Questions and Answers of Mechanics Of Materials

Determine the maximum deflection of the shaft. \(E I\) is constant. The bearings exert only vertical reactions on the shaft. 312 22 B
The beam is subjected to the loading shown. Determine the slope at \(B\) and displacement at \(C\). \(E I\) is constant. Ta Mo C b B
The two A-36 steel bars have a thickness of \(1 \mathrm{in}\). and a width of \(4 \mathrm{in}\). They are designed to act as a spring for the machine which exerts a force of 4 kip on them at \(A\)
The beam is made of a ceramic material. In order to obtain its modulus of elasticity, it is subjected to the elastic loading shown. If the moment of inertia is \(I\) and the beam has a measured
If the bearings at \(A\) and \(B\) exert only vertical reactions on the shaft, determine the displacement at \(C\) and the slopes at the bearings \(A\) and \(B\). EI is constant. 22 P
If the bearings at \(A\) and \(B\) exert only vertical reactions on the shaft, determine the maximum deflection within region \(A B\). \(E I\) is constant. -- 22 C P
If the bearings at \(A\) and \(B\) exert only vertical reactions on the shaft, determine the slope at \(A\) and the maximum deflection of the shaft. \(E I\) is constant. 50 lb-ft 50 lb-ft A B 2 ft 4
If the bearings at \(A\) and \(B\) only exert vertical reactions on the shaft, determine the slope at \(A\) and the displacement at C. EI is constant. A -a Mo Mo B C a
Determine the slope at \(A\) and the maximum deflection in the beam. \(E I\) is constant. 24 kip-ft 12 kip -6ft 6 ft- -12 ft- -6 ft- B
Determine the deflection and slope at \(C\). \(E I\) is constant. A B -L + L Mo
The two force components act on the tire of the automobile. The tire is xed to the axle, which is supported by bearings at \(A\) and \(B\). Determine the maximum deflection of the axle. Assume that
If the bearings at \(A\) and \(B\) exert only vertical reactions on the shaft, determine the slope at \(A\) and the maximum deflection. A La- P C -2a Mo - Pa D a B
The rod is constructed from two shafts for which the moment of inertia of \(A B\) is \(I\) and of \(B C\) is 2 I. Determine the maximum slope and displacement of the rod due to the loading. The
Determine the slope at point \(A\) and the maximum deflection of the simply supported beam. The beam is made of material having a modulus of elasticity \(E\). The moment of inertia of segments \(A
The W10 \(\times 15\) cantilever beam is made of A-36 steel and is subjected to the loading shown. Determine the slope and displacement at its end \(B\). A 3 kip/ft 6 ft. -6 ft B
Determine the slope at \(B\) and displacement at \(C . E I\) is constant. W W C02 312
The two bars are pin connected at \(D\). Determine the slope at \(A\) and the displacement at \(D\). \(E I\) is constant. B 212 L2
Determine the slope at \(C\) and displacement at \(B\). \(E I\) is constant. A a W B
The W10 \(\times 15\) cantilever beam is made of A-36 steel and is subjected to the loading shown. Determine the slope and displacement at its end \(B\). A 3 kip/ft -6 ft -6 ft - B
The W14 \(\times 30\) cantilever beam is made of A-36 steel and is subjected to the loading shown. Determine the slope and displacement at its end \(B\). 2 kip/ft A 6 ft 6 ft. B 30 kip-ft
The W14 \(\times 43\) simply supported beam is made of A992 steel and is subjected to the loading shown. Determine the displacement of its center \(C\). 60 kip-ft A -x T -12 ft- 3 kip/ft 12 ft B
The W14 \(\times 43\) simply supported beam is made of A992 steel and is subjected to the loading shown. Determine the slope at \(A\) and \(B\). 60 kip ft A 12 ft- C 3 kip/ft 12 ft B
The W12 \(\times 45\) simply supported beam is made of A-36 steel and is subjected to the loading shown. Determine the displacement of at its center \(C\). 50 kip-ft 12 kip A 12 ft C 12 ft B
The W14 \(\times 43\) simply supported beam is made of A-36 steel and is subjected to the loading shown. Determine the slope at \(A\) and \(B\). 2 kip/ft 10 ft C 10 ft B 40 kip-ft
Determine the slope at \(A\) and the displacement of at point \(C\) of the simply supported beam. The modulus of elasticity of the wood is \(E=10 \mathrm{GPa}\). A 3 kN 3 kN -1.5 m-1.5 m- 3 m. 100 mm
The simply supported beam is made of A-36 steel and is subjected to the loading shown. Determine the displacement of its center \(C\). Take \(I=0.1457\left(10^{-3}\right) \mathrm{m}^{4}\). 20 kN 4
The \(\mathrm{W} 10 \times 30\) cantilever beam is made of A-36 steel and is subjected to unsymmetrical bending caused by the applied moment. Determine the displacement of the centroid at its end
The W \(8 \times 24\) simply supported beam is made of A-36 steel and is subjected to the loading shown. Determine the displacement of its center \(C\). A 6 kip/ft C -8 ft- -8 ft- 5 kip-ft B
Determine the slope at \(B\) and the displacement of point \(C\) of the simply supported beam. Take \(E=200 \mathrm{GPa}\) and \(I=45.5\left(10^{6}\right) \mathrm{mm}^{4}\). A -3 m 10 kN 9 kN/m C 3 m
The simply supported beam is subjected to a uniform load of \(2 \mathrm{kip} / \mathrm{ft}\). Code restrictions, due to a plaster ceiling, require the maximum displacement not to exceed \(1 / 360\)
Determine the displacement at its end \(E\) of beam \(C D E\). The beams are made of wood having a modulus of elasticity of \(E=10 \mathrm{GPa}\). A E 1.5 m 1 m 2 m 1.5 m DB 75 mm . 150 mm Section
Determine the vertical displacement at the end \(A\) of the bracket. Assume that the bracket is fixed supported at its base \(B\) and neglect axial deflection. \(E I\) is constant. B A b
Determine the vertical displacement and slope at the end \(A\) of the bracket. Assume that the bracket is fixed supported at its base, and neglect the axial deformation of segment \(A B\). \(E I\) is
The wide-flange beam acts as a cantilever. Due to an error it is installed at an angle \(\theta\) with the vertical. Determine the ratio of its displacement in the \(x\) direction to its displacement
The beam is supported by a pin at \(A\), a roller at \(B\), and a post having a diameter of \(50 \mathrm{~mm}\) at \(C\). Determine the support reactions at \(A, B\), and \(C\). The post and the beam
Determine the moment reactions at the supports \(A\) and \(B\), then draw the shear and moment diagrams. \(E I\) is constant. A B L Mo
The beam has a constant \(E_{1} I_{1}\) and is supported by the fixed wall at \(B\) and the \(\operatorname{rod} A C\). If the rod has a cross-sectional area \(A_{2}\) and the material has a modulus
Determine the moment reactions at the supports \(A\) and \(B\), then draw the shear and moment diagrams. Solve by expressing the internal moment in the beam in terms of \(A_{y}\) and \(M_{A} . E I\)
The loading on a floor beam used in the airplane is shown. Use discontinuity functions and determine the reactions at the supports \(A\) and \(B\), and then draw the moment diagram for the beam. A 30
Determine the force in the spring of stiffness \(k . E I\) is constant. P A k 2 a C
Before the uniform distributed load is applied to the beam, there is a small gap of \(0.2 \mathrm{~mm}\) between the beam and the post at \(B\). Determine the support reactions at \(A, B\), and
The compound beam segments meet in the center using a smooth contact (roller). Determine the reactions at the fixed supports \(A\) and \(B\) when the load \(\mathbf{P}\) is applied. \(E I\) is
Determine the reactions at \(A\) and \(B\). Assume the support at \(A\) only exerts a moment on the beam. \(E I\) is constant. 22 212 B
The assembly consists of a steel and an aluminum bar, each of which is 1 in. thick, fixed at its ends \(A\) and \(B\), and pin connected to the rigid short link \(C D\). If a horizontal force of \(80
If the temperature of the 75 -mm-diameter post \(C D\) is increased by \(60^{\circ} \mathrm{C}\), determine the force developed in the post. The post and the beam are made of A-36 steel, and the
The beam is supported by a pin at \(A\), a spring having a stiffness \(k\) at \(B\), and a roller at \(C\). Determine the force the spring exerts on the beam. \(E I\) is constant. W L + L-
The beam has a constant \(E_{1} I_{1}\) and is supported by the fixed wall at \(B\) and the \(\operatorname{rod} A C\). If the rod has a cross-sectional area \(A_{2}\) and the material has a modulus
The rim on the flywheel has a thickness \(t\), width \(b\), and specific weight \(\gamma\). If the flywheel is rotating at a constant rate of \(\omega\), determine the maximum moment developed in the
The box frame is subjected to a uniform distributed loading \(w\) along each of its sides. Determine the moment developed in each corner. Neglect the deflection due to axial load. EI is constant. E A
The cantilever beam has a circular cross section. If it supports a force \(\mathbf{P}\) at its end, determine its radius y as a function of \(x\) so that it is subjected to a constant maximum bending
Select the lightest-weight wide-flange overhanging beam from Appendix B that will safely support the loading. Assume the support at \(A\) is a pin and the support at \(B\) is a roller. The allowable
The journal bearings at \(A\) and \(B\) exert only \(x\) and \(z\) components of force on the shaft. Determine the shaft's diameter to the nearest millimeter so that it can resist the loadings
The journal bearings at \(A\) and \(B\) exert only \(x\) and \(z\) components of force on the shaft. Determine the shaft's diameter to the nearest millimeter so that it can resist the loadings. Use
Select the lightest-weight wide-flange beam from Appendix B that will safely support the loading. The allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the allowable shear
The simply supported joist is used in the construction of a floor for a building. If the allowable shear stress is \(\tau_{\text {allow }}=\) 350 psi and the allowable bending stress is
The simply supported joist is used in the construction of a floor for a building. If the allowable shear stress is \(\tau_{\text {allow }}=350\) psi and the allowable bending stress is
The board's overhang beam is constructed using two 2-in. by 4-in. board braced as shown. If the allowable bending stress is \(\sigma_{\text {allow }}=600\) psi, determine the largest load \(P\) that
In the case of plane stress, where the in-plane principal strains are given by \(\epsilon_{1}\) and \(\epsilon_{2}\), show that the third principal strain can be obtained
The plate is made of material having a modulus of elasticity \(E=200 \mathrm{GPa}\) and Poisson's ratio \(u=\frac{1}{3}\). Determine the change in width \(a\), height \(b\), and thickness \(t\) when
The state of stress at a point is shown. If the material is machine steel having a yield stress of \(\sigma_{Y}=500 \mathrm{MPa}\), determine the factor of safety with respect to yielding if the
The state of stress stress at a critical point on a thin steel shell is shown. Determine if yielding has occurred using the maximum distortion energy theory. The yield stress for the steel is
The state of strain at the point on the bracket has components of \(\epsilon_{x}=350\left(10^{-6}\right), \quad \epsilon_{y}=-860\left(10^{-6}\right)\), \(\gamma_{x y}=250\left(10^{-6}\right)\). Use
The A-36 steel post is subjected to the forces shown. If the strain gages \(a\) and \(b\) at point \(A\) give readings of \(\epsilon_{a}=300\left(10^{-6}\right)\) and
A differential element is subjected to plane strain that has the following components: \(\epsilon_{x}=950\left(10^{-6}\right), \epsilon_{y}=420\left(10^{-6}\right)\), \(\gamma_{x
The state of strain at the point on the bracket has components of \(\epsilon_{x}=-130\left(10^{-6}\right), \quad \epsilon_{y}=280\left(10^{-6}\right)\), \(\gamma_{x y}=75\left(10^{-6}\right)\). Use
The state of plane strain on the element has components of \(\epsilon_{x}=400\left(10^{-6}\right), \epsilon_{y}=200\left(10^{-6}\right), \gamma_{x y}=-300\left(10^{-6}\right)\). Determine the
If the W \(310 \times 24\) beam is made from steel having an allowable normal stress of \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=60
Determine the minimum width of the beam to the nearest \(\frac{1}{4}\) in. that will safely support the loading of \(P=8\) kip. The allowable bending stress is \(\sigma_{\text {allow }}=24
Select the lightest-weight steel wide-flange beam from Appendix B that will safely support the machine loading shown. The allowable bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and
The simply supported beam is made of timber that has an allowable bending stress of \(\sigma_{\text {allow }}=960\) psi and an allowable shear stress of \(\tau_{\text {allow }}=75\) psi. Determine
The spreader beam \(A B\) is used to slowly lift the 3000 -lb pipe that is centrally located on the straps at \(C\) and \(D\). If the beam is a W12 \(\times 45\), determine if it can safely support
The supports only exert vertical forces on the beam. Determine the greatest magnitude of \(\mathbf{P}\) that can be applied. \(\sigma_{\text {allow }}=25 \mathrm{MPa}, \tau_{\text {allow }}=700
The simply supported beam is made of timber that has an allowable bending stress of \(\sigma_{\text {allow }}=1.20 \mathrm{ksi}\) and an allowable shear stress of \(\tau_{\text {allow }}=100
Select the lightest W360 shape section from Appendix B that can safely support the loading acting on the overhanging beam. The beam is made from steel having an allowable normal stress of
Investigate if the W250 \(\times 58\) shape section can safely support the loading acting on the overhanging beam. The beam is made from steel having an allowable normal stress of \(\sigma_{\text
The brick wall exerts a uniform distributed load of \(1.20 \mathrm{kip} / \mathrm{ft}\) on the beam. If the allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the allowable
The joists of a floor in a warehouse are to be selected using square timber beams made of oak. If each beam is to be designed to carry \(90 \mathrm{lb} / \mathrm{ft}\) over a simply supported span of
The timber beam has a width of 6 in. Determine its height \(h\) so that it simultaneously reaches an allowable bending stress of \(\sigma_{\text {allow }}=1.50 \mathrm{ksi}\) and an allowable shear
If the bearing pads at \(A\) and \(B\) support only vertical forces, determine the greatest magnitude of the uniform distributed loading \(w\) that can be applied to the beam. \(\sigma_{\text {allow
The beam is constructed from two boards. If each nail can support a shear force of \(200 \mathrm{lb}\), determine the maximum spacing of the nails, \(s, s^{\prime}\), and \(s^{\prime \prime}\), to
The simply supported beam is composed of two W12 \(\times 22\) sections built up as shown. Determine the maximum uniform loading \(w\) the beam will support if the allowable bending stress is
The simply supported beam is composed of two W12 \(\times 22\) sections built up as shown. Determine if the beam will safely support a loading of \(w=2 \mathrm{kip} / \mathrm{ft}\). The allowable
If \(P=800 \mathrm{lb}\), determine the minimum dimension \(a\) of the beam's cross section to the nearest \(\frac{1}{8}\) in. to safely support the load. The wood species has an allowable normal
If \(a=3 \mathrm{in}\). and the wood has an allowable normal stress of \(\sigma_{\text {allow }}=1.5 \mathrm{ksi}\), and an allowable shear stress of \(\tau_{\text {allow }}=150 \mathrm{psi}\),
The shaft is supported by a smooth thrust bearing at \(A\) and a smooth journal bearing at \(B\). If \(P=5 \mathrm{kN}\) and the shaft is made from steel having an allowable normal stress of
The shaft is supported by a smooth thrust bearing at A and a smooth journal bearing at B. If the shaft is made from steel having an allowable normal stress of \(\sigma_{\text {allow }}=150
Determine the minimum depth \(h\) of the beam to the nearest \(\frac{1}{8}\) in. that will safely support the loading shown.The allowable bending stress is \(\sigma_{\text {allow }}=2.1
Draw the shear and moment diagrams for the shaft, and determine its required diameter to the nearest \(\frac{1}{8}\) in. if \(\sigma_{\text {allow }}=30 \mathrm{ksi}\) and \(\tau_{\text {allow }}=15
Draw the shear and moment diagrams for the shaft, and determine its required diameter to the nearest \(\frac{1}{4}\) in. if \(\sigma_{\text {allow }}=30 \mathrm{ksi}\) and \(\tau_{\text {allow }}=15
Draw the shear and moment diagrams for the shaft, and determine its required diameter to the nearest \(\frac{1}{4} \mathrm{in}\). if \(\sigma_{\text {allow }}=7 \mathrm{ksi}\) and \(\tau_{\text
Determine the maximum uniform loading \(w\) the \(\mathrm{W} 12 \times 14\) beam will support if the allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the allowable shear
Determine if the \(\mathrm{W} 14 \times 22\) beam will safely support a loading of \(w=1.5 \mathrm{kip} / \mathrm{ft}\). The allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\)
Determine the maximum uniform distributed load \(w\) that can be safely supported on the T-beam if the allowable bending stress is \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and the allowable shear
The compound beam is made from two sections, which are pinned together at \(B\). Use Appendix B and select the lightest-weight wide-flange beam that would be safe for each section if the allowable
The beam is made from a plate that has a constant thickness \(t\). Determine the width \(w\) as a function of \(x\) so that it has a maximum bending stress \(\sigma_{\max }\) throughout its length
The tapered beam supports a uniform distributed load \(w\). If it is made from a plate and has a constant width \(b\), determine the absolute maximum bending stress in the beam. ho I 2 ho L L 2 2 W I
The beam is made from a plate having a constant thickness \(t\) and a width that varies as shown. If it supports a concentrated force \(\mathbf{P}\) at its center, determine the absolute maximum
The beam has a constant thickness \(b\). If it supports the distributed loading shown, determine the maximum bending stress \(\sigma_{\max }\) in the beam. ho 22 -- Wo 2ho I ho 22
Determine the variation in the depth \(d\) of the cantilever beam that supports the concentrated force \(\mathbf{P}\) so that it has the same maximum bending stress \(\sigma_{\max }\) throughout its
Determine the variation in the depth \(d\) of a cantilever beam that supports a concentrated force \(\mathbf{P}\) so that it has the same maximum bending stress \(\sigma_{\max }\) throughout its

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