It’s physics for computers, specifically the Direct Stiffness Method. The formal definition of what you send into a computer for stress analysis involves a whole lot of matrixes. You turn a structure into tiny little nodes not unlike pixels or voxels. Each point can be connected to other elements, and these connections have unique internal linear or twisting “stiffness”, like a spring has. Think how a spring and a stick of wood resist squishing and bending. They can be expressed as one massive square (important!) matrix. The equation in the third panel is essentially a mega version of Hooke’s law:

F = ku
“The vector of forces on the nodes = the matrix containing all information of the stiffness of the connections * the vector of positions of the nodes”.

This is a linear algebra problem, the easiest type of problem for a computer with a GPU. We can insert the known positions and forces on the bridge and solve for all unknown positions. If a truss on a bridge is calculated to experience too much force than it can handle, you can say that the bridge will fail under those conditions.

It’s the matrix