Questions and Answers of Mechanics Of Materials

Determine the maximum force \(P\) that can be applied to the handle so that the A-36 steel control rod \(B C\) does not buckle. The rod has a diameter of \(25 \mathrm{~mm}\). 350 mm A 250 mm B 45
The 2014-T6 aluminum rod \(B C\) has a diameter of 2 in. 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
If load \(C\) has a mass of \(500 \mathrm{~kg}\), determine the required minimum diameter of the solid L2-steel \(\operatorname{rod} A B\) to the nearest \(\mathrm{mm}\) so that it will not buckle.
If the diameter of the solid L2-steel \(\operatorname{rod} A B\) is \(50 \mathrm{~mm}\), determine the maximum mass \(C\) that the rod can support without buckling. Use F.S. \(=2\) against buckling.
The column is supported at \(B\) by a support that does not permit rotation but allows vertical displacement. Determine the critical load \(P_{\mathrm{cr}} . E I\) is constant. Per A L B
The members of the truss are assumed to be pin connected. If member \(A C\) is an \(\mathrm{A}-36\) steel rod of 2 in. diameter, determine the maximum load \(P\) that can be supported by the truss
The steel bar \(A B\) 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 \(B C\)
The two steel channels are to be laced together to form a 30 -ft-long bridge column assumed to be pin connected at its ends. Each channel has a cross-sectional area of \(A=3.10 \mathrm{in}^{2}\) and
The steel bar AB of the frame is assumed to be pin connected at its ends for y-y axis buckling. If w = 3 kN/m, determine the factor of safety with respect to y-y axis buckling. Take Est =200 GPa, σy
A 6061-T6 aluminum alloy solid circular rod of length \(4 \mathrm{~m}\) is pinned at both of its ends. If it is subjected to an axial load of \(15 \mathrm{kN}\) and F.S. \(=2\) against buckling,
A 6061-T6 aluminum alloy solid circular rod of length \(4 \mathrm{~m}\) is pinned at one end while fixed at the other end. If it is subjected to an axial load of \(15 \mathrm{kN}\) and F.S. \(=2\)
The members of the truss are assumed to be pin connected. If member \(B D\) is an \(\mathrm{A} 992\) steel rod having a radius of 2 in., determine the maximum load \(P\) that can be supported by the
Solve Prob. 13-36 for member \(A B\), which has a radius of 2 in.Data from Prob. 13-36The members of the truss are assumed to be pin connected. If member \(B D\) is an \(\mathrm{A} 992\) steel rod
The linkage is made using two A992 steel rods, each having a circular cross section. Determine the diameter of each rod to the nearest 1/8 in. that will support a load of P = 6 kip. Assume that the
The linkage is made using two A992 steel rods, each having a circular cross section. If each rod has a diameter of \(\frac{3}{4}\) in., determine the largest load it can support without causing any
The steel bar AB of the frame is assumed to be pin connected at its ends for \(y-y\) axis buckling. If \(P=18 \mathrm{kN}\), determine the factor of safety with respect to buckling. Take
The ideal column has a weight \(w\) (force/length) and is subjected to the axial load \(\mathbf{P}\). Determine the maximum moment in the column at midspan. \(E I\) is constant. Establish the
The ideal column is subjected to the force \(\mathbf{F}\) at its midpoint and the axial load \(\mathbf{P}\). Determine the maximum moment in the column at midspan. \(E I\) is constant. Hint:
The column with constant \(E I\) has the end constraints shown.Determine the critical load for the column. L
Consider an ideal column as in Fig. 13-10c, having both ends fixed. Show that the critical load on the column is \(P_{\text {cr }}=4 \pi^{2} E I / L^{2}\). Due to the vertical deflection of the top
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 \(P_{\text {cr }}=20.19 E I / L^{2}\). Hint: Due to the vertical
Determine the \(\operatorname{load} P\) required to cause the A-36 steel W8 \(\times 15\) column to fail either by buckling or by yielding.The column is fixed at its base and free at its top. 1 in. P
The tube is made of C86100 bronze and has an outer diameter of \(60 \mathrm{~mm}\) and a wall thickness of \(10 \mathrm{~mm}\). Determine the eccentric load \(P\) that it can support without failure.
Solve Prob. 13-47 if instead the tube is free at one end and fixed at the other.Data from Prob. 13-47The tube is made of C86100 bronze and has an outer diameter of \(60 \mathrm{~mm}\) and a wall
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
A column of intermediate length buckles when the compressive stress is \(40 \mathrm{ksi}\). If the slenderness ratio is 60 , determine the tangent modulus. 5 mm- 200 mm- L
The aluminum rod is fixed at its base and free at its top. If the eccentric load \(P=200 \mathrm{kN}\) is applied, determine the greatest allowable length \(L\) of the rod so that it does not buckle
The aluminum rod is fixed at its base and free at its top. If the length of the rod is \(L=2 \mathrm{~m}\), determine the greatest allowable load \(P\) that can be applied so that the rod does not
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.
Assume that the wood column is pinned top and bottom for movement about the \(x-x\) axis, and fixed at the bottom and free at the top for movement about the \(y-y\) axis. Determine the maximum
A W14 \(\times 30\) structural A992 steel column is pin connected at is ends and has a length \(L=12 \mathrm{ft}\). Determine the maximum eccentric load \(P\) that can be applied so the column does
A W16 \(\times 45\) structural A992 steel column is fixed at the base and free at the top and has a length \(L=8 \mathrm{ft}\). Determine the maximum eccentric load \(P\) that can be applied so the
Determine the \(\operatorname{load} P\) required to cause the steel \(\mathrm{W} 12 \times 50\) structural A-36 steel column to fail either by buckling or by yielding. The column is fixed at its
Solve Prob. 13-57 if the column is an A-36 steel W12 \(\times 16\) section.Data from Prob. 13-57Determine the \(\operatorname{load} P\) required to cause the steel \(\mathrm{W} 12 \times 50\)
The tube is made of copper and has an outer diameter of \(35 \mathrm{~mm}\) and a wall thickness of \(7 \mathrm{~mm}\). Determine the eccentric load \(\mathrm{P}\) that it can support without
The wood column is pinned at its base and top. If \(L=5 \mathrm{ft}\), determine the maximum eccentric load \(P\) that can be applied without causing the column to buckle or yield.
The brass rod is fixed at one end and free at the other end. If the eccentric load \(P=200 \mathrm{kN}\) is applied, determine the greatest allowable length \(L\) of the rod so that it does not
The brass rod is fixed at one end and free at the other end. If the length of the rod is \(L=2 \mathrm{~m}\), determine the greatest allowable load \(P\) that can be applied so that the rod does not
Determine the equation of the elastic curve. Use discontinuity functions. \(E I\) is constant. A -12 in-12 in 70 lb -36 in.- 180 lb B
Draw the bending-moment diagram for the shaft and then, from this diagram, sketch the deflection or elastic curve for the shaft's centerline. Determine the equations of the elastic curve using the
Determine the moment reactions at the supports \(A\) and \(B\). Use the method of integration. \(E I\) is constant. Wo 111 A L B
Determine the reactions, then draw the shear and moment diagrams. Use the moment-area theorems. \(E I\) is constant. A m -1 m 200 N B 2 m. C
Using the method of superposition, determine the magnitude of \(\mathbf{M}_{0}\) in terms of the distributed load \(w\) and dimension \(a\) so that the deflection at the center of the beam is zero.
Using the method of superposition, determine the displacement at \(C\) of beam \(A B\). The beams are made of wood having a modulus of elasticity of \(E=1.5\left(10^{3}\right) \mathrm{ksi}\). DA -a B
The column has a thickness of 4 in. and a width of 6 in. Using the NFPA equations of Sec. 13.6 and Eq. 13-30, determine the maximum allowable eccentric force \(P\) that can be applied.Assume that the
The column has a thickness of 4 in. and a width of 6 in. Using the NFPA equations of Sec. 13.6 and Eq. 13-30, determine the maximum allowable eccentric force \(P\) that can be applied. Assume that
A steel column has a length of \(5 \mathrm{~m}\) and is free at one end and fixed at the other end. If the cross-sectional area has the dimensions shown, determine the critical
The square structural A992 steel tubing has outer dimensions of 8 in. by 8 in. Its cross-sectional area is \(14.40 \mathrm{in}^{2}\) and its moments of inertia are \(I_{x}=I_{y}=131
If the A-36 steel solid circular rod \(B D\) has a diameter of 2 in., determine the allowable maximum force \(P\) that can be supported by the frame without causing the rod to buckle. Use F.S. \(=2\)
If \(P=15\) kip, determine the required minimum diameter of the A992 steel solid circular rod \(B D\) to the nearest \(\frac{1}{16} \mathrm{in}\). Use F.S. \(=2\) against buckling. A B 4 ft D 3 ft 3
The steel pipe is fixed supported at its ends. If it is \(4 \mathrm{~m}\) long and has an outer diameter of \(50 \mathrm{~mm}\), determine its required thickness so that it can support an axial force
The W200 \(\times 46\) wide-flange A992-steel column can be considered pinned at its top and fixed at its base. Also, the column is braced at its mid-height against weak axis buckling. Determine the
The wide-flange A992 steel column has the cross section shown. If it 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
The wide-flange A992 steel column has the cross section shown. If it is fixed at the bottom and free at the top, determine if the column will buckle or yield when the force \(P=10 \mathrm{kN}\) is
An L2 steel strap having a thickness of 0.125 in. and a width of \(2 \mathrm{in}\). is bent into a circular arc of radius \(600 \mathrm{in}\). Determine the maximum bending stress in the strap.
The L2 steel blade of the band saw wraps around the pulley having a radius of \(12 \mathrm{in}\). Determine the maximum normal stress in the blade. The blade has a width of 0.75 in. and a thickness
A picture is taken of a man performing a pole vault, and the minimum radius of curvature of the pole is estimated by measurement to be \(4.5 \mathrm{~m}\). If the pole is \(40 \mathrm{~mm}\) in
Determine the equation of the elastic curve and the maximum deflection of the cantilever beam. A x L Wo
Determine the displacement of end \(\mathrm{C}\) of the 100 -mm-diameter solid circular shaft. The shaft is made of steel having a modulus of elasticity of \(E=200 \mathrm{GPa}\). B C -2 m- 1 m- x2 6
Determine the maximum deflection of the 150 -mm-diameter solid circular shaft. The shaft is made of steel having \(E=200 \mathrm{GPa}\). 6 kNm A B -x1- 1 m 2 m 9 kN C
Determine the equation of the elastic curve in terms of the \(x_{1}\) and \(x_{2}\) coordinates. What is the deflection of end \(C\) of the shaft? \(E I\) is constant. Ix- L B 2x. Mo
Determine the equation of the elastic curve in terms of the \(x_{1}\) and \(x_{2}\) coordinates and the deflection of end \(C\) of the overhang beam. \(E I\) is constant. x1 L- W B C X2
A torque wrench is used to tighten the nut on a bolt. If the dial indicates that a torque of \(60 \mathrm{lb} \cdot \mathrm{ft}\) is applied when the bolt is fully tightened, determine the force
The pipe can be assumed roller supported at its ends and by a rigid saddle \(\mathrm{C}\) at its center. The saddle rests on a cable that is connected to the supports. Determine the force that should
Determine the equation of the elastic curve and determine the maximum deflection. \(E I\) is constant. 2Mo A Mo B -L-
Determine the maximum slope of the beam. \(E I\) is constant. A . We L B
Determine the maximum deflection of the beam. \(E I\) is constant. A L Wo B
Determine the maximum deflection of the solid circular shaft. The shaft is made of steel having \(E=200 \mathrm{GPa}\). It has a diameter of \(100 \mathrm{~mm}\). 6 kNm 8 kN -x 1.5 m 1.5 m B 6 kNm
Wooden posts used for a retaining wall have a diameter of 3 in. If the soil pressure along a post varies uniformly from zero at the top \(A\) to a maximum of \(300 \mathrm{lb} / \mathrm{ft}\) at the
Determine the displacement at the center of the beam and the slope at \(B\). \(E I\) is constant. Mo A |x- -L Mo B
The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of \(6 \mathrm{in}\).
The tapered beam has a rectangular cross section. Determine the deflection of its center in terms of the load \(P\), length \(L\), modulus of elasticity \(E\), and the moment of inertia \(I_{c}\) of
The beam is made of a material having a specific weight of \(\gamma\). Determine the displacement and slope at its end \(A\) due to its weight. The modulus of elasticity for the material is \(E\). L
The beam is made of a material having a specific weight \(\gamma\). Determine the displacement and slope at its end \(A\) due to its weight. The modulus of elasticity for the material is \(E\). h L A
The shaft is made of steel and has a diameter of \(15 \mathrm{~mm}\). Determine its maximum deflection. The bearings at \(A\) and \(B\) exert only vertical reactions on the shaft.
The shaft supports the two pulley loads shown. If the bearings only exert vertical reactions on the shaft, determine the equation of the elastic curve. EI is constant. 20 in. 40 lb B -20 in. -20 in.
Determine the maximum deflection of the simply supported beam. \(E=200 \mathrm{GPa}\) and \(I=65.0\left(10^{6}\right) \mathrm{mm}^{4}\). 30 kN 15 kN 2 m -2 m- m B
Determine the equation of the elastic curve. \(E I\) is constant. 20 kN -B 20 kN -1.5 m- -3 m. -1.5 m-
Determine the equations of the slope and elastic curve. \(E I\) is constant. 2 kN/m -5 m B -3 m- 8 kNm
Determine the equation of the elastic curve and the maximum deflection of the simply supported beam. \(E I\) is constant. -- Mo Mo B -- C -- D
Determine the equation of the elastic curve. \(E I\) is constant. 6 kN/m -1.5 m- 3 m- B 20 kN -1.5 m-
Determine the maximum deflection of the cantilever beam. Take \(E=200 \mathrm{GPa}\) and \(I=65.0\left(10^{6}\right) \mathrm{mm}^{4}\). A 30 kN/m -1.5 m- -1.5 m 15 kN
Determine the equation of the elastic curve. \(E I\) is constant. x 3 kN/m 50 kN 3 m. 3 m- 4 m B
Determine the displacement at \(x=7 \mathrm{~m}\) and the slope at \(A\).\(E I\) is constant. x 3 kN/m 50 kN 3 m 3 m 4 m B
Determine the equation of the elastic curve, the slope at \(A\), and the maximum deflection of the simply supported beam. \(E I\) is constant. A 3 13 3 B
Determine the equation of the elastic curve. \(E I\) is constant. A 4 kip 8 ft. 6 kip-ft 8 ft 6 kip-ft 8 ft B
Determine the equation of the elastic curve. \(E I\) is constant. 9 ft A -15 ft- 6 kip/ft B
Determine the displacement at each of the pulleys \(C, D\), and \(E\). The shaft is made of steel and has a diameter of \(30 \mathrm{~mm}\). The bearings at \(A\) and \(B\) exert only vertical
Determine the slope of the shaft at \(A\) and \(B\). The shaft is made of steel and has a diameter of \(30 \mathrm{~mm}\). The bearings only exert vertical reactions on the shaft.
Determine the equation of the elastic curve. Specify the slopes at \(A\) and \(B\). EI is constant. w B
The wooden beam is subjected to the load shown. Determine the equation of the elastic curve. Specify the deflection at the end C. \(E_{w}=1.6\left(10^{3}\right) \mathrm{ksi}\). A -x -9 ft 0.8 kip/ft
The wooden beam is subjected to the load shown. Determine the equation of the elastic curve. If \(E_{\mathrm{w}}=12 \mathrm{GPa}\), determine the displacement and the slope at end \(B\). A -3 m 6 kN
Determine the displacement of end \(B\) of the cantilever beam. \(E I\) is constant. 22 B
Determine the displacement at \(C\) and the slope of the beam at \(A, B\), and \(C\). \(E I\) is constant. A B 8 kNm -6 m + -3 m
The composite simply supported steel shaft is subjected to a force of \(10 \mathrm{kN}\) at its center. Determine its maximum deflection. \(E_{\mathrm{st}}=200 \mathrm{GPa}\). 200 mm A 200 mm 200 mm
Determine the magnitude of force \(\mathbf{F}\) that must be applied at the end of the overhang \(C\) so that when the force \(\mathbf{P}\) is applied, displacement at \(C\) is zero. \(E I\) is
Determine the slope at \(A\) and the maximum deflection. \(E I\) is constant. 20 kip.ft 6 ft A 12 ft- B 6 ft 20 kip-ft
Determine the maximum deflection of the 50 -mm-diameter A-36 steel shaft. 500 mm 800 mm 1200 mm 300 N 300 N 600 N 600 N B
Determine the slope of the 50 -mm-diameter A-36 steel shaft at the journal bearings at \(A\) and \(B\). The bearings exert only vertical reactions on the shaft. A 500 mm 800 mm 300 N 1200 mm D 300 N
Determine the slope at \(A\) of the simply supported beam.EI is constant. B - d --

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