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Questions and Answers of Mechanical Engineering

A steel member has a Brinell of HB = 250. Estimate the ultimate strength of the steel in MPa.
Brinell hardness tests were made on a random sample of 10 steel parts during processing. The results were HB values of 252 (2), 260, 254, 257 (2), 249 (3), and 251. Estimate the mean and standard
Repeat Prob. 2–15 assuming the material to be cast iron.
Toughness is a term that relates to both strength and ductility. The fracture toughness, for example, is defined as the total area under the stress-strain curve to fracture, . This area, called the
What is the material composition of AISI 4340 steel?
The symbol W is used in the various figure parts to specify the weight of an element. If not given, assume the parts are weightless. For each figure part, sketch a free-body diagram of each element,
Using the figure part selected by your instructor, sketch a free-body diagram of each element in the figure. Compute the magnitude and direction of each force using an algebraic or vector method, as
Find the reactions at the supports and plot the shear-force and bending-moment diagrams for each of the beams shown in the figure on page 123. Label the diagrams properly.
Repeat Prob. 3-3 using singularity functions exclusively (for reactions as well).
A beam carrying a uniform load is simply supported with the supports set back a distance a from the ends as shown in the figure. The bending moment at x can be found from summing moments to zero at
An artist wishes to construct a mobile using pendants, string, and span wire with eyelets as shown in the figure.(a) At what positions w, x, y, and z should the suspension strings be attached to the
For each of the plane stress states listed below, draw a Mohr’s circle diagram properly labeled, find the principal normal and shear stresses, and determine the angle from the x axis to σ1.
Repeat Prob. 3–8 for: (a) σx = −4, σy = 12, τx y = 7 ccw (b) σx = 6, σy = −5, τx y = 8 ccw (c) σx = −8, σy = 7, τx y = 6 cw (d)
Repeat Prob. 3–8 for: (a) σx = 20, σy = −10, τx y = 8 cw (b) σx = 30, σy = −10, τx y = 10 ccw (c) σx = −10, σy = 18, τx y = 9
For each of the stress states listed below, find all three principal normal and shear stresses. Draw a complete Mohr’s three-circle diagram and label all points of interest. (a) σx = 10,
Repeat Prob. 3–11 for: (a) σx = −80, σy = −30, τx y = 20 cw (b) σx = 30, σy = −60, τx y = 30 cw (c) σx = 40, σz = −30, τx y =
A ½ -in-diameter steel tension rod is 72 in long and carries a load of 2000 lbf. Find the tensile stress, the total deformation, the unit strains, and the change in the rod diameter.
Twin diagonal aluminum alloy tension rods 15 mm in diameter are used in a rectangular frame to prevent collapse. The rods can safely support a tensile stress of 135 MPa. If the rods are initially 3 m
Electrical strain gauges were applied to a notched specimen to determine the stresses in the notch. The results were ǫx = 0.0021 and ǫy = −0.00067. Find σx and σy if the
An engineer wishes to determine the shearing strength of a certain epoxy cement. The problem is to devise a test specimen such that the joint is subject to pure shear. The joint shown in the figure,
The state of stress at a point is σx = −2, σy = 6, σz = −4, τx y = 3, τyz = 2, and τz x = −5 kpsi. Determine the principal stresses, draw a complete
Repeat Prob. 3–17 with σx = 10, σy = 0, σz = 10, τx y = 20, τyz = −10√2, and τz x = 0 MPa.
Repeat Prob. 3–17 with σx = 1, σy = 4, σz = 4, τx y = 2, τyz = −4, and τz x = −2 kpsi.
The Roman method for addressing uncertainty in design was to build a copy of a design that was satisfactory and had proven durable. Although the early Romans did not have the intellectual tools to
Using our experience with concentrated loading on a simple beam, Prob. 3–20, consider a uniformly loaded simple beam (Table A–9–7). (a) Show that the stress-to-load equation for a
The Chicago North Shore & Milwaukee Railroad was an electric railway running between the cities in its corporate title. It had passenger cars as shown in the figure, which weighed 104.4 kip, had
For each section illustrated, find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and bottom surfaces. Suppose a positive bending
From basic mechanics of materials, in the derivation of the bending stresses, it is found that the radius of curvature of the neutral axis, ρ, is given by ρ = E I/M. Find the x and y
For each beam illustrated in the figure, find the locations and magnitudes of the maximum tensile bending stress and the maximum shear stress due to V.
The figure illustrates a number of beam sections. Use an allowable bending stress of 1.2 kpsi for wood and 12 kpsi for steel and find the maximum safe uniformly distributed load that each beam can
A pin in a knuckle joint carrying a tensile load F deflects somewhat on account of this loading, making the distribution of reaction and load as shown in part b of the figure. The usual designer’s
The figure illustrates a pin tightly fitted into a hole of a substantial member. A usual analysis is one that assumes concentrated reactions R and M at distance l from F. Suppose the reaction is
For the beam shown, determine (a) the maximum tensile and compressive bending stresses, (b) The maximum shear stress due to V, and (c) the maximum shear stress in the beam.
Consider a simply supported beam of rectangular cross section of constant width b and variable depth h, so proportioned that the maximum stress σx at the outer surface due to bending is
In Prob. 3-30, h →0 as x →0, which cannot occur. If the maximum shear stress τmax due to direct shear is to be constant in this region, show that the depth h at location x is given by
Consider a simply supported static beam of circular cross section of diameter d, so proportioned by varying the diameter such that the maximum stress σx at the surface due to bending is
Two steel thin-wall tubes in torsion of equal length are to be compared. The first is of square cross section, side length b, and wall thickness t. The second is a round of diameter b and wall
Begin with a 1-in-square thin-wall steel tube, wall thickness t = 0.05 in, length 40 in, then introduce corner radii of inside radii ri, with allowable shear stress τall of 11 500 psi, shear
An unequal leg angle shown in the figure carries a torque T. Show that
In Prob. 3–35 the angle has one leg thickness 1/16 in and the other 1/8 in, with both leg lengths 58 in. The allowable shear stress is τall = 12 000 psi for this steel angle. (a) Find the
Two 12 in long thin rectangular steel strips are placed together as shown. Using a maximum allowable shear stress of 12 000 psi, determine the maximum torque and angular twist, and the torsional
Using a maximum allowable shear stress of 60 MPa, find the shaft diameter needed to transmit35 kw when (a) The shaft speed is 2000 rev/min. (b) The shaft speed is 200 rev/min
A 15-mm-diameter steel bar is to be used as a torsion spring. If the torsional stress in the bar is not to exceed 110 MPa when one end is twisted through an angle of 30°, what must be the length of
A 3-in-diameter solid steel shaft, used as a torque transmitter, is replaced with a 3-in hollow shaft having a ¼ -in wall thickness. If both materials have the same strength, what is the percentage
A hollow steel shaft is to transmit 5400 N .m of torque and is to be sized so that the torsional stress does not exceed 150 MPa. (a) If the inside diameter is three-fourths of the outside diameter,
The figure shows an endless-belt conveyor drive roll. The roll has a diameter of 6 in and is driven at 5 rev/min by a geared-motor source rated at 1 hp. Determine a suitable shaft diameter dC for an
The conveyer drive roll in the figure for Prob. 3–42 is 150 mm in diameter and is driven at 8 rev/min by a geared-motor source rated at 1 kW. Find a suitable shaft diameter dC based on an allowable
For the same cross-sectional area A = s2 = πd2/4, for a square cross-sectional area shaft and a circular cross-sectional area shaft, in torsion which has the higher maximum shear stress, and by
For the same cross-sectional area A = s2 = πd2/4, for a square cross-sectional area shaft and a circular cross-sectional area shaft, both of length l, in torsion which has the greater angular
In the figure, shaft AB is rotating at 1000 rev/min and transmits 10 hp to shaft CD through a set of bevel gears contacting at point E. The contact force at E on the gear of shaft CD is determined to
Repeat the analysis of Prob. 3–46 for shaft AB. Let the diameter of the shaft be 1.0 in, and assume that bearing A is a thrust bearing.
A torque of T = 1000 lbf ?in is applied to the shaft EFG, which is running at constant speed and contains gear F. Gear F transmits torque to shaft ABCD through gear C, which drives the chain sprocket
If the tension-loaded plate of Fig. 3-29 is infinitely wide, then the stress state anywhere in the plate can be described in polar coordinates as For the radial, tangential, and shear components,
Considering the stress concentration at point A in the figure, determine the maximum normal and shear stresses at A if F = 200 lbf.
Develop the formulas for the maximum radial and tangential stresses in a thick-walled cylinder due to internal pressure only.
Repeat Prob. 3–51 where the cylinder is subject to external pressure only. At what radii do the maximum stresses occur?
Develop the stress relations for a thin-walled spherical pressure vessel.
A pressure cylinder has a diameter of 150 mm and has a 6-mm wall thickness. What pressure can this vessel carry if the maximum shear stress is not to exceed 25 Mpa?
A cylindrical pressure vessel has an outside diameter of 10 in and a wall thickness of 3/8 in. If the internal pressure is 350 psi, what is the maximum shear stress in the vessel walls?
An AISI 1020 cold-drawn steel tube has an ID of 1 ¼ in and an OD of 1 ¾ in. What maximum external pressure can this tube take if the largest principal normal stress is not to exceed 80 percent of
An AISI 1020 cold-drawn steel tube has an ID of 40 mm and an OD of 50 mm. What maximum internal pressure can this tube take if the largest principal normal stress is not to exceed 80 percent of the
Find the maximum shear stress in a 10-in circular saw if it runs idle at 7200 rev/min. The saw is 14 gauge (0.0747 in) and is used on a ¾ -in arbor. The thickness is uniform. What is the maximum
The maximum recommended speed for a 300-mm-diameter abrasive grinding wheel is 2069 rev/min. Assume that the material is isotropic; use a bore of 25 mm, ν = 0.24, and a mass density of 3320
An abrasive cutoff wheel has a diameter of 6 in, is 1/16 in thick, and has a 1-in bore. It weighs 6 oz and is designed to run at 10 000 rev/min. If the material is isotropic and ν = 0.20, find
A rotary lawn-mower blade rotates at 3000 rev/min. The steel blade has a uniform cross section 1/8 in thick by 1 ¼ in wide, and has a ½ -in-diameter hole in the center as shown in the
The table lists the maximum and minimum hole and shaft dimensions for a variety of standard press and shrink fits. The materials are both hot-rolled steel. Find the maximum and minimum values of the
The table gives data concerning the shrink fit of two cylinders of differing materials and dimensional specification in inches. Elastic constants for different materials may be found in Table
Force fits of a shaft and gear are assembled in an air-operated arbor press. An estimate of assembly force and torque capacity of the fit is needed. Assume the coefficient of friction is f, the fit
A utility hook was formed from a 1-in-diameter round rod into the geometry shown in the figure. What are the stresses at the inner and outer surfaces at section A-A if the load F is 1000 lbf?
The steel eyebolt shown in the figure is loaded with a force F of 100 lbf. The bolt is formed of ¼ -in-diameter wire to a 3/8 -in radius in the eye and at the shank. Estimate the stresses at
Shown in the figure is a 12-gauge (0.1094-in) by ¾ -in latching spring that supports a load of F = 3 lbf. The inside radius of the bend is 1/8 in. Estimate the stresses at the inner and outer
The cast-iron bell-crank lever depicted in the figure is acted upon by forces F1 of 250 lbf and F2 of 333 lbf. The section A-A at the central pivot has a curved inner surface with a radius of ri = 1
The crane hook depicted in Fig. 3–35 has a 1-in-diameter hole in the center of the critical section. For a load of 5 kip, estimate the bending stresses at the inner and outer surfaces at the
A 20-kip load is carried by the crane hook shown in the figure. The cross section of the hook uses two concave flanks. The width of the cross section is given by b = 2/r, where r is the radius from
An offset tensile link is shaped to clear an obstruction with a geometry as shown in the figure. The cross section at the critical location is elliptical, with a major axis of 4 in and a minor axis
A cast-steel C frame as shown in the figure has a rectangular cross section of 1 in by 1.6 in, with a 0.4-in-radius semicircular notch on both sides that forms midflank fluting as shown. Estimate A,
Two carbon steel balls, each 25 mm in diameter, are pressed together by a force F. In terms of the force F, find the maximum values of the principal stress, and the maximum shear stress, in MPa.
One of the balls in Prob. 3–81 is replaced by a flat carbon steel plate. If F = 18 N, at what depth does the maximum shear stress occur?
An aluminum alloy roller with diameter 1 in and length 2 in rolls on the inside of a cast-iron ring having an inside radius of 4 in, which is 2 in thick. Find the maximum contact force F that can be
Simplify Eqs. (3–70), (3–71), and (3–72) by setting z = 0 and finding σx /pmax , σy/pmax , σz/pmax , and τ2/3/pmax and, for cast iron, check the ordinate intercepts of the
A 6-in-diameter cast-iron wheel, 2 in wide, rolls on a flat steel surface carrying an 800-lbf load. (a) Find the Hertzian stresses σx, σy, σz, and τ2/3. (b) What happens to the
Structures can often be considered to be composed of a combination of tension and torsion members and beams. Each of these members can be analyzed separately to determine its force-deflection
The figure shows a torsion bar OA fixed at O, simply supported at A, and connected to a cantilever AB. The spring rate of the torsion bar is kT , in newton-meters per radian, and that of the
A torsion-bar spring consists of a prismatic bar, usually of round cross section, that is twisted at one end and held fast at the other to form a stiff spring. An engineer needs a stiffer one than
An engineer is forced by geometric considerations to apply the torque on the spring of Prob. 4–3 at the location x = 0.2l. For a uniform-diameter spring, this would cause the long leg of the span
A bar in tension has a circular cross section and includes a conical portion of length l , as Shown, the task is to find the spring rate of the entire bar. Equation (4–4) is useful for the outer
When a hoisting cable is long, the weight of the cable itself contributes to the elongation. If a cable has a weight per unit length of w, a length of l , and a load P attached to the free end, show
Use integration to verify the deflection equation given for the uniformly loaded cantilever beam of appendix Table A–9–3.
Use integration to verify the deflection equation given for the end moment loaded cantilever beam of appendix Table A–9–4.
When an initially straight beam sags under transverse loading, the ends contract because the neutral surface of zero strain neither extends nor contracts. The length of the deflected neutral surface
Using the results of Prob. 4–9, determine the end contraction of the uniformly loaded cantilever beam of appendix Table A–9–3.
Using the results of Prob. 4–9, determine the end contraction of the uniformly loaded simply supported beam of appendix Table A–9–7. Assume the left support cannot deflect in the x direction,
The figure shows a cantilever consisting of steel angles size 4 X 4 X ½ in mounted back to back, Using superposition, find the deflection at B and the maximum stress in the beam.
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 at midspan
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 values differ?
A rectangular steel bar supports the two overhanging loads shown in the figure. Using superposition, find the deflection at the ends and at the center.
Using the formulas in Appendix Table A–9 and superposition, find the deflection of the cantilever at B if I = 13 in4 and E = 30 Mpsi.
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.
Using superposition, determine the maximum deflection of the beam shown in the figure. The material is carbon steel.
Illustrated is a rectangular steel bar with simple supports at the ends and loaded by a force F at the middle; the bar is to act as a spring. The ratio of the width to the thickness is to be aboutb

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