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engineering
mechanics of materials
Mechanics Of Materials 11th Edition Russell C. Hibbeler - Solutions
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. 60 lb
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 reactions on the shaft. \(E_{\mathrm{st}}=200 \mathrm{GPa}\). A E B -250 mm- -250 mm- -250 mm- -250 mm-
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. \(E_{\mathrm{st}}=200 \mathrm{GPa}\). A E B |-250 -250 mm- 0mm- -250 mm- -250 mm- -250 mm- 150 N 60 N 150 N
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 -B 9 ft 1.5 kip [12 in. C 6 in.
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 2 kN/m 4 kN -1.5 m 1.5 m m- B
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 40 mm 200 mm B 20 mm 5 kN 5 kN
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 constant. A P a + F B C a
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 600 N 600 N B
Determine the slope at \(A\) of the simply supported beam.EI is constant. B - d --
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 \(A\) and \(B\). If the supports exert only vertical forces on the bars, determine the maximum deflection of
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 maximum deflection \(\Delta\), determine \(E\). The supports at \(A\) and \(D\) exert only vertical
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 ft D 2 ft
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 the bearings resist only vertical loads. The axle has a diameter of \(1.25 \mathrm{in}\). and is made
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 modulus of elasticity is \(E\). 27 27
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 \(A B\) and \(C D\) of the beam is \(I\), and the moment of inertia of segment \(B C\) is \(2 I\). B 12 --
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 B [200 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 kN/m 5 m C 5 m B
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 \(A\) due to the loading. Hint: Resolve the moment into components and use superposition. 15 ft. -30 PA
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 B
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 \(1 / 360\) of the span length. Select the lightest-weight A-36 steel wide-flange beam from Appendix B that will
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 a-a 3 kN
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 constant. 3 in. B C 20 lb/in. 4 in. A 80 lb
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 in the \(y\) direction at \(A\) when a load \(\mathbf{P}\) is applied at this point. The moments of
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 are made of the same material having a modulus of elasticity \(E=200 \mathrm{GPa}\), 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 of elasticity \(E_{2}\), determine the force in the rod. T L2 W -L1 B
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 \(M_{A} . E I\) is constant. A W L B
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 lb/in. 120 in. 120 in. B
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 \(C\). The post at \(B\) has a diameter of \(40 \mathrm{~mm}\), and the moment of inertia of the beam is
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 constant. A L C L- B
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 \(80 \mathrm{lb}\) is applied to the link as shown, determine the moments created at \(A\) and \(B .
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 moment of inertia of the beam is \(I=255\left(10^{6}\right) \mathrm{mm}^{4}\). A 3 m B - 3 m C D 3 m
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 of elasticity \(E_{2}\), determine the force in the rod. L2 W B
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 rim. Assume that the spokes do not deform. Due to symmetry of the loading, the slope of the rim at
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 L D B L
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 stress \(\sigma_{\max }\) throughout its length. P
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 bending stress is \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress is
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 without exceeding an allowable shear stress of \(\tau_{\text {allow }}=80 \mathrm{MPa}\). Use the maximum
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 the maximum distortion energy theory of failure with \(\sigma_{\text {allow }}=200 \mathrm{MPa}\). N
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 stress is \(\tau_{\text {allow }}=22 \mathrm{ksi}\). A 8 kip 10 kip 8 kip I I I -10 ft- -5 ft-5 ft-
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 \(\sigma_{\text {allow }}=1500\) psi, determine the height \(h\) of the notch so that the both allowable stresses
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 \(\sigma_{\text {allow }}=1700 \mathrm{psi}\), determine the smallest height \(h\) of the notch so that the beam
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 can be applied. Also, determine the maximum spacing of nails, \(s\), along the beam section \(A C\)
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 from\[\epsilon_{3}=\frac{-u\left(\epsilon_{1}+\epsilon_{2}\right)}{(1-u)}\]where \(u\) is Poisson's ratio for the material.
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 it is subjected to the uniform distributed loading shown. 400 mm t = 20 mm 2 MN/m 3 MN/m b = 300 mm
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 maximum shear stress theory is considered. 100 MPa -150 MPa
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 \(\sigma_{Y}=650 \mathrm{MPa}\). 340 MPa 65 MPa -55 MPa
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 strain transformation equations to determine the equivalent in-plane strains on an element
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 \(\epsilon_{b}=175\left(10^{-6}\right)\), determine the magnitudes of \(\mathbf{P}_{1}\) and \(\mathbf{P}_{2}\). 45 2 ft P2 -4 in-
A differential element is subjected to plane strain that has the following components: \(\epsilon_{x}=950\left(10^{-6}\right), \epsilon_{y}=420\left(10^{-6}\right)\), \(\gamma_{x y}=-325\left(10^{-6}\right)\). Use the strain transformation equations and determine (a) the principal strains and (b)
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 strain transformation equations to determine(a) the in-plane principal strains and(b) the maximum
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 equivalent state of strain, which represents(a) the principal strains, and(b) the maximum in-plane shear
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 \(\tau_{\text {allow }}=60 \mathrm{MPa}\), determine the maximum cable force \(P\) that can safely be supported by the beam. -1 m P 2
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 \(\sigma_{\text {allow }}=24 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=15 \mathrm{ksi}\). 6 in. [ P -6 ft -A
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 allowable shear stress is \(\tau_{\text {allow }}=14 \mathrm{ksi}\). 5 kip 5 kip 5 kip 5 kip
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 its dimensions if it is to be rectangular and have a height-to-width ratio of 1.25 . A 5 kip/ft -6 ft-
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 load. The allowable bending stress is \(\sigma_{\text {allow }}=22 \mathrm{ksi}\) and the
The supports only exert vertical forces on the beam. Determine the greatest magnitude of \(\mathbf{P}\) that can be applied. \(\sigma_{\text {allow }}=25 \mathrm{MPa}, \tau_{\text {allow }}=700 \mathrm{kPa}\). A 150 mm 30 mm 120 mm 4 m P 40 mm 4 m B
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 \(\tau_{\text {allow }}=100 \mathrm{ksi}\). Determine its smallest dimensions to the nearest \(\frac{1}{8} \mathrm{in}\). if it is
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 \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=80
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 \(\sigma_{\text {allow }}=150 \mathrm{MPa}\) and an allowable shear stress of \(\tau_{\text {allow }}=80
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