(a) Calculate the shear equation V (x) and the moment equation M(x) as a function of the length L and the two forces f1, f2 (Hint: Find the equivalent force and moment that f1 exerts on the structure) (b) Check your results from part (a), by verifying the following: - V(x) = M(x) - The shear equation V (x) and the moment equation M(x) satisfy the boundary conditions at the pivot (x = 0), and the free end condition at x = 4L. By boundary condition we mean that the shear force at the end points needs to be equal to the reaction force (left) and the applied force f2 (right). Similarly, the bending moment should equal zero at the ends (pivot can not support a moment and the free end can not support a moment) (c) Plot the shear equation V (x) and the moment equation M(x)) using f₁ = 1[N], f₂ = 2*f₁, and L = 1[m],

(a) Calculate the shear equation V (x) and the moment equation M(x) as a function of the length L and the two forces f1, f2 (Hint: Find the equivalent force and moment that f1 exerts on the structure) (b) Check your results from part (a), by verifying the following: - V(x) = M(x) - The shear equation V (x) and the moment equation M(x) satisfy the boundary conditions at the pivot (x = 0), and the free end condition at x = 4L. By boundary condition we mean that the shear force at the end points needs to be equal to the reaction force (left) and the applied force f2 (right). Similarly, the bending moment should equal zero at the ends (pivot can not support a moment and the free end can not support a moment) (c) Plot the shear equation V (x) and the moment equation M(x)) using f₁ = 1[N], f₂ = 2*f₁, and L = 1[m],

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

The beam in the figure below is supported by a pivot (left) and roller (right).
L
L
L
L
f₁
(a) Calculate the shear equation V (x) and the moment equation M(x) as a function of the length
L and the two forces f1, f2
(Hint: Find the equivalent force and moment that f1 exerts on the structure)
(b) Check your results from part (a), by verifying the following:
- V(x) = M(x)
The shear equation V (x) and the moment equation M(x) satisfy the boundary
conditions at the pivot (x = 0), and the free end condition at x = 4L. By boundary condition we
mean that the shear force at the end points needs to be equal to the reaction force (left) and the
applied force f2 (right). Similarly, the bending moment should equal zero at the ends (pivot can
not support a moment and the free end can not support a moment)
(c) Plot the shear equation V (x) and the moment equation M(x))
using f₁ = 1[N], f₂ = 2*f₁, and L= = 1[m],

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Step 5 Validation of shear and moment equations

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Step 6 Shear force and bending moments at ends

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