11405

Solving a Double Scissor Truss

This Demonstration uses the method of joints to solve the member forces in a double scissor truss. The point loads (, ) and reaction forces (, ) are shown in blue. Set the point loads with sliders. Check "show joint labels" to show the labels assigned to each joint. Arrows that point outward represent the member response to compression forces (green), and arrows that point inward represent the member response to tension forces (red). Compression acts to shorten the member, and tension acts to lengthen the member. Black members are zero members; that is, these members are neither in tension nor in compression, so the force is 0 kN. The purpose of zero members is to provide stability and extra support to the structure in case another member fails. The member forces are shown on the diagram in kN.

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DETAILS

The method of sections is used to determine the individual member forces in the scissor truss. First, write out the lengths of the members (Figure 1).
For the equilateral triangles:
;
for the scalene triangles:
,
where is the length of the hypotenuse.
Next, solve for the reaction forces. The sum of the moments about joint and the sum of the forces in the direction are taken.
,
,
where and are the vertical point load forces at joints and , and and are the reaction forces at joints and (all in kN).
Next, do the force balances at the joints in the and directions. The order in which the force balances are presented is the order in which they should be solved. The force balances around joints are done assuming we know which members are under tension and which are under compression before solving the truss. If we assume incorrectly, the force will be negative.
Joint
,
.
Joint
,
.
Joint
,
.
Joint
,
.
Joint
.
Figure 1.
Figure 2.
Reference
[1] R. C. Hibbeler, Engineering Mechanics: Statics, 12th ed., Upper Saddle River, NJ: Prentice Hall, 2010.
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