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
- Determine the equation for the support forces, R1
- 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.
- Combine the two equations into a single equation for V(x) using the bracket
- Integrate V(x) to find the equation for the internal momemt M(x).
- Integrate the equation E I y" = M(x) to find y(x).
- State the conditions from which to determine the integration
constants and determine the integration constants.
- Determine the equation for the deflection at x=L/2 in terms of
L and wo.