2.1.7 Calculating Truss Forces

Try not to cut through more than three members with unknown forces.

Pass an imaginary "cut" through the truss, slicing through the members you want to solve.

The cut must divide the truss into two completely separate pieces. 2.1.7 calculating truss forces

Solving these equations will give you the external forces holding the truss in place. Step 2: The Method of Joints

: AB = +5 kN → Tension (member is being stretched). AC = –7.07 kN → Compression (member is being shortened → risk of buckling). Try not to cut through more than three

Before calculations can commence, the engineer must establish a theoretical model of the truss. This requires three specific assumptions that simplify the complex reality of a physical structure into a solvable mathematical problem. First, all members are assumed to be straight, two-force members, meaning they are subjected to only axial forces—tension or compression—with no bending moments. Second, the joints are idealized as frictionless pins, allowing the members to rotate freely. Third, the self-weight of the members is often neglected, with the assumption that loads are applied solely at the joints. With these constraints in place, the calculation process begins by treating the entire truss as a rigid body to determine the external support reactions.

Once the external reactions are known, the internal forces can be determined. The two primary analytical methods used are the Method of Joints and the Method of Sections. The Method of Joints is the more granular of the two. It involves isolating a single joint—essentially a point where members converge—and drawing a free-body diagram (FBD) of that specific point. Because the joint is a particle in equilibrium, the forces acting on it must form a closed polygon. In practice, this requires applying the equilibrium equations ($\Sigma F_x = 0$ and $\Sigma F_y = 0$) to the joint. The analysis typically begins at a support where the reaction forces are known, solving for the two unknown member forces connected to it. The process then progresses joint by joint across the structure. While effective and exhaustive, this method can become tedious for large trusses, as it requires solving for every member sequentially to reach a specific interior member. Solving these equations will give you the external

You can often speed up your calculations by identifying "zero-force members" at a glance. These members carry no load under specific loading conditions but are necessary for stability and to prevent buckling.