Seismic Response Coefficient given Fundamental Period Solution

STEP 0: Pre-Calculation Summary
Formula Used
Seismic Response Coefficient = 1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Fundamental Period^(2/3))
Cs = 1.2*Cv/(R*T^(2/3))
This formula uses 4 Variables
Variables Used
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.
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.
Fundamental Period - (Measured in Second) - Fundamental Period is the time taken for one complete oscillation (back-and-forth) by the building.
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
Fundamental Period: 0.17 Second --> 0.17 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cs = 1.2*Cv/(R*T^(2/3)) --> 1.2*0.54/(6*0.17^(2/3))
Evaluating ... ...
Cs = 0.351931230429107
STEP 3: Convert Result to Output's Unit
0.351931230429107 --> No Conversion Required
FINAL ANSWER
0.351931230429107 0.351931 <-- Seismic Response Coefficient
(Calculation completed in 00.004 seconds)

Credits

Created by Mridul Sharma
Indian Institute of Information Technology (IIIT), Bhopal
Mridul Sharma has created this Calculator and 200+ more calculators!
Verified by Rithik Agrawal
National Institute of Technology Karnataka (NITK), Surathkal
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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
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 Fundamental Period
Go Seismic Response Coefficient = 1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Fundamental Period^(2/3))
Seismic Coefficient for Velocity Dependent Structures
Go Seismic Coefficient for Velocity Dependent = Seismic Response Coefficient*Response Modification Factor /2.5
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
Lateral Force
Go Lateral Force = Lateral Seismic Force/Vertical Distribution Factor
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
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 Eccentrically Braced 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 for Steel Frames
Go Fundamental Period = 0.035*Height of Building^(3/4)
Fundamental Period for Reinforced Concrete Frames
Go Fundamental Period = 0.03*Height of Building^(3/4)

Seismic Response Coefficient given Fundamental Period Formula

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

What is the Response Coefficient?

The response modification coefficient (R) is used to calculate the reduced design seismic forces of a structural system, and the deflection amplification factor (Cd) to convert elastic lateral displacements to total lateral displacements.

How to Calculate Seismic Response Coefficient given Fundamental Period?

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

How to calculate Seismic Response Coefficient given Fundamental Period using this online calculator? To use this online calculator for Seismic Response Coefficient given Fundamental Period, enter Seismic Coefficient for Short Period Structures (Cv), Response Modification Factor (R) & Fundamental Period (T) and hit the calculate button. Here is how the Seismic Response Coefficient given Fundamental Period calculation can be explained with given input values -> 0.351931 = 1.2*0.54/(6*0.17^(2/3)).

FAQ

What is Seismic Response Coefficient given Fundamental Period?
The Seismic response Coefficient given Fundamental Period formula calculates the seismic response coefficient when we have a prior info of the fundamental period and is represented as Cs = 1.2*Cv/(R*T^(2/3)) or Seismic Response Coefficient = 1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Fundamental Period^(2/3)). 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 & Fundamental Period is the time taken for one complete oscillation (back-and-forth) by the building.
How to calculate Seismic Response Coefficient given Fundamental Period?
The Seismic response Coefficient given Fundamental Period formula calculates the seismic response coefficient when we have a prior info of the fundamental period is calculated using Seismic Response Coefficient = 1.2*Seismic Coefficient for Short Period Structures/(Response Modification Factor*Fundamental Period^(2/3)). To calculate Seismic Response Coefficient given Fundamental Period, you need Seismic Coefficient for Short Period Structures (Cv), Response Modification Factor (R) & Fundamental Period (T). With our tool, you need to enter the respective value for Seismic Coefficient for Short Period Structures, Response Modification Factor & Fundamental Period 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 Seismic Response Coefficient?
In this formula, Seismic Response Coefficient uses Seismic Coefficient for Short Period Structures, Response Modification Factor & Fundamental Period. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Seismic Response Coefficient = Lateral Force/Total Dead Load
  • Seismic Response Coefficient = 2.5*Seismic Coefficient for Velocity Dependent/Response Modification Factor
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