16.4 THE METHOD OF JOINTS

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The basic steps when solving problems with the method of joints is,

1. Draw an FBD for each joint as if it is a particle.

2. Solve for the applied forces with the "joint particle" in equilibrium. The simplest joints are often the best to start with.

We can see an example of a two force member below being used to support a canopy,

[picture]

This method is best shown using a sample problem, ([Hibbeler, 1992], prob 6-7, pg. )

[picture]

This problem can also be solved using matrices techniques by framing the truss members as linear equations.

********************** Solve in Mathcad *********************

Try the problem below,

16.4.1 Practice Problems

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1. Determine the force in each member of the truss shown. Indicate tension or compression.

2. Determine the force in each member of the truss shown. Indicate tension or compression.

3. Find the forces in each of the beams of the structure below (indicate tension or compression). Assume all joints are pinned.

4. For the frame below, find the tension/compression in each member, under the loading conditions given, and assuming all joints are pinned. (Note: you must clearly indicate tension or compression when dealing with this type of problem)

(ans. EF=515lb(C), BC=515(C), CD=125(C), AB=774(T), AE=401(C), BD=1563(T), BE=625(C), DE=1289(C)

5. Given the frame below, find the tension/compression in each member.

6. Find the forces in each beam of the bridge shown. (As usual, clearly indicate tension or compression)

7. Find the tension/compression in each member of the frame below, (HINT: look for 6 zero force members and use symmetry)

16.4.2 References

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Beer, F.P., Johnson, E.R., Statics & Mechanics of Materials, McGraw-Hill, 1992.

Hibbeler, R.C., Engineering Mechanics: Statics and Dynamics, 6th edition, MacMillan Publishing Co., New York, USA, 1992.