How Do You Model the Forces Acting on a Structure?

Model the forces acting on a structure by drawing a free-body diagram, showing all external loads and support reactions, and applying the conditions of static equilibrium. You can then identify how forces travel through the structure and the internal effects they produce.

First, simplify the structure into an idealized two-dimensional or three-dimensional model. Replace supports with their corresponding reaction forces, and represent loads as vectors showing magnitude, direction, and point of application.

For a stationary structure, use the equilibrium equations:

$$\sum F_x = 0, \qquad \sum F_y = 0, \qquad \sum M = 0$$

For example, consider a simply supported beam of length $4\text{ m}$ carrying a central downward load of $1000\text{ N}$. If the vertical reactions are $R_A$ and $R_B$, taking moments about support A gives:

$$R_B(4) - 1000(2) = 0$$

Therefore, $R_B = 500\text{ N}$. From $\sum F_y = 0$, .

The model should also show the load path: how the applied load is transferred through members to the supports and then to the ground. Depending on their position and loading, members may experience tension, compression, shear, bending, or torsion.

A common misconception is that equilibrium means no forces are acting. It actually means that the resultant force and resultant moment are both zero.

In an IB Design Technology HL response on B3.2, draw a labelled free-body diagram, state any simplifying assumptions, calculate reactions with equilibrium equations, and explain how the resulting internal forces influence structural-system or material selection.