Scribd
Upload
56 views6 pages

Shear and Moment Diagram

This document defines beams and explains that they can be statically determinate or indeterminate. Statically determinate beams have reactions that can be determined through static equilibrium equations, while indeterminate beams require additional equations based on elastic deformation. The document also describes different types of loads that can act on beams, including concentrated, uniform, and varying loads. It provides an example of calculating shear and moment diagrams for a beam under a uniform load, defining shear and moment values and their signs. Finally, it presents three example problems of drawing shear and moment diagrams for beams with different loading configurations.

Uploaded by

Glyrah Marie Dela Torre
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
56 views6 pages

Shear and Moment Diagram

This document defines beams and explains that they can be statically determinate or indeterminate. Statically determinate beams have reactions that can be determined through static equilibrium equations, while indeterminate beams require additional equations based on elastic deformation. The document also describes different types of loads that can act on beams, including concentrated, uniform, and varying loads. It provides an example of calculating shear and moment diagrams for a beam under a uniform load, defining shear and moment values and their signs. Finally, it presents three example problems of drawing shear and moment diagrams for beams with different loading configurations.

Uploaded by

Glyrah Marie Dela Torre
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 6

Shear & Moment in Beams

DEFINITION OF A BEAM

A beam is a bar subject to forces or couples that lie in a plane containing the

longitudinal of the bar. According to determinacy, a beam may be determinate or

indeterminate.

STATICALLY DETERMINATE BEAMS

Statically determinate beams are those beams in which the reactions of the supports

may be determined by the use of the equations of static equilibrium. The beams shown

below are examples of statically determinate beams.

STATICALLY INDETERMINATE BEAMS

If the number of reactions exerted upon a beam exceeds the number of equations in

static equilibrium, the beam is said to be statically indeterminate. In order to solve the

reactions of the beam, the static equations must be supplemented by equations based

upon the elastic deformations of the beam.

The degree of indeterminacy is taken as the difference between the umber of reactions

to the number of equations in static equilibrium that can be applied. In the case of the

propped beam shown, there are three reactions R1, R2, and M and only two equations

( M = 0 and sum;Fv = 0) can be applied, thus the beam is indeterminate to the first
TYPES OF LOADING

Loads applied to the beam may consist of a concentrated load (load applied at a point),

uniform load, uniformly varying load, or an applied couple or moment. These loads are

shown in the following figures.


Shear and Moment Diagrams
Consider a simple beam shown of length L that

carries a uniform load of w (N/m) throughout its

length and is held in equilibrium by reactions R1

and R2. Assume that the beam is cut at point C a

distance of x from he left support and the portion of

the beam to the right of C be removed. The portion

removed must then be replaced by vertical

shearing force V together with a couple M to hold

the left portion of the bar in equilibrium under the

action of R1 and wx. The couple M is called the resisting moment or moment and the

force V is called the resisting shear or shear. The sign of V and M are taken to be

positive if they have the senses indicated above.

Solved Problems in Shear and Moment Diagrams


INSTRUCTION

Write shear and moment equations for the beams in the following problems. In each

problem, let x be the distance measured from left end of the beam. Also, draw shear

and moment diagrams, specifying values at all change of loading positions and at points

of zero shear. Neglect the mass of the beam in each problem.

Problem 403

Beam loaded as shown in Fig. P-403.


Solution 403
Problem 404

Beam loaded as shown in Fig. P-404.

Solution 404
Problem 405

Beam loaded as shown in Fig. P-405.

Solution 405

You might also like