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mechanical engineering

Questions and Answers of Mechanical Engineering

Illustrated in the figure is a 1 ½ -in-diameter steel countershaft that supports two pulleys. Pulley A delivers power to a machine causing a tension of 600 lbf in the tight side of the belt
The figure shows a steel countershaft that supports two pulleys. Pulley C receives power from a motor producing the belt tensions shown. Pulley A transmits this power to another machine through the
The structure of a diesel-electric locomotive is essentially a composite beam supporting a deck. Above the deck are mounted the diesel prime mover, generator or alternator, radiators, switch gear,
The designer of a shaft usually has a slope constraint imposed by the bearings used. This limit will be denoted as ξ . If the shaft shown in the figure is to have a uniform diameter d except in
A shaft is to be designed so that it is supported by roller bearings. The basic geometry is shown in the figure. The allowable slope at the bearings is 0.001 mm/mm without bearing life penalty. For a
Determine the maximum deflection of the shaft of Prob. 4–24.
For the shaft shown in the figure, let a1 = 4 in, b1 = 12 in, a2 = 10 in, F1 = 100 lbf, F2 = 300 lbf, and E = 30 Mpsi. The shaft is to be sized so that the maximum slope at either bearing A or
If the diameter of the beam for Prob. 4–26 is 1.375 in, determine the deflection of the beam at x = 8 in.
See Prob. 4–26 and the accompanying figure. The loads and dimensions are F1 = 3.5 kN, F2 = 2.7 kN, a1 = 100 mm, b1 = 150 mm, and a2 = 175 mm. Find the uniform shaft diameter necessary to limit the
Shown in the figure is a uniform-diameter shaft with bearing shoulders at the ends; the shaft is subjected to a concentrated moment M = 1200 lbf ?in. The shaft is of carbon steel and has a = 5 in and
The rectangular member OAB, shown in the figure, is held horizontal by the round hooked bar AC. The modulus of elasticity of both parts is 10 Mpsi. Use superposition to find the deflection at B due
The figure illustrates a torsion-bar spring O A having a diameter d = 12 mm. The actuating cantilever AB also has d = 12 mm. Both parts are of carbon steel. Use superposition and find the spring rate
Consider the simply supported beam with an intermediate load in Appendix A–9–6. Determine the deflection equation if the stiffness of the left and right supports are k1 and k2, respectively.
Consider the simply supported beam with a uniform load in Appendix A–9–7. Determine the deflection equation if the stiffness of the left and right supports are k1 and k2, respectively.
Prove that for a uniform-cross-section beam with simple supports at the ends loaded by a single concentrated load, the location of the maximum deflection will never be outside the range of 0.423l
Solve Prob. 4–12 using singularity functions. Use statics to determine the reactions.
Solve Prob. 4–13 using singularity functions. Use statics to determine the reactions.
Solve Prob. 4–14 using singularity functions. Use statics to determine the reactions.
Consider the uniformly loaded simply supported beam with an overhang as shown. Use singularity functions to determine the deflection equation of the beam. Use statics to determine the reactions.
Solve Prob. 4–15 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
Solve Prob. 4–30 using singularity functions. Use statics to determine the reactions.
Determine the deflection equation for the steel beam shown using singularity functions. Since the beam is symmetric, write the equation for only half the beam and use the slope at the beam center as
Determine the deflection equation for the cantilever beam shown using singularity functions. Evaluate the deflections at B and C and compare your results with Example 4€“11.
Examine the expression for the deflection of the cantilever beam, end-loaded, shown in Appendix Table A€“9€“1 for some intermediate point, x = a, as
A steel shaft of uniform 2-in diameter has a bearing span l of 23 in and an overhang of 7 in on which a coupling is to be mounted. A gear is to be attached 9 in to the right of the left bearing and
Use Castigliano’s theorem to verify the maximum deflection for the uniformly loaded beam of Appendix Table A–9–7. Neglect shear.
Solve Prob. 4–17 using Castigliano’s theorem. Hint: Write the moment equation using a position variable positive to the left starting at the right end of the beam.
Solve Prob. 4–30 using Castigliano’s theorem.
Solve Prob. 4–31 using Castigliano’s theorem.
Determine the deflection at midspan for the beam of Prob. 4–41 using Castigliano’s theorem.
Using Castigliano€™s theorem, determine the deflection of point B in the direction of the force F for the bar shown. The solid bar has a uniform diameter, d. Neglect bending shear.
A cable is made using a 16-gauge (0.0625-in) steel wire and three strands of 12-gauge (0.0801-in) copper wire. Find the stress in each wire if the cable is subjected to a tension of 250 lbf.
The figure shows a steel pressure cylinder of diameter 4 in which uses six SAE grade 5 steel bolts having a grip of 12 in. These bolts have a proof strength (see Chap. 8) of 85 kpsi for this size of
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
A rectangular aluminum bar 12 mm thick and 50 mm wide is welded to fixed supports at the ends, and the bar supports a load W = 3.5 kN, acting through a pin as shown. Find the reactions at the
The steel shaft shown in the figure is subjected to a torque of 50 lbf-in applied at point A. Find the torque reactions at O and B
Repeat Prob. 4–55 with the diameters of section OA being 1.5 in and section AB being 1.75 in.
In testing the wear life of gear teeth, the gears are assembled by using a pretorsion. In this way, a large torque can exist even though the power input to the tester is small. The arrangement shown
The figure shows a 3/8 - by 1 ½ -in rectangular steel bar welded to fixed supports at each end. The bar is axially loaded by the forces FA = 10 kip and FB = 5 kip acting on pins at A and
For the beam shown, determine the support reactions using superposition and procedure 1 from Sec. 4€“10.
Solve Prob. 4–59 using Castigliano’s theorem and procedure 1 from Sec. 4–10.
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 12 mm. The second area moment of the beam is I = 8(105) mm4. A force
The steel beam ABCD shown is supported at C as shown and supported at B and D by steel bolts each having a diameter of 5/16 in. The lengths of BE and DF are 2 and 2.5 in, respectively. The beam has a
The horizontal deflection of the right end of the curved bar of Fig. 4–12 is given by Eq. (4–35) for R/h > 10. For the same conditions, determine the vertical deflection.
A cast-iron piston ring has a mean diameter of 81 mm, a radial height h = 6 mm, and a thickness b = 4 mm. The ring is assembled using an expansion tool that separates the split ends a distance
For the wire form shown use Castigliano€™s method to determine the vertical deflection of point A. Consider bending only and assume Eq. (4€“28) applies for the curved part.
For the wire form shown determine the vertical deflections of points A and B. Consider bending only and assume Eq. (4€“28) applies.
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 =
For the wire form shown, determine(a) The reactions at points A and B,(b) How the bending moment varies along the wire, and(c) the deflection of the load F. Assume that the entire energy is described
For the curved beam shown, F = 30 kN. The material is steel with E = 207 iGPa and G = 79 GPa. Determine the relative deflection of the applied forces.
For the curved beam shown, F = 30 kN. The material is steel with E = 207 GPa and G = 79 GPa. Determine the relative deflection of the applied forces.
A thin ring is loaded by two equal and opposite forces F in part a of the figure. A free-body diagram of one quadrant is shown in part b. This is a statically indeterminate problem, because the
Find the increase in the diameter of the ring of Prob. 4–71 due to the forces F and along the y axis.
A round tubular column has outside and inside diameters of D and d, respectively, and a diametral ratio of K = d/D. Show that buckling will occur when the outside diameter is
For the conditions of Prob. 4€“73, show that buckling according to the parabolic formula will occur when the outside diameter is
Link 2, shown in the figure, is 1 in wide, has 1 2 -in-diameter bearings at the ends, and is cut from low-carbon steel bar stock having a minimum yield strength of 24 kpsi. The end-condition
The hydraulic cylinder shown in the figure has a 3-in bore and is to operate at a pressure of 800 psi. With the clevis mount shown, the piston rod should be sized as a column with both ends rounded
The figure shows a schematic drawing of a vehicular jack that is to be designed to support a maximum mass of 400 kg based on the use of a design factor nd = 2.50. The opposite-handed threads on the
If drawn, a figure for this problem would resemble that for Prob. 4–52. A strut that is a standard hollow right circular cylinder has an outside diameter of 4 in and a wall thickness of 3/8 in and
Find expressions for the maximum values of the spring force and deflection y of the impact system shown in the figure. Can you think of a realistic application for this model?
As shown in the figure, the weight W1 strikes W2 from a height h. Find the maximum values of the spring force and the deflection of W2. Name an actual system for which this model might be used.
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, what would be the maximum
The figure shows a horizontal steel bar 3/8 in thick loaded in steady tension and welded to a vertical support. Find the load F that will cause a shear stress of 20 kpsi in the throats of the
For the weldment of Prob. 9–1 the electrode specified is E7010. For the electrode metal, what is the allowable load on the weldment?
The members being joined in Prob. 9–1 are cold-rolled 1018 for the bar and hot-rolled 1018 for the vertical support. What load on the weldment is allowable because member metal is incorporated into
A 5/16 -in steel bar is welded to a vertical support as shown in the figure. What is the shear stress in the throat of the welds if the force F is 32 kip? br>
A ¾ -in-thick steel bar, to be used as a beam, is welded to a vertical support by two fillet welds as illustrated.(a) Find the safe bending force F if the permissible shear stress in the welds
The figure shows a weldment just like that of Prob. 9€“5 except that there are four welds instead of two. Show that the weldment is twice as strong as that of Prob. 9€“5. br>
The weldment shown in the figure is subjected to an alternating force F. The hot-rolled steel bar is 10 mm thick and is of AISI 1010 steel. The vertical support is likewise of 1010 steel. The
The permissible shear stress for the weldment illustrated is 140 MPa. Estimate the load, F, that will cause this stress in the weldment throat. br>
In the design of weldments in torsion it is helpful to have a hierarchical perception of the relative efficiency of common patterns. For example, the weld-bead patterns shown in Table 9€“1
The space available for a weld-bead pattern subject to bending is a ?a. Place the patterns of Table 9€“2 in hierarchical order of efficiency of weld metal placement to resist bending. A
Among the possible forms of weldment problems are the following:€¢ The attachment and the member(s) exist and only the weld specifications need to be decided.€¢ The members exist,
The attachment shown carries a bending load of 3 kip. The clearance a is to be 6 in. The load is a static 3000 lbf. Specify the weldment (give the pattern, electrode number, type of weld, length of
The attachment in Prob. 9€“12 has not had its length determined. The static force is 3 kip; the clearance a is to be 6 in. The member is 4 in wide. Specify the weldment (give the pattern,
A vertical column of A36 structural steel (Sy = 36 kpsi, Sut = 58€“80 kpsi) is 10 in wide. An attachment has been designed to the point shown in the figure. The static load of 20 kip is
Write a computer program to assist with a task such as that of Prob. 9–14 with a rectangular weld bead pattern for a torsional shear joint. In doing so solicit the force F, the clearance a, and the
Fillet welds in joints resisting bending are interesting in that they can be simpler than those resisting torsion. From Prob. 9–10 you learned that your objective is to place weld metal as far away
For a rectangular weld-bead track resisting bending, develop the necessary equations to treat cases of vertical welds, horizontal welds, and weld-all-around patterns with depth d and width b and
When comparing two different weldment patterns it is useful to observe the resistance to bending or torsion and the volume of weld metal deposited. Measure of effectiveness, defined as second moment
A torque T = 20(103) lb .in is applied to the weldment shown. Estimate the maximum shear stress in the weld throat. br>
Find the maximum shear stress in the throat of the weld metal in the figure. br>
The figure shows a welded steel bracket loaded by a static force F. Estimate the factor of safety if the allowable shear stress in the weld throat is 120 MPa. br>
The figure shows a formed sheet-steel bracket. Instead of securing it to the support with machine screws, welding has been proposed. If the combined stress in the weld metal is limited to 900 psi,
Without bracing, a machinist can exert only about 100 lbf on a wrench or tool handle. The lever shown in the figure has t = ½ in and w = 2 in. We wish to specify the fillet-weld size to secure
Estimate the safe static load F for the weldment shown in the figure if an E6010 electrode is used and the design factor is to be 2. Use conventional analysis. br>
Brackets, such as the one shown, are used in mooring small watercraft. Failure of such brackets is usually caused by bearing pressure of the mooring clip against the side of the hole. Our purpose
For the sake of perspective it is always useful to look at the matter of scale. Double all dimensions in Prob. 9–5 and find the allowable load. By what factor has it increased? First make a guess,
For a balanced double-lap joint cured at room temperature, Volkersen€™s equation simplifies to
A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 50 kpsi. Using the distortion-energy and maximum-shear-stress theories determine the factors of safety for
Repeat Prob. 5–1 for: (a) σA = 12 kpsi, σB = 12 kpsi (b) σA = 12 kpsi, σB = 6 kpsi (c) σA = 12 kpsi, σB = −12 kpsi (d) σA = −6 kpsi, σB =
Repeat Prob. 5–1 for a bar of AISI 1020 cold-drawn steel and: (a) σx = 180 MPa, σy = 100 MPa (b) σx = 180 MPa, τx y = 100 MPa (c) σx = −160 MPa, τx y = 100
Repeat Prob. 5–1 for a bar of AISI 1018 hot-rolled steel and: (a) σA = 100 MPa, σB = 80 MPa (b) σA = 100 MPa, σB = 10 MPa (c) σA = 100 MPa, σB = −80 MPa (d)
Repeat Prob. 5–3 by first plotting the failure loci in the σA , σB plane to scale; then, for each stress state, plot the load line and by graphical measurement estimate the factors of
Repeat Prob. 5–4 by first plotting the failure loci in the σA , σB plane to scale; then, for each stress state, plot the load line and by graphical measurement estimate the factors of
An ASTM cast iron has minimum ultimate strengths of 30 kpsi in tension and 100 kpsi in compression. Find the factors of safety using the MNS, BCM, and MM theories for each of the following stress
For Prob. 5–7, case (d), estimate the factors of safety from the three theories by graphical measurements of the load line.
Among the decisions a designer must make is selection of the failure criteria that is applicable to the material and its static loading. A 1020 hot-rolled steel has the following properties: Sy = 42
A 4142 steel Q&T at 80◦F exhibits Syt = 235 kpsi, Syc = 275 kpsi, and εf = 0.06. Choose and plot the failure locus and, for the static stresses at the critical locations, which are 10
For grade 20 cast iron, Table A–24 gives Sut = 22 kpsi, Suc = 83 kpsi. Choose and plot the failure locus and, for the static loadings inducing the stresses at the critical locations of Prob. 5–9,

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