Analysis & loading · Seismic & dynamic
Earthquake: equivalent static storey forces (AS 1170.4) calculator
Fundamental period, spectral shape factor for the site class, base shear and its distribution to storeys with the height exponent k, plus storey shears and the overturning moment.
Standard: AS 1170.4-2007 (Amdt 2) · T1 = 1.25kt·hn^0.75 · C(T) = kpZ·Ch(T) · V = C(T)·Sp/μ·W · storey distribution kF,i
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Probability factor kp (1/500 → 1.0) | 1/500 (1.0) | |
| Hazard factor Z (e.g. Gold Coast, Brisbane 0.05) | 0.05 | |
| Site sub-soil class | Ce shallow soil | |
| Period coefficient kt | 0.075 concrete moment frame | |
| Sp/μ | 0.38 limited ductile (μ = 2, Sp = 0.77) | |
| Storeys from the base: height above base (m), seismic weight G + ψcQ (kN) | 3.5, 2800 7.0, 2800 10.5, 2800 14.0, 2200 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Structure height hn | 14.00 | m |
| Total seismic weight | 10,600 | kN |
| Period T1 = 1.25kt·hn^0.75 | 0.679 | s |
| kpZ (minimum 0.08) | 0.080 | |
| Spectral shape factor Ch(T1) | 1.84 | |
| Elastic site coefficient C(T1) = kpZ·Ch | 0.147 | |
| Design action coefficient Cd = C·Sp/μ | 0.056 | |
| Base shear V = Cd·W | 593.6 | kN |
| Height exponent k | 1.09 | |
| Overturning moment ΣF·h | 6,115 | kNm |
| Force at top level | 211.3 | kN |
| V/W | 0.056 | |
| Result: base shear V | 593.6 | kN |
- ✓ Height within the equivalent static method limit (≤ 50 m)
Method, formulas and assumptions
- Structure height hn = MAX([t.h]) = 14 m
- Total seismic weight = SUM([t.W]) = 10600 kN
- Period T1 = 1.25kt·hn^0.75 = 1.25*0.075*14^0.75 = 0.67853 s
- kpZ (minimum 0.08) = MAX(1*0.05,0.08) = 0.08
- Spectral shape factor Ch(T1) = CHOOSE(3,IF(0.67853<0.1,0.8+15.5*0.67853,IF(0.67853<=1.5,MIN(0.704/0.67853,2.35),1.056/0.67853^2)),IF(0.67853<0.1,1+19.4*0.67853,IF(0.67853<=1.5,MIN(0.88/0.67853,2.94),1.32/0.67853^2)),IF(0.67853<0.1,1.3+23.8*0.67853,IF(0.67853<=1.5,MIN(1.25/0.67853,3.68),1.874/0.67853^2)),IF(0.67853<0.1,1.1+25.8*0.67853,IF(0.67853<=1.5,MIN(1.98/0.67853,3.68),2.97/0.67853^2)),IF(0.67853<0.1,1.1+25.8*0.67853,IF(0.67853<=1.5,MIN(3.08/0.67853,3.68),4.62/0.67853^2))) = 1.8422
- Elastic site coefficient C(T1) = kpZ·Ch = 0.08*1.8422 = 0.14738
- Design action coefficient Cd = C·Sp/μ = 0.14738*0.38 = 0.056004
- Base shear V = Cd·W = 0.056004*10600 = 593.64 kN
- Height exponent k = IF(0.67853<=0.5,1,IF(0.67853>=2.5,2,1+(0.67853-0.5)/2)) = 1.0893
- Overturning moment ΣF·h = SUM([s.Mi]) = 6114.5 kNm
- Force at top level = INDEX([s.F],COUNT([s.F])) = 211.28 kN
- V/W = 593.64/10600 = 0.056004
- Result: base shear V = 593.64 = 593.64 kN
- Check the Earthquake Design Category (Table 2.1) first: EDC I structures may use the simple 0.1W provision; EDC III needs dynamic analysis.
- Ch(T) formulae as in the site's AS 1170.4 response spectrum demo. Apply the storey forces at the centre of mass ± 0.1b accidental eccentricity.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.