Les fermes simples

A simple truss is a framework of slender members connected at joints, with all members lying in a single two-dimensional plane called a planar truss. The basic simple truss comprises three members arranged in a triangular formation, which is inherently stable and rigid. This triangular configuration serves as the foundation for creating larger truss structures by strategically adding two members and a joint at a time.

External loads are assumed to act at joints because this simplification ensures truss members act as two-force members experiencing only axial compression or tension. When a member's weight is significant, half its magnitude is applied as equally distributed vertical forces at both ends. This assumption, combined with treating joints as smooth pins, makes structural analysis tractable and reliable.

Although truss members connect via welded, bolted, or riveted joints, they are assumed to be smooth pins provided the centerlines of joining members are concurrent. This assumption allows members to rotate freely at joints without transmitting bending moments, ensuring they experience only axial forces. This simplification is critical for accurate analysis and design of simple trusses.

For a simple truss to be statically determinate and stable, the number of members (m) and joints (j) must satisfy the equation m = 2j - 3. This relationship ensures there are enough members to resist deformation under load while maintaining structural stability. If a truss does not satisfy this equation, it is either indeterminate or unstable, which can lead to structural failure.

A simple triangular truss can be expanded by strategically adding two members and one joint to the existing framework. This process can be repeated multiple times to create larger truss structures capable of supporting greater loads over longer spans. The configuration of members is critical in determining the overall strength and stability of the expanded structure.

The two key assumptions are: first, external loads are applied only at joints and member weight is negligible; second, joints are treated as smooth pins provided member centerlines are concurrent. These assumptions ensure truss members act as two-force members experiencing only axial compression or tension. Together, they simplify analysis while maintaining accuracy for design and evaluation purposes.

The method of joints analyzes truss member forces by examining equilibrium at each joint individually. Since joints are assumed as smooth pins and members carry only axial forces, force equations at each joint can be solved systematically. This approach is fundamental for determining tension and compression in each member, and students can practice this technique through method of joints problem solving.