It is the night before your statics exam, you are staring at a truss with seven members, and the textbook example somehow skipped the one step you actually needed. If that is you, take a breath. The method of joints is genuinely one of the most learnable topics in engineering — it just gets taught badly.
This walkthrough solves a complete truss from start to finish, explains the sign conventions that trip everyone up, and shows you how to check your own answer. If you want to verify your working afterwards, our Truss Calculator solves any 2D truss and shows every member force.
The One Idea Everything Rests On
A truss does not move. That is it. That single fact is the whole method.
If the structure is not accelerating, every force on it must cancel out. And crucially, that is true not just for the truss as a whole, but for every single joint in it. Zoom in on any pin, draw the forces pulling on it, and they must sum to zero.
At each joint you get two equations:
ΣFx = 0 (horizontal forces balance)
ΣFy = 0 (vertical forces balance)
Two equations means you can solve for at most two unknown members at a time. That constraint is not a limitation — it is your roadmap. It tells you exactly which joint to attack next.
Before You Start: Is It Even Solvable?
Check static determinacy first. Thirty seconds here saves an hour of frustration:
m + r = 2j
where m = members, r = reaction components, j = joints.
If m + r = 2j, the method of joints will solve it. If m + r > 2j, the truss is statically indeterminate and no amount of joint equations will crack it — you need stiffness methods. If m + r < 2j, the structure is a mechanism and will collapse.
Students lose real marks by grinding away at an indeterminate truss. Check first.
Step 1: Find the Support Reactions
Before touching any joint, treat the whole truss as one rigid body and find the reactions.
Our example: a simple triangular truss. Span of 6 m. Pin support at A on the left, roller at B on the right. A downward load of 1000 N at joint C, at the apex, directly in the middle.
Because the load sits exactly at midspan and the geometry is symmetric, taking moments about A gives:
ΣMA = 0 → (By × 6) − (1000 × 3) = 0 → By = 500 N
Then vertically: ΣFy = 0 → Ay + 500 − 1000 = 0 → Ay = 500 N
Both supports carry half. Symmetry gave us that for free — and when your answer respects the symmetry of the problem, that is your first sign you are on track.
Step 2: The Sign Convention (Read This Twice)
Here is where most people lose marks, so let us be very precise.
Always assume every unknown member is in tension. Draw the force arrow pulling away from the joint, along the member.
Then solve. If the answer comes out positive, the member really is in tension. If it comes out negative, the member is in compression — and you do not redraw anything or start over. The minus sign is the answer.
This one habit — assume tension, always, everywhere, and let the algebra tell you the truth — eliminates the single largest source of errors in truss problems. Students who guess the direction each time get lost by the third joint.
Step 3: Pick the Right Joint to Start
Start at a joint with no more than two unknown members. Usually that is a support.
Start at joint A. It has the reaction Ay = 500 N pushing up, plus two members: AC (the inclined top member) and AB (the bottom chord). Two unknowns, two equations. Perfect.
Say member AC rises at 60° from horizontal.
Vertical: ΣFy = 0
500 + FAC × sin(60°) = 0
FAC = −500 ÷ 0.866 = −577 N
Negative, so AC carries 577 N in compression. That should feel right: the top members of a loaded truss get squashed.
Horizontal: ΣFx = 0
FAB + FAC × cos(60°) = 0
FAB = −(−577 × 0.5) = +289 N
Positive, so AB is in tension at 289 N. Also intuitive: the bottom chord is being stretched as the truss tries to flatten out.
Step 4: Move Along and Use Symmetry
Move to joint B. By symmetry, member BC mirrors AC exactly: 577 N in compression. You do not need to redo the algebra — but if you are being marked, show the equations anyway.
Joint C is now your free check. Every force there should balance, because you already know all three members meeting at it. If joint C does not close, you have an arithmetic error upstream. This is the most useful habit in the whole topic: the last joint is your proof.
Zero-Force Members: Free Marks
Larger trusses hide members carrying nothing at all. Two rules find them instantly:
Rule 1: At a joint with exactly two members, not in a straight line, and no external load — both members are zero-force.
Rule 2: At a joint with three members where two are collinear, and no external load — the third (the odd one out) is zero-force.
Spot these first and a fourteen-member truss can collapse into six real calculations. Examiners include them deliberately to reward students who look before they grind.
A common misconception worth clearing up: zero-force members are not useless. They brace the structure, stop long members buckling, and carry load under different load cases. They are zero for this loading, not zero forever.
Mistakes That Cost Marks
Skipping the reactions. You cannot start at a support without knowing its reaction. Always do the whole-body equilibrium first.
Starting at a joint with three unknowns. Two equations cannot solve three unknowns. If every joint has three, you need the method of sections instead.
Sloppy angles. sin and cos get swapped constantly. Draw the triangle. Label it. Do not do it in your head at 1 a.m.
Redrawing after a negative. Negative means compression. Write it down and move on.
Check Your Answer
Once you have worked it by hand, verify it. Enter your nodes, members, supports and loads into our free Truss Calculator and it returns every member force, colour-coded for tension and compression, plus the support reactions. Comparing your hand solution against it is how the method actually sticks — you find your own mistake instead of being told the answer.
Frequently Asked Questions
How do you calculate truss forces using the method of joints?
Find the support reactions from whole-body equilibrium, then work joint by joint. At each joint apply ΣFx = 0 and ΣFy = 0, solving no more than two unknown members at a time, until every member is known.
Which joint should I start with?
Any joint with two or fewer unknown members — usually a support, once you have found its reaction. If every joint has three or more unknowns, use the method of sections to cut through the truss first.
How do I know if a member is in tension or compression?
Assume tension for every unknown and draw the force pulling away from the joint. A positive result means it really is tension; a negative result means compression. Do not redraw — the sign is the answer.
What is a zero-force member?
A member carrying no load under the current loading. At an unloaded joint with two non-collinear members, both are zero-force; at an unloaded joint with three members where two are collinear, the third is zero-force. They still matter structurally.
What is the difference between the method of joints and the method of sections?
The method of joints solves every member by working through each joint, and suits problems where you need all the forces. The method of sections cuts an imaginary line through the truss and solves a whole free body at once — far faster when you only need two or three specific members.
When does the method of joints not work?
When the truss is statically indeterminate (m + r > 2j). Joint equilibrium alone cannot solve it, and you need a stiffness or finite element approach instead. Always check m + r = 2j before you start.