Stiffness can be measured through various practical methods. One common method is testing where a load is applied to the structure and the deformation is measured. Another method is vibration testing, where the natural frequency of the structure is determined and used to calculate stiffness. Specialized tools such as strain gauges and accelerometers can also be used to measure strain and vibration.
However, the stiffness of a single beam under a specific load can be quite accurately calculated using relevant formulas found in standards or literature. Alternatively, stiffness values can also be obtained from tables of section properties. Specially developed programs, or Finite Element Method (FEM), can be used to evaluate stiffness and deflection for more complex structures.
For example, the stiffness of a horizontal cantilever beam with a vertical point load at the free end can be calculated using the formula below.
where
E = modulus of elasticity of the material
I = moment of inertia (or second moment of area) of the beam's cross-section
L = length of the beam.
The values for E and I can be obtained from material data tables or calculated using appropriate equations. The SSAB Design handbook can be used to calculate I as well as other examples how to calculate the stiffness for other geometries.