Bending Stress Lecture 3 ME EN 372 Andrew Ning aning@byu.edu - PDF document

Bending Stress Lecture 3 ME EN 372 Andrew Ning aning@byu.edu Outline Axial Stress Bending Stress

Axial Stress F σ x = F A A

Bending Stress Pure Bending M z M z

M z M z M z y M z y

y M z M z y ZZ y 2 dA I z = A M z I z σ x y neutral axis σ x ( y ) = − M z y I z

Flexure formula: σ x = − M z y I z Simplified (ignore coordinate system subscripts and only include max value) σ max = Mc I

Neutral Axis Neutral axis is at y-centroid. � ydA A y = ¯ � dA A few common moments of inertia Rectangle: I = bh 3 12 Circle: I = πr 4 4 Thin Shell: I = πr 3 t

Parallel Axis Theorem I = I c + Ad 2 Example: moment of inertia 4 in 0.875 in 2.5 in 0.875 in

Example: wind turbine tower Bidirectional Bending σ x = − M z y + M y z I z I y