MT-16.20 a.2002 Use per unit length since entire equation is of this form. Thus d/d EI dx dx2 dx dx p -mw or ddw El m=p:(233) x Beam Bending Equation often f=0 and this becomes E mw =p dx dx This is a fourth order differential equation in X -- Need four boundary conditions This is a second order differential equation in time Need two initial conditions Paul A. Lagace @2001 Unit 23-3w MIT - 16.20 Fall, 2002 Use per unit length since entire equation is of this form. Thus: 2 d 2 EI dw  dx2  dx2  − d F dw  = pz − m ˙˙ dx  dx  or: 2 d 2 EI dw  ˙˙ dx2  dx2  − d F dw  + mw = pz (23-3) dx  dx  Beam Bending Equation often, F = 0 and this becomes: 2 d 2 2 EI dw  + mw = pz dx  dx2  ˙˙ --> This is a fourth order differential equation in x --> Need four boundary conditions --> This is a second order differential equation in time --> Need two initial conditions Paul A. Lagace © 2001 Unit 23 - 3