Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4, Problem 99P
Solve Prob. 4–98 using Castigliano’s theorem and procedure 1 from Sec. 4–10.
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6-28 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 surface finish corresponds closely to a hot-
rolled finish. Ignore curvature effects on the bending stress. What number of applica-
tions is likely to cause failure? Solve using:
(a) Goodman criterion.
(b) Gerber criterion.
= 40 lbf
max
12 in-
= 20 lbf
min
Problem 6-28
Solve only Problem 4-53
After recording the applied twisting moment and resulted angle, fill the following
table
MT
(N.m)
T.
MPa
(degree)
(rad.)
Now, the twisting moment-twisting angle and shear stress-shear strain curves can
be plotted, then determine maximum shear stress, shear stress at proportional limit
and modulus of rigidity.
4-6 Problem
The following torsion test data were obtained for AA6061-T6 aluminum alloy has a
round cross section with 30mm outer diameter, 0 inner diameter and 100 length.
0 32
130
Twisted angle (): 0 1
Torque (N.m):
286
347 487
5.5
591
786
910
1105 1163 1235 1222
3.5
6.5
7.5
9.
10.5 13.5 16.5 21.5 25.5
> Plot the torque-twisted angle curve and determine the proportional limit on it.
Plot the shear stress-strain curve the determine the shearing strength and
modulus of rigidity.
Prof. Adnan N. Abood
Asst. Lec. Zainah Waheed
25
Chapter 4 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Ch. 4 - The figure shows a torsion bar OA fixed at O,...Ch. 4 - For Prob. 41, if the simple support at point A...Ch. 4 - A torsion-bar spring consists of a prismatic bar,...Ch. 4 - An engineer is forced by geometric considerations...Ch. 4 - A bar in tension has a circular cross section and...Ch. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - Derive the equations given for beam 2 in Table A9...Ch. 4 - Derive the equations given for beam 5 in Table A9...Ch. 4 - The figure shows a cantilever consisting of steel...
Ch. 4 - A simply supported beam loaded by two forces is...Ch. 4 - Using superposition, find the deflection of the...Ch. 4 - A rectangular steel bar supports the two...Ch. 4 - An aluminum tube with outside diameter of 2 in and...Ch. 4 - The cantilever shown in the figure consists of two...Ch. 4 - Using superposition for the bar shown, determine...Ch. 4 - A simply supported beam has a concentrated moment...Ch. 4 - Prob. 18PCh. 4 - Using the results of Prob. 418, use superposition...Ch. 4 - Prob. 20PCh. 4 - Consider the uniformly loaded simply supported...Ch. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - 429 to 434 For the steel countershaft specified in...Ch. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - For the steel countershaft specified in the table,...Ch. 4 - For the steel countershaft specified in the table,...Ch. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - The cantilevered handle in the figure is made from...Ch. 4 - Prob. 42PCh. 4 - The cantilevered handle in Prob. 384, p. 154, is...Ch. 4 - A flat-bed trailer is to be designed with a...Ch. 4 - The designer of a shaft usually has a slope...Ch. 4 - Prob. 46PCh. 4 - If the diameter of the steel beam shown is 1.25...Ch. 4 - For the beam of Prob. 4-47, plot the magnitude of...Ch. 4 - Prob. 49PCh. 4 - 4-50 and 4-51 The figure shows a rectangular...Ch. 4 - and 451 the ground at one end and supported by a...Ch. 4 - The figure illustrates a stepped torsion-bar...Ch. 4 - Consider the simply supported beam 5 with a center...Ch. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Solve Prob. 410 using singularity functions. Use...Ch. 4 - Prob. 57PCh. 4 - Prob. 58PCh. 4 - Prob. 59PCh. 4 - Solve Prob. 413 using singularity functions. Since...Ch. 4 - Prob. 61PCh. 4 - Solve Prob. 419 using singularity functions to...Ch. 4 - Using singularity functions, write the deflection...Ch. 4 - Determine the deflection equation for the...Ch. 4 - Use Castiglianos theorem to verify the maximum...Ch. 4 - Use Castiglianos theorem to verify the maximum...Ch. 4 - Solve Prob. 415 using Castiglianos theorem.Ch. 4 - Solve Prob. 452 using Castiglianos theoremCh. 4 - Determine the deflection at midspan for the beam...Ch. 4 - Using Castiglianos theorem, determine the...Ch. 4 - Solve Prob. 441 using Castiglianos theorem. Since...Ch. 4 - Solve Prob. 442 using Castiglianos theorem.Ch. 4 - The cantilevered handle in Prob. 384 is made from...Ch. 4 - Solve Prob. 450 using Castiglianos theorem.Ch. 4 - Solve Prob. 451 using Castiglianos theorem.Ch. 4 - The steel curved bar shown has a rectangular cross...Ch. 4 - Repeat Prob. 476 to find the vertical deflection...Ch. 4 - For the curved steel beam shown. F = 6.7 kips....Ch. 4 - A steel piston ring has a mean diameter of 70 mm....Ch. 4 - For the steel wire form shown, use Castiglianos...Ch. 4 - 4-81 and 4-82 The part shown is formed from a...Ch. 4 - 4-81 and 4-82 The part shown is formed from a...Ch. 4 - Repeat Prob. 481 for the vertical deflection at...Ch. 4 - Repeat Prob. 482 for the vertical deflection at...Ch. 4 - A hook is formed from a 2-mm-diameter steel wire...Ch. 4 - The figure shows a rectangular member OB, made...Ch. 4 - Prob. 87PCh. 4 - For the wire form shown, determine the deflection...Ch. 4 - Prob. 89PCh. 4 - Prob. 90PCh. 4 - Prob. 91PCh. 4 - Prob. 92PCh. 4 - Solve Prob. 492 using Castiglianos method and...Ch. 4 - An aluminum step bar is loaded as shown. (a)...Ch. 4 - The steel shaft shown in the figure is subjected...Ch. 4 - Repeat Prob. 495 with the diameters of section OA...Ch. 4 - The figure shows a 12- by 1-in rectangular steel...Ch. 4 - For the beam shown, determine the support...Ch. 4 - Solve Prob. 498 using Castiglianos theorem and...Ch. 4 - Consider beam 13 in Table A9, but with flexible...Ch. 4 - Prob. 101PCh. 4 - The steel beam ABCD shown is simply supported at C...Ch. 4 - Prob. 103PCh. 4 - A round tubular column has outside and inside...Ch. 4 - For the conditions of Prob. 4104, show that...Ch. 4 - Link 2, shown in the figure, is 25 mm wide, has...Ch. 4 - Link 3, shown schematically in the figure, acts as...Ch. 4 - The hydraulic cylinder shown in the figure has a...Ch. 4 - The figure shows a schematic drawing of a...Ch. 4 - If drawn, a figure for this problem would resemble...Ch. 4 - Design link CD of the hand-operated toggle press...Ch. 4 - Find the maximum values of the spring force and...Ch. 4 - As shown in the figure, the weight W1 strikes W2...Ch. 4 - Part a of the figure shows a weight W mounted...
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- Repeat Problem 3.3-1, but now use a circular tube with outer diameter d0= 2.5 in. and inner diameter di= 1.5 in.arrow_forwardRepeat Problem 6.4-14 but use the configuration of channel shapes and loading shown in the figure. Use P = 250 N.arrow_forward-15 Repeat the preceding problem using ??. = - 750 psi.arrow_forward
- Repeat Problem 11.2-3 assuming that R= 10 kN · m/rad and L = 2 m.arrow_forwardRepeat Problem 11.3-9. Use two C 150 × 12.2 steel shapes and assume that E = 205 GPa and L = 6 m.arrow_forward4-67. Compute the angle of twist of the free end rela- tive to the fixed end of the steel bar shown in Figure P4-67.arrow_forward
- 4-67. Figure P4-67 shows a shaft carrying three gears that rotates at 1150 rpm. Gear A delivers 20 kW to a mat- ing gear that drives a mixer. Gear C delivers 12 kW to a different mating gear that drives a circular saw. All power comes into the shaft through gear B. Consider- ing only torsion, compute the shearing stress in each part of the shaft. Consider stress concentrations.arrow_forwardL length of the adjustable wrench in the figure; Choose a number from 152 to 252 mm that does not end with a zero. F force also; Choose from 122 to 292 N as a non-zero number. Find the torque and direction of the wrench applied to the bolt. ?arrow_forwardSolve the preceding problem for the element shown in the figure.arrow_forward
- Solve the preceding problem for the following data: b = 6 in., b = 10 in, L = 110 ft, tan a = 1/3, and q = 325 lb/ft.arrow_forwardCompare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?arrow_forwardPipe 2 has been inserted snugly into Pipe I. but the holes Tor a connecting pin do not line up; there is a gap s. The user decides to apply either force P:lo Pipe I or force P-, to Pipe 2, whichever is smaller. Determine the following using the numerical properties in the box. (a) If only P{is applied, find Pt{tips} required to close gap s; if a pin is then inserted and Ptremoved, what are reaction forces RAand RBfor this load case? (b) If only P2is applied, find P2{kips) required to close gap a; if a pin is inserted and P2removed, what are reaction forces R^ and RBfor this load case? (c) What is the maximum shear stress in the pipes, for the loads in parts (a) and (b)? (d) If a temperature increase IT is to be applied to the entire structure to close gaps{instead of applying forces Ptand P2), find the AT required to close the gap. If a pin is inserted after the gaphas closed, what are reaction forces .''.', and RBfor this case? (e) Finally, if the structure (with pin inserted) then cools to the original ambient temperature, what are reaction forces Rtand Parrow_forward
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