Truss Analysis Calculator: Member Forces by the Method of Joints, Tension and Compression, Support Reactions
Member forces and reactions for a pin-jointed truss.
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How this calculator works
Type each joint as x then y, one per line, and each member as the two joints it joins.
Type the joint loads, and choose the pin and the roller support joints.
The calculator solves the equilibrium of every joint and lists the force in each member, marked tension or compression.
Formulas used
- \Sigma F_x = 0,\ \Sigma F_y = 0\ \text{at every joint}
- m + r = 2j
- T_i > 0\ \text{tension},\ T_i < 0\ \text{compression}
Worked example
With the default numbers in the calculator above:
- Reaction at the pin (joint 1), horizontal: 0 kN
- Reaction at the pin (joint 1), vertical: 10 kN
- Reaction at the roller (joint 3): 10 kN
- Check: the forces left over after adding the loads and reactions (should be zero): 0 kN
- Force in every member (joint-joint): 1-2: 6.667 kN tension; 2-3: 6.667 kN tension; 4-5: 13.33 kN compression; 1-4: 12.02 kN compression; 4-2: 12.02 kN tension; 2-5: 12.02 kN tension; 5-3: 12.02 kN compression
- Largest tension: 12.019 kN in member 4-2
- Largest compression: 13.333 kN in member 4-5
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is the method of joints?
It finds the force in each member by writing the horizontal and vertical equilibrium of each joint. Each joint gives two equations, and the equations are solved together.
How do I know if a truss can be solved by statics alone?
The number of members plus the number of support reactions (3 for a pin and a roller) must equal twice the number of joints. If it is less the truss is a mechanism, and if it is more it is statically indeterminate.
What is a zero-force member?
A member that carries no load for the given loading. It still keeps the shape stable and carries load if the loads change.
Does the calculator check buckling?
No. Long compression members can buckle, so check them with the Euler column calculator.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any statics text (analysis of trusses, the method of joints).
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