NSR-10 design spectrum
The elastic acceleration spectrum of section A.2.6, for your municipality, your soil and your use.
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The NSR-10 design spectrum gives the acceleration Sa, as a fraction of gravity, for which a building is designed according to its vibration period T. It is built from the municipality's Aa and Av, the soil profile's Fa and Fv coefficients and the occupancy group's importance factor I: it equals 2.5·Aa·Fa·I up to TC and then decays as 1.2·Av·Fv·I/T (A.2.6).
- Code
- NSR-10, A.2.6
- Damping
- 5 % of critical
- Units
- Fraction of g
Barranquilla (Atlántico), soil profile D, occupancy group I
- Fa
- 1.60
- Fv
- 2.40
- I
- 1.00
- T0
- 0.15 s
- TC
- 0.72 s
- TL
- 5.76 s
- Sa max.
- 0.400 g
- Ta (15 m)
- 0.54 s
- Sa(Ta)
- 0.400 g
How is the NSR-10 design spectrum calculated?
The curve has three branches, separated by two periods that depend only on Aa, Av, Fa and Fv. The importance factor I scales the whole curve.
| Branch | Equation | Reference |
|---|---|---|
| Short periods, T ≤ TC | Sa = 2.5·Aa·Fa·I | A.2.6-3 |
| Intermediate periods, TC < T ≤ TL | Sa = 1.2·Av·Fv·I / T | A.2.6-1 |
| Long periods, T > TL | Sa = 1.2·Av·Fv·TL·I / T² | A.2.6-5 |
| End of the plateau | TC = 0.48·Av·Fv / (Aa·Fa) | A.2.6-2 |
| Start of the long-period branch | TL = 2.4·Fv | A.2.6-4 |
| Higher modes in dynamic analysis, T < T0 | Sa = 2.5·Aa·Fa·I·(0.4 + 0.6·T/T0), with T0 = 0.1·Av·Fv / (Aa·Fa) | A.2.6-6 and A.2.6-7 |
What soil profile does my lot have?
The geotechnical engineer defines it from the top 30 m of ground, by the shear wave velocity vs, the blow count N or the undrained shear strength su (A.2.4.4). First profile F is ruled out, then 3 m or more of soft clay are looked for, which make the profile E (A.2.4.5). We explain it in soil profile in the NSR-10.
| Profile | Description | Criterion, in the top 30 m |
|---|---|---|
| A | Competent rock | vs ≥ 1,500 m/s |
| B | Medium-stiffness rock | 760 ≤ vs < 1,500 m/s |
| C | Very dense soil or soft rock | 360 ≤ vs < 760 m/s, or N ≥ 50, or su ≥ 100 kPa |
| D | Stiff soil | 180 ≤ vs < 360 m/s, or 15 ≤ N < 50, or 50 ≤ su < 100 kPa |
| E | Soft soil | vs < 180 m/s, or more than 3 m of soft clay (PI > 20, w ≥ 40 %, su < 50 kPa) |
| F | Require site evaluation | Liquefiable or collapsible soils, peats and organic clays, very high plasticity clays, more than 36 m of soft to medium clay |
What are the values of Fa and Fv?
They amplify the rock spectrum to account for the soil: Fa at short periods and Fv at intermediate periods. For intermediate values of Aa or Av, interpolate linearly, as this tool does (A.2.4.5.5 and A.2.4.5.6).
| Fa | Aa ≤ 0.1 | 0.2 | 0.3 | 0.4 | ≥ 0.5 |
|---|---|---|---|---|---|
| A | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |
| B | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |
| C | 1.2 | 1.2 | 1.1 | 1.0 | 1.0 |
| D | 1.6 | 1.4 | 1.2 | 1.1 | 1.0 |
| E | 2.5 | 1.7 | 1.2 | 0.9 | 0.9 |
| Fv | Av ≤ 0.1 | 0.2 | 0.3 | 0.4 | ≥ 0.5 |
|---|---|---|---|---|---|
| A | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 |
| B | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |
| C | 1.7 | 1.6 | 1.5 | 1.4 | 1.3 |
| D | 2.4 | 2.0 | 1.8 | 1.6 | 1.5 |
| E | 3.5 | 3.2 | 2.8 | 2.4 | 2.4 |
Which importance factor should I use?
The one for the building's occupancy group (table A.2.5-1). We explain it in occupancy groups.
| Occupancy group | Examples (A.2.5.1) | I |
|---|---|---|
| IV, essential facilities | Hospitals and clinics with surgery, intensive care or emergency services; airports; telecommunications centers; emergency shelters | 1.50 |
| III, community services | Fire stations, police, civil defense; daycare centers, schools and universities | 1.25 |
| II, special occupancy | Halls for more than 200 people, shopping centers with more than 500 m² per floor, government buildings | 1.10 |
| I, normal occupancy | All others, such as housing and offices | 1.00 |
What does this tool not include?
The spectrum is elastic: the design forces of the members are reduced by the energy dissipation capacity coefficient R = φa·φp·φr·R0, which depends on the structural system and its irregularities (A.3.3). The coefficients Fa and Fv do not include hillside effects (A.2.4.5.7), and where the municipality has adopted a seismic microzonation study, its regulations replace sections A.2.4 and A.2.6 (A.2.9.1). The period Ta is an estimate: the model's period may not exceed Cu·Ta, with Cu = 1.75 − 1.2·Av·Fv and not less than 1.2 (A.4.2.1).
Frequently asked questions
What is the design spectrum?
It is the curve that gives the maximum horizontal design acceleration, as a fraction of gravity, of a single-degree-of-freedom system according to its vibration period T, for 5 % damping. The NSR-10 defines it in section A.2.6, and the seismic design forces are calculated from it.
What is TC in the NSR-10 spectrum?
It is the period where the plateau ends: TC = 0.48·Av·Fv/(Aa·Fa) (equation A.2.6-2). For shorter periods, Sa stays at 2.5·Aa·Fa·I; for longer ones, it decays with 1/T. In Barranquilla, with soil profile D, TC = 0.72 s.
How is the approximate period Ta calculated?
With Ta = Ct·h^α, where h is the height in meters from the base to the top floor, and Ct and α depend on the structural system: 0.047 and 0.9 for concrete frames, 0.072 and 0.8 for steel frames, and 0.049 and 0.75 for wall systems and all others (table A.4.2-1).
What if my soil is type F?
The NSR-10 gives no Fa or Fv for that profile: it requires a site-specific seismic study, by the geotechnical engineer, with a wave amplification analysis (A.2.10).
Can this spectrum be used for a dynamic analysis?
Yes: it is the same spectrum as section A.2.6. For modes other than the fundamental one with periods shorter than T0, the code allows the ramp of equation A.2.6-7 to be used (A.2.6.1.3), which the chart shows dotted.
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