Internal
forces
As
one can calculate the forces and moments transmitted through joints between
members, one can also calculate the internal forces which one part of a member
exerts on another. To calculate these internal forces, simply draw a freebody
diagram of only part of the member, cutting through the member at the point you
are interested in knowing the forces and moments. For example, consider the
following member

If
you are interested in knowing the forces and moments that are transmitted
through the member at point D, you
can draw the freebodydiagram of the portion to the left of D to get

For
the body to be in equilibrium one must have
_{}
In
this example, _{} is the axial force
exerted by the right side of the bar on the left side of the bar at D, _{} is the shear load
exerted by the right side of the bar on the left side of the bar at D, _{} is the bending moment
exerted by the right side of the bar on the left side of the bar at D.
The
example shows the basic elements of how one find the internal forces at a given
point in a member. Like any other constraint, one must introduce a force or a
moment for every way in which the motion of one side of the point is restricted
by the other side. For example, in the above the right side of D restricts the left side from freely
moving along the axial direction, and the transverse to the axial direction,
and also restricts free rotation. Consequently, two forces and one moment are
introduced to enforce the restriction.
Note: the forces and moment
applied by the lefthand side onto the righthand side are equal in magnitude
but opposite in direction to the forces and moments applied by the righthand
side on the lefthand side.
ã Mehrdad Negahban and the University of Nebraska, 19962000.
All rights reserved
Copy and distribute freely for personal use only
Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 685880526