3. A beam is loaded as shown. El is constant. The vertical reactions at B and C are equal to 80KN. For items a, b and c, use the coordinate system shown, with x=0 at point A. a. Derive the moment function, M(x), in terms of El, using Macaulay Functions. b. Derive the slope function, 0(x) in terms of El. С. Derive the deflection function, y(x) in terms of El. The modulus of elasticity is 200 GPa. d. Determine the required moment of inertia, I, if i. The absolute value of the maximum deflection should not exceed 6mm; and ii. The absolute value of the slope should not exceed 0.01 radians at A.

3. A beam is loaded as shown. El is constant. The vertical reactions at B and C are equal to 80KN. For items a, b and c, use the coordinate system shown, with x=0 at point A. a. Derive the moment function, M(x), in terms of El, using Macaulay Functions. b. Derive the slope function, 0(x) in terms of El. С. Derive the deflection function, y(x) in terms of El. The modulus of elasticity is 200 GPa. d. Determine the required moment of inertia, I, if i. The absolute value of the maximum deflection should not exceed 6mm; and ii. The absolute value of the slope should not exceed 0.01 radians at A.

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

System of Forces

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.

Question

3. A beam is loaded as shown. El is constant. The
vertical reactions at B and C are equal to 80kN. For
items a, b and c, use the coordinate system shown,
with x=0 at point A.
a. Derive the moment function, M(x), in
terms of El, using Macaulay Functions.
b. Derive the slope function, 0(x) in terms
of El.
С.
Derive the deflection function, y(x) in
terms of El.
The modulus of elasticity is 200 GPa.
d. Determine the required moment of inertia,
I, if
i. The absolute value of the
maximum deflection should not
exceed 6mm; and
ii. The absolute value of the slope
should not exceed 0.01 radians at
А.
40 kN
40 kN
10 kN/m
А
В
D
2 m
8 m
2 m

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