Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
9th Edition
ISBN: 9781337594318
Author: Barry J. Goodno; James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 10, Problem 10.4.2P
A fixed-end beam AB carries point load P acting at point C. The beam has a rectangular cross section (b = 75 mm, h = 150 mm). Calculate the reactions of the beam and the displacement at point C. Assume that E = 190 GPa.
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Problem For the beam shown in Figure
A. Find the reaction at support B (RB)
B. Find the reaction at support D (RD)
Home Work:
1. Determine the maximum deflection d in a simply supported beam of length L
carrying a uniformly distributed load of intensity w, applied over its entire length.
2. For the beam loaded as shown in the Figure, compute the moment of area of the
M diagrams between the reactions about both the left and the right reaction. (Hint:
Draw the moment diagram by parts from right to left).
500 N
2 m
1 m
1 m
400 N/m
B
R1
R2
Please solve according to
the exporters of a typical
solution.
1
M
E*I
3. Moment Diagram by Parts
but
ds = pd0
M
de
M
ds
E*I
1
The construction of moment diagram by parts depends on two basic principles:
1) The resultant bending moment at any section caused by any load system is the
algebraic sum of the bending moment at that section caused by each load acting
separately.
= de =
%3D
E*I
ds
but
ds = dx
(Flat curve)
M
Σ
. de =
-) M. =
MR
M =
E * I
1
(M * dx
EML,EMR : Sum of the moment caused by all the forces to the left and right
section respectively.
.. 0 =
E * I
2)…
Home Work:
1. Determine the maximum deflection d in a simply supported beam of length L
carrying a uniformly distributed load of intensity w, applied over its entire length.
2. For the beam loaded as shown in the Figure, compute the moment of area of the
M diagrams between the reactions about both the left and the right reaction. (Hint:
Draw the moment diagram by parts from right to left).
500 N
2 m
1 m
1 m
400 N/m
R1
R2
Please solve according to
the exporters of a typical
solution.
1
E*I
3. Moment Diagram by Parts
but
ds = pd0
M
de
M
ds
E*I
1
The construction of moment diagram by parts depends on two basic principles:
1) The resultant bending moment at any section caused by any load system is the
= de =
%3D
E*I
ds
algebraic sum of the bending moment at that section caused by each load acting
separately.
but
ds = dx
(Flat curve)
M
=) M2 =
Σ
= OP **
E * I
MR
1
[M * dx
EM,EMR : Sum of the moment caused by all the forces to the left and right
section respectively.
:. 0 =
E * I
2) The…
Chapter 10 Solutions
Bundle: Mechanics Of Materials, Loose-leaf Version, 9th + Mindtap Engineering, 1 Term (6 Months) Printed Access Card
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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_forwardCantilever beam AB carries an upward uniform load of intensity q1from x = 0 to L/2 (see Fig. a) and a downward uniform load of intensity q from x = L/2 to L. Find q1in terms of q if the resulting moment at A is zero. Draw V and M diagrams for the case of both q and qtas applied loadings. Repeat part (a) for the case of an upward triangularly distributed load with peak intensity q0(see Fig. b). For part (b), find q0, instead of q1arrow_forwardDraw the shear-force and bending-moment diagrams for a cantilever beam AB acted upon by two different load cases. A distributed load with linear variation and maximum intensity q0(see figure part a). A distributed load with parabolic variation and maximum intensity q0(see figure part b).arrow_forward
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