The first practical step in truss analysis is solving for the external reactions at the supports. This is accomplished by applying the three equations of static equilibrium to the truss as a whole: the sum of forces in the horizontal direction ($\Sigma F_x = 0$), the sum of forces in the vertical direction ($\Sigma F_y = 0$), and the sum of moments about any point ($\Sigma M = 0$). For instance, determining the vertical reaction force at a roller support involves summing the moments about a pin support on the opposite side of the truss. These reaction forces are critical; without correctly identifying the external forces acting on the system, any subsequent calculation of internal member forces would be invalid. This stage grounds the analysis in the broader context of Newton’s Laws, ensuring that the structure is externally stable.

Choose a pivot point (usually a pin support) and set the to zero: to find the remaining reaction forces at the supports. 2. Choose an Analysis Method Depending on what you need to find, use one of two methods:

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

If you only need to find the force in a few specific members located in the middle of a large truss, the Method of Sections is much faster. The Process:

| Mistake | Consequence | |---------|-------------| | Drawing member force wrong direction in FBD | Sign reversal (tension vs compression swapped) | | Forgetting to convert angles correctly | Wrong force components | | Using joint with >2 unknowns | Cannot solve – stuck | | Misidentifying support reaction type (e.g., roller has vertical only) | Wrong reaction values propagate | | Using method of sections but cutting through >3 unknown members | Unsolvable without extra equations |