Questions and Answers of Mechanics Of Materials

Determine the displacement of point \(C\). The beam is made from A992 steel and has a moment of inertia of \(I=53.8 \mathrm{in}^{4}\). 8 kip A B -5 ft- -10 ft 5 ft-
Determine the slope at \(B\). The beam is made from A992 steel and has a moment of inertia of \(I=53.8 \mathrm{in}^{4}\). 8 kip A B -5 ft- 10 ft- -5 ft-
The beam is made of Douglas fir. Determine the slope at \(C\). 8 kN BO -1.5m 1.5m- -1.5 m- 180 mm H 120 mm
Determine the displacement at pulley \(B\). The A992 steel shaft has a diameter of \(30 \mathrm{~mm}\). 4 kN B 3 kN 0.4 m 0.4 m 0.3 m 1 kN 1 kN 0.3 m C
Determine the displacement at point \(D\). The A992 steel beam has a moment of inertia of \(I=125\left(10^{6}\right) \mathrm{mm}^{4}\). 18 kNm A 4m- D B3m 3m 41 4 m- 18 kNm
Determine the slope at \(A\). The A992 steel beam has a moment of inertia of \(I=125\left(10^{6}\right) \mathrm{mm}^{4}\). 18 kNm A -4 m- D B3m 3m 4m m- 18 kNm
Determine the slope at \(B\). The A992 structural steel beam has a moment of inertia of \(I=125\left(10^{6}\right) \mathrm{mm}^{4}\). 18 kNm A 4m- D 1-3m-3m-Ca 4 m. 18 kNm
Determine the displacement of end \(C\) of the overhang Douglas fir beam. A a 400 lb -8 ft. La 3 in. H 6 6 in. Section a-a B -4 ft 400 lb-ft
Determine the slope at \(A\) of the overhang white spruce beam. A a 400 lb -8 ft La 3 in. H 16 in. Section a-a B -4 ft. 400 lb-ft
Determine the slope at \(A\) of the 2014-T6 aluminum shaft having a diameter of \(100 \mathrm{~mm}\). A T 1 m C B 0.5 m 0.5 m 8 kN 8 kN 1 m
Determine the displacement at point \(C\) of the 2014-T6 aluminum shaft having a diameter of \(100 \mathrm{~mm}\). A 1 m 1 m 0.5 m 0.5 m 8 kN 8 kN B
Determine the displacement at point \(C\) of the W14 \(\times 26\) beam made from A992 steel. 8 kip A -5 ft 5 ft. B C -5 ft 5 ft- 8 kip D
Determine the slope at \(A\) of the W14 \(\times 26\) beam made from A992 steel. 8 kip A -5 ft 5 ft- B 8 kip C -5 ft 5 ft- D
Determine the slope at \(C\) of the overhang white spruce beam. A .D a La -4 ft. -4 ft 150 lb/ft 300 lb B -4 ft. C 3 in. H in. Section a-a
Determine the displacement at point \(D\) of the overhang white spruce beam. A -4 ft. 150 lb/ft 300 lb D La -4 ft -B 3 in. H 16 in. Section a-a -4 ft- C
Determine the maximum deflection of the beam caused only by bending, and caused by both bending and shear. Take \(E=3 G\). I W 7
The beam is made of oak, for which \(E_{0}=11 \mathrm{GPa}\). Determine the slope and displacement at point \(A\). 200 mm 400 mm I A 4 kN/m -3 m- + -3 m- B
Determine the slope of the shaft at the bearing support \(A\). \(E I\) is constant. 22 Wo C B
Determine the vertical displacement of point \(A\) on the angle bracket due to the concentrated force \(\mathbf{P}\). The bracket is fixed connected to its support. EI is constant. Consider only the
Determine the vertical displacement of point \(C\). The frame is made using A-36 steel W250 \(\times 45\) members. Consider only the effect of bending. 15 kN D 15 kN/m 5 m A B C -2.5 m- -2.5 m-
Determine the horizontal displacement of end \(B\). The frame is made using A-36 steel W \(250 \times 45\) members. Consider only the effect of bending. 15 kN 5 m A 15 kN/m B C -2.5 m- -2.5 m
The L-shaped frame is made from two segments, each of length \(L\) and flexural stiffness \(E I\). Determine the horizontal displacement of point \(C\). W C L A B- -L-
The L-shaped frame is made from two segments, each of length \(L\) and flexural stiffness \(E I\). Determine the vertical displacement of point \(B\). W C L A B -L-
Determine the vertical displacement of the ring at point \(B\). \(E I\) is constant. B P A
Determine the horizontal displacement of the roller at \(A\) due to the loading. \(E I\) is constant. PA B
The 6-ft-long column has the cross section shown and is made of material which has a stress-strain diagram that can be approximated by the two line segments. If the column is pinned at both ends,
The 6-ft-long column has the cross section shown and is made of material which has a stress-strain diagram that can be approximated by the two line segments. If the column is fixed at both ends,
The stress-strain diagram for the material of a column can be approximated as shown. Plot \(P / A\) versus \(K L / r\) for the column. (MPa) 350- 200- (in./in.) 0 0.001 0.004
Construct the buckling curve, \(P / A\) versus \(L / r\), for a column that has a bilinear stress-strain curve in compression as shown. The column is pinned at its ends. 260 (MPa) 140 E (mm/mm)
The stress-strain diagram of a material can be approximated by the two line segments. If a bar having a diameter of \(80 \mathrm{~mm}\) and a length of \(1.5 \mathrm{~m}\) is made from this material,
The stress-strain diagram for a material can be approximated by the two line segments. If a bar having a diameter of \(80 \mathrm{~mm}\) and a length of \(1.5 \mathrm{~m}\) is made from this
The stress-strain diagram for a material can be approximated by the two line segments. If a bar having a diameter of 80 \(\mathrm{mm}\) and length of \(1.5 \mathrm{~m}\) is made from this material,
The stress-strain diagram for a material can be approximated by the two line segments. If a bar having a diameter of \(80 \mathrm{~mm}\) and length of \(1.5 \mathrm{~m}\) is made from this material,
Determine the largest length of a structural A-36 steel rod if it is fixed supported and subjected to an axial load of \(100 \mathrm{kN}\). The rod has a diameter of \(50 \mathrm{~mm}\). Use the AISC
Use the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is \(14 \mathrm{ft}\) long and supports an axial load of 40 kip. The ends are pinned. Take
Using the AISC equations, select from Appendix B the lightest-weight structural A-36 steel column that is \(24 \mathrm{ft}\) long and supports an axial load of 100 kip. The ends are fixed.
Using the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is \(12 \mathrm{ft}\) long and supports an axial load of 20 kip. The ends are pinned.
Determine the longest length of a W10 \(\times 12\) structural A992 steel section if it is fixed supported and is subjected to an axial load of \(28 \mathrm{kip}\). Use the AISC equations.
Using the AISC equations, select from Appendix B the lightest-weight wide-flange A992 steel column that is \(30 \mathrm{ft}\) long and supports an axial load of \(200 \mathrm{kip}\). The ends are
A W8 \(\times 24\) A-36 steel column is \(30 \mathrm{ft}\) long and is pinned at both ends and braced against its weak axis at mid height. Determine the allowable axial force \(P\) that can be safely
Check if a W10 \(\times 39\) column can safely support an axial force of \(P=250 \mathrm{kip}\). The column is \(20 \mathrm{ft}\) long and is pinned at both ends and braced against its weak axis at
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.
Using the AISC equations, determine the longest length of a W8 \(\times 31\) column. The column is made of A992 steel and it supports 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 \(1500 \mathrm{kN}\). The column has a length of \(4 \mathrm{~m}\), is made from A992 steel,
If the maximum anticipated hoist load is 12 kip, determine if the W8 \(\times 31\) wide-flange A-36 steel column is adequate for supporting the load. The hoist travels along the bottom flange of the
The 2014-T6 aluminum hollow section has the cross section shown. If the column is \(10 \mathrm{ft}\) long and is fixed at both ends, determine the allowable axial force \(P\) that can be safely
The 2014-T6 aluminum hollow section has the cross section shown. If the column is fixed at its base and pinned at its top, and is subjected to the axial force \(P=100\) kip, determine the maximum
The column is made of wood. It is fixed at its bottom and free at its top. Use the NFPA formulas to determine its greatest allowable length if it supports an axial force of \(P=6\) kip. 3 in. y x. P
The column is made of wood. It is fixed at its bottom and free at its top. Use the NFPA formulas to determine the largest allowable axial force \(P\) that it can support if it has a length \(L=6
The 2014-T6 aluminum column is \(3 \mathrm{~m}\) long and has the cross section shown. If the column is pinned at both ends and braced against the weak axis at its mid height, determine the allowable
The 2014-T6 aluminum column has the cross section shown. If the column is pinned at both ends and subjected to an axial force \(P=100 \mathrm{kN}\), determine the maximum length of the column. 15 mm]
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 force that it can support. 6 in. y. x P 6 in. x 10 ft P
The tube is 0.25 in. thick, is made of a 2014-T6 aluminum alloy, and is fixed connected at its ends. Determine the largest axial force that it can support. 6 in. y 6 in. x 10 ft P
The tube is 0.25 in. thick, is made of a 2014-T6 aluminum alloy and is pin connected at its ends. Determine the largest axial force it can support. 6 in. y 10 ft P 6 in. x P
A rectangular wooden column has the cross section shown. If the column is \(6 \mathrm{ft}\) long and subjected to an axial force of \(P=15\) kip, determine the required minimum dimension \(a\) of its
A rectangular wooden column has the cross section shown. If \(a=3\) in. and the column is \(12 \mathrm{ft}\) long, determine the allowable axial force \(P\) that can be safely supported by the column
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
The wooden column is formed by gluing together the 6 in. \(X\) 0.5 in. boards. If the column is pinned at both ends and is subjected to an axial force of \(P=20 \mathrm{kip}\), determine the required
The bar is made from a 2014-T6 aluminum alloy. Determine its thickness \(b\) if its width is \(1.5 b\). Assume that it is fixed connected at its ends. b 800 lb 5 ft 800 lb 1.5b
The timber column has a length of \(18 \mathrm{ft}\) and is pin connected at its ends. Use the NFPA formulas to determine the largest axial force \(P\) that it can support. 6 in. 5 -5 in. P 18 ft
The timber column has a length of \(18 \mathrm{ft}\) and is fixed connected at its ends. Use the NFPA formulas to determine the largest axial force \(P\) that it can support. 6 in. P -5 in. P 18 ft
The W8 \(\times 15\) 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
Solve Prob. 13-107 if the column is fixed at its bottom and pinned at its top.Data from Prob. 13-107The W8 \(\times 15\) wide-flange A-36 steel column is assumed to be pinned at its top and bottom.
The W10×19 structural A992 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
The W12 \(\times 50\) 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
The W14 \(\times 43\) structural 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
The W10 \(\times 45\) structural A-36 steel column is fixed at its bottom and free at its top. If it is subjected to a load of \(P=2\) kip, determine if it is safe based on the AISC equations of Sec.
The W14 \(\times 22\) structural A-36 steel column is fixed at its top and bottom. If a horizontal load (not shown) causes it to support end moments of \(M=10 \mathrm{kip} \cdot \mathrm{ft}\),
The W14 \(\times 22\) column is fixed at its top and bottom. If a horizontal load (not shown) causes it to support end moments of \(M=15 \mathrm{kip} \cdot \mathrm{ft}\), determine the maximum
The W14 \(\times 53\) structural A-36 steel column supports an axial load of 80 kip in addition to an eccentric load \(P\). Determine the maximum allowable value of \(P\) based on the AISC equations
The W12 \(\times 45\) structural A-36 steel column supports an axial load of 80 kip in addition to an eccentric load of \(P=60\) kip. Determine if the column fails based on the AISC equations of Sec.
A 20 -ft-long column is made from a 2014-T6 aluminum alloy. If it is pinned at its top and bottom, and a compressive force \(\mathbf{P}\) is applied at point \(A\), determine the maximum allowable
A 20-ft-long column is made of aluminum alloy 2014-T6. If it is pinned at its top and bottom, and a compressive force \(\mathbf{P}\) is applied at point \(A\), determine the maximum allowable
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 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
The rectangular wooden column can be considered fixed at its base and pinned at its top. Also, the column is braced at its mid height against the weak axis. Determine the maximum eccentric force
The rectangular wooden column can be considered fixed at its base and pinned at its top. Also, the column is braced at its mid height against the weak axis. Determine the maximum eccentric force
Check if the column is adequate for supporting the eccentric force of \(P=800 \mathrm{lb}\) applied at its top. It is fixed at its base and free at its top. Use the NFPA equations of Sec. 13.6 and
Determine the maximum allowable eccentric force \(P\) that can be applied to the 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. 5 in.
The 10-in.-diameter utility pole supports the transformer that has a weight of \(600 \mathrm{lb}\) and center of gravity at \(G\). If the pole is fixed to the ground and free at its top, determine if
Determine if the column can support the eccentric compressive load of \(1.5 \mathrm{kip}\). Assume that the ends are pin connected. Use the NFPA equations in Sec. 13.6 and Eq. 13-30. 3 in 1.5 kip 12
Determine if the column can support the eccentric compressive load of \(1.5 \mathrm{kip}\). Assume that the bottom is fixed and the top is pinned. Use the NFPA equations in Sec. 13.6 and Eq. 13-30. 3
Determine the total axial and bending strain energy in the A992 steel beam. \(A=2300 \mathrm{~mm}^{2}, I=9.5\left(10^{6}\right) \mathrm{mm}^{4}\). 1.5 kN/m 10 m 15 kN
The 200-kg block \(D\) is dropped from rest at a height \(h=1 \mathrm{~m}\) onto end \(C\) of the A992 steel W200 \(\times 36\) overhang beam. If the spring at \(B\) has a stiffness \(k=200
Determine the maximum height \(\mathrm{h}\) from which the \(200-\mathrm{kg}\) block \(D\) can be dropped from rest without causing the A992 steel W200 \(\times 36\) overhang beam to yield. The
The A992 steel bars are pin connected at \(B\) and \(C\). If they each have a diameter of \(30 \mathrm{~mm}\), determine the slope at \(E\). Neglect the axial load in each member. A 300 N-m B C E 3m
The steel chisel has a diameter of \(0.5 \mathrm{in}\). and a length of \(10 \mathrm{in}\). It is struck by a hammer that weighs \(3 \mathrm{lb}\), and at the instant of impact it is moving at \(12
Determine the total axial and bending strain energy in the A992 structural steel W8 \(\times 58\) beam. 5 kip -10 ft 10 ft- 30 3 kip
Determine the vertical displacement of joint \(C\). The truss is made from A992 steel rods each having a diameter of 1 in. 60 60 12 kip B 6 ft
Determine the horizontal displacement of joint \(B\). The truss is made from A992 steel rods each having a diameter of 1 in. A 60 60 12 kip B 6 ft
The cantilevered beam is subjected to a couple moment \(\mathbf{M}_{0}\) applied at its end. Determine the slope of the beam at \(B\). \(E I\) is constant. Use the method of virtual work. A -L B Mo
Solve Prob. R14-9 using Castigliano’s theorem.Data from Prob. R14-9The cantilevered beam is subjected to a couple moment \(\mathbf{M}_{0}\) applied at its end. Determine the slope of the beam at
Determine the slope and displacement at point \(C\). \(E I\) is constant. W AQ -2a B W a C
A material is subjected to a general state of plane stress. Express the strain energy density in terms of the elastic constants \(E, G\), and \(u\) and the stress components \(\sigma_{x},
The strain energy density for plane stress must be the same whether the state of stress is represented by \(\sigma_{x}, \sigma_{y}\), and \(\tau_{x y}\), or by the principal stresses \(\sigma_{1}\)
The A-36 steel bar consists of two segments, one of circular cross section of radius \(r\), and one of square cross section. If the bar is subjected to the axial loading of \(P\), determine the
Determine the strain energy in the rod assembly. Portion \(A B\) is steel, \(B C\) is brass, and \(C D\) is aluminum. \(E_{\mathrm{st}}=200 \mathrm{GPa}, E_{\mathrm{br}}=101 \mathrm{GPa}\), and
Using bolts of the same material and cross-sectional area, two possible attachments for a cylinder head are shown. Compare the strain energy developed in each case, and then explain which design is
If \(P=150 \mathrm{kN}\), determine the total strain energy stored in the truss. Each member has a cross-sectional area of \(8.0\left(10^{3}\right) \mathrm{mm}^{2}\) and is made of A-36 steel. P D -3
Determine the maximum force \(P\) and the corresponding maximum total strain energy stored in the truss without causing any of the members to have permanent deformation. Each member has the

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