Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 5, Problem 5.5.9P
A seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick.
What is the maximum bending stress in the board?
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For the problem shown below (left), W = 51 lbs while
L1 = 4.4 inches and L2 = 12 inches. This results in the
shear force diagram as shown on the right, where A, is
the reaction force in the vertical direction at point A.
Based on this shear diagram, what is the maximum
moment in the portion of the horizontal beam from x =
O to x = L1 in units of lb-in to two decimal places. (Be
sure to use a negative sign to designate a negative
moment if necessary.)
A
|--L1-——————— L2
Ay lb
0
-Ay lb
W
L1
L2
W
-L1-
BO
L1-
-X
The rectangular section used for the simply supported beam shown in Figure Q2 is 250 mm
deep and 320 mm wide. Determine the uniformly distributed load per metre that the beam may
carry over a distance of 6 m from the left end support if the bending stress is not to exceed 140
N/ mm.
w/m length
6 m
3 m
(a) The Figure la show the cross-section of a beam. All dimension are in cm.
10
2
10
Figure la
(i) Calculate the centroid of the cross-section measured from the bottom of the
cross section.
(ii) Calculate the moment of inertia, I, for this cross-section.
(iii)A pure bending moment of magnitude 1.0 kN.m is applied to the cross-
section, generating compression above the neutral axis, and tension below.
Calculate the maximum values of the tensile and compressive stress.
(iv)The bending moment is removed. The same beam cross-section is now subject
to a vertical shear force of 2.5 kN acting in the downward. Calculate the
maximum horizontal shear stress. Where does it occur?
Chapter 5 Solutions
Mechanics of Materials (MindTap Course List)
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