curved beam strength Rice University（莱斯大学曲梁力量）.pdf

Bending of Curved Beams – Strength of Materials Approach M σ θθ N V r cross-section must be symmetric but does not have θ to be rectangular assume plane sections remain plane and just rotate about the neutral axis, as for a straight beam, and that the only significant stress is the hoop stress σθθ neutral axis Let ∆φ= rotation of the centroid cross-section B B R R n N r P M R −r n A P ∆θ ∆φ A R = radius to centroid R = radius to neutral axis n ∆l (Rn −r )∆φ ⎛Rn ⎞ r = radius to general fiber in the beam eθθ ω⎜ −1⎟ l r∆θ ⎝ r ⎠ N, M = normal force and bending moment ∆φ ω computed from centroid ∆θ Reference: Advanced Mechanics of Materials : Boresi, Schmidt, and Sidebottom From Hooke’s law