Analysis of Statically Determinate Trusses

Method of Joints

Support Reactions: To solve for the support reactions the free-body diagram of the truss, as a unified structure, is drawn first (move the mouse over the figure to see the free-body diagram). This free-body diagram shows the external shape of the truss with the applied and reaction forces clearly identified. The reaction forces, shown in green, are drawn in the positive x and y directions. The correct direction of each reaction will be determined from the equilibrium equations.

We begin the solution procedure by writing the moment equilibrium equation. Moments should be summed about a joint with the most reactions (i.e., unknowns). In this case, it would be wise to select joint 1 as the moment center and the origin of the coordinates xyz. Using the counter clockwise direction as positive, we obtain the following equation with one unknown (R4-y)

We then write the force equilibrium equation in the x direction to solve for R1-x.

Thus, R1-x is in the -x direction because of the negative sign in front of its magnitude.

Finally, we write the force equilibrium equation in the y direction to solve for R1-y.

Example 1