**Understanding Transverse Deflection in an Elastic Beam**This section explains the transverse deflection of an elastic beam with constant flexural rigidity EI and length L. The transverse deflection \( v(x) \) for the beam is described by the equation:\[ v(x) = \frac{M_0 (x^3 - x^2L)}{4EIL} \]In this equation, \( M_0 \) is the applied couple.Given:- Length, \( L = 100 \) mm- Applied couple, \( M_0 = 100 \) N-mmWe are tasked with finding the magnitude of the shear force (in Newtons) at the middle of the beam.**Diagram Explanation:**The accompanying diagram depicts an elastic beam aligned along the x-axis. The variables illustrated in the diagram are as follows:- \( v(x) \): Transverse deflection at a distance x from the origin.- \( O \): Origin point of the beam.- \( x \): Variable representing the distance from the origin to a specific point on the beam.- \( L \): Total length of the beam.The diagram helps visualize the geometry and deformation of the beam, essential for understanding the underlying mechanics of beam deflection and shear forces.

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Engineering

Civil Engineering

ows an elastic be igidity EI and deflection v(x) d by an equation

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

**Understanding Transverse Deflection in an Elastic Beam**

This section explains the transverse deflection of an elastic beam with constant flexural rigidity EI and length L. The transverse deflection \( v(x) \) for the beam is described by the equation:

\[ v(x) = \frac{M_0 (x^3 - x^2L)}{4EIL} \]

In this equation, \( M_0 \) is the applied couple.

Given:
- Length, \( L = 100 \) mm
- Applied couple, \( M_0 = 100 \) N-mm

We are tasked with finding the magnitude of the shear force (in Newtons) at the middle of the beam.

**Diagram Explanation:**
The accompanying diagram depicts an elastic beam aligned along the x-axis. The variables illustrated in the diagram are as follows:
- \( v(x) \): Transverse deflection at a distance x from the origin.
- \( O \): Origin point of the beam.
- \( x \): Variable representing the distance from the origin to a specific point on the beam.
- \( L \): Total length of the beam.

The diagram helps visualize the geometry and deformation of the beam, essential for understanding the underlying mechanics of beam deflection and shear forces.

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