Characteristics of structural mechanics

Structural mechanics is the branch of mechanics that studies how structures respond to loads, i.e. the forces, stresses, strains and displacements produced in them.

Characteristics of structural mechanics

1. It is based on three fundamental conditions: equilibrium of forces, compatibility of displacements, and the material's force-displacement relation (Hooke's law).
2. It idealises real structures into simple models: members as lines (beams, columns, bars), supports as hinges, rollers or fixed supports, and loads as point, line or distributed loads.
3. It assumes materials are homogeneous, isotropic and linearly elastic, and that displacements are small.
4. It uses the principle of superposition for linear structures.
5. It divides structures into statically determinate (solved by equilibrium alone) and indeterminate (needing compatibility as well).
6. It supplies the data (forces and displacements) needed for the design of members and for checking serviceability.

Two basic approaches of structural analysis

Force (flexibility) method: The unknowns are redundant forces. Example: a propped cantilever carrying a UDL is made determinate by removing the prop at B. The upward deflection at B caused by the prop reaction, $\dfrac{R_BL^3}{3EI}$, is set equal to the downward deflection of the cantilever under the UDL, $\dfrac{wL^4}{8EI}$, since the net deflection at the prop is zero. This gives the prop reaction:

$$R_B = \frac{3wL}{8}$$

Displacement (stiffness) method: The unknowns are joint displacements. Example: in a continuous beam, the support rotation $\theta_B$ is taken as the unknown and found from joint moment equilibrium, $\sum M_B = 0$ (slope-deflection method); the member end moments are found afterwards.