Earthquake damage to buildings
Earthquake waves shake the ground horizontally and vertically. The building mass resists, creating an inertia force F = m·a on every floor. Typical damage:
- Soft storey: an open floor (parking, shop) is much weaker than the floors above, so the drift concentrates there and the floor collapses.
- Short column: a column held by a half-height wall is stiff and attracts a huge force; it fails in shear.
- Pounding: neighbouring buildings sway out of step and hit each other.
- Torsion: an uneven plan (L-shaped, stair at one corner) makes the building twist.
- Weak joints and brittle materials: unreinforced masonry, poorly tied roofs, badly detailed beam-column joints.
- Soil: soft or sandy wet soil can liquefy and tilt a building.
Overview of seismic design
Aim of design: a small quake causes no damage, a moderate quake only repairable damage, and the strongest expected quake must not cause collapse, so people can escape.
Lateral load: base shear V = C × W, where W is the building weight and C a seismic coefficient from the zone, soil, building type and period. The force is shared among floors in proportion to weight × height (an inverted triangle).
- Strength and stiffness: shear walls, braced frames, rigid frames to keep drift small.
- Ductility: steel bars, confined concrete and strong-column weak-beam design let the building bend without breaking.
- Regularity: simple, symmetric shape; equal stiffness on all floors; no heavy top.
- Load path: floors tied to walls, walls tied to the foundation.
- Isolation and damping: base isolators let the ground slide under the building; dampers soak up energy.
Natural period of a frame building is about T = 0.1 × (number of storeys) seconds. When the ground shakes near this period, the building sways the most (resonance).
Seismic retrofit
Retrofit strengthens an existing building without rebuilding it. First an engineer checks the weak points (soft storey, weak joints, poor soil, no ties). Then choose:
- Add shear walls or steel braces to make weak floors stiff.
- Jacketing: wrap columns with concrete, steel or carbon-fibre sheets so they become ductile.
- Tie roof and floors to the walls; add bands and stitching to masonry.
- Strengthen footings, or fit base isolators under the building.
- Remove heavy parapets, tanks or chimneys at the top; fill gaps between neighbours.
Retrofit costs far less than rebuilding and is most useful for schools, hospitals and old homes.
Key formulas and definitions
- F = m × a (inertia force on a floor)
- Base shear V = C × W
- Floor force share ∝ weight × height (4 equal floors: 10 %, 20 %, 30 %, 40 %)
- Storey drift ratio = relative displacement ÷ storey height
- Natural period T ≈ 0.1 × n seconds (n = storeys)
- Soft storey: stiffness k small gives drift = V / k large
Worked examples
1. A floor has a mass of 50 tonnes. The ground acceleration is 0.3 g. Find the inertia force (g = 9.81 m/s²).
m = 50 000 kg. a = 0.3 × 9.81 = 2.94 m/s². F = m a = 50 000 × 2.94 = 147 000 N ≈ 147 kN.
2. A 4-floor building (equal floors) weighs W = 4000 kN and C = 0.1. Find the base shear and the force on each floor.
V = 0.1 × 4000 = 400 kN. Shares 10, 20, 30, 40 %: floor forces 40, 80, 120, 160 kN (bottom to top).
3. Floor 2 moves 24 mm relative to floor 1. The storey height is 3 m. Find the drift ratio.
Drift ratio = 24 / 3000 = 0.008 = 0.8 %. Many codes keep this under about 1 to 2 %.
4. A ground storey has 1/4 the stiffness of the others. The same shear gives 0.8 % drift in a normal storey. What drift will it get?
Drift = V / k, so with k four times smaller the drift is 4 times larger: 0.8 × 4 = 3.2 %. That is a danger sign.
5. Estimate the natural period of a 4-storey and a 12-storey frame building.
T ≈ 0.1 n: 4 storeys gives 0.4 s; 12 storeys gives 1.2 s. Taller buildings sway more slowly.
6. Bracing makes a storey 2.5 times stiffer. The drift was 0.81 %. Find the new drift.
New drift = 0.81 / 2.5 = 0.32 %.
Common mistakes
- Thinking the building is pushed by the earthquake from outside. The force is its own inertia: heavier means more force.
- Believing a stronger building alone is enough. It also needs ductility and a regular shape.
- Leaving the ground floor open and weak for parking without extra walls or bracing (soft storey).
- Ignoring the roof: heavy water tanks high up add a lot of force.