Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Chapter 5, Problem 163RP
(a)
To determine
Express b in terms of x, L, and
(b)
To determine
Find the smallest value of h.
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Students have asked these similar questions
Beam DE rests on the cantilever beam AC as shown. Knowing that a square rod of side 10 mm is used for each
beam, determine the deflection at end C if the 25-N-m couple is applied (a) to end E of the beam DE, (b) to end
C of the beam AC. Use E = 200 GPa.
10 mm
D
E
A
B
25 N-m
120 mm
180 mm
ANS.
(a) 5.94 mm ↓. (b) 6.75 mm ↓.
10 mm
Please solve correctl
Homework
A timber beam AB of length L and rectangular cross section carries
a single concentrated load P at its midpoint C. (a) Show that the ratio
Tm/Tm of the maximum values of the shearing and normal stresses in
the beam is equal to h/2L, where h and L are, respectively, the depth
and the length of the beam. (b) Determine the depth h and the width
b of the beam, knowing that L = 2 m, P = 40 kN, 7m = 960 kPa,
and om = 12 MPa.
|P
L/2 -
- L/2·
A
В
Chapter 5 Solutions
Mechanics of Materials, 7th Edition
Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...
Ch. 5.1 - 5.11 and 5.12 Draw the shear and bending-moment...Ch. 5.1 - 5.11 and 5.12 Draw the shear and bending-moment...Ch. 5.1 - 5.13 and 5.14 Assuming that the reaction of the...Ch. 5.1 - 5.13 and 5.14 Assuming that the reaction of the...Ch. 5.1 - 5.15 and 5.16 For the beam and loading shown,...Ch. 5.1 - 5.15 and 5.16 For the beam and loading shown,...Ch. 5.1 - For the beam and loading shown, determine the...Ch. 5.1 - For the beam and loading shown, determine the...Ch. 5.1 - 5.19 and 5.20 For the beam and loading shown,...Ch. 5.1 - 5.19 and 5.20 For the beam and loading shown,...Ch. 5.1 - Draw the shear and bending-moment diagrams for the...Ch. 5.1 - 5.22 and 5.23 Draw the shear and bending-moment...Ch. 5.1 - 5.22 and 5.23 Draw the shear and bending-moment...Ch. 5.1 - 5.24 and 5.25 Draw the shear and bending-moment...Ch. 5.1 - 5.24 and 5.25 Draw the shear and bending-moment...Ch. 5.1 - Knowing that W = 12 kN, draw the shear and...Ch. 5.1 - Determine (a) the magnitude of the counterweight W...Ch. 5.1 - Determine (a) the distance a for which the...Ch. 5.1 - Knowing that P = Q = 480 N, determine (a) the...Ch. 5.1 - Solve Prob. 5.29, assuming that P = 480 N and Q =...Ch. 5.1 - Determine (a) the distance a for which the...Ch. 5.1 - A solid steel rod of diameter d is supported as...Ch. 5.1 - A solid steel bar has a square cross section of...Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.1a....Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.2a....Ch. 5.2 - Prob. 36PCh. 5.2 - Prob. 37PCh. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.5a....Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.6a....Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.7. 5.7...Ch. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.8. 5.7...Ch. 5.2 - Prob. 42PCh. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.10....Ch. 5.2 - 5.44 and 5.45 Draw the shear and bending-moment...Ch. 5.2 - 5.44 and 5.45 Draw the shear and bending-moment...Ch. 5.2 - Prob. 46PCh. 5.2 - Prob. 47PCh. 5.2 - Prob. 48PCh. 5.2 - Using the method of Sec. 5.2, solve Prob. 5.20....Ch. 5.2 - 5.50 and 5.51 Determine (a) the equations of the...Ch. 5.2 - 5.50 and 5.51 Determine (a) the equations of the...Ch. 5.2 - 5.52 and 5.53 Determine (a) the equations of the...Ch. 5.2 - 5.52 and 5.53 Determine (a) the equations of the...Ch. 5.2 - 5.54 and 5.55 Draw the shear and bending-moment...Ch. 5.2 - 5.54 and 5.55 Draw the shear and bending-moment...Ch. 5.2 - 5.56 and 5.57 Draw the shear and bending-moment...Ch. 5.2 - 5.56 and 5.57 Draw the shear and bending-moment...Ch. 5.2 - 5.58 and 5.59 Draw the shear and bending-moment...Ch. 5.2 - 5.58 and 5.59 Draw the shear and bending-moment...Ch. 5.2 - Knowing that beam AB is in equilibrium under the...Ch. 5.2 - Knowing that beam AB is in equilibrium under the...Ch. 5.2 - The beam AB supports two concentrated loads P and...Ch. 5.2 - The beam AB supports a uniformly distributed load...Ch. 5.2 - Beam AB supports a uniformly distributed load of 2...Ch. 5.3 - 5.65 and 5.66 For the beam and loading shown,...Ch. 5.3 - 5.65 and 5.66 For the beam and loading shown,...Ch. 5.3 - 5.67 and 5.68 For the beam and loading shown,...Ch. 5.3 - 5.67 and 5.68 For the beam and loading shown,...Ch. 5.3 - 5.69 and 5.70 For the beam and loading shown,...Ch. 5.3 - 5.69 and 5.70 For the beam and loading shown,...Ch. 5.3 - 5.71 and 5.72 Knowing that the allowable normal...Ch. 5.3 - 5.71 and 5.72 Knowing that the allowable normal...Ch. 5.3 - 5.73 and 5.74 Knowing that the allowable normal...Ch. 5.3 - 5.73 and 5.74 Knowing that the allowable normal...Ch. 5.3 - 5.75 and 5.76 Knowing that the allowable normal...Ch. 5.3 - 5.75 and 5.76 Knowing that the allowable normal...Ch. 5.3 - 5.77 and 5.78 Knowing that the allowable normal...Ch. 5.3 - 5.77 and 5.78 Knowing that the allowable normal...Ch. 5.3 - A steel pipe of 100-mm diameter is to support the...Ch. 5.3 - Two metric rolled-steel channels are to be welded...Ch. 5.3 - Two rolled-steel channels are to be welded back to...Ch. 5.3 - Two L4 3 rolled-steel angles are bolted together...Ch. 5.3 - Assuming the upward reaction of the ground to be...Ch. 5.3 - Assuming the upward reaction of the ground to be...Ch. 5.3 - Determine the largest permissible distributed load...Ch. 5.3 - Solve Prob. 5.85, assuming that the cross section...Ch. 5.3 - Determine the largest permissible value of P for...Ch. 5.3 - Solve Prob. 5.87, assuming that the T-shaped beam...Ch. 5.3 - Beams AB, BC, and CD have the cross section shown...Ch. 5.3 - Beams AB, BC, and CD have the cross section shown...Ch. 5.3 - Each of the three rolled-steel beams shown...Ch. 5.3 - A 54-kip load is to be supported at the center of...Ch. 5.3 - A uniformly distributed load of 66 kN/m is to be...Ch. 5.3 - A roof structure consists of plywood and roofing...Ch. 5.3 - Solve Prob. 5.94, assuming that the 6-kN...Ch. 5.3 - Prob. 96PCh. 5.3 - Assuming that the front and rear axle loads remain...Ch. 5.4 - 5.98 through 5.100 (a) Using singularity...Ch. 5.4 - 5.98 through 5.100 (a) Using singularity...Ch. 5.4 - 5.98 through 5.100 (a) Using singularity...Ch. 5.4 - 5.101 through 5.103 (a) Using singularity...Ch. 5.4 - Prob. 102PCh. 5.4 - Prob. 103PCh. 5.4 - Prob. 104PCh. 5.4 - Prob. 105PCh. 5.4 - Prob. 106PCh. 5.4 - Prob. 107PCh. 5.4 - Prob. 108PCh. 5.4 - Prob. 109PCh. 5.4 - Prob. 110PCh. 5.4 - Prob. 111PCh. 5.4 - Prob. 112PCh. 5.4 - 5.112 and 5.113 (a) Using singularity functions,...Ch. 5.4 - Prob. 114PCh. 5.4 - 5.114 and 5.115 A beam is being designed to be...Ch. 5.4 - 5.116 and 5.117 A timber beam is being designed to...Ch. 5.4 - Prob. 117PCh. 5.4 - Prob. 118PCh. 5.4 - Prob. 119PCh. 5.4 - 5.118 through 5.121 Using a computer and step...Ch. 5.4 - Prob. 121PCh. 5.4 - 5.122 and 5.123 For the beam and loading shown and...Ch. 5.4 - 5.122 and 5.123 For the beam and loading shown and...Ch. 5.4 - 5.124 and 5.125 For the beam and loading shown and...Ch. 5.4 - Prob. 125PCh. 5.5 - 5.126 and 5.127 The beam AB, consisting of a...Ch. 5.5 - Prob. 127PCh. 5.5 - 5.128 and 5.129 The beam AB, consisting of a...Ch. 5.5 - 5.128 and 5.129 The beam AB, consisting of a...Ch. 5.5 - Prob. 130PCh. 5.5 - Prob. 131PCh. 5.5 - Prob. 132PCh. 5.5 - 5.132 and 5.133 A preliminary design on the use of...Ch. 5.5 - Prob. 134PCh. 5.5 - Prob. 135PCh. 5.5 - Prob. 136PCh. 5.5 - Prob. 137PCh. 5.5 - Prob. 138PCh. 5.5 - Prob. 139PCh. 5.5 - Assuming that the length and width of the cover...Ch. 5.5 - Two cover plates, each 12 in. thick, are welded to...Ch. 5.5 - Two cover plates, each 12 in. thick, are welded to...Ch. 5.5 - Prob. 143PCh. 5.5 - Prob. 144PCh. 5.5 - Two cover plates, each 7.5 mm thick, are welded to...Ch. 5.5 - Prob. 146PCh. 5.5 - Prob. 147PCh. 5.5 - For the tapered beam shown, determine (a) the...Ch. 5.5 - Prob. 149PCh. 5.5 - Prob. 150PCh. 5.5 - Prob. 151PCh. 5 - Draw the shear and bending-moment diagrams for the...Ch. 5 - Draw the shear and bending-moment diagrams for the...Ch. 5 - Determine (a) the distance a for which the...Ch. 5 - For the beam and loading shown, determine the...Ch. 5 - Draw the shear and bending-moment diagrams for the...Ch. 5 - Beam AB, of length L and square cross section of...Ch. 5 - Prob. 158RPCh. 5 - Knowing that the allowable normal stress for the...Ch. 5 - Prob. 160RPCh. 5 - (a) Using singularity functions, find the...Ch. 5 - Prob. 162RPCh. 5 - Prob. 163RP
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- Homework A timber beam AB of length L and rectangular cross section carries a single concentrated load P at its midpoint C. (a) Show that the ratio Tm/Tm of the maximum values of the shearing and normal stresses in the beam is equal to h/2L, where h and L are, respectively, the depth and the length of the beam. (b) Determine the depth h and the width b of the beam, knowing that L = 2 m, P = 40 KN, T, = 960 kPa, and om = 12 MPa. m · L/2 C - L/2· A Вarrow_forwardL=800mm, b=25mm, w0=300kN/m, σall=200 MPaarrow_forwardA 5-m-long, simply supported steel beam AD is to carry the distributed and concentrated loads shown. Knowing that the allowable normal stress for the grade of steel is 160 MPa, select the wide-flange shape to be used.arrow_forward
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- For the loading shown, and knowing that beams AB and DE have the same flexural rigidity, determine the reaction (a) at B, (b) at Earrow_forwardThe 6 *12-in. timber beam has been strengthened by bolt-ing to it the steel reinforcement shown. The modulus of elasticity for wood is 1.8 * 106 psi and for steel 29 *106 psi. Knowing that the beam is bent about a horizontal axis by a couple of moment 450 kip·in., determine the maximum stress in (a) the wood, (b) the steel.arrow_forwardA cable AB of span L and a simple beam A'B' of the same span are subjected to identical vertical loadings as shown. Show that the magnitude of the bending moment at a point C' in the beam is equal to the product T0h, where T0 is the magnitude of the horizontal component of the tension force in the cable and h is the vertical distance between point C and the chord joining the points of support A and B.arrow_forward
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