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engineering
mechanical engineering
Shigleys Mechanical Engineering Design 9th edition Richard G. Budynas, J. Keith Nisbett - Solutions
For the steel countershaft specified in the table, assume the bearings have a maximum slope specification of 0.06° for good bearing life. Determine the minimum shaft diameter.Problem 3-70, A countershaft carrying two V-belt pulleys is shown in the figure. Pulley A receives power from a motor
For the steel countershaft specified in the table, assume the bearings have a maximum slope specification of 0.06° for good bearing life. Determine the minimum shaft diameter.Problem 3-71, A countershaft carrying two V-belt pulleys is shown in the figure. Pulley A receives power from a motor
For the steel countershaft specified in the table, assume the bearings have a maximum slope specification of 0.06° for good bearing life. Determine the minimum shaft diameter.Problem 3-73, A gear reduction unit uses the countershaft shown in the figure. Gear A receives power from another gear
For the steel countershaft specified in the table, assume the bearings have a maximum slope specification of 0.06° for good bearing life. Determine the minimum shaft diameter.Problem 3-73, A gear reduction unit uses the countershaft shown in the figure. Gear A receives power from another gear
The cantilevered handle in the figure is made from mild steel that has been welded at the joints. For Fy = 200 lbf, Fx = Fz = 0, determine the vertical deflection (along the y axis) at the tip. Use superposition.See the discussion on p. 102 for the twist in the rectangular cross section in
For the cantilevered handle in Prob. 4€“41, let Fx = ˆ’150 lbf, Fy = 0 lbf, Fz = ˆ’100 lbf. Find the deflection at the tip along the x axis.In Prob. 4€“41, The cantilevered handle in the figure is made from mild steel that has been welded at the joints. For
The cantilevered handle in Prob. 3–84, p. 140, is made from mild steel. Let Fy = 250 lbf, Fx = Fz = 0. Determine the angle of twist in bar OC, ignoring the fillets but including the changes in diameter along the 13-in effective length. Compare the angle of twist if the bar OC is simplified to be
A flat-bed trailer is to be designed with a curvature such that when loaded to capacity the trailer bed is flat. The load capacity is to be 3000 lbf/ft between the axles, which are 25 ft apart, and the second-area moment of the steel structure of the bed is I = 485 in4. Determine the equation for
A steel shaft is to be designed so that it is supported by roller bearings. The basic geometry is shown in the figure from Prob. 4€“45, with l = 300 mm, a = 100 mm, and F = 3 kN. The allowable slope at the bearings is 0.001 mm/mm without bearing life penalty. For a design factor of 1.28,
If the diameter of the steel beam shown is 1.25 in, determine the deflection of the beam atx = 8in.
For the beam of Prob. 4€“47, plot the magnitude of the displacement of the beam in 0.1-in increments. Approximate the maximum displacement and the value of x where it occurs.Prob. 4€“47, If the diameter of the steel beam shown is 1.25 in, determine the deflection of the beam atx
Shown in the figure is a uniform-diameter shaft with bearing shoulders at the ends; the shaft is subjected to a concentrated moment M = 1000 lbf ˆ™ in. The shaft is of carbon steel and has a = 4 in and l = 10 in. The slope at the ends must be limited to 0.002 rad.Find a suitable diameterd.
The figure shows a rectangular member OB, made from ¼-in-thick aluminum plate, pinned to the ground at one end and supported by a ½ -in-diameter round steel rod with hooks formed on the ends. A load of 100 lbf is applied as shown.Use superposition to determine the vertical deflection
The figure shows a rectangular member OB, made from ¼-in-thick aluminum plate, pinned to the ground at one end and supported by a ½ -in-diameter round steel rod with hooks formed on the ends. A load of 100 lbf is applied as shown.Use superposition to determine the vertical deflection
The figure illustrates a stepped torsion-bar spring OA with an actuating cantilever AB. Both parts are of carbon steel. Use superposition and find the spring rate k corresponding to a force F acting atB.
Consider the simply supported beam 5 with a center load in Appendix A–9. Determine the deflection equation if the stiffness of the left and right supports are k1 and k2, respectively.
Consider the simply supported beam 10 with an overhanging load in Appendix A–9. Determine the deflection equation if the stiffness of the left and right supports are k1 and k2, respectively.
Solve Prob. 4€“10 using singularity functions. Use statics to determine the reactions.Prob. 4€“10, The figure shows a cantilever consisting of steel angles size 100 × 100 × 12 mm mounted back to back.Using superposition, find the deflection at B and the
Solve Prob. 4–11 using singularity functions. Use statics to determine the reactions.Prob. 4–11, A simply supported beam loaded by two forces is shown in the figure. Select a pair of structural steel channels mounted back to back to support the loads in such a way that the deflection
Solve Prob. 4€“12 using singularity functions. Use statics to determine the reactions.Prob. 4€“12, Using superposition, find the deflection of the steel shaft at A in the figure. Find the deflection at midspan.By what percentage do these two valuesdiffer?
Solve Prob. 4–21 using singularity functions to determine the deflection equation of the beam. Use statics to determine the reactions.Prob. 4–21, Consider the uniformly loaded simply supported steel beam with an overhang as shown. The second-area moment of the beam is I = 0.05 in 4.
Solve Prob. 4€“13 using singularity functions. Since the beam is symmetric, only write the equation for half the beam and use the slope at the beam center as a boundary condition. Use statics to determine the reactions.Prob. 4€“13, A rectangular steel bar supports the two
Solve Prob. 4€“17 using singularity functions. Use statics to determine the reactions.Prob. 4€“17, A simply supported beam has a concentrated moment MA applied at the left support and a concentrated force F applied at the free end of the overhang on the right.Using
Solve Prob. 4€“19 using singularity functions to determine the deflection equation of the beam. Use statics to determine the reactions.Prob. 4€“19, Using the results of Prob 4€“18, use superposition to determine the deflection equations for the three regions of the
Using singularity functions, write the deflection equation for the steel beam shown. Since the beam is symmetric, write the equation for only half the beam and use the slope at the beam center as a boundary condition.Plot your results and determine the maximum deflection.
Use Castigliano’s theorem to verify the maximum deflection for the uniformly loaded cantilever beam 3 of Appendix Table A–9. Neglect shear.
Solve Prob. 4–15 using Castigliano’s theorem.Prob. 4–15, The cantilever shown in the figure consists of two structural-steel channels size 3 in, 5.0 lbf/ft.Using superposition, find the deflection at A. Include the weight of thechannels.
Solve Prob. 4€“52 using Castigliano€™s theorem.Prob. 4€“52, The figure illustrates a stepped torsion-bar spring OA with an actuating cantilever AB. Both parts are of carbon steel. Use superposition and find the spring rate k corresponding to a force F acting atB.
Using Castigliano€™s theorem, determine the deflection of point B in the direction of the force F for the steel barshown.
Solve Prob. 4€“41 using Castigliano€™s theorem. Since Eq. (4€“18) for torsional strain energy was derived from the angular displacement for circular cross sections, it is not applicable for section BC. You will need to obtain a new strain energy equation for the
Solve Prob. 4€“42 using Castigliano€™s theorem.Prob. 4€“42, For the cantilevered handle in Prob. 4€“41, let Fx = ˆ’150 lbf, Fy = 0 lbf, Fz = ˆ’100 lbf. Find the deflection at the tip along the x axis.In Prob. 4€“41, The
The cantilevered handle in Prob. 3–84 is made from mild steel. Let Fy = 250 lbf and Fx = Fz = 0. Using Castigliano’s theorem, determine the vertical deflection (along the y axis) at the tip. Repeat the problem with shaft OC simplified to a uniform diameter of 1 in for its entire
Solve Prob. 4€“50 using Castigliano€™s theorem.Prob. 4€“50, The figure shows a rectangular member OB, made from ¼-in-thick aluminum plate, pinned to the ground at one end and supported by a ½ -in-diameter round steel rod with hooks formed on the ends. A
Solve Prob. 4€“51 using Castigliano€™s theorem.Prob. 4€“51, The figure shows a rectangular member OB, made from ¼-in-thick aluminum plate, pinned to the ground at one end and supported by a ½ -in-diameter round steel rod with hooks formed on the ends. A
The steel curved bar shown has a rectangular cross section with a radial height h = 6 mm, and a thickness b = 4 mm. The radius of the centroidal axis is R = 40 mm. A force P = 10 N is applied as shown. Find the vertical deflection at B. Use Castigliano€™s method for a curved flexural
Repeat Prob. 4€“76 to find the vertical deflection at A.Prob. 4€“76, The steel curved bar shown has a rectangular cross section with a radial height h = 6 mm, and a thickness b = 4 mm. The radius of the centroidal axis is R = 40 mm. A force P = 10 N is applied as shown. Find the
For the curved steel beam shown, F = 6.7 kips. Determine the relative deflection of the appliedforces.
A steel piston ring has a mean diameter of 70 mm, a radial height h = 4.5 mm, and a thickness b = 3 mm. The ring is assembled using an expansion tool that separates the split ends a distance δ by applying a force F as shown. Use Castigliano€™s theorem and determine the force
For the steel wire form shown, use Castigliano€™s method to determine the horizontal reaction forces at A and B and the deflection atC.
The part shown is formed from a 1/8 -in diameter steel wire, with R = 5 in and l = 4 in. A force is applied with P = 1 lbf. Use Castigliano’s method to estimate the horizontal deflection at point A.Justify any components of strain energy that you choose toneglect.
The part shown is formed from a 1/8 -in diameter steel wire, with R = 5 in and l = 4 in. A force is applied with P = 1 lbf. Use Castigliano€™s method to estimate the horizontal deflection at point A.Justify any components of strain energy that you choose toneglect.
Repeat Prob. 4€“81 for the vertical deflection at point A.Prob. 4€“81, The part shown is formed from a 1/8 -in diameter steel wire, with R = 5 in and l = 4 in. A force is applied with P = 1 lbf. Use Castigliano€™s method to estimate the horizontal deflection at point
Repeat Prob. 4€“82 for the vertical deflection at point A.Prob. 4€“82, The part shown is formed from a 1/8 -in diameter steel wire, with R = 5 in and l = 4 in. A force is applied with P = 1 lbf. Use Castigliano€™s method to estimate the horizontal deflection at point
A hook is formed from a 2-mm-diameter steel wire and fixed firmly into the ceiling as shown. A 1-kg mass is hung from the hook at point D. Use Castigliano€™s theorem to determine the vertical deflection of pointD.
The figure shows a rectangular member OB, made from ¼ -in-thick aluminum plate, pinned to the ground at one end, and supported by a ½ -in-diameter round steel rod that is formed into an arc and pinned to the ground at C. A load of 100 lbf is applied at B. Use Castigliano€™s
Repeat Prob. 4–86 for the vertical deflection at point A.Prob. 4–86, The figure shows a rectangular member OB, made from ¼ -in-thick aluminum plate, pinned to the ground at one end, and supported by a ½ -in-diameter round steel rod that is formed into an arc and pinned to the
For the wire form shown, determine the deflection of point A in the y direction. Assume R/h > 10 and consider the effects of bending and torsion only. The wire is steel with E = 200 GPa, ν = 0.29, and has a diameter of 6 mm.Before application of the 250-N force the wire form is in the
A 100-ft cable is made using a 12-gauge (0.1055-in) steel wire and three strands of 10-gauge (0.1019-in) copper wire. Find the deflection of the cable and the stress in each wire if the cable is subjected to a tension of 400 lbf.
The figure shows a steel pressure cylinder of diameter 5 in that uses six SAE grade 4 steel bolts having a grip of 10 in. These bolts have a proof strength of 65 kpsi. Suppose the bolts are tightened to 75 percent of this strength.(a) Find the tensile stress in the bolts and the compressive stress
A torsion bar of length L consists of a round core of stiffness (GJ)c and a shell of stiffness (GJ)s . If a torque T is applied to this composite bar, what percentage of the total torque is carried by the shell?
A rectangular aluminum bar 10 mm thick and 60 mm wide is welded to fixed supports at the ends, and the bar supports a load W = 4 kN, acting through a pin as shown. Find the reactions at the supports and the deflection of pointA.
Solve Prob. 4–92 using Castigliano’s method and procedure 1 from Sec. 4–10.Prob. 4–92, A rectangular aluminum bar 10 mm thick and 60 mm wide is welded to fixed supports at the ends, and the bar supports a load W = 4 kN, acting through a pin as shown. Find the reactions
An aluminum step bar is loaded as shown.(a) Verify that end C deflects to the rigid wall, and(b) Determine the wall reaction forces, the stresses in each member, and the deflection ofB.
The steel shaft shown in the figure is subjected to a torque of 200 lbf ˆ™ in applied at point A. Find the torque reactions at O and B; the angle of twist at A, in degrees; and the shear stress in sections OA andAB.
Repeat Prob. 4€“95 with the diameters of section OA being 0.5 in and section AB being 0.75 in.Prob. 4€“95, The steel shaft shown in the figure is subjected to a torque of 200 lbf ˆ™ in applied at point A. Find the torque reactions at O and B; the angle of twist at A,
The figure shows a ½ - by 1-in rectangular steel bar welded to fixed supports at each end. The bar is axially loaded by the forces FA = 12 kip and FB = 6 kip acting on pins at A and B. Assuming that the bar will not buckle laterally, find the reactions at the fixed supports, the stress in
For the beam shown, determine the support reactions using superposition and procedure 1 from Sec.4€“10.
Solve Prob. 4€“98 using Castigliano€™s theorem and procedure 1 from Sec. 4€“10.Prob. 4€“98, For the beam shown, determine the support reactions using superposition and procedure 1 from Sec.4€“10.
Consider beam 13 in Table A–9, but with flexible supports. Let w = 500 lbf/ft, l = 2 ft, E = 30 Mpsi, and I = 0.85 in4. The support at the left end has a translational spring constant of k1 = 1.5(106) lbf/in and a rotational spring constant of k2 = 2.5(106) lbf ∙ in. The right support has a
The steel beam ABCD shown is simply supported at A and supported at B and D by steel cables, each having an effective diameter of 0.5 in. The second area moment of the beam is I = 1.2 in4. A force of 5 kips is applied at point C. Using procedure 2 of Sec. 4€“10 determine the stresses in
The steel beam ABCD shown is supported at C as shown and supported at B and D by shoulder steel bolts, each having a diameter of 8 mm. The lengths of BE and DF are 50 mm and 65 mm, respectively. The beam has a second area moment of 21(103) mm4. Prior to loading, the members are stress-free. A force
Link 2, shown in the figure, is 25 mm wide, has 12-mm-diameter bearings at the ends, and is cut from low-carbon steel bar stock having a minimum yield strength of 165 MPa. The end-condition constants are C = 1 and C = 1.2 for buckling in and out of the plane of the drawing, respectively.(a) Using a
The hydraulic cylinder shown in the figure has a 2-in bore and is to operate at a pressure of 1500 psi. With the clevis mount shown, the piston rod should be sized as a column with both ends rounded for any plane of buckling. The rod is to be made of forged AISI 1030 steel without further heat
The figure shows a schematic drawing of a vehicular jack that is to be designed to support a maximum mass of 300 kg based on the use of a design factor nd = 3.50. The opposite-handed threads on the two ends of the screw are cut to allow the link angle θ to vary from 15 to
If drawn, a figure for this problem would resemble that for Prob. 4–90. A strut that is a standard hollow right circular cylinder has an outside diameter of 3 in and a wall thickness of ¼ in and is compressed between two circular end plates held by four bolts equally spaced on a bolt circle of
Find the maximum values of the spring force and deflection of the impact system shown in the figure if W = 30 lbf, k = 100 lbf/in, and h = 2 in. Ignore the mass of the spring and solve using energyconservation.
As shown in the figure, the weight W1 strikes W2 from a height h. If W1 = 40 N, W2 = 400 N, h = 200 mm, and k = 32 kN/m, find the maximum values of the spring force and the deflection of W2. Assume that the impact between W1 and W2 is inelastic, ignore the mass of the spring, and solve using
Part a of the figure shows a weight W mounted between two springs. If the free end of spring k1 is suddenly displaced through the distance x = a, as shown in part b, determine the maximum displacement y of the weight. Let W = 5 lbf, k1 = 10 lbf/in, k2 = 20 lbf/in, and a = 0.25 in.Ignore the mass of
A 10-mm drill rod was heat-treated and ground. The measured hardness was found to be 300 Brinell. Estimate the endurance strength in MPa if the rod is used in rotating bending.
Estimate S'e in kpsi for the following materials:(a) AISI 1035 CD steel.(b) AISI 1050 HR steel.(c) 2024 T4 aluminum.(d) AISI 4130 steel heat-treated to a tensile strength of 235 kpsi.
A steel rotating-beam test specimen has an ultimate strength of 120 kpsi. Estimate the life of the specimen if it is tested at a completely reversed stress amplitude of 70 kpsi.
A steel rotating-beam test specimen has an ultimate strength of 1600 MPa. Estimate the life of the specimen if it is tested at a completely reversed stress amplitude of 900 MPa.
A steel rotating-beam test specimen has an ultimate strength of 230 kpsi. Estimate the fatigue strength corresponding to a life of 150 kcycles of stress reversal.
Repeat Prob. 6–5 with the specimen having an ultimate strength of 1100 MPa.Repeat Prob. 6–5, A steel rotating-beam test specimen has an ultimate strength of 230 kpsi. Estimate the fatigue strength corresponding to a life of 150 kcycles of stress reversal.
A steel rotating-beam test specimen has an ultimate strength of 150 kpsi and a yield strength of 135 kpsi. It is desired to test low-cycle fatigue at approximately 500 cycles. Check if this is possible without yielding by determining the necessary reversed stress amplitude.
Derive Eq. (6–17). Rearrange the equation to solve for N.Sf ≥ Sut N(log f )/3 1 ≤ N ≤ 103
Estimate the endurance strength of a 1.5-in-diameter rod of AISI 1040 steel having a machined finish and heat-treated to a tensile strength of 110 kpsi.
A 1-in-diameter solid round bar has a groove 0.1-in deep with a 0.1-in radius machined into it. The bar is made of AISI 1020 CD steel and is subjected to a purely reversing torque of 1800 lbf ∙ in.For the S-N curve of this material, let f = 0.9.(a) Estimate the number of cycles to failure.(b) If
A solid square rod is cantilevered at one end. The rod is 0.6 m long and supports a completely reversing transverse load at the other end of ±2kN. The material is AISI 1080 hot-rolled steel. If the rod must support this load for 104 cycles with a factor of safety of 1.5, what dimension should the
A rectangular bar is cut from an AISI 1020 cold-drawn steel flat. The bar is 2.5 in wide by 3/8 in thick and has a 0.5-in-dia. hole drilled through the center as depicted in Table A–15–1. The bar is concentrically loaded in push-pull fatigue by axial forces Fa, uniformly distributed across the
A solid round bar with diameter of 2 in has a groove cut to a diameter of 1.8 in, with a radius of 0.1 in. The bar is not rotating. The bar is loaded with a repeated bending load that causes the bending moment at the groove to fluctuate between 0 and 25 000 lbf · in. The bar is hot-rolled AISI
The rotating shaft shown in the figure is machined from AISI 1020 CD steel. It is subjected to a force of F = 6 kN. Find the minimum factor of safety for fatigue based on infinite life. If the life is not infinite, estimate the number of cycles.Be sure to check for yielding.
The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F1 = 2500 lbf and F2 = 1000 lbf. Determine the minimum fatigue factor of safety based on achieving infinite life. If infinite life
Solve Prob. 6–17 except with forces F1 = 1200 lbf and F2 = 2400 lbf.Prob. 6–17, The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F1 = 2500 lbf and F2 = 1000 lbf.
Bearing reactions R1 and R2 are exerted on the shaft shown in the figure, which rotates at 950rev/min and supports an 8-kip bending force. Use a 1095 HR steel. Specify a diameter d using a design factor of nd = 1.6 for a life of 10 hr.The surfaces are machined.
A bar of steel has the minimum properties Se = 40 kpsi, Sy = 60 kpsi, and Sut = 80 kpsi. The bar is subjected to a steady torsional stress of 15 kpsi and an alternating bending stress of 25 kpsi. Find the factor of safety guarding against a static failure, and either the factor of safety guarding
Repeat Prob. 6–20 but with a steady torsional stress of 20 kpsi and an alternating bending stress of 10 kpsi.Repeat Prob. 6–20, A bar of steel has the minimum properties Se = 40 kpsi, Sy = 60 kpsi, and Sut = 80 kpsi. The bar is subjected to a steady torsional stress of 15 kpsi and an
Repeat Prob. 6–20 but with a steady torsional stress of 15 kpsi, an alternating torsional stress of 10 kpsi, and an alternating bending stress of 12 kpsi.Repeat Prob. 6–20, A bar of steel has the minimum properties Se = 40 kpsi, Sy = 60 kpsi, and Sut = 80 kpsi. The bar is subjected to a steady
Repeat Prob. 6–20 but with an alternating torsional stress of 30 kpsi.Repeat Prob. 6–20, A bar of steel has the minimum properties Se = 40 kpsi, Sy = 60 kpsi, and Sut = 80 kpsi. The bar is subjected to a steady torsional stress of 15 kpsi and an alternating bending stress of 25 kpsi. Find the
Repeat Prob. 6–20 but with an alternating torsional stress of 15 kpsi and a steady bending stress of 15 kpsi.Repeat Prob. 6–20, A bar of steel has the minimum properties Se = 40 kpsi, Sy = 60 kpsi, and Sut = 80 kpsi. The bar is subjected to a steady torsional stress of 15 kpsi and an
The cold-drawn AISI 1040 steel bar shown in the figure is subjected to a completely reversed axial load fluctuating between 28 kN in compression to 28 kN in tension. Estimate the fatigue factor of safety based on achieving infinite life, and the yielding factor of safety. If infinite life is not
Repeat Prob. 6€“25 for a load that fluctuates from 12 kN to 28 kN. Use the Modified Goodman, Gerber, and ASME-elliptic criteria and compare their predictions.Repeat Prob. 6€“25, The cold-drawn AISI 1040 steel bar shown in the figure is subjected to a completely reversed axial
Repeat Prob. 6€“25 for each of the following loading conditions:(a) 0 kN to 28 kN(b) 12 kN to 28 kN(c) €“28 kN to 12 kNRepeat Prob. 6€“25, The cold-drawn AISI 1040 steel bar shown in the figure is subjected to a completely reversed axial load fluctuating between 28 kN
The figure shows a formed round-wire cantilever spring subjected to a varying force. The hardness tests made on 50 springs gave a minimum hardness of 400 Brinell. It is apparent from the mounting details that there is no stress concentration. A visual inspection of the springs indicates that the
The figure is a drawing of a 4- by 20-mm latching spring. A preload is obtained during assembly by shimming under the bolts to obtain an estimated initial deflection of 2 mm. The latching operation itself requires an additional deflection of exactly 4 mm. The material is ground high-carbon steel,
The figure shows the free-body diagram of a connecting-link portion having stress concentration at three sections. The dimensions are r = 0.25 in, d = 0.40 in, h = 0.50 in, w1 = 3.50 in, and w2 = 3.0 in. The forces F fluctuate between a tension of 5 kip and a compression of 16 kip.Neglect column
Solve Prob. 6–30 except let w1 = 2.5 in, w2 = 1.5 in, and the force fluctuates between a tension of 16 kips and a compression of 4 kips.Prob. 6–30, The figure shows the free-body diagram of a connecting-link portion having stress concentration at three sections. The dimensions are r =
For the part in Prob. 6€“30, recommend a fillet radius r that will cause the fatigue factor of safety to be the same at the hole and at the fillet.In Prob. 6€“30, The figure shows the free-body diagram of a connecting-link portion having stress concentration at three sections.
The torsional coupling in the figure is composed of a curved beam of square cross section that is welded to an input shaft and output plate. A torque is applied to the shaft and cycles from zero to T. The cross section of the beam has dimensions of 3/16 × 3/16 in, and the centroidal
Repeat Prob. 6€“33 ignoring curvature effects on the bending stress.Repeat Prob. 6€“33, The torsional coupling in the figure is composed of a curved beam of square cross section that is welded to an input shaft and output plate. A torque is applied to the shaft and cycles from
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