Story Drift Determination Elastic Analysis of a Building

[scotty409]

ASCE 7, 2002 edition, 9.5.5.7.1 calls for the design story drift to be determined by the difference of the deflections at the top and bottom of the story under consideration. Then it gives a formula to calculate the deflection at level x. One of the variables of the formula is the deflections determined by an elastic analysis. But gives no further guidance on how to conduct this analysis or what it entails.

I am writing an article for a non-profit trade association magazine and would like to at least describe in a paragraph what an engineer would do to perform an elastic analysis.

Any help you can provide would be greatly appreciated.

J. Scott Mitchell
Fire Protection Engineer

 

[Qshake]

I would say that you're chewing off a bit more than you'd like if you're writing an article but never performed the calculation before.

In it's simplest form the elastic analysis means an analysis in which all of the materials obey Hooke's law. Otherwise stated that the stress is proportional to the strain; moreover force is proportional to displacement.

Having noted the above, you may not analyze material which will undergo yielding resulting in permanent displacements. Under such loading, the force (or stress) is no longer proportional. This is a non-linear behavior and doesn't follow Hooke's law. While there is more to this, its best to re-focus on the elastic analysis.

In a very simple case such as an inverted pendulum. Where you would have a large mass, M, atop some structural element (column) with stiffness, K and fixity at the base. Further, if you applied a load to the top of the column of stiffness, K the deflection would be equal to delta = Ph^3/3EI. Which is a rather famous formula for a cantilever deflection with a load, P, applied at the free end. That is elastic, for every load, P, there is one and one only displacement, delta.

The matter is only slightly more complicated when you extend this to single story frames as you now have to consider the interaction of the beams and columns. However, a junior course in structural analysis will assist with the proper methods of determining the displacement. Virtual work or Castigliano's theorems come to mind as do some others.

However to represent larger buildings or taller, multi-story buildings it is nearly impossible to do by hand. So at this point you'll wish to invest in a structural program for the elastic analysis. For the type of analysis that you're looking for you will apply a psuedo-static load as prescribed by the building code which is inversly proportional to the height of the building and based on story weight and overall building weight.

There are other means of elastic earthquake analysis such as elastic response spectrum analysis or even elastic time-history analysis but these are far advanced topics.

A good reference for you is the Seismic Design Handbook by Farzad Naiem.


Regards,
Qshake

Eng-Tips Forums:Real Solutions for Real Problems Really Quick.