Dynamic amplification factor (DAF) or dynamic increase factor (DIF) refers to the ratio of the dynamic response of a structure to its static response. Moreover, the value of this ratio, which is a dimensionless number, depicts the effect of dynamic loading on a structure. In this article, you will learn what a dynamic amplification factor is, its use in the Eurocode, and its application in offshore lifting.

## What is Dynamic Amplification Factor

Every structure experiences static loading from its own weight, and that of other entities it carries. As a result, it has deflections and stresses due to these loads. Moreover, if the structure comes under dynamic loading from wind, waves, or any form of vibration, deflections and stresses increase. So, the factor by which these deflections and stresses increase is what the dynamic amplification factor depicts. Therefore, it is important to estimate what this value is, to ensure a structurally sound bridge, building, etc.

Generally, the magnitude of the DAF depends on the response of the structure to loading. For a single-degree-of-freedom (SDOF) system, there is limited movement. Thus, the maximum value of DAF is 2, as most design guidelines recommend. However, systems with multiple-degree-of-freedom (MDOF) experience relatively more dynamic effects. As a result, such systems may record DAF values more than two. This further highlights the need to accurately quantify this value.

### Formula

The formula for determining the DAF varies from one application to the other. However, it always involves taking the ratio of a structure’s dynamic response to that of its static response. For example, the DAF for a bridge subject to dynamic forces from moving vehicles is the ratio of its maximum dynamic strain (*ε _{dyn}*) to its maximum static strain (

*ε*).

_{static}

## Dynamic Amplification Factor Use in Eurocode

The Eurocode is a design code with high levels of adoption amongst EU nations. Moreover, it is specifically for harmonizing structural design rules within the region. It has ten sections, but it is the Eurocode 1 (EN 1991), containing rules on actions on structures, that elaborates on DAF. Generally, this section assumes a high level of dependence of the DAF value on a bridge span length. Other factors such as the natural frequency of a vehicle, roadway roughness, and the expansion joint’s condition also influence it. In addition, this design code has load models with built-in values for a 2-line bridge roadway as the figure below shows.

Even though the Eurocode enjoys wide acceptance, studies show that its estimation of DAF values is too conservative. For instance, results from dynamic load tests in Europe spanning 21 years, show that 90% of DAF values are smaller than those in the code. Also, these studies show that the estimated values depend more on road roughness and speed, rather than bridge span length. Nevertheless, this does not discredit the recommendations in this design code. Rather, it highlights that following the codes will overestimate loads, which in turn will lead to a safer design. But this may be more expensive to implement. Thus, it is advisable to always perform a dynamic analysis to accurately estimate the dynamic effects and balance project safety and cost.

## Dynamic Amplification Factor Use in Offshore Lifting

Accurate estimation of the dynamic amplification factor is very important in offshore lifting operations. This is due to the high dynamic loading common in this application along with equally high static loads. In addition, some applications require the installation of equipment several hundreds of feet below sea level. So, without accurate predicted loads, difficulty and danger may ensue. The DNV code (DNV-RP-H103) states that for a subsea lifting operation, the static response will be the weight (mg) of the equipment. The dynamic response (*F _{total}*) is the aggregate of the maximum static load (

*F*), the characteristic hydrodynamic force (

_{max-static}*F*), and the characteristic snap force (

_{hyd}*F*).

_{snap}

Many offshore lifting operations involve lifting equipment onboard, then unto the seafloor using a crane. As soon as the equipment raises into the air, it is subject to dynamic loading from wind and vessel heave. Then, it undergoes significant hydrodynamic loading during lowering through the splash zone. As a result, the slings undergo alternating tensioning and loosening. Hence, the application of DAF in the lifting system design helps avoid failure. Two of the ways that lifting systems compensate for this phenomenon are:

**Heave compensation:**This involves using a control system to keep the load motionless with respect to the seabed or another vessel.**Constant tension:**The constant tension system uses a control system, but includes a winch to ensure a constant line pull. If the load cell of the control system detects any change in tension, the winch automatically adjusts to maintain the preset value.