Modeling wall's behaviour Sorry if the quesiton is inconvenient, but I judged the physics forum would be the best place to go. My house is divided in two parts by a wall, and there's some tree pushing it, so the wall is about to crack. I already asked for some specialized people to fix, but just for curiosity I wanted to know how I can find a function, equation, etc. that models, in 3D, the behaviour of the wall with time, so the solution could be find mathematically. I think something involving plane equation would do (because I have to "find" the function that describes the wall physically in the plane first right?) but I lack the time for working on it. Any suggestions?
Thanks for your time, have a nice day.


 A: A full 3D model might be too complex for this case, because then you need to know everything about the wall, and the tree, and the interaction between the two in great detail. I think a simplified approach might be more suitable. I'm not sure if this is oversimplified, but let me take a swing at it:
If we assume the tree is supported by both the ground and the wall we have the following equations, see image below:
$$F_{ground_y}+F_{wall_y}=F_{tree_y}$$
$$F_{ground_x}+F_{wall_x}=0$$
and resulting from the moments
$$F_{wall_y} \cdot x_{wall} + F_{wall_x} \cdot y_{wall} - F_{tree_y} \cdot x_{tree} =0$$
We also assume that the tree will only carry loads in line with the centerline of the tree:
$$tan(\alpha)=\frac{F_{ground_y}}{F_{ground_x}}$$
Combining all the equations above, and noting that $F_{wall_y}=m_{tree}g$ gives:
$$F_{ground_x}=\frac{m_{tree}g\left( x_{tree} - x_{wall} \right)}{\tan (\alpha) x_{wall}+y_{wall} } $$
This is equal to $-F_{wall_x}$, and it is possible to solve for all the other variables as well.
At the bottom, the moment induced by this force is equal to:
$$M=F_{wall_x} y_{wall}$$
This will induce the following maximum stress:
$$\sigma=-\frac{M (0.5 t_{wall})}{I_{wall}}+\frac{F_{wall_y}}{A_{wall}}$$
Where the moment of inertia of the wall $I_{wall}$, and the area of the wall $A_{wall}$ are determined by the wall geometry.
If the geometry of the problem and the weight of the tree are known, it is possible to determine $\sigma$.
This value should be lower than the maximum allowable stress of the wall, $\sigma_{wall_{max}}.$
The difficult part is to determine the value of $\sigma_{wall_{max}}$, perhaps values for bricks can be used.

