Structural Dynamics / module 13
Earthquake ground motion and base excitation
How ground motion excites structural response, and how mass enters the equation written in relative coordinates.
What you will understand
- Derive the base-excitation equation and explain why üg appears as an effective force
- Distinguish relative from absolute response and say which quantity matters for what
- Explain why the equation is written in relative displacement
- Describe how amplitude, duration and frequency content each affect the response
- Explain why records are baseline-corrected and filtered, and what that costs
- Recognise the limits of a uniform base-excitation idealisation
Lessons
The base-excitation equation
Where −m üg comes from, why the equation is written in relative displacement, and the distinction between two answers that are routinely interchanged.
Module summary
- m ü + c u̇ + k u = −m üg, with u the displacement RELATIVE to the ground
- The ground acceleration acts as an effective force −m üg — mass is the multiplier
- Relative displacement damages the structure; absolute acceleration damages its contents
- The spring and damper connect the mass to the GROUND, so they see relative motion
- For MDOF the effective force is −Mι üg, with ι the influence vector
- A rigid structure rides with the ground; a very flexible one is left behind
- Amplitude, duration and frequency content are three separate properties of a record
- Every processed record has been filtered, and the corner frequency is a processing choice
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Practice
A 12-storey building has a total seismic mass of 9 600 tonnes. At an instant the ground acceleration is 2.5 m/s². What is the total effective earthquake force, in MN?
Check yourself
A structure's relative displacement peaks at 95 mm, and the record's peak ground displacement is 110 mm. What is the peak absolute displacement?
Check yourself
Two records have the same peak ground acceleration. One lasts 8 s and the other 40 s. For which type of structure does the difference matter most?
Practice
Ground motion is harmonic at 25 mm and 1 Hz. A structure has a natural frequency of 0.5 Hz and 5% damping. What is its relative displacement amplitude, in mm?