Boundary Conditions

The number of boundary conditions usually matches the number of constants in the solution of the differential equation.

1. Clamped ends
   
   In this case, the deflection u and the slope u' must vanish. Hence at the end considered, where x=0 we have: u(0) = 0 and u'(0) = 0

2. Simply supported ends
   
   In this case, no deflection u nor moment M can exist at the end of the beam. Hence, u(0) = 0 and EI u''(0) = 0

3. Free ends
   
   At such a free end, there is no moment nor shear. Hence,
   EI u''(0) = 0 and EI u'''(0) = 0

Index

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