Truss calculator (method of joints)
Enter your values. The answer and the full worked solution update as you type.
Result
| Member | Length (m) | Force (kN) | Type |
|---|---|---|---|
| AB | 4 | 13.33 | tension |
| BC | 4 | 13.33 | tension |
| CD | 3.606 | 24.04 | compression |
| DE | 4 | 20 | compression |
| EA | 3.606 | 24.04 | compression |
| BE | 3.606 | 12.02 | tension |
| BD | 3.606 | 12.02 | tension |
Positive member forces are tension, negative ones compression. Members are assumed pin-jointed and loaded only at the joints.
Solve a statically determinate planar truss. Enter the joints with their coordinates, the members, the supports (pins and rollers) and the loads. The calculator checks determinacy with m + r = 2j, finds the support reactions, solves every member force and shows the joint equations of the method of joints in the order you would solve them by hand. The diagram marks tension and compression members and the force in each.
Truss and member forces
Step-by-step solution
Determinacy
Support reactions from the equilibrium of the whole truss
Method of joints (tension positive)
Key formulas
- Method of joints
- ΣFx = 0, ΣFy = 0 at each joint
- Method of sections
- ΣM = 0 about a cut point
- Member force
- positive = tension, negative = compression
How to analyse a truss with the method of joints
- Check determinacy: with m members, r reaction components and j joints, a solvable truss needs m + r = 2j and a stable geometry.
- Find the reactions from the equilibrium of the whole truss: ΣFx = 0, ΣFy = 0 and ΣM = 0 about a support.
- Start at a joint with at most two unknown member forces. Assume every member is in tension, pulling away from the joint.
- Write ΣFx = 0 and ΣFy = 0 for that joint, using the direction cosines of the members, and solve for the two unknowns.
- Move to the next joint with at most two unknowns. A negative answer means the member is in compression.
Questions and answers
How do I enter the truss?
Joints as name x y, separated by semicolons, for example A 0 0; B 4 0; C 2 3. Members as pairs of joint names, AB or A-B, separated by commas. Supports as A pin, B roller (vertical reaction) or B xroller (horizontal reaction). Loads as joint Fx Fy, with downward loads negative.
What are zero-force members?
Members that carry no force under the given loads. At an unloaded joint with two members that are not in line, both are zero-force members; at an unloaded joint with three members of which two are in line, the third is.
What does “statically indeterminate” mean?
There are more unknown forces than equilibrium equations (m + r > 2j), so the forces also depend on the stiffness of the members. Such trusses need methods such as the force method or a stiffness analysis.
Why can a truss with m + r = 2j still be unstable?
Counting is necessary but not sufficient. If the members or the reactions are arranged badly, for example all reactions parallel or a panel without a diagonal, the truss can move, and the equations have no unique solution. The calculator reports this.
When should I use the method of sections instead?
When you only need the forces in a few members in the middle of a large truss. Cut through at most three members with unknown forces and take moments about the point where two of them meet.
Practise it yourself
Practise Truss: method of joints
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.