Fundamental Period given Seismic Response Coefficient Calculator

✖The Seismic Coefficient for Short Period Structures is for acceleration dependent structures.ⓘ Seismic Coefficient for Short Period Structures [C_v]			+10% -10%
✖Response Modification Factor is the ratio of base shear that would be developed in the lateral load resisting system to the design base shear.ⓘ Response Modification Factor [R]			+10% -10%
✖Seismic Response Coefficient calculates reduced design seismic forces of structural system and deflection amplification factor to convert elastic lateral displacements to total lateral displacements.ⓘ Seismic Response Coefficient [C_s]			+10% -10%

✖Fundamental Period is the time taken for one complete oscillation (back-and-forth) by the building.ⓘ Fundamental Period given Seismic Response Coefficient [T]

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Formula

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Fundamental Period given Seismic Response Coefficient

Formula

`"T" = (1.2*"C"_{"v"}/("R"*"C"_{"s"}))^(3/2)`

Example

`"0.171409s"=(1.2*"0.54"/("6"*"0.35"))^(3/2)`

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Fundamental Period given Seismic Response Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fundamental Period = (1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Seismic Response Coefficient))^(3/2)
T = (1.2*C_v/(R*C_s))^(3/2)
This formula uses 4 Variables

Variables Used

Fundamental Period - (Measured in Second) - Fundamental Period is the time taken for one complete oscillation (back-and-forth) by the building.
Seismic Coefficient for Short Period Structures - The Seismic Coefficient for Short Period Structures is for acceleration dependent structures.
Response Modification Factor - Response Modification Factor is the ratio of base shear that would be developed in the lateral load resisting system to the design base shear.
Seismic Response Coefficient - Seismic Response Coefficient calculates reduced design seismic forces of structural system and deflection amplification factor to convert elastic lateral displacements to total lateral displacements.

STEP 1: Convert Input(s) to Base Unit

Seismic Coefficient for Short Period Structures: 0.54 --> No Conversion Required
Response Modification Factor: 6 --> No Conversion Required
Seismic Response Coefficient: 0.35 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = (1.2*C_v/(R*C_s))^(3/2) --> (1.2*0.54/(6*0.35))^(3/2)

Evaluating ... ...

T = 0.171408978472175

STEP 3: Convert Result to Output's Unit

0.171408978472175 Second --> No Conversion Required

FINAL ANSWER

0.171408978472175 ≈ 0.171409 Second <-- Fundamental Period

(Calculation completed in 00.004 seconds)

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has created this Calculator and 200+ more calculators!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

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< 21 Seismic Loads Calculators

Fundamental Period given Seismic Response Coefficient

Go Fundamental Period = (1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Seismic Response Coefficient))^(3/2)

Seismic Coefficient for Short Period Structures

Go Seismic Coefficient for Short Period Structures = (Seismic Response Coefficient*(Response Modification Factor*Fundamental Period^(2/3)))/1.2

Seismic Response Coefficient given Fundamental Period

Go Seismic Response Coefficient = 1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Fundamental Period^(2/3))

Response Modification Factor

Go Response Modification Factor = 1.2*Seismic Coefficient for Short Period Structures/(Seismic Response Coefficient*Fundamental Period^(2/3))

Seismic Response Coefficient given Seismic Coefficient for Velocity Dependent Structures

Go Seismic Response Coefficient = 2.5*Seismic Coefficient for Velocity Dependent/Response Modification Factor

Response Modification Factor by Velocity Dependent Structures

Go Response Modification Factor = 2.5*Seismic Coefficient for Velocity Dependent/Seismic Response Coefficient

Seismic Coefficient for Velocity Dependent Structures

Go Seismic Coefficient for Velocity Dependent = Seismic Response Coefficient*Response Modification Factor/2.5

Vertical Distribution Factor given Lateral Force

Go Vertical Distribution Factor = Lateral Seismic Force/Lateral Force

Lateral Seismic Force

Go Lateral Seismic Force = Vertical Distribution Factor*Lateral Force

Lateral Force

Go Lateral Force = Lateral Seismic Force/Vertical Distribution Factor

Total Lateral Force Acting in Direction of each of Principal Axis

Go Lateral Force = Seismic Response Coefficient*Total Dead Load

Seismic Response Coefficient given Base Shear

Go Seismic Response Coefficient = Lateral Force/Total Dead Load

Total Dead Load given Base Shear

Go Total Dead Load = Lateral Force/Seismic Response Coefficient

Building Height for Steel Frame given Fundamental Period

Go Height of Building = (Fundamental Period/0.035)^(4/3)

Building Height for Steel Eccentrically Braced Frames given Fundamental Period

Go Height of Building = (Fundamental Period/0.03)^(4/3)

Building Height for Reinforced Concrete Frames given Fundamental Period

Go Height of Building = (Fundamental Period/0.03)^(4/3)

Building Height for other Buildings given Fundamental Period

Go Height of Building = (Fundamental Period/0.02)^(4/3)

Fundamental Period for Steel Frames

Go Fundamental Period = 0.035*Height of Building^(3/4)

Fundamental Period for Steel Eccentrically Braced Frames

Go Fundamental Period = 0.03*Height of Building^(3/4)

Fundamental Period for Reinforced Concrete Frames

Go Fundamental Period = 0.03*Height of Building^(3/4)

Fundamental Period for other Buildings

Go Fundamental Period = 0.02*Height of Building^(3/4)

Fundamental Period given Seismic Response Coefficient Formula

Fundamental Period = (1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Seismic Response Coefficient))^(3/2)
T = (1.2*C_v/(R*C_s))^(3/2)

What is the Fundamental Period of a Structure?

Depending on mass and stiffness, the fundamental period is a global characteristic describing the behaviour of building under seismic loads. Usually, they are height-depend relationships setting up considering the total height of buildings or their number of storeys.

How to Calculate Fundamental Period given Seismic Response Coefficient?

Fundamental Period given Seismic Response Coefficient calculator uses Fundamental Period = (1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Seismic Response Coefficient))^(3/2) to calculate the Fundamental Period, The Fundamental Period given Seismic Response Coefficient is defined as the fundamental period when we have a prior info of seismic response coefficient. Fundamental Period is denoted by T symbol.

How to calculate Fundamental Period given Seismic Response Coefficient using this online calculator? To use this online calculator for Fundamental Period given Seismic Response Coefficient, enter Seismic Coefficient for Short Period Structures (C_v), Response Modification Factor (R) & Seismic Response Coefficient (C_s) and hit the calculate button. Here is how the Fundamental Period given Seismic Response Coefficient calculation can be explained with given input values -> 0.171409 = (1.2*0.54/(6*0.35))^(3/2).

FAQ

What is Fundamental Period given Seismic Response Coefficient?

The Fundamental Period given Seismic Response Coefficient is defined as the fundamental period when we have a prior info of seismic response coefficient and is represented as T = (1.2*C_v/(R*C_s))^(3/2) or Fundamental Period = (1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Seismic Response Coefficient))^(3/2). The Seismic Coefficient for Short Period Structures is for acceleration dependent structures, Response Modification Factor is the ratio of base shear that would be developed in the lateral load resisting system to the design base shear & Seismic Response Coefficient calculates reduced design seismic forces of structural system and deflection amplification factor to convert elastic lateral displacements to total lateral displacements.

How to calculate Fundamental Period given Seismic Response Coefficient?

The Fundamental Period given Seismic Response Coefficient is defined as the fundamental period when we have a prior info of seismic response coefficient is calculated using Fundamental Period = (1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Seismic Response Coefficient))^(3/2). To calculate Fundamental Period given Seismic Response Coefficient, you need Seismic Coefficient for Short Period Structures (C_v), Response Modification Factor (R) & Seismic Response Coefficient (C_s). With our tool, you need to enter the respective value for Seismic Coefficient for Short Period Structures, Response Modification Factor & Seismic Response Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Fundamental Period?

In this formula, Fundamental Period uses Seismic Coefficient for Short Period Structures, Response Modification Factor & Seismic Response Coefficient. We can use 4 other way(s) to calculate the same, which is/are as follows -

Fundamental Period = 0.035*Height of Building^(3/4)
Fundamental Period = 0.03*Height of Building^(3/4)
Fundamental Period = 0.03*Height of Building^(3/4)
Fundamental Period = 0.02*Height of Building^(3/4)

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