Statics Activities

Stress  Force per unit area (  ) Typical engineering units – psi (lb f /in 2 ) – N/m 2 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/m 2

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 / L o 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 =  (0.04) 2 = m 2  = 200N/0.005m 2 = 40000N/m N A =  r 2

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 (  ) The ratio of change in length (  L) to original length (L o ) (dimensionless)  =  L/L o 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 =  /  = (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).