Truss Systems

A truss is an assemblage of slender straight members connected at joints, loaded only at joints, so each member is a two-force member carrying only axial tension (positive, elongates) or compression (negative, shortens). This makes trusses efficient for long spans with minimal bending. Ideal truss assumptions: 1) members connected by frictionless pins, 2) loads and reactions applied only at joints, 3) members straight and centroidal axes concurrent at joint, 4) self-weight negligible or lumped at joints. Real gusset plates introduce secondary moments, but primary analysis remains axial. Static determinacy (planar, simple truss): m + r = 2j for externally + internally determinate, where m = members, r = reaction components (3 for simply supported), j = joints. Internally, simple truss built from triangle satisfies m = 2j - 3. If m < 2j-3 → mechanism (unstable), m = 2j-3 → internally determinate, m > 2j-3 → internally indeterminate to (m - (2j-3)) degrees. Analysis principles: Method of joints: equilibrium at each joint ΣFx=0, ΣFy=0 (2 equations per joint). Start at joint with ≤2 unknowns. Method of sections: cut through ≤3 unknown members, apply ΣFx=0, ΣFy=0, ΣM=0 to one side - efficient for specific members. Sign convention: tension pulls away from joint, compression pushes into joint. Zero-force members: Rule 1: If only two non-collinear members meet at unloaded joint, both are zero-force. Rule 2: If three members meet at unloaded joint and two are collinear, third is zero-force. Rule 3: If two collinear members plus external load perpendicular to them, zero-force does not apply. Zero-force members provide stability during erection and brace compression chords against buckling. Limitations: Analysis assumes small deflections, elastic, and that buckling of compression members (Euler Fcr = π²EI/(KL)²) is checked separately - truss analysis gives force, not capacity. Joint rigidity and eccentricities cause secondary bending in real structures.