Trusses: Classical Truss Theory

General

• Triangulation: Using triangulation, it is possible to form a stable assembly with pin connections only.

• Rectangles require moment-resisting connections to be stable.

  • The connections are more expensive to make, and the resulting moments require larger members.

Classical Truss Theory

• "Classical Truss Theory" is a set of simplifying assumptions that make it easy to analyze trusses by hand.

  • Assume members are pin connected.

  • Assume assembly is loaded at joints.

• Two-force member: These assumptions lead to the conclusion that each member is a two-force member, meaning that the end forces are equal, opposite and in-line.

  • Axial force only, no moment, no shear. This, in turn, leads to the conclusion that the members act either in pure tension or pure compression, with no internal shears or moments.

  • This simplifies analysis since it reduces the number of unknown internal forces to solve for.

• Classical truss theory leads to two basic approaches to determining the forces in truss members:

  • The Method of Joints, which considers free body diagrams of individual joints.

  • The Method of Sections, which considers free body diagrams of portions of a truss.

• The method of joints is primarily useful in learning to visualize the action of members (e.g. whether they are in tension or compression) and in mentally predicting the effect of changes in geometry.

• The method of sections is useful for investigating the forces in a particular critical member of a truss.

• Computer-based methods are well suited to the task of finding all member forces in a truss.

Interpreting Truss Form and Behavior

• The behavior of a parallel-chord truss can be interpreted in terms of the shear and moment diagram for a beam with the same span and loading condition. (the top and bottom edge members of a truss are often called chords)

  • The moment corresponds to the a couple created by the tension and compression in the chord forces. The chord forces will be maximum in the region where the moment is maximum.

    • The sense of the bending moment can also tell whether the tension chord is on the top or bottom, with the compression chord on the opposite side.

  • The shear corresponds to the vertical component of forces in the vertical and diagonal members (often called the web members of a truss). The web forces will be maximum in the region where the shear is maximum.

    • The sense of the shear racking can be used to tell whether the diagonals are in tension or compression.