Method of Joints to Solve a Truss Problem

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration solves a truss using the method of joints, which involves doing force balances around one joint at a time.


1. Select "reaction forces" to see how the reaction forces and are calculated.

2. Then, under the drop-down menu, select "calculate moment" to see the moment balance around joint and calculate the reaction force at joint . Move the mouse over the equations to see an explanation of the moment balance.

3. Next, select "-force balance" to do a force balance in the -direction at joint . Note that joint is fixed but joint can move in the -direction.

4. Select "-force balance" to determine the reaction force at joint .

5. Select "balances at joints" and select joint . Check "focus on joint" to zoom in on the members around the joint and display the force balances. Note that the direction of the arrows are drawn in "focus on joint" because we know the correct direction. If the arrows were drawn assuming all members were under tension, then a negative force would result, indicating the direction should be reversed.

6. Repeat step 5 for the other joints.

7. When "solved" is selected from the joints, the compression (green) and tension (red) forces are shown on the full diagram. Arrows that point outward represent the member's response to compression forces, which act to shorten the member. Arrows that point inward represent the member's response to tension forces, which act to lengthen the member.

When doing balances around the joints, the signs on all of the forces are positive because we assume we can determine which members are under tension and which are under compression before solving the truss. This is done by starting at joint , seeing that the reaction force points upward and knowing that the member force must point downward for the truss to remain stationary.


Contributed by: Rachael L. Baumann (September 2017)
Additional contributions by: John L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.