There are two segments to the beam: (1) Point A to Point C, and (2) Point C to Point B. Establish a coordinate system such that x = 0 at Point A. (a) Draw a Free Body that extends from Point A for a distance x such that x<1.5 m. Solve for the internal forces V(x) and M(x) as functions of x. Use the F.B. and the Equations of Equilibrium to find these internal forces. (b) Draw a Free Body that extends from Point A for a distance x such that x>1.5 m. Solve for the internal forces V(x) and M(x) as functions of x. Use the F.B. and Equations of Equilibrium to find these functions. (c) Draw a 3rd Free Body from a point x (x>1.5) to Point B. In other words draw a free body of the right hand portion of the beam. This segment should have length = 3m – x. Use this F.B. and equations of equilibrium to solve for internal force V(x) and M(x) as functions of x. Prove to yourself that the V(x) and M(x) functions found in Part II.(c) are equal to those found in Part II.(b). 8 kN/m 4 kN/m А 1.5 m 1.5 m

There are two segments to the beam: (1) Point A to Point C, and (2) Point C to Point B. Establish a coordinate system such that x = 0 at Point A. (a) Draw a Free Body that extends from Point A for a distance x such that x<1.5 m. Solve for the internal forces V(x) and M(x) as functions of x. Use the F.B. and the Equations of Equilibrium to find these internal forces. (b) Draw a Free Body that extends from Point A for a distance x such that x>1.5 m. Solve for the internal forces V(x) and M(x) as functions of x. Use the F.B. and Equations of Equilibrium to find these functions. (c) Draw a 3rd Free Body from a point x (x>1.5) to Point B. In other words draw a free body of the right hand portion of the beam. This segment should have length = 3m – x. Use this F.B. and equations of equilibrium to solve for internal force V(x) and M(x) as functions of x. Prove to yourself that the V(x) and M(x) functions found in Part II.(c) are equal to those found in Part II.(b). 8 kN/m 4 kN/m А 1.5 m 1.5 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

There are two segments to the beam: (1) Point A to Point C, and (2) Point C to
Point B.
Establish a coordinate system such that x = 0 at Point A.
(a) Draw a Free Body that extends from Point A for a distance x such that x<1.5
m.
Solve for the internal forces V(x) and M(x) as functions of x. Use the F.B. and
the Equations of Equilibrium to find these internal forces.
(b) Draw a Free Body that extends from Point A for a distance x such that x>1.5
m.
Solve for the internal forces V(x) and M(x) as functions of x. Use the F.B. and
Equations of Equilibrium to find these functions.
(c) Draw a 3rd Free Body from a point x (x>1.5) to Point B. In other words draw a
free body of the right hand portion of the beam. This segment should have
length
= 3m – x. Use this F.B. and equations of equilibrium to solve for internal force
V(x) and M(x) as functions of x. Prove to yourself that the V(x) and M(x)
functions found in Part II.(c) are equal to those found in Part II.(b).
8 kN/m
4 kN/m
В
1.5 m
1.5 m

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