Attention - understanding this example may be aided by reading the theoretical introduction and watching the video course on Example 8.

We assume a coordinate system. If we write moment functions from the left side, there is no need to calculate support reactions.

\begin{aligned}&EJw''=-M_G\\ \end{aligned} \begin{aligned}&M_G=-20x\\ &EJw''=20x\\ &EJw'=20 \frac{x^2}{2} + C\\ &EJw=20 \frac{x^3}{2\cdot3} + Cx + D\\ \end{aligned}

Boundary Conditions

\begin{aligned}&w'(x=10m)=0 &=> 0=20\cdot \frac{l0^2}{2}+C &=> &C=-1000 [kNm^2]\\ &w(x=10m)=0 &=> 0=20\cdot \frac{10^3}{6}+10C+D &=> &D=6666.67 [kNm^3]\\ \end{aligned}

Bending of the beam at point A

\begin{aligned}&w_A(x=0)=\frac{D}{EJ}=\frac{6666.67}{EJ}\\ \end{aligned}