Determination of the Internal Forces in Truss Members
.
2- Method of Sections
Sometimes there
is no need to determine the forces in all of the members of a truss. For
example, if several forces are only required, then the method of sections used
instead of the method of joints to save time and efforts.
In this
method, the truss is divided by a cut into parts. The cut has to be made in
such a way that it either passes through three members that do not all belong
to the same joint, or passes through one joint and one member, e.g. you have to
select a section such that there are no more than three unknowns. After cutting
and support reactions are computing, the free-body diagram for each part of the
truss contains only three unknown forces that can be determined by the three
conditions of equilibrium.
To illustrate the method, we consider the truss shown in(Fig. 1a- in the attached file) with the objective of determining the forces in members 1,2 and 3. As a first step, the reactions at supports A and B are computed by applying the conditions of equilibrium to the free-body diagram of the whole truss. In the second step, we pass an imaginary section through the members 1-3, cutting the truss into two parts. Fig. 6.10b (in the attached file) shows the free-body diagrams of the two partsof the truss. The internal forces in members 1-3 act as external forces in the free-body diagrams; they are assumed to be tensile forces.
Please see the attached file
By The Lecturer
Khalid Safaa Al-Khalidy
References
1- Dietmar Gross, et., al., 2009
"Engineering Mechanics 1-Static"Springer Heidelberg Dordrecht London
New York.
2-
R.C. Hibbeler, 2004
" Engineering Mechanics – Static", Pearson Education. Inc (United
States of America).