Calculating loads in a truss


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There are plenty of resources on the web for reading about how to calculate stresses in a system of trusses. West Point has an activity I'd like to try in a physics class. Below is an example I have started to illustrate.


truss2

In the truss above, all horizontal members have length and vertical members have length The system is statically determinate if where is the number of joints, is the number of members, and is the number of reaction forces. There are 7 joints, 11 members, and the pin at has 2 reaction forces (vertical and horizontal), and the roller at has 1 reaction force (vertical). So the system is determinate.

Here we have added the reaction forces to our diagram:

truss2

To find the tensions in the members:

  1. Ensure net vertical force is zero. Since , we know that .
  2. Ensure net moment is zero. The moment about is , so .
  3. Ensure net horizontal force is zero. So .
  4. Now we look at the forces at the joints, choosing joints in the order we can solve them. We treat tensions as positive forces. has two reaction forces, and two unknown tensions and and so is a good starting point. We could draw a FBD, but since horizontal forces must net to zero, And since vertical forces net to zero,
  5. Now we have enough information to look at . Draw the FBD. Net the vertical forces:

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