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 : w_{o}
Moment of inertia of crosssection :
Young's modulus : E

 Determine the equation for the support forces, R_{1}
and R_{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.
 Combine the two equations into a single equation for V(x) using the bracket
function
 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 w_{o}.