C5.2 Beams – Internal Forces

So far we’ve only looked at action and reaction forces; forces that act externally on the body.

Question Image

But internally within the body, we have what we call internal forces that act to resist the external action and reaction forces.

C5.2 Beams – Internal Forces

So far we’ve only looked at action and reaction forces; forces that act externally on the body.

Question Image

But internally within the body, we have what we call internal forces that act to resist the external action and reaction forces.

To illustrate internal forces further, consider the simply-supported beam below. It’s made out of 3 segments “fixed” together:

Illustration of internal forces: simply-supported beam with 3 segments fixed together, with 3 reactions forces acting at the fixed joints

If we isolate the segments, then for each segment we will have the external forces acting on it, plus the reaction forces for the “fixed” joint supports: R_x, R_y, M.

Technically, all beams are “fixed” together through intermolecular forces to form a continuous body. Therefore if we make a section cut along any portion of the beam, we have the “reaction” forces that would result from a “fixed” support.

Except that since these come from within the structure itself, we call them “internal forces”.

The 3 internal forces corresponding to the 3 reaction forces of a fixed support have special names:

Normal force, N (x-direction like R_x; units: N for force)
Shear force, V (y-direction like R_y; units: N for force)
Bending moment, BM or just M (units: Nm for moment)

The sign convention is particularly important, especially when we proceed to shear force and bending moment diagrams. The positive directions for the internal forces are shown below for both the left- and right-portions of any section cut:

Positive sign convention of internal forces in a section cut

A simpler way of expressing the sign convention is as follows:

Simpler representation of the positive sign convention for internal forces

It’s okay if these all seem too confusing; it will make more sense through an example.

To illustrate internal forces further, consider the simply-supported beam below. It’s made out of 3 segments “fixed” together:

Illustration of internal forces: simply-supported beam with 3 segments fixed together, with 3 reactions forces acting at the fixed joints

If we isolate the segments, then for each segment we will have the external forces acting on it, plus the reaction forces for the “fixed” joint supports: R_x, R_y, M.

Technically, all beams are “fixed” together through intermolecular forces to form a continuous body. Therefore if we make a section cut along any portion of the beam, we have the “reaction” forces that would result from a “fixed” support.

Except that since these come from within the structure itself, we call them “internal forces”.

The 3 internal forces corresponding to the 3 reaction forces of a fixed support have special names:

Normal force, N (x-direction like R_x; units: N for force)
Shear force, V (y-direction like R_y; units: N for force)
Bending moment, BM or just M (units: Nm for moment)

The sign convention is particularly important, especially when we proceed to shear force and bending moment diagrams. The positive directions for the internal forces are shown below for both the left- and right-portions of any section cut:

Positive sign convention of internal forces in a section cut

A simpler way of expressing the sign convention is as follows:

Simpler representation of the positive sign convention for internal forces

It’s okay if these all seem too confusing; it will make more sense through an example.