Statics Activities

Stress ( )s

• Force per unit area (s)• Typical engineering units– psi (lbf/in2)– N/m2

• Stress = Force/Area– Applied by external agents– Area is X-section area

• Same definition as pressure

Stress (σ)

• applied to the material by external agents• force per unit area (same definition as pressure)• stress = force / area = F / A• unit: N/m2

Types of Stress

• tensile: object is pulled apart• compressive: object is pushed together• shear: equal and opposite forces applied across

object’s faces

Strain (ε)

• material’s response to the stress• ratio of the change in length to the original length• strain = change in length / original length• strain = ΔL / Lo

• units: dimensionless

Stress

• Example– Calculate the stress in a cylindrical rod if a 200N

force is applied to one end. The radius of the cylinder is 4cm.

A = p(0.04)2 = 0.0.05m2

s = 200N/0.005m2 = 40000N/m2

200 N

A = pr2

Shear stress

• When stress develops in an area parallel to the force direction

• Sometimes when a force affects surfaces, or materials with “grain” (i.e. wood, some crystals, shale rock), or specific geometries.

Strain (e)

• The ratio of change in length (DL) to original length (Lo) (dimensionless)e = DL/Lo

• Brought about by a stress in a material

• Can be temporary or permanent deformation

Strain

Elastic Modulus

• Elastic modulus (E) (or Young’s modulus)• Indicator of relative strength of material

E = s/e = (stress/strain)

Modes of Failure

• Materials can fail– Damaged (excessive

strain- ductile failure)– Catastrophic (fracture)

Ultimate Strength & Fracture

• Ultimate Strength – A level of stress in a material that causes failure– Compression– Tension– Shear

• Safety factors are applied to protect against reaching this level (2x,3x,4x, and higher).