A prismatic beam of mass density p, cross-sectional area A, and length L rests upon a fixed pinned support at A and roller support B, as shown. The beam is symmetrically positioned with overhanging sections of length a to the left and right of A and B, respectively. L-a 2 A a- -L- B g Questions: (a) Sketch a free-body diagram of the beam, labeling all dimensions, external forces, and reactions due to the gravitational "self-weight" of the beam. (b) Compute the reaction forces due to the beam's self-weight expressed in terms of the given variables. (c) Compute the value or formula for the shear force V(x) and bending moment M(x) deformation distributions within specific beam intervals.

A prismatic beam of mass density p, cross-sectional area A, and length L rests upon a fixed pinned support at A and roller support B, as shown. The beam is symmetrically positioned with overhanging sections of length a to the left and right of A and B, respectively. L-a 2 A a- -L- B g Questions: (a) Sketch a free-body diagram of the beam, labeling all dimensions, external forces, and reactions due to the gravitational "self-weight" of the beam. (b) Compute the reaction forces due to the beam's self-weight expressed in terms of the given variables. (c) Compute the value or formula for the shear force V(x) and bending moment M(x) deformation distributions within specific beam intervals.

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

A prismatic beam of mass density p, cross-sectional area A, and length L rests upon a
fixed pinned support at A and roller support B, as shown. The beam is symmetrically
positioned with overhanging sections of length a to the left and right of A and B,
respectively.
L-a
2
A
a-
-L-
B
g
Questions:
(a) Sketch a free-body diagram of the beam, labeling all dimensions, external forces,
and reactions due to the gravitational "self-weight" of the beam.
(b) Compute the reaction forces due to the beam's self-weight expressed in terms of
the given variables.
(c) Compute the value or formula for the shear force V(x) and bending moment
M(x) deformation distributions within specific beam intervals.
(d) Sketch graphs of the shear force and bending moment distributions. Line up
the shear force plot directly over the bending moment plot with equivalently
scaled horizontal axes. Label all critical points, such as zero crossings, and local
maxima and minima in each plot.

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