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 9, Problem 9.6.9P
A simple beam AB is subjected to a load in the form of a couple M0 acting at end B (see figure). Determine the angles of rotation
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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)…
3. Two beams are supported as shown in the diagram below, each 150mm x 200mm x 6 meters. Beam CD is a
cantilever beam carrying a uniformly distributed load of 6 KN/m freely supported on beam AB. Beam AB is
freely supported on each ends. E = 13.8 GPa for both beam. Neglect the weight of the beam.
a. Compute the reaction at D.
b. Compute the deflection at D.
c. Compute the bending stress of beam CD.
6 ka lm
бт
6m
6m
A
LAB
Show Transcribed Text
B
W
L
LBC
X
H
W360 x 72
A W360x72 standard steel shape is used to support the loads shown on the beam in the figure. The shape is oriented so
that bending occurs about the weak axis as shown.[P = 8 kN, w = 24 kN/m, a = 1 m, b = 5.5 m]
1.)Determine the maximum absolute value of negative moment in the beam.
2.)Determine the maximum positive moment in the beam.
3.)Determine the maximum stress at any point along the beam.
Chapter 9 Solutions
Mechanics of Materials (MindTap Course List)
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Calculate the deflection at point C of a beam...Ch. 9 - Compound beam ABC is loaded by point load P = 1.5...Ch. 9 - The compound beam shown in the figure consists of...Ch. 9 - -33 Find the horizontal deflection hand verti cal...Ch. 9 - The fr a me A BCD shown in the heure is squeezed...Ch. 9 - A framework A BCD is acted on by counterclockwise...Ch. 9 - A framework A BCD is acted on by force P at 2L/3...Ch. 9 - A beam ABCDE has simple supports at B and D and...Ch. 9 - A frame ABC is loaded at point C by a force P...Ch. 9 - The wing of a large commercial jet is represented...Ch. 9 - The wing of a small plane is represented by a...Ch. 9 - Find an expression for required moment MA(in terms...Ch. 9 - Find an expression for required moment MA(in terms...Ch. 9 - Find required distance d (in terms of L) so that...Ch. 9 - A cantilever beam has two triangular loads as...Ch. 9 - -1 A cantilever beam AB is subjected to a uniform...Ch. 9 - The load on a cantilever beam AB has a triangular...Ch. 9 - A cantilever beam AB is subjected to a...Ch. 9 - Determine the angle of rotation BBand the...Ch. 9 - -5 Calen1ate the deflections S 3a ndCh. 9 - A cantileverbeam^Cßsupportstwo concentrated loads...Ch. 9 - Obtain formulas for the angle of rotation 0Aat...Ch. 9 - A simple beam AB supports two concentrated loads P...Ch. 9 - A simple beam AB is subjected to a load in the...Ch. 9 - -10 The simple beam AB shown in the figure...Ch. 9 - A simple beam AB is subjected to couples M0and 2A0...Ch. 9 - The cantilever beam ACB shown in the figure has...Ch. 9 - The cantilever beam ACB shown in the figure...Ch. 9 - Beam ACB hangs from two springs, as shown in the...Ch. 9 - -4 A simple beam ABCD has moment of inertia I near...Ch. 9 - A beam ABC has a rigid segment from A to B and a...Ch. 9 - A simple beam ABC has a moment of inertia 1,5 from...Ch. 9 - The tapered cantilever beam AB shown in the figure...Ch. 9 - The tapered cantilever beam AB shown in the figure...Ch. 9 - A tapered cantilever beam A B supports a...Ch. 9 - A tapered cantilever beam AB supports a...Ch. 9 - Repeat Problem 97-10, but now use the tapered...Ch. 9 - A simple beam ACE is constructed with square cross...Ch. 9 - A uniformly loaded simple beam AB (see figure) of...Ch. 9 - A simple beam AB of length L supports a...Ch. 9 - A propped cantilever beam AB of length L and with...Ch. 9 - A simple beam AB of length L is subjected to loads...Ch. 9 - A beam ABC with simple supports at A and B and an...Ch. 9 - A simple beam ACB supporting a uniform load q over...Ch. 9 - The frame shown in the figure consists of a beam...Ch. 9 - A simple beam AB of length L is loaded at the...Ch. 9 - The simple beam shown in the figure supports a...Ch. 9 - An overhanging beam ABC supports a concentrated...Ch. 9 - The cantilever beam shown in the figure supports a...Ch. 9 - A simple beam ACB supports a uniform load of...Ch. 9 - A cantilever beam ACB supports two concentrated...Ch. 9 - The cantilever beam A CB shown in the hgure is...Ch. 9 - The frame A BC support s a concentrated load P at...Ch. 9 - A simple beam ABC DE supports a uniform load of...Ch. 9 - An overhanging beam ABC is subjected to a couple...Ch. 9 - An overhanging beam ABC rests on a simple support...Ch. 9 - A symmetric beam A BCD with overhangs at both ends...Ch. 9 - A heavy object of weight W is dropped onto the...Ch. 9 - An object of weight Wis dropped onto the midpoint...Ch. 9 - A cantilever beam AB of length L = 6 It is...Ch. 9 - A weight W = 20 kN falls through a height h = 1,0...Ch. 9 - A weight W = 4000 lb falls through a height h =...Ch. 9 - An overhanging beam ABC with a rectangular cross...Ch. 9 - A heavy flywheel rotates at an angular speed m...Ch. 9 - A simple beam AB of length L and height /;...Ch. 9 - A cantilever beam JA of length Land height/; (see...Ch. 9 - An overhanging beam ABC of height h has a sliding...Ch. 9 - A simple beam AB of length L and height h (see...Ch. 9 - Beam AB has an elastic support kR at A, pin...
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