be assumed fixed at its base and pinned at its top. Determine the largest axial force P that can be applied without causing it to buckle.

An A992 steel W200 X 46 column of length 9 m is fixed at one end and free at its other end. Determine the allowable axial load the column can support if F.S. = 2 against buckling.

The 10-ft wooden rectangular column has the dimensions shown. Determine the critical load if the ends are assumed to be pin connected. \(E_{\mathrm{w}}=1.6\left(10^{3}\right) \mathrm{ksi}\), \(\sigma_{Y}=5 \mathrm{ksi}\).

The 10-ft wooden column has the dimensions shown. Determine the critical load if the bottom is fixed and the top is pinned. \(E_{\mathrm{w}}=1.6\left(10^{3}\right) \mathrm{ksi}\), \(\sigma_{Y}=5 \mathrm{ksi}\).

Determine the maximum force P that can be applied to the handle so that the A992 steel control rod AB does not buckle. The rod has a diameter of 1.25 in. It is pin connected at its ends.

The A-36 steel pipe has an outer diameter of 2 in. and a thickness of 0.5 in. If it is held in place by a guywire, determine the largest vertical force P that can be applied without causing the pipe to buckle. Assume that the ends of the pipe are pin connected.

The A-36 steel pipe has an outer diameter of 2 in. If it is held in place by a guywire, determine its required inner diameter to the nearest \(\frac{1}{8} \text { in }\)., so that it can support a maximum vertical load of P = 4 kip without causing the pipe to buckle. Assume the ends of the pipe are pin connected.

The deck is supported by the two 40-mm-square columns. Column AB is pinned at A and fixed at B, whereas CD is pinned at C and D. If the deck is prevented from sidesway, determine the greatest weight of the load that can be applied without causing the deck to collapse. The center of gravity of the load is located at d = 2 m. Both columns are made from Douglas Fir.

The deck is supported by the two 40-mm-square columns. Column AB is pinned at A and fixed at B, whereas CD is pinned at C and D. If the deck is prevented from sidesway, determine the position d of the center of gravity of the load and the load’s greatest magnitude without causing the deck to collapse. Both columns are made from Douglas Fir.

The beam is supported by the three pin-connected suspender bars, each having a diameter of 0.5 in. and made from A-36 steel. Determine the greatest uniform load w that can be applied to the beam without causing AB or CB to buckle.

The W14 X 30 A992 steel column is assumed pinned at both of its ends. Determine the largest axial force P that can be applied without causing it to buckle.

The A992 steel bar AB has a square cross section. If it is pin connected at its ends, determine the maximum allowable load P that can be applied to the frame. Use a factor of safety with respect to buckling of 2.

The linkage is made using two A992 steel rods, each having a circular cross section. Determine the diameter of each rod to the nearest \(\frac{1}{8} \text { in }\). that will support a load of P = 10 kip. Assume that the rods are pin connected at their ends. Use a factor of safety with respect to buckling of 1.8.

The linkage is made using two A992 steel rods, each having a circular cross section. If each rod has a diameter of 2 in., determine the largest load it can support without causing any rod to buckle if the factor of safety against buckling is 1.8. Assume that the rods are pin connected at their ends.

The linkage is made using two A-36 steel rods, each having a circular cross section. Determine the diameter of each rod to the nearest \(\frac{1}{8} \text { in }\). that will support the 900-lb load. Assume that the rods are pin connected at their ends. Use a factor of safety with respect to buckling of F.S. = 1.8.

The linkage is made using two A-36 steel rods, each having a circular cross section. If each rod has a diameter of \(\frac{3}{4} \text { in }\)., determine the largest load it can support without causing any rod to buckle. Assume that the rods are pin connected at their ends.

The steel bar AB has a rectangular cross section. If it is pin connected at its ends, determine the maximum allowable intensity w of the distributed load that can be applied to BC without causing AB to buckle. Use a factor of safety with respect to buckling of 1.5. \(E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=360 \mathrm{MPa}\).

Determine if the frame can support a load of P = 20 kN if the factor of safety with respect to buckling of member AB is F.S. = 3. Assume that AB is made of steel and is pinned at its ends for x–x axis buckling and fixed at its ends for y–y axis buckling. \(E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=360 \mathrm{MPa}\).

Determine the maximum allowable load P that can be applied to member BC without causing member AB to buckle. Assume that AB is made of steel and is pinned at its ends for x–x axis buckling and fixed at its ends for y–y axis buckling. Use a factor of safety with respect to buckling of F.S. = 3. \(E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=360 \mathrm{MPa}\).

A 6061-T6 aluminum alloy solid circular rod of length 4 m is pinned at both of its ends. If it is subjected to an axial load of 15 kN and F.S. = 2 against buckling, determine the minimum required diameter of the rod to the nearest mm.

A 6061-T6 aluminum alloy solid circular rod of length 4 m is pinned at one end while fixed at the other end. If it is subjected to an axial load of 15 kN and F.S. = 2 against buckling, determine the minimum required diameter of the rod to the nearest mm.

The members of the truss are assumed to be pin connected. If member BD is an A992 steel rod of radius 2 in., determine the maximum load P that can be supported by the truss without causing the member to buckle.

Solve Prob. 13–36 for member AB, which has a radius of 2 in. The members of the truss are assumed to be pin connected. If member BD is an A992 steel rod of radius 2 in., determine the maximum load P that can be supported by the truss without causing the member to buckle.

The truss is made from A992 steel bars, each of which has a circular cross section with a diameter of 1.5 in. Determine the maximum force P that can be applied without causing any of the members to buckle. The members are pin connected at their ends.

The truss is made from A992 steel bars, each of which has a circular cross section. If the applied load P = 10 kip, determine the diameter of member AB to the nearest \(\frac{1}{8} \text { in }\). that will prevent this member from buckling. The members are pin connected at their ends.

The steel bar AB of the frame is assumed to be pin connected at its ends for y–y axis buckling. If P = 18 kN, determine the factor of safety with respect to buckling about the y–y axis. \(E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=360 \mathrm{MPa}\).

The ideal column has a weight w (force>length) and is subjected to the axial load P. Determine the maximum moment in the column at midspan. EI is constant. Hint: Establish the differential equation for deflection, Eq. 13–1, with the origin at the midspan. The general solution is \(v=C_{1} \sin k x+C_{2} \cos k x+(w /(2 P)) x^{2}-(w L /(2 P)) x-\left(w E I / P^{2}\right) \text { where } k^{2}=P / E I\).

The ideal column is subjected to the force F at its midpoint and the axial load P. Determine the maximum moment in the column at midspan. EI is constant. Hint: Establish the differential equation for deflection, Eq. 13–1. The general solution is \(v=C_{1} \sin k x+C_{2} \cos k x-c^{2} x / k^{2}\), where \(c^{2}=F / 2 E I, k^{2}=P / E I\).

The column with constant EI has the end constraints shown. Determine the critical load for the column.

Consider an ideal column as in Fig. 13–10c, having both ends fixed. Show that the critical load on the column is \(P_{\mathrm{cr}}=4 \pi^{2} E I / L^{2}\). Hint: Due to the vertical deflection of the top of the column, a constant moment \(\mathbf{M}^{\prime}\) will be developed at the supports. Show that \(d^{2} v / d x^{2}+(P / E I) v=M^{\prime} / E I\). The solution is of the form \(v=C_{1} \sin (\sqrt{P / E I} x)+C_{2} \cos (\sqrt{P / E I} x)+M^{\prime} / P\).

Consider an ideal column as in Fig. 13–10d, having one end fixed and the other pinned. Show that the critical load on the column is \(P_{\mathrm{cr}}=20.19 E I / L^{2}\). Hint: Due to the vertical deflection at the top of the column, a constant moment M will be developed at the fixed support and horizontal reactive forces \(\mathbf{R}^{\prime}\) will be developed at both supports. Show that \(d^{2} v / d x^{2}+(P / E I) v=\left(R^{\prime} / E I\right)(L-x)\). The solution is of the form \(v=C_{1} \sin (\sqrt{P / E I} x)+C_{2} \cos (\sqrt{P / E I} x)+\left(R^{\prime} / P\right)(L-x)\). After application of the boundary conditions show that tan \((\sqrt{P / E I} L)=\sqrt{P / E I} L\). Solve numerically for the smallest nonzero root.

The wood column is ixed at its base and free at its top. Determine the load P that can be applied to the edge of the column without causing the column to fail either by buckling or by yielding. \(E_{\mathrm{w}}=12 \mathrm{GPa}, \sigma_{Y}=55 \mathrm{MPa}\).

The W10 X 12 structural A-36 steel column is used to support a load of 4 kip. If the column is ixed at the base and free at the top, determine the sidesway delection at the top of the column due to the loading.

The W10 X 12 structural A-36 steel column is used to support a load of 4 kip. If the column is ixed at its base and free at its top, determine the maximum stress in the column due to this loading.

The aluminum column is fixed at the bottom and free at the top. Determine the maximum force P that can be applied at A without causing it to buckle or yield. Use a factor of safety of 3 with respect to buckling and yielding. \(E_{\mathrm{al}}=70 \mathrm{GPa}, \sigma_{Y}=95 \mathrm{MPa}\).

A column of intermediate length buckles when the compressive stress is 40 ksi. If the slenderness ratio is 60, determine the tangent modulus.

The aluminum rod is fixed at its base and free at its top. If the eccentric load P = 200 kN is applied, determine the greatest allowable length L of the rod so that it does not buckle or yield. \(E_{\mathrm{al}}=72 \mathrm{GPa}, \sigma_{Y}=410 \mathrm{MPa}\).

The aluminum rod is fixed at its base and free and at its top. If the length of the rod is L = 2 m, determine the greatest allowable load P that can be applied so that the rod does not buckle or yield. Also, determine the largest sidesway deflection of the rod due to the loading. \(E_{\mathrm{al}}=72 \mathrm{GPa}, \sigma_{Y}=410 \mathrm{MPa}\).

Assume that the wood column is pin connected at its base and top. Determine the maximum eccentric load P that can be applied without causing the column to buckle or yield. \(E_{w}=1.8\left(10^{3}\right) \mathrm{ksi}\), \(\sigma_{Y}=8 \mathrm{ksi}\).

Assume that the wood column is pinned top and bottom for movement about the x-y axis, and fixed at the bottom and free at the top for movement about the y-y axis. Determine the maximum eccentric load P that can be applied without causing the column to buckle or yield. \(E_{w}=1.8\left(10^{3}\right) \mathrm{ksi}\), \(\sigma_{Y}=8 \mathrm{ksi}\).

The wood column is pinned at its base and top. If the eccentric force P = 10 kN is applied to the column, investigate whether the column is adequate to support this loading without buckling or yielding. Take E = 10 GPa and \(\sigma_{Y}=15 \mathrm{MPa}\).

The wood column is pinned at its base and top. Determine the maximum eccentric force P the column can support without causing it to either buckle or yield. Take E = 10 GPa and \(\sigma_{Y}=15 \mathrm{MPa}\).

The A992 steel rectangular hollow section column is pinned at both ends. If it has a length of L = 14 ft, determine the maximum allowable eccentric force P it can support without causing it to either buckle or yield.

The A992 steel rectangular hollow section column is pinned at both ends. If it is subjected to the eccentric force P = 45 kip, determine its maximum allowable length L without causing it to either buckle or yield.

The tube is made of copper and has an outer diameter of 35 mm and a wall thickness of 7 mm. Determine the eccentric load P that it can support without failure.The tube is pin supported at its ends. \(E_{\mathrm{cu}}=120 \mathrm{GPa}, \sigma_{Y}=750 \mathrm{MPa}\).

The wood column is pinned at its base and top. If L = 5 ft, determine the maximum eccentric load P that can be applied without causing the column to buckle or yield. \(E_{w}=1.8\left(10^{3}\right) \mathrm{ksi}, \sigma_{Y}=8 \mathrm{ksi}\).

The brass rod is ixed at one end and free at the other end. If the eccentric load P = 200 kN is applied, determine the greatest allowable length L of the rod so that it does not buckle or yield. \(E_{br}=101 \mathrm{GPa}, \sigma_{Y}=69 \mathrm{MPa}\).

The brass rod is fixed at one end and free at the other end. If the length of the rod is L = 2 m, determine the greatest allowable load P that can be applied so that the rod does not buckle or yield. Also, determine the largest sidesway delection of the rod due to the loading. \(E_{br}=101 \mathrm{GPa}, \sigma_{Y}=69 \mathrm{MPa}\).

A W12 X 26 structural A992 steel column is pin connected at its ends and has a length L = 11.5 ft. Determine the maximum eccentric load P that can be applied so the column does not buckle or yield. Compare this value with an axial critical load \(P^{\prime}\) applied through the centroid of the column.

A W14 X 30 structural A-36 steel column is pin connected at its ends and has a length L = 10 ft. Determine the maximum eccentric load P that can be applied so the column does not buckle or yield. Compare this value with an axial critical load \(P^{\prime}\) applied through the centroid of the column.

Determine the maximum eccentric load P the 2014-T6-aluminum-alloy strut can support without causing it either to buckle or yield. The ends of the strut are pin connected.

The 6061-T6 aluminum alloy solid shaft is ixed at one end but free at the other end. If the shaft has a diameter of 100 mm, determine its maximum allowable length L if it is subjected to the eccentric force P = 80 kN.

The 6061-T6 aluminum alloy solid shaft is ixed at one end but free at the other end. If the length is L = 3 m, determine its minimum required diameter if it is subjected to the eccentric force P = 60 kN.

The W14 X 53 structural A992 steel column is fixed at its base and free at its top. If P = 75 kip, determine the sidesway deflection at its top and the maximum stress in the column.

The W14 X 53 column is fixed at its base and free at its top. Determine the maximum eccentric load P that it can support without causing it to buckle or yield. \(E_{st}=29\left(10^{3}\right) \mathrm{ksi}\), sY = 50 ksi.

The stress–strain diagram for a material can be approximated by the two line segments shown. If a bar having a diameter of 80 mm and a length of 1.5 m is made from this material, determine the critical load provided the ends are pinned. Assume that the load acts through the axis of the bar. Use Engesser’s equation.

The stress–strain diagram for a material can be approximated by the two line segments shown. If a bar having a diameter of 80 mm and a length of 1.5 m is made from this material, determine the critical load provided the ends are fixed. Assume that the load acts through the axis of the bar. Use Engesser’s equation.

The stress–strain diagram for a material can be approximated by the two line segments shown. If a bar having a diameter of 80 mm and length of 1.5 m is made from this material, determine the critical load provided one end is pinned and the other is fixed. Assume that the load acts through the axis of the bar. Use Engesser’s equation.

The stress–strain diagram for the material of a column can be approximated as shown. Plot P/A vs. KL/r for the column.

Construct the buckling curve, P/A versus L/r, for a column that has a bilinear stress–strain curve in compression as shown.

The stress–strain diagram of the material can be approximated by the two line segments. If a bar having a diameter of 80 mm and a length of 1.5 m is made from this material, determine the critical load provided the ends are pinned. Assume that the load acts through the axis of the bar. Use Engesser’s equation.

The stress–strain diagram of the material can be approximated by the two line segments. If a bar having a diameter of 80 mm and a length of 1.5 m is made from this material, determine the critical load provided the ends are fixed. Assume that the load acts through the axis of the bar. Use Engesser’s equation.

The stress–strain diagram of the material can be approximated by the two line segments. If a bar having a diameter of 80 mm and a length of 1.5 m is made from this material, determine the critical load provided one end is pinned and the other is fixed. Assume that the load acts through the axis of the bar. Use Engesser’s equation.

Determine the largest length of a W10 X 12 structural A992 steel section if it is pin supported and is subjected to an axial load of 28 kip. Use the AISC equations.

Using the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is 14 ft long and supports an axial load of 40 kip. The ends are fixed.

Using the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is 14 ft long and supports an axial load of 40 kip. The ends are pinned. Take \(\sigma_{Y}=50 \mathrm{ksi}\).

Determine the longest length of a W8 X 31 structural A992 steel section if it is pin supported and is subjected to an axial load of 130 kip. Use the AISC equations.

Using the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is 12 ft long and supports an axial load of 20 kip. The ends are pinned.

Determine the longest length of a W10 X 12 structural A992 steel section if it is fixed supported and is subjected to an axial load of 28 kip. Use the AISC equations.

Using the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is 30 ft long and supports an axial load of 200 kip. The ends are fixed.

Determine the longest length of a W8 X 31 structural A992 steel section if it is pin supported and is subjected to an axial load of 18 kip. Use the AISC equations.

Using the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is 12 ft long and supports an axial load of 40 kip. The ends are fixed.

A 5-ft-long rod is used in a machine to transmit an axial compressive load of 3 kip. Determine its smallest diameter if it is pin connected at its ends and is made of a 2014-T6 aluminum alloy.

Determine the longest length of a W8 X 31 structural A992 steel column if it is to support an axial load of 10 kip. The ends are pinned.

Using the AISC equations, check if a column having the cross section shown can support an axial force of 1500 kN. The column has a length of 4 m, is made from A992 steel, and its ends are pinned.

The beam and column arrangement is used in a railroad yard for loading and unloading cars. If the maximum anticipated hoist load is 12 kip, determine if the W8 X 31 wide-lange A-36 steel column is adequate for supporting the load. The hoist travels along the bottom lange of the beam, 1 ft ? x ? 25 ft, and has negligible size. Assume the beam is pinned to the column at B and pin supported at A. The column is also pinned at C and it is braced so it will not buckle out of the plane of the loading.

The bar is made of a 2014-T6 aluminum alloy. Determine its smallest thickness b if its width is 5b. Assume that it is pin connected at its ends.

The bar is made of a 2014-T6 aluminum alloy. Determine its smallest thickness b if its width is 5b. Assume that it is fixed connected at its ends.

The 1-in.-diameter rod is used to support an axial load of 5 kip. Determine its greatest allowable length L if it is made of 2014-T6 aluminum. Assume that the ends are pin connected.

The 1-in.-diameter rod is used to support an axial load of 5 kip. Determine its greatest allowable length L if it is made of 2014-T6 aluminum. Assume that the ends are ixed connected.

The tube is 0.5 in. thick, is made of aluminum alloy 2014-T6, and is ixed connected at its ends. Determine the largest axial load that it can support.

The tube is 0.5 in. thick, is made from aluminum alloy 2014-T6, and is ixed at its bottom and pinned at its top. Determine the largest axial load that it can support.

The tube is 0.25 in. thick, is made of a 2014-T6 aluminum alloy, and is fixed at its bottom and pinned at its top. Determine the largest axial load that it can support.

The tube is 0.25 in. thick, is made of a 2014-T6 aluminum alloy, and is ixed connected at its ends. Determine the largest axial load that it can support.

The tube is 0.25 in. thick, is made of 2014-T6 aluminum alloy and is pin connected at its ends. Determine the largest axial load it can support.

A rectangular wooden column has the cross section shown. If the column is 6 ft long and subjected to an axial force of P = 15 kip, determine the required minimum dimension a of its cross-sectional area to the nearest \(\frac{1}{16} \text { in }\). so that the column can safely support the loading. The column is pinned at both ends.

A rectangular wooden column has the cross section shown. If a = 3 in. and the column is 12 ft long, determine the allowable axial force P that can be safely supported by the column if it is pinned at its top and fixed at its base.

A rectangular wooden column has the cross section shown. If a = 3 in. and the column is subjected to an axial force of P = 15 kip, determine the maximum length the column can have to safely support the load. The column is pinned at its top and fixed at its base.

The timber column has a square cross section and is assumed to be pin connected at its top and bottom. If it supports an axial load of 50 kip, determine its smallest side dimension a to the nearest \(\frac{1}{2} \text { in }\). Use the NFPA formulas.

The bar is made of aluminum alloy 2014-T6. Determine its thickness b if its width is 1.5b. Assume that it is fixed connected at its ends.

The timber column has a length of 18 ft and is pin connected at its ends. Use the NFPA formulas to determine the largest axial force P that it can support.

The timber column has a length of 18 ft and is fixed connected at its ends. Use the NFPA formulas to determine the largest axial force P that it can support.

The W8 X 15 wide-flange A-36 steel column is assumed to be pinned at its top and bottom. Determine the largest eccentric load P that can be applied using Eq. 13–30 and the AISC equations of Sec. 13.6.

Solve Prob. 13–107 if the column is fixed at its top and bottom. The W8 X 15 wide-flange A-36 steel column is assumed to be pinned at its top and bottom. Determine the largest eccentric load P that can be applied using Eq. 13–30 and the AISC equations of Sec. 13.6.

Solve Prob. 13–107 if the column is fixed at its bottom and pinned at its top. The W8 X 15 wide-flange A-36 steel column is assumed to be pinned at its top and bottom. Determine the largest eccentric load P that can be applied using Eq. 13–30 and the AISC equations of Sec. 13.6.

The W12 X 50 wide-flange A-36 steel column is fixed at its bottom and free at its top. Determine the greatest eccentric load P that can be applied using Eq. 13–30 and the AISC equations of Sec. 13.6.

The W8 X 15 wide-flange A992 steel column is fixed at its top and bottom. If it supports end moments of \(M=5 \mathrm{kip} \cdot \mathrm{ft}\), determine the axial force P that can be applied. Bending is about the x–x axis. Use the AISC equations of Sec. 13.6 and Eq. 13–30.

The W8 X 15 wide-flange A992 steel column is fixed at its top and bottom. If it supports end moments of \(M=23 \mathrm{kip} \cdot \mathrm{ft}\), determine the axial force P that can be applied. Bending is about the x–x axis. Use the interaction formula with \(\left(\sigma_{b}\right)_{\text {allow }}=24 \mathrm{ksi}\).

The W12 X 22 wide-flange A-36 steel column is fixed at its bottom and free at its top. Determine the greatest eccentric load P that can be applied using Eq. 13–30 and the AISC equations of Sec. 13.6.

The W10 X 15 wide-flange A-36 steel column is fixed at its bottom and free at its top. Determine the greatest eccentric load P that can be applied using Eq. 13–30 and the AISC equations of Sec. 13.6.

The W10 X 15 wide-flange A-36 steel column is fixed at its bottom and free at its top. If it is subjected to a load P = 2 kip, determine if it is safe based on the AISC equations of Sec. 13.6 and Eq. 13–30.

The W12 * 22 wide-flange A-36 steel column is fixed at its bottom and free at its top. If it is subjected to a load P = 4 kip, determine if it is safe based on the AISC equations of Sec. 13.6 and Eq. 13–30.

A 20-ft-long column is made of aluminum alloy 2014-T6. If it is pinned at its top and bottom, and a compressive load P is applied at point A, determine the maximum allowable magnitude of P using the equations of Sec. 13.6 and Eq. 13–30.

A 20-ft-long column is made of aluminum alloy 2014-T6. If it is pinned at its top and bottom, and a compressive load P is applied at point A, determine the maximum allowable magnitude of P using the equations of Sec. 13.6 and the interaction formula with \(\left(\sigma_{b}\right)_{\text {allow }}=20 \mathrm{ksi}\).

The 2014-T6 aluminum hollow column is fixed at its base and free at its top. Determine the maximum eccentric force P that can be safely supported by the column. Use the allowable stress method. The thickness of the wall for the section is t = 0.5 in.

The 2014-T6 aluminum hollow column is fixed at its base and free at its top. Determine the maximum eccentric force P that can be safely supported by the column. Use the interaction formula. The allowable bending stress is \(\left(\sigma_{b}\right)_{\text {allow }}=30 \mathrm{ksi}\). The thickness of the wall for the section is t = 0.5 in.

The 10-ft-long bar is made of aluminum alloy 2014-T6. If it is fixed at its bottom and pinned at the top, determine the maximum allowable eccentric load P that can be applied using the formulas in Sec. 13.6 and Eq. 13–30.

The 10-ft-long bar is made of aluminum alloy 2014-T6. If it is fixed at its bottom and pinned at the top, determine the maximum allowable eccentric load P that can be applied using the equations of Sec. 13.6 and the interaction formula with \(\left(\sigma_{b}\right)_{\text {allow }}=18 \mathrm{ksi}\).

Check if the wood column is adequate for supporting the eccentric load of P = 800 lb applied at its top. It is fixed at its base and free at its top. Use the NFPA equations of Sec. 13.6 and Eq. 13–30.

Determine the maximum allowable eccentric load P that can be applied to the wood column. The column is fixed at its base and free at its top. Use the NFPA equations of Sec. 13.6 and Eq. 13–30.

The 10-in.-diameter utility pole supports the transformer that has a weight of 600 lb and center of gravity at G. If the pole is fixed to the ground and free at its top, determine if it is adequate according to the NFPA equations of Sec. 13.6 and Eq. 13–30.

Using the NFPA equations of Sec. 13.6 and Eq. 13–30, determine the maximum allowable eccentric load P that can be applied to the wood column. Assume that the column is pinned at both its top and bottom.

Using the NFPA equations of Sec. 13.6 and Eq. 13–30, determine the maximum allowable eccentric load P that can be applied to the wood column. Assume that the column is pinned at the top and fixed at the bottom.