Drawing Shear Diagrams

A s

hear

diagram is

a graphical representation of how V (shear force) varies over a loaded

beam.

Rules:

1.

The application of a concentrated load will either increase or decrease (depending

on direction of load) the shear in the bea

m by the magnitude of the force applied.

2.

The increase/decrease occurs at the point of application.

3.

A uniformly distributed load will change the shear force (V) at a uniform rate

equal to the intensity of the load (lbs/ft) or (kN/m). This results in a

“diagonal”

line representing the change in shear across the beam where the uniform load is

applied.

Drawing

Bending Moment Diagrams

Similar to the shear force diagram, the bending moment diagram is a graphical

representation of how the bending varies along the length of a beam. There is a

relationship between the shear and bending moment diagram:

**

The bending moment at any point along the beam can be found by summing the

areas contained under the shear diagram. (Left to right works best).

Some general rules for building a bending moment diagram:

a.

The bending moment diagram should be constructed bel

ow a shear diagram.

b.

The location of zero shear on the shear diagram will be a location of maximum or

minimum moment.

c.

A rectangular area in the shear diagram will indicate a sloping straight (diagonal)

line on the bending moment diagram. A positive shear v

alue indicates a positive

slope of the diagonal line on the bending moment diagram. A negative shear

value indicates a negative slope on the bending moment diagram.

d.

A triangular, trapezoidal or other type of area under the shear diagram will

translate int

o curved (parabolic) line on the moment diagram. The same rules

apply with regard to slope of the moment diagram line.

The M at any point = ∑V

area

(start left go right)

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