1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: MDOF Earthquake Response

  1. May 16, 2016 #1
    1. The problem statement, all variables and given/known data
    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.


    2. Relevant equations
    Modal Mass, M* = ∫m.φ^2(x) dx

    3. 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
  2. jcsd
  3. May 21, 2016 #2
    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?
  4. May 24, 2016 #3
    I've managed to solve the problem now. Thank you for the concern though!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted