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 5.5, Problem 136P
To determine
Express the variable diameter d in terms of x, L, and
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2.4 An 18-m-long steel wire of 5-mm diameter is to be used in the
manufacture of a prestressed concrete beam. It is observed that
the wire stretches 45 mm when a tensile force P is applied. Know-
ing that E = 200 GPa, determine (a) the magnitude of the force
P, (b) the corresponding normal stress in the wire.
2.36 A 250-mm bar of 150 x 30-mm rectangular cross section consists
of two aluminum layers, 5 mm thick, brazed to a center brass layer
of the same thickness. If it is subjected to centric forces of magni-
tude P = 30 kN, and knowing that E, = 70 GPa and E, = 105 GPa,
determine the normal stress (a) in the aluminum layers, (b) in the
brass layer.
P'
250 mm
5 mm
5 mm
5 mm
Aluminum
Brass
Aluminum
P
30 mm
Fig. P2.36
5.86 The cast iron inverted T-section supports two concentrated loads of magni-
tude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and
30 MPa in shear. (a) Show that the neutral axis of the cross section is located at
d = 48.75 mm and that the moment of inertia of the cross-sectional area about this
axis is I = 11.918 x 106 mm“. (b) Find the maximum allowable value of P.
1.0 m
1.0 m
15 mm
3 m
150 mm
NA-
d
15 mm
150 mm
FIG. P5.86
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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