(Situation 1) Consider the following beam: X y max W B (a) Determine the support reactions at A and B. (b) Draw the shear and bending moment diagram of the beam. (c) Using DIM with Macaulay brackets, derive the equations for the slope and deflection of the beam at any location x from A. Assume El to be constant. (d) Using the derived equations from (c), determine the slope at the supports, as well as the location and magnitude of the maximum deflection.

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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Hi, please kindly answer the situation 1. Thank you
(Situation 1) Consider the following beam:
A
A
X
37 kN/m
5 m
L
(a) Determine the support reactions at A and B.
(b) Draw the shear and bending moment diagram of the beam.
(c) Using DIM with Macaulay brackets, derive the equations for the slope and deflection of the beam at any location x from A. Assume El to be
constant.
(d) Using the derived equations from (c), determine the slope at the supports, as well as the location and magnitude of the maximum deflection.
(Situation 2) Consider the following beam (Assume A to be fixed, B to be an internal hinge, and C to be roller.):
I= 1680 x 106 mm4
Ymax
B
Hinge
-2.5 m-
W
E constant = 205 GPa
B
2
155 KN
-2.5 m-
I= 1260 x 106 mm4
(a) Determine the support reactions at A and C.
(b) Draw the bending moment diagram-by-parts of the beam. Use A as the reference point.
(c) Using MAM, determine the slope and deflection at D.
(Situation 3) Consider the same beam in Situation 2. Determine the deflection at D using virtual work method.
D
Transcribed Image Text:(Situation 1) Consider the following beam: A A X 37 kN/m 5 m L (a) Determine the support reactions at A and B. (b) Draw the shear and bending moment diagram of the beam. (c) Using DIM with Macaulay brackets, derive the equations for the slope and deflection of the beam at any location x from A. Assume El to be constant. (d) Using the derived equations from (c), determine the slope at the supports, as well as the location and magnitude of the maximum deflection. (Situation 2) Consider the following beam (Assume A to be fixed, B to be an internal hinge, and C to be roller.): I= 1680 x 106 mm4 Ymax B Hinge -2.5 m- W E constant = 205 GPa B 2 155 KN -2.5 m- I= 1260 x 106 mm4 (a) Determine the support reactions at A and C. (b) Draw the bending moment diagram-by-parts of the beam. Use A as the reference point. (c) Using MAM, determine the slope and deflection at D. (Situation 3) Consider the same beam in Situation 2. Determine the deflection at D using virtual work method. D
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