Principles of mechanics; perfectly rigid assumption

Principles of applied mechanics

• Newton's first law: a body continues in its state of rest or of uniform straight-line motion unless an external force compels it to change.
• Newton's second law: the acceleration produced is directly proportional to the resultant force and in the same direction, so F = ma.
• Newton's third law: for every action there is an equal and opposite reaction. Forces between two bodies in contact are equal, opposite and collinear.
• Law of gravitation: two particles of masses m₁ and m₂ at distance r attract each other with F = G m₁m₂/r². The weight of a body is W = mg.
• Parallelogram law: the resultant R of two forces P and Q acting at a point is given in magnitude and direction by the diagonal of the parallelogram, R = √(P² + Q² + 2PQ cos α).
• Principle of transmissibility: a force may be moved anywhere along its line of action without changing its external effect on a rigid body.

Why a solid body is taken as perfectly rigid in statics

• Real solids deform only slightly under load, so the shape and dimensions can be taken as unchanged. The moment arms and angles then stay as in the original geometry.
• The equilibrium equations can be applied directly to the undeformed body, which makes the analysis simple.
• Transmissibility is valid only for rigid bodies.
• The small error is acceptable, because the purpose of statics is to find the external forces and support reactions. The deformation itself is studied in strength of materials.