Lecture 35

Lecture 35:

Moment (M) and Moment Diagrams

The Moment (M) within a beam is a representation of the magnitude of the internal couple found within the beam at any given point.

A moment diagram is a graphic representation of the moment at every point along the length of the member. To plot a moment diagram of a beam, one must determine the magnitude of the moment at each point along the length of the beam and then determine whether it is a positive or negative moment. Positive values are shown above and negative values below a reference axis.

Sign convention is probably the most troublesome part of moment diagrams. In North America, if the moment tends to cause the beam to curve upward it is positive; if the moment tends to cause it to curve downward it is negative. This is the opposite of the conventions for most of the rest of the world.

The sign of the moment diagram is not necessarily the same sign of the moment found in the FBD or in the moment equation when determining its magnitude.
three beam types and their moment diagrams

A simplly supported beam with gravity load always has a positive moment.

A cantilever with gravity load always has a negative moment.

A continuous beam with an overhang subject to a gravity load experiences both positive and negative moments.

How to draw a MOMENT DIAGRAM

Start at the left end and plot the bending moment values due to external loads and reactions with regard to the following:

The moment diagram is the graphic representation of the magnitude of the bending moment at successive points along the beam.
The bending moment for the moment diagram (M) at any point equals the sum of moments of the forces to the left about that point.
Since the entire beam is in equilibrium (sum of M=0), the bending moment diagram must close to zero at the right side.
Consider the values of successive incremental ordinates along the length of the beam in order to determine the shape of the curve:

if the magnitudes of successive shear ordinates are constant, the moment curve has a constant slope at that increment.
if the magnitudes of successive shear ordinates increase, the slope of the moment curve is positive (it approaches the vertical).
if the magnitudes of successive shear ordinates decreases, the slope of the moment curve is negative (it approaches the horizontal).
Abrupt changes in the shear diagram will produce abrupt changes in the slope of the moment curve. Concentrated moments produce vertical lines in the moment curve.

Moment Diagrams