MT-1620 al.2002 a) Assume plane sections remain plane and perpendicular to the midplane after deformation Bernouilli - Euler Hypothesis"* 1750 b)For small angles, this implies the following for deflections l(x,y,二)≈ z≈-2 (13-1) d x total derivative dx since it does not vary with y or z Figure 13.4 Representation of movement in x-direction of two points on same plane in beam u=-z sin note direction of u relative to +x direction Paul A Lagace @2001 Unit 13-7MIT - 16.20 Fall, 2002 a) Assume plane sections remain plane and perpendicular to the midplane after deformation “Bernouilli - Euler Hypothesis” ~ 1750 b) For small angles, this implies the following for deflections: dw u x( , y,) z ≈ − zφ ≈ − z (13 - 1) dx total derivative  φ = dw since it does not  dx  vary with y or z Figure 13.4 on same plane in beam Note direction of u relative to +x direction Representation of movement in x-direction of two points ⇒ u = -z sin φ Paul A. Lagace © 2001 Unit 13 - 7