Let us start with the fundamental relation of structural engineering:
where, k: stiffness, E: Modulus of elasticity, I: Moment of inertia of area, L: Linear dimension, delta: deflection, F: Force
In a structural design problem, the minimum force is usually defined by a code, usually decided by the owner or the laws of the country. The constitution of the country forms the codes to safeguard the interest of the citizens. Sometimes, the owner may choose to design the structure for a higher load. In the design process, the engineer usually limits the deflection by providing adequate stiffness, k. So actually, our domain of structural engineering evolves around fixing the stiffness value.
We know further:
What are the things we can play around in a design problem? Modulus of elasticity comes from material science. That is why we also need to study the physics and chemistry to address different issues. Moment of inertia of area is defines the cross section properties. We can design a column, circular or rectangular in cross section. We can vary the span (L) of the beam or column height or any other structural elements. In all these operations, we take the immense help of mathematics.
Then one can just wonder that the similar relation is even narrated in Hook's law that we study in high school!
In fluid mechanics, we narrate the fluid flow in a closed conduit as:
An electrical engineer will write the equation about narrating the flow of electricity as:
and so on.
If the system that we are solving is quite large, perhaps you will need to solve a set of such above equations. We will impose the boundary conditions and assume that the system is in equilibrium. The process is identical for whether we solve flow problem in a network of pipes, truss analysis, frame analysis, electric circuit analysis or what else? We will then go to the mathematician to have a solution. He will help us in solving a system of linear equations! What else an engineer can do?
So, no wonder, the knowledge base that we deal around finally merges towards a unity. Perhaps there is one Creator who created all these systems in the universe at a single moment. So His creation is also a unique and structured.