Dynamic Factor for Vertical Impact

For an idealized linearly elastic system without energy losses, when a weight falls from height $h$ and then deforms the structure, the maximum displacement can be expressed through the static displacement $\delta_{st}$ caused by the same weight $P$:

$$\delta_{max}=K_d\delta_{st},$$

where the dynamic factor is:

$$K_d=1+\sqrt{1+\frac{2h}{\delta_{st}}}.$$

If stresses in the linear system are proportional to load:

$$\sigma_{dyn}=K_d\sigma_{st}.$$

• $P$ — weight acting as the reference static force;
• $h$ — drop height;
• $\delta_{st}$ — static displacement under $P$;
• $\delta_{max}$ — maximum displacement during impact;
• $K_d$ — dynamic factor;
• $\sigma_{st}$, $\sigma_{dyn}$ — static and maximum dynamic stresses.

For suddenly applied loading with zero initial velocity, $h=0$ and therefore $K_d=2$. The formula assumes elastic behavior, negligible energy loss, and a correctly determined static compliance in the impact direction.

Because $K_d$ is dimensionless and has no separate quantity in the registry, the calculator uses the equivalent displacement relation without treating $K_d$ as a variable.