Problem # p020

Deflection of Beam under continuous load, bracket function.

Use the bracket function to find the equation for the deflection of the shown beam at its center, x=L/2.

Consider as given :
Length of beam : L
Weight per unit lenth : wo
Moment of inertia of cross-section :
Young's modulus : E


  1. Determine the equation for the support forces, R1 and R2.
  2. Sketch the two Free Body Diagrams you are using to determine the equation for the internal shear force V(x), one for a cut to the left and one for a cut to the right of the center of the beam.
  3. Combine the two equations into a single equation for V(x) using the bracket function
  4. Integrate V(x) to find the equation for the internal momemt M(x).
  5. Integrate the equation E I y" = M(x) to find y(x).
  6. State the conditions from which to determine the integration constants and determine the integration constants.
  7. Determine the equation for the deflection at x=L/2 in terms of L and wo.