(3) By means of an example, compare and prove the best method out of available numerical integration methods. (You may compare any two or three methods (1) A 10-m beam is subjected to a load, and the shear force follows the equationV(x) = 5 + 0.25.x?where V is the shear force and x is length in distance along the beam.V = dM/dx,We know thatand M is the bending moment. Integration yields the relationshipM = M, +V dxIf Mo is zero andx=10 m, Calculate M using (a) analytical integration, (b) trapezoidal rule (c) Simpson's1/3rd rule. (Use1m increments).

Answered: Image /qna-images/answer/ef0be23e-e74a-4325-b19b-95025c4148e8.jpg

1) A 10-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25.x2 e V is the shear force and x is length in distance along the beam. V = dM/dx, now that and M is the bending moment. Integration yields the relation

1) A 10-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25.x2 e V is the shear force and x is length in distance along the beam. V = dM/dx, now that and M is the bending moment. Integration yields the relation

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

Design of structures using FEA

An arrangement, in which various members are interconnected with their constrained relative motion, the whole arrangement is then known as a structure. The degree of freedom of such a structure is zero. In such a structure, the load can act throughout the length of the structure or at the joints.

Question

(3) By means of an example, compare and prove the best method out of available numerical integration methods. (You may compare any two or three methods

(1) A 10-m beam is subjected to a load, and the shear force follows the equation
V(x) = 5 + 0.25.x?
where V is the shear force and x is length in distance along the beam.
V = dM/dx,
We know that
and M is the bending moment. Integration yields the relationship
M = M, +
V dx
If Mo is zero andx=10 m, Calculate M using (a) analytical integration, (b) trapezoidal rule (c) Simpson's
1/3rd rule. (Use1m increments).

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