Capacity Spectrum Calculator

✖Spacing of Secondary Members can be described as the space in between the secondary members.ⓘ Spacing of Secondary Members [S]			+10% -10%
✖Length of Secondary Member can be described as the measurement of the secondary element in length.ⓘ Length of Secondary Member [L_s]			+10% -10%
✖Moment of Inertia of Secondary Member can be described as the quantity expressed by the body resisting angular acceleration.ⓘ Moment of Inertia of Secondary Member [I_s]			+10% -10%

✖Capacity Spectrum can be defined as the capacity curve transformed from shear force vs. roof displacement coordinates into spectral acceleration vs. spectral displacement coordinates.ⓘ Capacity Spectrum [C_s]

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Formula

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Capacity Spectrum

Formula

`"C"_{"s"} = (32*"S"*"L"_{"s"}^4)/(10^7*"I"_{"s"})`

Example

`"5.555556"=(32*"2.5m"*("0.5m")^4)/(10^7*"90mm⁴/mm")`

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Download Bearing, Stresses, Plate Girders & Ponding Considerations Formulas PDF

Capacity Spectrum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member)
C_s = (32*S*L_s^4)/(10^7*I_s)
This formula uses 4 Variables

Variables Used

Capacity Spectrum - Capacity Spectrum can be defined as the capacity curve transformed from shear force vs. roof displacement coordinates into spectral acceleration vs. spectral displacement coordinates.
Spacing of Secondary Members - (Measured in Meter) - Spacing of Secondary Members can be described as the space in between the secondary members.
Length of Secondary Member - (Measured in Meter) - Length of Secondary Member can be described as the measurement of the secondary element in length.
Moment of Inertia of Secondary Member - (Measured in Meter⁴ per Meter) - Moment of Inertia of Secondary Member can be described as the quantity expressed by the body resisting angular acceleration.

STEP 1: Convert Input(s) to Base Unit

Spacing of Secondary Members: 2.5 Meter --> 2.5 Meter No Conversion Required
Length of Secondary Member: 0.5 Meter --> 0.5 Meter No Conversion Required
Moment of Inertia of Secondary Member: 90 Millimeter⁴ per Millimeter --> 9E-08 Meter⁴ per Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_s = (32*S*L_s^4)/(10^7*I_s) --> (32*2.5*0.5^4)/(10^7*9E-08)

Evaluating ... ...

C_s = 5.55555555555556

STEP 3: Convert Result to Output's Unit

5.55555555555556 --> No Conversion Required

FINAL ANSWER

5.55555555555556 ≈ 5.555556 <-- Capacity Spectrum

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Design of Steel Structures » Bearing, Stresses, Plate Girders & Ponding Considerations » Ponding Considerations in Buildings » Capacity Spectrum

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Created by M Naveen

National Institute of Technology (NIT), Warangal

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Verified by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< 7 Ponding Considerations in Buildings Calculators

Length of Primary Member using Collapse Prevention Level

Go Length of Primary Member = ((Collapse Prevention Level*10^7*Moment of Inertia of Primary Member)/(32*Length of Secondary Member))^(1/4)

Length of Secondary Member given Capacity Spectrum

Go Length of Secondary Member = (Capacity Spectrum*10^7*Moment of Inertia of Secondary Member/(32*Spacing of Secondary Members))^(1/4)

Moment of Inertia of Primary Member using Collapse Prevention Level

Go Moment of Inertia of Primary Member = (32*Length of Primary Member^4*Length of Secondary Member)/(10^7*Collapse Prevention Level)

Length of Secondary Member using Collapse Prevention Level

Go Length of Secondary Member = (Collapse Prevention Level*10^7*Moment of Inertia of Primary Member)/(32*Length of Primary Member^4)

Collapse Prevention Level

Go Collapse Prevention Level = (32*Length of Primary Member^4*Length of Secondary Member)/(10^7*Moment of Inertia of Primary Member)

Moment of Inertia of Secondary Member given Capacity Spectrum

Go Moment of Inertia of Secondary Member = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Capacity Spectrum)

Capacity Spectrum

Go Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member)

Capacity Spectrum Formula

Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member)
C_s = (32*S*L_s^4)/(10^7*I_s)

What is Capacity Spectrum?

The Capacity Spectrum can be defined as the capacity curve transformed from shear force vs. roof displacement coordinates into spectral acceleration vs. spectral displacement coordinates.

What is Collapse Prevention Level?

The Collapse Prevention Level is defined as the building performance level consisting of the structural collapse prevention level with no consideration of nonstructural vulnerabilities, except that parapets and heavy appendages are rehabilitated.

How to Calculate Capacity Spectrum?

Capacity Spectrum calculator uses Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member) to calculate the Capacity Spectrum, The Capacity Spectrum formula is defined as the capacity curve transformed from shear force vs. roof displacement coordinates into spectral acceleration vs. spectral displacement coordinates. Capacity Spectrum is denoted by C_s symbol.

How to calculate Capacity Spectrum using this online calculator? To use this online calculator for Capacity Spectrum, enter Spacing of Secondary Members (S), Length of Secondary Member (L_s) & Moment of Inertia of Secondary Member (I_s) and hit the calculate button. Here is how the Capacity Spectrum calculation can be explained with given input values -> 5.555556 = (32*2.5*0.5^4)/(10^7*9E-08).

FAQ

What is Capacity Spectrum?

The Capacity Spectrum formula is defined as the capacity curve transformed from shear force vs. roof displacement coordinates into spectral acceleration vs. spectral displacement coordinates and is represented as C_s = (32*S*L_s^4)/(10^7*I_s) or Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member). Spacing of Secondary Members can be described as the space in between the secondary members, Length of Secondary Member can be described as the measurement of the secondary element in length & Moment of Inertia of Secondary Member can be described as the quantity expressed by the body resisting angular acceleration.

How to calculate Capacity Spectrum?

The Capacity Spectrum formula is defined as the capacity curve transformed from shear force vs. roof displacement coordinates into spectral acceleration vs. spectral displacement coordinates is calculated using Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member). To calculate Capacity Spectrum, you need Spacing of Secondary Members (S), Length of Secondary Member (L_s) & Moment of Inertia of Secondary Member (I_s). With our tool, you need to enter the respective value for Spacing of Secondary Members, Length of Secondary Member & Moment of Inertia of Secondary Member and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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