Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 4, Problem 4.3.17P
Find expressions for shear force V and moment Mat x = 2L/3 of beam (a) in terms of peak load intensity q0 and beam length variable L. Repeat for beam (b).
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An I-beam has a flange width b = 400 mm , height hℎ = 400 mm , web thickness tw = 13 mm , and flange thickness tf = 21 mm . Use the following steps to calculate the shear flow at the point shown, where x = 55 mm .
A) The formula for the shear flow includes the moment of inertia of the whole cross section, I, about the neutral axis. Calculate the moment of inertia.
B) The shear flow at the point depends on the value of Q for the portion of the upper flange to the right of the point. Calculate the value of Q
C) Use the results from Parts A and B to calculate the shear flow at the point in the upper flange 55 mm to the right of the web if the shear force on the section is V = 4.6 kN
A beam segment subjected to internal bending moments at sections A and B is shown along with a sketch of the cross-sectional dimensions. The beam segment is subjected to internal bending moments of MA = 1390 N·m and MB = 3080 N·m. The segment length is Δx = 180 mm. Consider area (2) and use cross-sectional dimensions of b = 92 mm, d = 240 mm, and d2 = 68 mm. (a) sketch a side view of the beam segment and plot the distribution of bending stresses acting at sections A and B. Indicate the magnitudes of key bending stresses on the sketch, including the stresses at the top and bottom of area (2) on both sections A and B. Tensile stresses are positive, while compressive stresses are negative. (b) determine the resultant forces acting in the x direction on the specified area at sections A and B, and show these resultant forces on the sketch. Tensile forces are positive, while compressive forces are negative. (c) determine the magnitude of the horizontal force required to satisfy equilibrium…
An I-beam has a flange width b = 400 mm , height h = 400 mm , web thickness tw = 13 mm , and flange thickness tf = 21 mm . Use the following steps to calculate the shear flow at the point shown, where x = 55 mm .
A) The formula for the shear flow includes the moment of inertia of the whole cross section, I, about the neutral axis. Calculate the moment of inertia.
B) The shear flow at the point depends on the value of Q for the portion of the upper flange to the right of the point. Calculate the value of Q
C) Use the results from Parts A and B to calculate the shear flow at the point in the upper flange 55 mm to the right of the web if the shear force on the section is V = 4.6 kN
Chapter 4 Solutions
Mechanics of Materials (MindTap Course List)
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- A fixed-end beam AB of a length L is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.arrow_forwardFind expressions for shear force V and moment M at mid-span of beam AB in terms of peak load intensity q0and beam length variables a and L Let a = 5L/b.arrow_forwardThe hollow box beam shown in the figure is subjected to a bending moment M of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment M if the dimensions of the cross section are A = 15 in., A] = 12.75 in., h = 9 in., and ey =7.5 in. Also, the yield stress is eY = 33 ksi. (b) What percent of the moment M is produced by the elastic core?arrow_forward
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