MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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Textbook Question
Chapter 11.2, Problem 4FP
of the beam's cross section to safely support the load. The wood has an allowable normal stress of σallow = 2 ksi and an allowable shear stress of τallow = 200 psi.
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Consider the bar, shown in Figure 1 that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.10-3 m², and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
x=0.0
x=2.0
2.0m
10 kN
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x))
-) +1(x) = 0.
d.x
dx
What are the accompanying boundary conditions for this bar?
b) Using the mesh in Figure 2, form the basis functions associated with element 2 and write the FEM
approximation over the element.
1
2
3
1
2
1m
1m
Figure 2: Mesh of 2 elements. Elements are numbered with underlines.
c) The general form of the element stiffness matrix system, with nodes indexed by i and j, is,
AE
Uj
N;(x)l(x)dx
– Ng(0)f(0)
¥ [4]}]{{}}={{{}\(\\+} + {N(2)f(2) = N (0)5() },
(1)
0, respectively.
L
=
(2)
where f(2) and f(0) denote the boundary forces at positions x 2 and x
Evaluate…
answer please
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Question 1
Consider the bar, shown in Figure 1, that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.103 m2, and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
10 kN
X
x=0.0
x=2.0
2.0m
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x)) + 1(x) = 0.
dx
dx
What are the accompanying boundary conditions for this bar?
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DII
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F6
F7
F8
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F3
F4
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Chapter 11 Solutions
MECHANICS OF MATERIALS
Ch. 11.2 - Determine the minimum dimension a to the nearest...Ch. 11.2 - of the rod to safely support the load. The rod is...Ch. 11.2 - The wood has an allowable normal stress of allow =...Ch. 11.2 - of the beam's cross section to safely support the...Ch. 11.2 - Determine the minimum dimension b to the nearest...Ch. 11.2 - The beam is made of steel having an allowable...Ch. 11.2 - Determine the minimum width of the beam to the...Ch. 11.2 - if P=10 kip.Ch. 11.2 - The beam has an allowable normal stress of allow...Ch. 11.2 - If each beam is to be designed to carry 90 lb/ft...
Ch. 11.2 - Determine its height h so that it simultaneously...Ch. 11.2 - to safely support the load. The wood has an...Ch. 11.2 - and the wood has an allowable normal stress of...Ch. 11.2 - if allow = 30 ksi and allow = 15 ksi. The journal...Ch. 11.2 - if allow = 30 ksi and allow = 15 ksi. The journal...Ch. 11.2 - The tapered beam supports a uniform distributed...Ch. 11.2 - Determine the variation in the depth d of a...Ch. 11.2 - Prob. 41PCh. 11.2 - The pulleys fixed to the shaft are loaded as...Ch. 11.2 - Prob. 43PCh. 11.2 - Prob. 44PCh. 11 - The cantilevered beam has a circular cross...Ch. 11 - Select the lightest-weight wide-flange overhanging...Ch. 11 - Prob. 3RPCh. 11 - Determine the shaft's diameter to the nearest...Ch. 11 - Select the lightest-weight wide-flange beam from...Ch. 11 - The simply supported joist is used in the...Ch. 11 - The simply supported joist is used in the...Ch. 11 - by 4-in. pieces of wood braced as shown. If the...
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