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# Dynamic Amplification Factor

## Definition

The Dynamic Amplification Factor (DAF) is also sometimes referred to as the Dynamic Load Factor (DLF). It is defined as the ratio of the displacement obtained when a load is applied dynamically compared to the displacement that would be obtained if the same load was applied statically.

The DAF is a function of the load-time history, and varies depending on the shape of the load pulse, the duration of the pulse td and the natural period of the structure T. The following graphs give the value of DAFs for different shapes of load / pressure pulses.

## Triangular Pulses

### Shock Triangular Pulses (tr / td = 0.0)

In a shock triangular pulse, the rise time tr is 0, i.e. the peak load / pressure is reached instantaneously. As the duration of the pulse increases with respect to the natural period, the DAF increases up to a maximum value of 2.0. Shock triangular pressure pulses are typically encountered in blast detonations.

### Isosceles Triangular Pulses (tr / td = 0.5)

In an isosceles triangular pulse, the rise time tr is half of the pulse duration td. The maximum value of the DAF for this type of pulse is 1.5, which occurs at a ratio of the pulse duration to the natural period of about 0.9. Isosceles triangular pressure pulses are typically encountered in blast deflagrations.

## Rectangular Pressure Pulses

In a rectangular pressure pulse, the rise time tr is 0, i.e. the peak pressure is reached instantaneously. As the duration of the pulse increases with respect to the natural period, the DAF increases up to a maximum value of 2.0. Because the pressure also drops suddenly from its maximum value to zero, the maximum negative DAF that can happen is a minimum value of -2.0.  