= (a) A beam ABC of length L is supporting the point force F at B (x: diagram of the beam is drawn below it. Y M M FL- FL- L L F B F Given that EI is the flexural rigidity of the beam, show that the deflection of the beam at B is given by UB - -FL³/(48EI) by considering only half of the beam. + B (b) Now, a beam ABCD of length 3L/2 is supporting the point force F at B (x = L/2). The bending- moment diagram of the beam is drawn below it. L + L L L -X >X L L/2). The bending-moment D X Given that EI is the flexural rigidity of the beam, determine the deflection of the beam at D.

= (a) A beam ABC of length L is supporting the point force F at B (x: diagram of the beam is drawn below it. Y M M FL- FL- L L F B F Given that EI is the flexural rigidity of the beam, show that the deflection of the beam at B is given by UB - -FL³/(48EI) by considering only half of the beam. + B (b) Now, a beam ABCD of length 3L/2 is supporting the point force F at B (x = L/2). The bending- moment diagram of the beam is drawn below it. L + L L L -X >X L L/2). The bending-moment D X Given that EI is the flexural rigidity of the beam, determine the deflection of the beam at D.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Equilibrium and Support Reactions

Civil engineers deal with structures that are composed of several members connected or with individual members such as beams and columns. To analyze such structures, the condition of statics must be applied. Under the static condition, the members are considered to be in equilibrium under the action of forces, that is, the members are assumed to be having negligible velocity.

Question

(a) A beam ABC of length L is supporting the point force F at B (x = L/2). The bending-moment
diagram of the beam is drawn below it.
Y
1/L
M
M
FL-
FL-
L
F
B
B
Given that EI is the flexural rigidity of the beam, show that the deflection of the beam at B is
given by vB = −FL³/(48EI) by considering only half of the beam.
+
+
(b) Now, a beam ABCD of length 3L/2 is supporting the point force F at B (x = L/2). The bending-
moment diagram of the beam is drawn below it.
L
L
L
L
L
L
X
L
32
X
D
-X
→X
Given that EI is the flexural rigidity of the beam, determine the deflection of the beam at D.

The simple truss ABCDEFGH is supporting two 12-kN loads at G and H, and supported at A and F
by pinned and roller joints, respectively, as shown below.
3m
Bo
3m 3 m
A
3 m
3 m
3 m
ID
www
H
G
12 kN 12 kN
3m
E
4m
(a) Determine the reactions at A and E by analysing an appropriate free-body diagram.
(b) Determine the forces on members CG and GH by analysing an appropriate free-body diagram.
State whether they are under compression or tension.

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