Similar to 2-D trusses, 3-D trusses (space trusses) require all members to have a pin joint at each end. Also, all loads must act at the joints.

The above two conditions insure that member forces act in the direction of the members. Without knowing the direction of the load, truss problems could not be solved using just static equilibrium equations.

Method of Joints

Method of Joints

Space truss problems can be solved by choosing a joint with only three unknown member forces and one or more known load forces. The forces at the joint are summed in all three directions which will produce three equations and three unknowns.

     ΣF_x = 0     ΣF_y = 0     ΣF_z = 0

The method of joints is usually the easiest method since the moment equilibrium equations are difficult to apply in 3D.

Vector notation should be used with 3-D problems because of the complexity of 3-D geometry.

Method of Sections

If only a single-member load is needed, then the method of sections can be used, just like with 2D planar trusses. However, with 3D trusses, the section that is cut will have three moment equations in addition to the three force equations to find the unknowns.

     ΣF_x = 0     ΣF_y = 0     ΣF_z = 0

     ΣM_x = 0     ΣM_y = 0     ΣM_z = 0