Statics/Method of Joints

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The method of joints is a way to find unknown forces in a truss structure. The principle behind this method is that all forces acting on a joint must add to zero. If there were a net force, the joint would move.

Example 1[edit | edit source]

Question[edit | edit source]

Find the force in member BC of the truss pictured to the right.

Answer[edit | edit source]

Using the method of joints, the force could be found by isolating the joint at either end of the member (joint B or C). Neither joint can be solved without further analysis; however, joint B can be solved if the force in member and is found.

To find force analyze joint A. This joint has an external vertical force of 300N which must be countered by the members attached to the joint. Member cannot possibly support any vertical load, otherwise it would not be loaded axially and the entire structure would no longer be a truss. If has no load then member is in 300N of tension.

When joint H is analyzed it is found that the force in members and must be zero. The reason why neither member can carry any load is that member can only take a vertical load and member can only take a horizontal load. In a real world application this structure might be useful if there was a load applied at joint . Now joint can be analyzed.

The picture to the left shows the forces affecting joint B.

Substitution[edit | edit source]

From analysis of joint

From analysis of joint

Put values for and into the equilibrium equations for joint B.

Now can be inserted in place of in , which gives:

Finally, can be solved for as follows: