nk is directed towards the other
extremity, the stress on the link is called pressure and the link is
called a "strut." If it is directed away from the other extremity, the
stress on the link is called tension and the link is called a "tie."
In this case, therefore, the only stress acting in a link is a
pressure or a tension in the direction of the straight line which
represents it in the diagram of the frame, and all that we have to do
is to find the magnitude of this stress. In the actual structure
gravity acts on every part of the link, but in the diagram we
substitute for the actual weight of the different parts of the link
two weights which have the same resultant acting at the extremities of
the link.

We may now treat the diagram of the frame as composed of links without
weight, but loaded at each joint with a weight made up of portions of
the weights of all the links which meet in that joint. If any link has
more than two joints we may substitute for it in the diagram an
imaginary stiff frame, consisting of links, each of which has only two
joints. The diagram of the frame is now reduced to a system of points,
certain pairs of which are joined by straight lines, and each point is
in general acted on by a weight or other force acting between it and
some point external to the system. To complete the diagram we may
represent these external forces as links, that is to say, straight
lines joining the points of the frame to points external to the frame.
Thus each weight may be represented by a link joining the point of
application of the weight with the centre of the earth.

But we can always construct an imaginary frame having its joints in
the lines of action of these external forces, and this frame, together
with the real frame and the links representing external forces, which
join points in the one frame to points in the other frame, make up
together a complete self-strained system in equilibrium, consisting of
points connected by links acting by pressure or tension. We may in
this way reduce any real structure to the case of a system of points
with attractive or repulsive forces acting between certain pairs of
these points, and keeping them in equilibrium. The direction of each
of these forces is sufficiently indicated by that of the line joining
the points, so that we have only to determine its magnitude. We might
do this by calculation, an