Lesson 12: Statics

What are the conditions for static equilibrium?

(1) ΣF = 0 — net force is zero (translational equilibrium) AND (2) Στ = 0 — net torque is zero (rotational equilibrium)

What does ΣFx = 0 and ΣFy = 0 mean in statics?

The sum of all force components in both the x and y directions must each equal zero independently

How do you choose a pivot point for torque in statics problems?

Choose it at the location of an unknown force to eliminate that force from the torque equation and simplify solving

What is the sign convention for torque in statics?

Counterclockwise (CCW) torques are positive, clockwise (CW) torques are negative

Where does gravity act on an object in statics problems?

At the center of gravity (same as center of mass for uniform gravitational fields) — treat all weight as acting at that single point

What is stress?

σ = F/A — Force applied per unit area. Units: Pascal (Pa = N/m²)

What is strain?

ε = ΔL/L₀ — Fractional change in length (or dimension); dimensionless ratio

What is Young's Modulus (Elastic Modulus)?

Y = stress/strain = (F/A)/(ΔL/L₀) — Measures a material's stiffness under tension or compression. Units: Pa

What is Shear Modulus?

S = shear stress / shear strain = (F/A)/(Δx/h) — Resistance to deformation by shear forces. Units: Pa

What is Bulk Modulus?

B = -ΔP/(ΔV/V₀) — Resistance to uniform compression on all sides; negative sign because volume decreases with pressure increase. Units: Pa

What is the elastic region on a stress-strain curve?

The region where stress is proportional to strain (Hooke's Law applies) — material returns to original shape when force is removed

What is the proportional limit?

The point up to which stress and strain are perfectly proportional — beyond this the relationship becomes nonlinear

What is the elastic limit?

The maximum stress a material can experience and still return to its original shape (no permanent deformation)

What is the yield point?

The stress at which permanent (plastic) deformation begins — material will not return to original shape

What is the breaking point?

The stress at which the material fractures or fails completely

What is the difference between elasticity and plasticity?

Elasticity: material returns to original shape after stress is removed. Plasticity: material is permanently deformed after stress exceeds the elastic limit.

What is a ductile material?

A material that undergoes significant plastic deformation before breaking (e.g., most metals like copper, steel)

What is a brittle material?

A material that fractures with little to no plastic deformation (e.g., glass, ceramic, cast iron)