Stresses in the rods of a framework — A/L Combined Mathematics

What must I remember about Stresses in the rods of a framework?

• Pin-Jointed Truss / Framework: A rigid structure composed of light rods smoothly pinned (hinged) together at their ends, carrying loads applied exclusively at the joints.
• Stresses in rods: Light rods can only carry internal axial forces along their length: Tension (T > 0, rod is stretched, pulls inward on joint pins) or Compression / Thrust (C > 0, rod is compressed, pushes outward against joint pins).
• Statical Determinacy criterion: For a planar pin-jointed truss with j joints and m members, the framework is statically determinate and internally rigid if m = 2j - 3.
• Method of Joints (Equilibrium of pins): Treat each joint pin as a particle in equilibrium under external loads and axial rod stresses; resolve forces along two orthogonal directions: ∑ X = 0 and ∑ Y = 0 at joints with at most two unknown stresses.
• Bow's Notation: System of lettering spaces between external forces and internal triangular cells to construct Cremona-Maxwell stress diagrams.

Test yourself (1 minute)

1. Zero-force member recognition rules

   1) If only two non-collinear rods meet at an unloaded joint, stress in BOTH rods is ZERO; 2) If three rods meet at an unloaded joint where two are collinear, stress in the third rod is ZERO.

2. Method of Sections (Ritter's Method)

   Cut the framework through at most three rods whose stresses are unknown; treat either isolated sub-structure as a rigid body in equilibrium, resolving and taking moments about rod intersection points.

3. Support reactions determination

   Always calculate external support reactions first by treating the ENTIRE truss as a single rigid body before analyzing internal joints.

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Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 4

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Year 2 · Term 2