In the Statics - Truss Page, we ended with a sample truss example in which we determined the external forces acting on the truss and the internal forces in several members by Method of Joints. For example 2, we would like to use the same truss and solve for several internal forces by Method of Sections. And since we previously solved for the external support reactions, we will not repeat that portion, but begin with the external support forces given and move to determine the internal forces in the selected members.
Example 1: In Diagram 1 we have a truss supported by a pinned joint at Point A and supported by a roller at point D. A vertical load of 500 lb. acts at point F, and a horizontal load of 800 lb. acts at Point C. The support reactions acting on the structure at points A and D are shown. For this structure we wish to determine the values of the internal force (tension/compression) in members BC, EC, and EF.
In Method of Sections, we will 'cut' the truss into two sections by drawing a line through the truss.
This line may be vertical, horizontal, at some angle, or even curved depending on the
problem. The criteria for this line is that we would like to cut through the unknown
members (whose internal force value we wish to determine), but not to cut through more
than three unknowns (since we will have three equilibrium conditions equations, we can
only solve for three unknowns). In this example, cutting the truss once will enable us to
find our selected unknowns, however, in some trusses, or for finding more internal forces,
one may have to repeat Method of Sections several times to determine all the unknowns.
In Diagram 2, we have cut through the original truss with a vertical line
just to the right of member BE. This vertical line cuts through members BC, EC, and EF
(the selected members whose internal forces we wish to determine). We have shown the
section of the truss to the left of the cut. We now treat this section of the truss as if
it were a completely new structure. The internal forces in members BC, EC, and EF now
become external forces with respect to this section. We have represented these forces with
the arrows shown. The forces must act along the direction of the cut member (since all
members in a truss are axial members), and we have selected an initial direction either
into or away from the section for each of the forces. If we have selected an incorrect
initial direction for a force, when we solve for the value of the force, the value will be
negative indicating the force acts in the opposite direction of the one chosen initially.
We may now proceed with the analysis of this structure using standard Static's techniques.
I. Draw a Free Body Diagram of the structure (section), showing and labeling all external forces, and indicating needed dimensions and angles. (Diagram 3)
II. Resolve (break) all forces into their x and
y-components.
III. Apply the Equilibrium Equations :
and solve for the unknown forces.
(Here
we sum the x-forces)
(Sum of y-forces, including load forces.)
(Sum of Torque
with respect to point E.)
Solving we obtain: BC = 44 lb. (T), EC = -50 lb.
(T), EF = 712 lb. (T) (The negative sign for force EC means that
we initially chose it in the incorrect direction. EC acts out of the section and so is in
tension, not into the section as shown in the FBD). Thus, we have solved for the internal
forces in the members BC, EC, and EF by method of sections.
Return to Topic 2.2 - Trusses
Continue to Example 2
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Topic 2: Statics II - Applications-Topic Table of Contents