Bending Line animations.
This is built in order to show how a modeled joist would bend under the incluence of a certain force. There are several different examples for different bearings.
The goal is to play around a bit and develop an intuition for what is going to happen with the joist. I also show the equation for the bending line above each example. I have calculated most myself, so it is pretty likely there are some mistakes. 😅
One-side firmly attached joint
$$w(x)=\frac{F}{6\mathrm{EI}_y}\left(3ax^2-x^3\right), \quad 0 \le x \le a \quad \mathrm{\mathbf{and}} \quad
w(x)=\frac{F}{6\mathrm{EI}_y}\left(3a^2x-a^3\right), \quad a \le x \le l$$
Joist on two bearings 
$$w(x)=\frac{F(l-a)}{6\mathrm{EI}_y l}\left(l^2x-(l-a)^2x-x^3\right), \ 0 \le x \le a \quad \mathrm{\mathbf{and}} \quad
w(x)=\frac{F(l-a)}{6\mathrm{EI}_y l}\left(\frac{l}{l-a}(x-a)^3+\left(l^2-(l-a)^2\right)x-x^3\right), \ a \le x \le l$$
One-side firmly attached joist with line load
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