Lessons · Engineering · a truss by the method of joints
A truss, one joint at a time
At a pin joint the member forces and the load add to zero, so a joint with two unknown members is solved by ΣF_x = 0 and ΣF_y = 0. Assume tension; a negative answer is compression.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A roof truss, a crane jib, a bridge: they are all pins and bars. Which bar is in compression decides which one can buckle, and the method of joints is how that is found without a computer.
How to think about it
Find a joint with only two unknown member forces. Draw it free, every member pulling away from the joint (tension). Write the two force sums and solve. Carry the answers to the next joint that now has two unknowns.
Worked example
Joint C: 8 kN down; member CB runs horizontally to the left; member CA runs up and to the left at 45°Two members, one load. This joint can be solved alone.
ΣF_y = 0: F_CA sin 45° − 8 = 0 → F_CA = 8 / 0.7071 = 11.31 kNOnly CA has a vertical part, so it alone holds the load up. Positive: tension.
ΣF_x = 0: −F_CB − F_CA cos 45° = 0 → F_CB = −11.31 × 0.7071 = −8 kNBoth members pull left if in tension, and nothing pulls right, so one of them must push.
F_CB = 8 kN in compressionThe sign says it. A member in compression is the one that can buckle, and that is why the sign matters.
Your turn
A joint with 6 kN down, one member rising at 60° and one horizontal. Write the vertical equation.
F sin − 6 = 0
Solve one, graded on the server
The trap
Starting at a joint with three unknown members. Two equations cannot solve three unknowns; find a joint with two, often at a support or under a load at the end, and the rest follow from it.