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mechanics of materials

Mechanics Of Materials 11th Edition Russell C. Hibbeler - Solutions

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 \(P\) that can be safely supported by the column using the allowable stress method. 5 ft 5 ft 6 in. 6
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 \(P\) that can be safely supported by the column using the interaction formula. The allowable bending
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 Eq. \(13-30\). 5 in. P 3 in.. 6 in. 6 ft
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. P 3 in. 6 in. 6 ft
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 it is adequate according to the NFPA equations of Sec. 13.6 and Eq. 13-30. 15 in. 18 ft
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 in. -1.5 in. 1.5 kip 6 ft
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 in. 1.5 kip 1.5 kip 12 in. 6 ft -1.5 in.
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 \(k=200 \mathrm{kN} / \mathrm{m}\), determine the maximum bending stress developed in the beam. A 4 m B h D 2 m C
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 spring at \(B\) has a stiffness \(\mathrm{k}=200 \mathrm{kN} / \mathrm{m}\). 4 m T h D B k C 2 m
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 2m 2m 3m D
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 \(12 \mathrm{ft} / \mathrm{s}\). Determine the maximum compressive stress in the chisel, assuming that
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 \(B\). \(E I\) is constant. Use the method of virtual work. A L- B Mo
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 \(\sigma_{x}, \sigma_{y}\), and \(\tau_{x y}\). y Txy
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 \(\sigma_{1}\) and \(\sigma_{2}\). This being the case, equate the strain energy expressions for each of these two
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 dimensions \(a\) of the square segment so that the strain energy within the square segment is the same as
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 \(E_{\mathrm{al}}=73.1 \mathrm{GPa}\). 20 mm 3 kN 15 mm 2 kN B A | 2 kN 25 mm 5 kN CD 5 kN -300 mm- 400
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 better for resisting an axial shock or impact load. (a) -L2- (b)
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 m 4 m A B C
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 cross-sectional area of \(8.0\left(10^{3}\right) \mathrm{mm}^{2}\) and is made of A-36 steel. 4 m -3 m A BY C
Determine the torsional strain energy in the 2014-T6 aluminum shaft. The tube shaft has an outer and inner diameter of \(60 \mathrm{~mm}\) and \(40 \mathrm{~mm}\), respectively. 12 kNm 10 kNm 6 kNm 0.8 m 9.6 m 0.61 m
Determine the torsional strain energy in the A-36 steel shaft. The shaft has a radius of \(40 \mathrm{~mm}\). 8 kNm 6 kNm 12 kNm 0.6 m 0.4 m 0.5 m
Determine the torsional strain energy stored in the tapered rod when it is subjected to the torque \(\mathbf{T}\). The rod is made of material having a modulus of rigidity of \(G\). L 2ro To T
Determine the bending strain energy in the A-36 steel beam. \(I=99.2\left(10^{6}\right) \mathrm{mm}^{4}\). 6 m 9 kN/m
If \(P=10\) kip, determine the total strain energy in the truss. Each member has a diameter of \(2 \mathrm{in}\). and is made of A992 steel. 4 ft A 3 ft B VP 3 ft- C
Determine the maximum force \(P\) and the corresponding maximum total strain energy that can be stored in the truss without causing any of the members to have permanent deformation. Each member of the truss has a diameter of \(2 \mathrm{in}\). and is made of A-36 steel. 4 ft 3 ft. B 3 ft- VP C
Consider the thin-walled tube of Fig. 5-26. Use the formula for shear stress, \(\tau_{\text {avg }}=T / 2 t A_{m}\), Eq. 5-18, and the general equation of shear strain energy, Eq. 14-11, to show that the angle of twist of the tube is given by Eq. 5-20. Hint: Equate the work done by the torque \(T\)
Determine the ratio of shearing strain energy to bending strain energy for the rectangular cantilever beam when it is subjected to the loading shown. The beam is made of material having a modulus of elasticity of \(E\) and Poisson's ratio of \(v\). -a -L La I h Section a-a
Determine the bending strain energy in the beam. \(E I\) is constant. T 22
Determine the bending strain energy in the A-36 steel beam due to the distributed load. \(I=122\left(10^{6}\right) \mathrm{mm}^{4}\). A -3 m- 15 kN/m B
Determine the bending strain energy in the beam due to the loading shown. \(E I\) is constant. Mo -- B 22 -- C
Determine the bending strain energy in the 2-in.-diameter A-36 steel rod. 80 lb 2 ft 2 ft 80 lb
Determine the bending strain energy in the beam and the axial strain energy in each of the two rods. The beam is made of 2014-T6 aluminum and has a square cross section \(50 \mathrm{~mm}\) by \(50 \mathrm{~mm}\). The rods are made of A-36 steel and have a circular cross section with a
The beam shown is tapered along its width. If a force \(\mathbf{P}\) is applied to its end, determine the strain energy in the beam and compare this result with that of a beam that has a constant rectangular cross section of width \(b\) and height \(h\). h L P
The pipe lies in the horizontal plane. If it is subjected to a vertical force \(\mathbf{P}\) at its end, determine the strain energy due to bending and torsion. Express the results in terms of the cross-sectional properties \(I\) and \(J\), and the material properties \(E\) and \(G\). x Z C A P 22 B
Determine the bending strain energy in the cantilever beam. Solve the problem two ways. (a) Apply Eq. 14-17. (b) The load \(w d x\) acting on a segment \(d x\) of the beam is displaced a distance \(v\), where \(v=w\left(-x^{4}+4 L^{3} x-3 L^{4}\right) /(24 E I)\), the equation of the elastic curve.
Determine the bending strain energy in the simply supported beam. Solve the problem two ways. (a) Apply Eq. 14-17. (b) The load \(w d x\) acting on the segment \(d x\) of the beam is displaced a distance \(v\), where \(v=w\left(-x^{4}+2 L x^{3}-L^{3} x\right) /(24 E I)\), the equation of the
Determine the horizontal displacement of joint \(C . A E\) is constant. L P L A -L. B
Determine the horizontal displacement of joint \(D . A E\) is constant. P D A C L 0.6 L 0.8 L B
Determine the horizontal displacement of joint \(A\). Each bar is made of A992 steel and has a cross-sectional area of \(1.5 \mathrm{in}^{2}\). 10 kip A 3 ft D 3 ft -- B C - 4 ft.
Determine the vertical displacement of joint \(C\). The members of the truss are 2014-T6 aluminum, \(40 \mathrm{~mm}\) diameter rods. 1.5 m A 2 m- D B 2 m 30 kN
Determine the slope at the end \(B\) of the A-36 steel beam. \(I=80\left(10^{6}\right) \mathrm{mm}^{4}\). A 8 m 6 kNm
Determine the slope of the beam at the pin support \(A\). \(E I\) is constant. Mo L B
Determine the vertical displacement of point \(B\) on the A992 steel beam. Take \(I=80\left(10^{6}\right) \mathrm{mm}^{4}\). A 3m- 20 kN B -5 m- C
The cantilever beam is subjected to a couple moment \(M_{0}\) applied at its end. Determine the slope of the beam at \(B\). EI is constant. -L- B Mo
Determine the displacement of point \(B\) on the A992 steel beam. \(I=250 \mathrm{in}^{4}\). A 15 ft 8 kip B -10 ft- C
The A-36 steel bars are pin connected at \(B\). If each has a square cross section, determine the vertical displacement of \(B\). 800 lb A B D 8 ft 4 ft 10 ft 2 in. H I2 I 2 in.
The A992 steel bars are pin connected at \(C\). If they each have a diameter of 2 in., determine the displacement of point \(E\). 2 kip E B C -6 ft 6ft 10 ft 8 ft D
Determine the vertical displacement of point \(C\) of the simply supported 6061-T6 aluminum beam. Consider both shearing and bending strain energy. A 100 kip C La -1.5 ft- -1.5 ft- B
Determine the deflection of the beam at its center caused by shear. The shear modulus is \(G\). I 27 - 22
The curved rod has a diameter \(d\). Determine the vertical displacement of end \(B\) of the rod. The rod is made of material having a modulus of elasticity of \(E\). Consider only bending strain energy. A P B
The rod has a circular cross section with a moment of inertia \(I\). If a vertical force \(\mathbf{P}\) is applied at \(A\), determine the vertical displacement at this point. Only consider the strain energy due to bending. The modulus of elastcity is \(E\). A P
The rod has a circular cross section with a polar moment of inertia \(J\) and moment of inertia \(I\). If a vertical force \(\mathbf{P}\) is applied at \(A\), determine the vertical displcement at this point. Consider the strain energy due to bending and torsion. The material constants are \(E\)
Determine the vertical displacement of end \(B\) of the frame.Consider only bending strain energy. The frame is made using two A-36 steel W460 \(\times 68\) wide-flange sections. 4 m A -3 m- B 20 kN
A bar is \(4 \mathrm{~m}\) long and has a diameter of \(30 \mathrm{~mm}\). Determine the total amount of elastic energy that it can absorb from an impact loading if (a) it is made of steel for which \(E_{\mathrm{st}}=200 \mathrm{GPa}, \sigma_{Y}=800 \mathrm{MPa}\), and (b) it is made from an
Determine the diameter of a red brass C83400 bar that is \(8 \mathrm{ft}\) long if it is to be used to absorb \(800 \mathrm{ft} \cdot \mathrm{lb}\) of energy in tension from an impact loading. No yielding occurs.
Determine the speed \(v\) of the \(50-\mathrm{Mg}\) mass when it is just over the top of the steel post, if after impact, the maximum stress developed in the post is \(550 \mathrm{MPa}\). The post has a length of \(L=1 \mathrm{~m}\) and a cross-sectional area of \(0.01 \mathrm{~m}^{2}\). Take
The collar has a weight of \(50 \mathrm{lb}\) and falls from rest down the titanium bar. If the bar has a diameter of 0.5 in., determine the maximum stress developed in the bar if the weight is (a) dropped from a height of \(h=1 \mathrm{ft}\), (b) released from a height \(h \approx 0\), and (c)
A steel cable having a diameter of 0.4 in. wraps over a drum and is used to lower an elevator having a weight of \(800 \mathrm{lb}\). The elevator is \(150 \mathrm{ft}\) below the drum and is descending at the constant rate of \(2 \mathrm{ft} / \mathrm{s}\) when the drum suddenly stops. Determine
The diver weighs \(150 \mathrm{lb}\) and, while holding himself rigid, strikes the end of the wooden diving board. Determine the maximum height \(h\) from which he can jump from rest onto the board so that the maximum bending stress in the wood does not exceed \(6 \mathrm{ksi}\). The board has a
The \(50-\mathrm{kg}\) block is dropped from rest at a height of \(h=600 \mathrm{~mm}\) onto the bronze C86100 tube. Determine the minimum length \(L\) the tube can have without causing the tube to yield. 30 mm Section a-a A 20 mm h = 600 mm a L a L B
The \(50-\mathrm{kg}\) block is dropped from rest at a height of \(h=600 \mathrm{~mm}\) onto the bronze C86100 tube. If \(L=900 \mathrm{~mm}\) determine the maximum normal stress developed in the tube. 30 mm 20 mm A Section a-a a a B h = 600 mm L
The sack of cement has a weight of \(90 \mathrm{lb}\). If it is dropped from rest at a height of \(h=4 \mathrm{ft}\) onto the center of the W10 \(\times 39\) structural steel A-36 beam, determine the maximum bending stress developed in the beam due to the impact. Also, what is the impact factor? T
The sack of cement has a weight of \(90 \mathrm{lb}\). Determine the maximum height \(h\) from which it can be dropped from rest onto the center of the \(\mathrm{W} 10 \times 39\) structural steel A-36 beam so that the maximum bending stress due to impact does not exceed \(30 \mathrm{ksi}\). 9 T h
A cylinder having the dimensions shown is made from magnesium Am 1004-T61. If it is struck by a rigid block having a weight of \(800 \mathrm{lb}\) and traveling at \(2 \mathrm{ft} / \mathrm{s}\), determine the maximum stress in the cylinder. Neglect the mass of the cylinder. 0.5 ft 1.5 ft 2 ft/s
The composite aluminum 2014-T6 bar is made from two segments having diameters of \(7.5 \mathrm{~mm}\) and \(15 \mathrm{~mm}\). Determine the maximum axial stress developed in the bar if the \(10-\mathrm{kg}\) collar is dropped from rest at a height of \(h=100 \mathrm{~mm}\). 7.5 mm- 300 mm 15 mm
The composite aluminum 2014-T6 bar is made from two segments having diameters of \(7.5 \mathrm{~mm}\) and \(15 \mathrm{~mm}\). Determine the maximum height \(h\) from which the 10-kg collar should be dropped from rest so that it produces a maximum axial stress in the bar of \(\sigma_{\max }=300
The 50-lb weight is falling \(3 \mathrm{ft} / \mathrm{s}\) at the instant it is \(2 \mathrm{ft}\) above the spring and post assembly. Determine the maximum stress in the post if the spring has a stiffness of \(k=200 \mathrm{kip} / \mathrm{in}\). The post has a diameter of \(3 \mathrm{in}\). and a
A 20-lb weight is dropped from rest at a height of \(h=3 \mathrm{ft}\) onto end \(A\) of the \(\mathrm{A} 992\) steel cantilever beam. If the beam is a W16 \(\times 50\), determine the maximum bending stress developed in the beam. h A 9 ft B
If the maximum allowable bending stress for the W16 \(\times 50\) structural A992 steel beam is \(\sigma_{\text {allow }}=30 \mathrm{ksi}\), determine the maximum height \(h\) from which a 30-lb weight can be released from rest and strike the end \(A\) of the beam. T h A 9 ft B
A 20-lb weight is dropped from rest at a height of \(h=3 \mathrm{ft}\) onto end \(A\) of the \(\mathrm{A} 992\) steel cantilever beam. If the beam is a W16 \(\times 50\), determine the slope of its end \(A\) due to the impact. h A 9 ft B
The simply supported W10 \(\times 15\) structural A-36 steel beam is in the horizontal plane and acts as a shock absorber for the 500-lb block which is traveling toward it at \(5 \mathrm{ft} / \mathrm{s}\). Determine the maximum deflection of the beam and the maximum stress in the beam during the
The 5 - \(\mathrm{kg}\) block is traveling with the speed of \(v=4 \mathrm{~m} / \mathrm{s}\) just before it strikes the 6061-T6 aluminum stepped cylinder. Determine the maximum normal stress developed in the cylinder. -300 mm- -300 mm- C B 20 mm 40 mm
The 2014-T6 aluminum bar \(A B\) can slide freely along the guides mounted on the rigid crash barrier. If the railcar of mass \(10 \mathrm{Mg}\) is traveling with a speed of \(v=1.5 \mathrm{~m} / \mathrm{s}\), determine the maximum bending stress developed in the bar. The springs at \(A\) and \(B\)
The 2014-T6 aluminum bar \(A B\) can slide freely along the guides mounted on the rigid crash barrier. Determine the maximum speed \(v\) of the \(10-\mathrm{Mg}\) railcar without causing the bar to yield when it is struck by the railcar. The springs at \(A\) and \(B\) have a stiffness of \(k=15
The \(50-\mathrm{kg}\) block \(C\) is dropped from rest at \(h=1.5 \mathrm{~m}\) onto the simply supported beam. If the beam is an A-36 steel W250 × 45 wide-flange section, determine the maximum bending stress developed in the beam. A C h 4 m 2 m B
Rods \(A B\) and \(A C\) have a diameter of \(20 \mathrm{~mm}\) and are made of 6061-T6 aluminum alloy. They are connected to the rigid collar \(A\) which slides freely along the vertical guide rod. If the \(50-\mathrm{kg}\) block \(D\) is dropped from rest at a height of \(h=200 \mathrm{~mm}\)
Rods \(A B\) and \(A C\) have a diameter of \(20 \mathrm{~mm}\) and are made of 6061-T6 aluminum alloy. They are connected to the rigid collar which slides freely along the vertical guide rod. Determine the maximum height \(h\) from which the \(50 \mathrm{~kg}\) block \(D\) can be dropped from rest
A 40-lb weight is dropped from rest at a height of \(h=2 \mathrm{ft}\) onto the center of the W10 \(\times 15\) structural A992 steel beam. Determine the maximum bending stress in the beam. A -5 ft- T h B 5 ft
If the maximum allowable bending stress for the \(\mathrm{W} 10 \times 15\) structural A992 steel beam is \(\sigma_{\text {allow }}=20 \mathrm{ksi}\), determine the maximum height \(h\) at which a 50-lb weight can be released from rest and strike the center of the beam. T h 5 ft. -5 ft B
A 40-lb weight is dropped from rest at a height of \(h=2 \mathrm{ft}\) onto the center of the W10 \(\times 15\) structural A992 steel beam. Determine the vertical displacement of its end \(B\) due to the impact. T h B 5 ft. 5 ft
The car bumper is made of polycarbonate polybutylene terephthalate. If \(E=2.0 \mathrm{GPa}\), determine the maximum deflection and maximum stress in the bumper if it strikes the rigid post when the car is coasting at \(v=0.75 \mathrm{~m} / \mathrm{s}\). The car has a mass of \(1.80 \mathrm{Mg}\),
Determine the vertical displacement of joint \(A\). Each A992 steel member has a cross-sectional area of \(400 \mathrm{~mm}^{2}\). A B -1.5 m E 40 kN 60 kN -3 m- 2 m
Determine the horizontal displacement of joint \(B\). Each A-36 steel member has a cross-sectional area of \(2 \mathrm{in}^{2}\). A 60 B 5 ft 800 lb 30
Determine the vertical displacement of joint \(B\). Each A992 steel member has a cross-sectional area of \(4.5 \mathrm{in}^{2}\). A F E 8 ft B -8 ft 5 kip 6 ft
Determine the horizontal displacement of joint \(B\). Each A992 steel member has a cross-sectional area of \(400 \mathrm{~mm}^{2}\). 5 kN -2 m- 4 kN C B D A 1.5 m
Determine the vertical displacement of joint \(C\). The truss is made from A-36 steel bars having a cross-sectional area of \(150 \mathrm{~mm}^{2}\). Af H F 2 m B -1.5 m 1.5m C 1.5 m-1.5 m 6 kN 6 kN 12 kN E 2 m
Determine the vertical displacement of joint \(G\). The truss is made from A-36 steel bars having a cross-sectional area of \(150 \mathrm{~mm}^{2}\) H Aro B D 15m 5m1.5m1.5m-1.5 m -1.5m- 6 kN 6 kN 12 kN E 2 m 2 m
The W14 \(\times 26\) structural A-36 steel member is used as a 20 -ft-long column that is assumed to be fixed at its top and fixed at its bottom. If the 15-kip load is applied at an eccentric distance of 10 in., determine the maximum stress in the column. 15 kip -10 in. 20 ft
The W14 \(\times 26\) structural A-36 steel member is used as a column that is assumed to be fixed at its top and pinned at its bottom. If the 15-kip load is applied at an eccentric distance of 10 in., determine the maximum stress in the column. H 15 kip 10 in. 20 ft
Determine the maximum eccentric load \(P\) the 2014-T6aluminum-alloy strut can support without causing it either to buckle or yield. The ends of the strut are pin connected. a $150 mm 150 mm 100 mm 3m- La 50 mm 100 mm Section a-a
The W250 28 A-36 steel column is fixed at its base. Its top is constrained to rotate about the \(y-y\) axis and free to move along the \(y-y\) axis. If \(e=350 \mathrm{~mm}\), determine the allowable eccentric force \(P\) that can be applied without causing the column either to buckle or yield. Use
The W250 \(\times 28\) A-36 steel column is fixed at its base. Its top is constrained to rotate about the \(y-y\) axis and free to move along the \(y-y\) axis. Determine the force \(\mathbf{P}\) and its eccentricity \(e\) so that the column will yield and buckle simultaneously. 6 m x.
The W14 \(\times 53\) structural A992 steel column is fixed at its base and free at its top. If \(P=\) kip, determine the sidesway displacement at its top and the maximum stress in the column. 10 in. P 18 ft
The W14 \(\times 53\) 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. Take \(E_{\mathrm{st}}=\) \(29\left(10^{3}\right) \mathrm{ksi}, \sigma_{Y}=50 \mathrm{ksi}\). 10 in. P 18 ft

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