Using conjugate beam method find the vertical deflection at D and slope at A for the S.S. beam loaded as shown in fig. in terms of EI.

(1) Support rxn calculation

$\sum M_A=0$

$50\times 4-V_B\times 5.5=0$

$V_B=36.36kN$

$\sum F_y=0$

$V_A-50+36.36=0$

$V_A=13.64kN$

(2)Draw BMD

$B.M_A=0$

$B.M_C=13.64\times 2=27.28kN.m$

$B.M_D=36.36\times 1.5=54.54 kN.m$

$B.M_B=0 ![enter image description here][2]$

(3)Draw $\frac{M}{EI}$ diagram

(4)Draw conjugate beam and consider $\frac{M}{EI}$ diagram as loading on the beam

$\sum M_A=0$

$(\frac{1}{2}\times 2\times \frac{27.28}{EI})(\frac{2}{3}\times 2)+(\frac{1}{2}\times 2\times \frac{13.6}{EI})(2+\frac{2}{3}\times …