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Problem 7.7

This document derives equations for shear force V and bending moment M at any location of a simply supported beam under a distributed load. It then plots the shear-force and bending-moment diagrams and reports that the maximum bending moment is 240 kN-m located at x=6m.

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194 views2 pages

Problem 7.7

This document derives equations for shear force V and bending moment M at any location of a simply supported beam under a distributed load. It then plots the shear-force and bending-moment diagrams and reports that the maximum bending moment is 240 kN-m located at x=6m.

Uploaded by

S M B
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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7.

7 For the simply supported beam subjected to the


loading shown,
(a) Derive equations for the shear force V and the
bending moment M for any location in the beam.
(Place the origin at point A.)
(b) Plot the shear-force and bending-moment
diagrams for the beam using the derived functions.
(c) Report the maximum bending moment and its
location.
Fig. P7.7

Solution
Beam equilibrium:
M A  (50 kN)(3 m)  (75 kN)(6 m)  Dy (10 m)  0
 Dy  60 kN
Fy  Ay  Dy  50 kN  75 kN  0
 Ay  65 kN

Section a-a:
For the interval 0 ≤ x < 3 m:
Fy  Ay  V  65 kN  V  0  V  65 kN
M a  a   Ay x  M  (65 kN)x  M  0  M  (65 kN) x

Section b-b:
For the interval 3 m ≤ x < 6 m:
Fy  Ay  50 kN  V  65 kN  50 kN  V  0
 V  15 kN
M b  b   Ay x  (50 kN)(x  3 m)  M
 (65 kN)x  (50 kN)(x  3 m)  M  0
 M  (15 kN) x  150 kN-m

Section c-c:
For the interval 6 m ≤ x < 10 m:
Fy  Ay  50 kN  75 kN  V
 65 kN  50 kN  75 kN  V  0
 V  60 kN

M c  c  Ay x  (50 kN)(x  3 m)  (75 kN)(x  6 m)  M


 (65 kN)x  (50 kN)(x  3 m)  (75 kN)(x  6 m)  M  0
 M  (60 kN) x  600 kN-m
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(b) Shear-force and bending-moment diagrams (c) Maximum bending moment
and its location

Mmax = 240 kN-m @ x = 6 m

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to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

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