Statics Reference

    Trusses

    Trusses are support members that are joined together at the ends. The function of a truss is to transmit loads to a support joint. In this section, we will analyze a simplified version of planar trusses called simple trusses, which consist of two-force members connected by frictionless joints/pins.

    Truss Assumptions

    The main assumptions for trusses and truss structures are:
    1. All loading is applied at the joints.
    2. The weight of the truss is negligible.

    Because of these assumptions, all trusses are two force members, with the forces on the truss acting along the axis of the member.

    Two Force Member

    A two force member is a rigid body that has two forces (no moments) acting on it in two locations, say \(A\) and \(B\). Equilibrium of the two-force member implies

    $$ \vec{F_A} + \vec{F_B} = \vec 0, $$
    resulting in
    1. \(|F_A| = |F_B|\)
    2. \( \vec{F_A} \) and \( \vec{F_B} \) act along the same line of action.
    Examples of different two force members.

    Zero Force Member

    Zero force members are members in a truss structure that experience no force. They act as support trusses to add stability, but are not load bearing. There are 2 cases where zero force members occur:
    1. Two noncolinear members share a pin with no support or external forces (Zero force member example, left)
    2. Two colinear forces with a third noncolinear force on a pin (zero force member example, right)
    Examples of different zero force members, highlighted in red.

    These rules will help us simplify trusses and solve for the internal forces in the desired members.

    Drawing free-body diagrams on trusses is simple. As mentioned in the beginning, we will choose the entire truss as our system and draw the free-body diagram to determine the reaction forces on pinned/roller joints. Note we will need more equations and free-body diagrams on individual truss members to fully determine the reaction forces. See statics reference pages on how that is done. The following is a diagram showcasing eliminating zero-force members as well as the free-body diagram on the truss.

    Stage: 0

    Truss Analysis: Joints

    Method of joints for truss analysis:
    1. Draw a free-body diagram for the entire truss and solve for the external reaction forces and moments at the supports
    2. Draw a free-body diagram of a joint with at least 1 known force and at most two unknown forces
    3. Use the equations of equilibrium for the joint to solve for the unknown forces
    4. Repeat steps 2 and 3 to find the forces in the trusses you are interested in.

    Note: Remember that truss members that are in compression "push back" on the pin joints, and truss members that are in tension "pull" on the pin joints.

    Truss Analysis: Sections

    Example of methods of sections for joint analysis