# MDOF Earthquake Response

## Homework Statement

The question is featured in the image below. I know the methods to calculate modal mass, stiffness etc, I'm just not too sure how to model both the distributed and lumped masses together. ## Homework Equations

Modal Mass, M* = ∫m.φ^2(x) dx

## The Attempt at a Solution

Say for instance, that the tower had no lumped mass at the top, so we only had to consider the distributed load (m = 3000 kg/m), the solution would be:
M* = m∫φ^2(x) dx (limits of integration are from 0 to L(=80m))
∫φ^2(x) dx = ∫(1-cos((πx)/(2L))^2 dx = L - 4L/π + L/2
M* = 3000 x (80 - 320/π +40) = 54423kg

My issue is not knowing how to combine the distributed and lumped masses together for this calculation. Any help is greatly appreciated

## Answers and Replies

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

I've managed to solve the problem now. Thank you for the concern though!