Building Design and Construction Handbook - Merritt - Ventech!

STRUCTURAL THEORY 5.65
FIGURE 5.47 Method of joints applied to the roof truss shown in (a).
Stresses in members at each joint are determined graphically in sucession (b)
to (e).
write the following two equations, one for the vertical components and the second
for the horizontal components:
�V � 0.6S � 8 � 0.6S � 0.6S � 0
FA BH HG
�H � 0.8S � 0.8S � 0.8S � 0
FA BH HG
Both unknown stresses are assumed to be compressive; i.e., acting toward the joint.
The stress in the vertical does not appear in these equations, because it was already
determined to be zero. The stress in FA, S FA, was found from analysis of joint 1 to
be 20 kips. Simultaneous solution of the two equations yields S HG � 6.7 kips and
S BH � 13.3 kips. (If these stresses had come out with a negative sign, it would
have indicated that the original assumption of their directions was incorrect; they
would, in that case, be tensile forces instead of compressive forces.) See also Art.
5.9.4.
All the force polygons in Fig. 5.47 can be conveniently combined into a single
stress diagram. The combination (Fig. 5.47ƒ) is called a Maxwell diagram.