Geotechnical Engineering Course

 Derivation of Functional Relationships

Using Calculator to easily solve problems of Duhamel's integrals

 Using a calculator to easily solve numerical problems of Duhamel's integrals

Problems involving Duhamel's Integral in Structural Dynamics require evaluating the integral between the limits. Instead of adopting the lengthy numerical methods found in classical books, a shortcut is presented that uses the integration feature of modern calculators.

Let us consider the example of a tower subjected to blast loading, as shown below

The mathematical formulation for displacement response is as follows

Similarly, responses at other times within the force duration and beyond the force duration (0.06s) can be calculated very easily