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Capacity Spectrum Formula

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

C s = \frac{32 \cdot S \cdot {L s}^{4}}{10^{7} \cdot I s}

C_s - Capacity Spectrum?S - Spacing of Secondary Members?L_s - Length of Secondary Member?I_s - Moment of Inertia of Secondary Member?

Capacity Spectrum Example

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With units

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Here is how the Capacity Spectrum equation looks like with Values.

Here is how the Capacity Spectrum equation looks like with Units.

Here is how the Capacity Spectrum equation looks like.

5.5556 = \frac{32 \cdot 2.5 \cdot {0.5}^{4}}{10^{7} \cdot 90}

5.5556 = \frac{32 \cdot 2.5m \cdot {0.5m}^{4}}{10^{7} \cdot 90mm⁴/mm}

5.5556 = \frac{32 \cdot 2.5 \cdot {0.5}^{4}}{10^{7} \cdot 90}

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Capacity Spectrum Solution

Follow our step by step solution on how to calculate Capacity Spectrum?

FIRST Step Consider the formula

C s = \frac{32 \cdot S \cdot {L s}^{4}}{10^{7} \cdot I s}

Next Step Substitute values of Variables

∴

C s = \frac{32 \cdot 2.5m \cdot {0.5m}^{4}}{10^{7} \cdot 90mm⁴/mm}

Next Step Convert Units

∴

C s = \frac{32 \cdot 2.5m \cdot {0.5m}^{4}}{10^{7} \cdot 9E-8m⁴/m}

Next Step Prepare to Evaluate

∴

C s = \frac{32 \cdot 2.5 \cdot {0.5}^{4}}{10^{7} \cdot 9E-8}

Next Step Evaluate

∴

C s = 5.55555555555556

LAST Step Rounding Answer

∴

C s = 5.5556

Capacity Spectrum Formula Elements

Variables

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.

Symbol: C_s

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Capacity Spectrum

Spacing of Secondary Members

Spacing of Secondary Members can be described as the space in between the secondary members.

Symbol: S

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Spacing of Secondary Members

Length of Secondary Member

Length of Secondary Member can be described as the measurement of the secondary element in length.

Symbol: L_s

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Secondary Member

Moment of Inertia of Secondary Member

Moment of Inertia of Secondary Member can be described as the quantity expressed by the body resisting angular acceleration.

Symbol: I_s

Measurement: Moment of Inertia per Unit LengthUnit: mm⁴/mm

Note: Value can be positive or negative.

Formulas to find Moment of Inertia of Secondary Member

Other formulas in Ponding Considerations in Buildings category

Go Collapse Prevention Level

C p = \frac{32 \cdot {L p}^{4} \cdot L s}{10^{7} \cdot I p}

Go Length of Secondary Member using Collapse Prevention Level

L s = \frac{C p \cdot 10^{7} \cdot I p}{32 \cdot {L p}^{4}}

Go Length of Primary Member using Collapse Prevention Level

L p = {(\frac{C p \cdot 10^{7} \cdot I p}{32 \cdot L s})}^{\frac{1}{4}}

Go Length of Secondary Member given Capacity Spectrum

L s = {(C s \cdot 10^{7} \cdot \frac{I s}{32 \cdot S})}^{\frac{1}{4}}

How to Evaluate Capacity Spectrum?

Capacity Spectrum evaluator uses Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member) to evaluate 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 evaluate Capacity Spectrum using this online evaluator? To use this online evaluator 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.

FAQs on Capacity Spectrum

What is the formula to find Capacity Spectrum?

The formula of Capacity Spectrum is expressed as Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member). Here is an example- 5.555556 = (32*2.5*0.5^4)/(10^7*9E-08).

How to calculate Capacity Spectrum?

With Spacing of Secondary Members (S), Length of Secondary Member (L_s) & Moment of Inertia of Secondary Member (I_s) we can find Capacity Spectrum using the formula - Capacity Spectrum = (32*Spacing of Secondary Members*Length of Secondary Member^4)/(10^7*Moment of Inertia of Secondary Member).

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Capacity Spectrum Formula

Capacity Spectrum Example

Capacity Spectrum Solution

Capacity Spectrum Formula Elements

Other formulas in Ponding Considerations in Buildings category

How to Evaluate Capacity Spectrum?

FAQs on Capacity Spectrum

Variable Name