Subject : Structural Analysis 1

Topic : Deflection of beam

Difficulty : High

$M_B=0\\ M_A=\frac{-1}{2}\times3\times30\times\frac{2}{3}\times3=\underline{-90\ kNm} \\ y_B=y_{max}=\frac{A\bar{x}}{EI}\\ A=b\times h\left( \frac{1}{h+1}\right)=3\times90\left[\frac{1}{3+1}\right]=67.5\\ \bar{x}=b-\frac{b}{n+2}=3-\frac{3}{3+2}=2.4\\ \boxed{\therefore y_B=\frac{67.5\times2.4}{EI}=\frac{162}{EI}}$