The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. The slopedeflection equations relate the moments at the ends of the member to the rotations and displacements of its end and the external loads applied to the member. There are different methods to find slope and deflection of a beam.
B Slope deflection equations.
Slope Deflection Equation i The slope deflection equation at the end A for member AB can be written as. SolutionEnd A is fixed hence A0 End B is Hinged hence B0 Assume both ends are fixed and therefore fixed end moments are 12 wL F 12 wL F 2 BA 2 AB The Slope deflection equations for final moment at each end are 2 L 4EI 12 wL 2 L 2EI M F 1 L 2EI 12 wL 2 L 2EI M F B 2 BA BA B A B 2 AB AB A B. Hence there is only o ne unknown q B. The maximum deflection of beams occurs where slope is zero.