Statics Summary (Equations)

Statics Summary
2D Force Systems 3D Force Systems
Rectangular Components Rectangular Components
𝐹 = 𝐹𝑥 + 𝐹𝑦 𝐹 = 𝐹𝑥 + 𝐹𝑦 + 𝐹𝑧
𝐹𝑥 = 𝐹 𝑐𝑜𝑠 𝜃 𝐹𝑥𝑦 = 𝐹 𝑐𝑜𝑠 ϕ
𝐹𝑦 = 𝐹 𝑠𝑖𝑛 𝜃 𝐹𝑥𝑦 = 𝐹 𝑠𝑖𝑛 ϕ
𝐹𝑥 = 𝐹𝑥𝑦 cos 𝜃
𝐹= 𝐹𝑥2 + 𝐹𝑦2
𝐹𝑦 = 𝐹𝑥𝑦 𝑠𝑖𝑛 𝜃
𝐹𝑦
𝜃 = 𝑡𝑎𝑛−1 Angle between Vectors
𝐹𝑥
𝑷∙𝑸
Moment 𝛼 = 𝑐𝑜𝑠 −1
𝑃𝑄
𝑀 = 𝑑𝐹 = 𝑟𝑠𝑖𝑛ϕ𝐹
Moment
𝑀 = 𝑟𝐴 𝐹1 + 𝑟𝐵 𝐹2 𝑀𝑥 = 𝑟𝑦 𝐹𝑧 − 𝑟𝑧 𝐹𝑦

Resultants 𝑀𝑦 = 𝑟𝑧 𝐹𝑥 − 𝑟𝑥 𝐹𝑧
𝑅 = 𝐹1 + 𝐹2 𝑀𝑧 = 𝑟𝑥 𝐹𝑦 − 𝑟𝑦 𝐹𝑥

𝑅𝑥 = ෍ 𝐹𝑥
2D Equilibrium
𝑅𝑦 = ෍ 𝐹𝑦 ෍ 𝐹𝑥 = 0 Collinear

෍ 𝐹𝑥 = 0 ෍ 𝐹𝑦 = 0 Concurrent
2 2
at a point
𝑅= ෍ 𝐹𝑥 + ෍ 𝐹𝑦
෍ 𝐹𝑥 = 0 ෍ 𝑀𝑧 = 0 Parallel

෍𝐹𝑦
෍ 𝐹𝑥 = 0 ෍ 𝐹𝑦 = 0
𝜃 = tan−1
σ 𝐹𝑥 General
෍ 𝑀𝑧 = 0