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CHAPTER Xi 
STRESS DIAGRAMS 
177. Stress Diagrams for Framed Structures.—It will be assumed 
that the framed structures considered are made up of bars which are 
connected by frictionless pin joints at their ends. It will also be assumed 
that the loads on the structure are concentrated at the joints. If a bar 
carries a load uniformly distributed over its length this load is divided 
into two equal parts, and one-part is placed at each end of the bar. Ifa 
bar carries a load concentrated at an intermediate point, this load is 
divided into two parts, which are to one another as the distances of the 
oad from the ends of the bar; these parts are then placed one at each 
end of the bar, the greater part being at that end of the bar which is 
nearest to the original load. 
In studying the equilibrium of a structure, two kinds of forces 
have to be considered, (1) the external forces, which for the whole 
structure must balance one another, and (2) the internal forces. As 
a consequence of the two assumptions mentioned at the beginning 
of this Article, the bars forming the structure are subjected either 
to direct compression or to direct tension under the action of the 
external forces. It follows, therefore, that the lines of action of 
‘the internal forces are the lines which represent the bars on the 
diagram of the structure ( called the frame diagram). At any joint, 
therefore, the forces acting are the internal forces acting along the 
bars meeting at that joint, and the external forces, if there are any, 
acting at that joint. 
If a sufficient number of the forces acting at any joint are known, the 
Si ygon of forces for that joint can be drawn and the unknown forces 
x ined. 
_ he general method of drawing the complete stress diagram for 
a framed structure will be understood by reference to the example 
worked out in Fig. 262. A simple roof truss is shown carrying 
, load AB at its apex. The other external forces are the reactions 
BC and CA at the supports. The internal forces are the forces 
acting along the bars AD, BD, and CD. The lines of action of all 
the forces are known, but AB is the only force whose magnitude is 
known as yet. 
At each joint there are three forces acting, and the polygon of forces 
for each joint is therefore a triangle. The triangle of forces for the joint 
2 or for the joint 3 cannot yet be drawn, because the magnitudes of all 
the forces at these joints are as yet unknown, but the triangle of forces 
for ‘the joint 1 may be drawn, and this is shown at (m). This triangle 
termines the magnitudes bd and da of the internal forces in the bars 
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