Engineering Stress

Engineering Stress • Tensile stress, s: • Shear stress, t: F F F t t Area, A F s Area, A F s F t F F t s F t = F lb N t s = A = f or o 2 2 in m A o original area before loading  Stress has units: N/m2 or lbf/in2

Common States of Stress F F A = cross sectional o area (when unloaded) F = s s s A o M F s A o A c F s = t A o M 2R • Simple tension: cable • Torsion (a form of shear): drive shaft Note: t = M/AcR here.

OTHER COMMON STRESS STATES A o Canyon Bridge, Los Alamos, NM (photo courtesy P.M. Anderson) F = s Balanced Rock, Arches A National Park o • Simple compression: Note: compressive structure member (s < 0 here). (photo courtesy P.M. Anderson)

OTHER COMMON STRESS STATES Fish under water s > 0 q s< 0 s > 0 z h • Bi-axial tension: • Hydrostatic compression: Pressurized tank (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson)

Engineering Strain d /2 L e = L L w o w o o d /2 L g = Dx/y= tan q • Tensile strain: • Lateral strain: - d • Shear strain: q x y 90º - q Strain is always dimensionless. 90º

F • Hooke's Law: s = Ee s E F e simple Linear- tension test elastic Linear Elastic Properties (If there is a linear response)

Modulus of Elasticity • Modulus of Elasticity, E: (also known as Young's modulus) “Stiffness” of the material Linear behavior typically seen in metals and ceramics Units: Pressure (psi) Other materials do not have linear response (Grey cast iron, concrete, most polymers) • Tangent modulus: slope of stress strain curve • at some specified level of stress Secant modulus: slope of a secant drawn form the origin to some point on the stress strain curve

Atomic Behavior • Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal

Effect of Temperature E = f(T)

Engineering Stress