Cumulative tutorial 10
From modes to base shear
Turn a modal output and a spectrum into a force, then check it is credible.
The three-storey building is to be assessed against a synthetic firm-ground record. The modal analysis is done; the spectrum has been generated. Convert them into a base shear, then apply the check that catches most errors in this chain.
The record is generated for teaching and is not a real strong-motion record.
What you are given
- Total seismic mass 1 200 tonnes
- Mode 1: T = 0.3157 s, effective mass 91.41%, spectral acceleration 5.104 m/s²
- Mode 2: T = 0.1127 s, effective mass 7.488%, spectral acceleration 4.778 m/s²
- Mode 3: T = 0.0780 s, effective mass 1.104%, spectral acceleration 4.465 m/s²
Tutorial 10
Work the problem
4 questions
Question 1
What base shear does mode 1 contribute, in MN?
Question 2
What base shear does mode 2 contribute, in MN?
Question 3
Combining all three modes by SRSS, what is the total base shear, in MN?
Question 4
The seismic weight is 11.77 MN. What is the base shear coefficient V/W?
What this establishes
The coefficient is the single most informative check in the chain, because it tests the mass, the spectrum, the units and the combination all at once. Compute it before looking at a single member force.