Area of Concrete Section given Prestress Drop Solution

STEP 0: Pre-Calculation Summary
Formula Used
Concrete Occupied Area = Modular Ratio for Elastic Shortening*Prestress Force/(Prestress Drop)
Ac = mElastic*PB/(Δfp)
This formula uses 4 Variables
Variables Used
Concrete Occupied Area - (Measured in Square Meter) - Concrete Occupied Area is area of concrete in design of section.
Modular Ratio for Elastic Shortening - Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material.
Prestress Force - (Measured in Kilonewton) - Prestress Force is the force acted on the tendon B if multiple tendons are used in a section.
Prestress Drop - (Measured in Newton per Square Millimeter) - Prestress Drop is the drop in applied prestress force due to strain in tendons.
STEP 1: Convert Input(s) to Base Unit
Modular Ratio for Elastic Shortening: 0.6 --> No Conversion Required
Prestress Force: 200 Kilonewton --> 200 Kilonewton No Conversion Required
Prestress Drop: 10 Megapascal --> 10 Newton per Square Millimeter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ac = mElastic*PB/(Δfp) --> 0.6*200/(10)
Evaluating ... ...
Ac = 12
STEP 3: Convert Result to Output's Unit
12 Square Meter --> No Conversion Required
FINAL ANSWER
12 Square Meter <-- Concrete Occupied Area
(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad
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13 Post-Tensioned Members Calculators

Variation of Eccentricity on Tendon A
Go Eccentricity Variation of Tendon A = Eccentricity at End for A+(4*Change in Eccentricity at A*Distance from Left End/Length of Beam in Prestress)*(1-(Distance from Left End/Length of Beam in Prestress))
Variation of Eccentricity of Tendon B
Go Eccentricity Variation of Tendon B = Eccentricity at End for B+(4*Change in Eccentricity B*Distance from Left End/Length of Beam in Prestress)*(1-(Distance from Left End/Length of Beam in Prestress))
Prestress Drop given Stress in concrete at Same Level due to Prestressing Force
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*Stress in Concrete Section/Modulus of Elasticity Concrete
Prestress Drop given Strain due to Bending and Compression in Two Parabolic Tendons
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*(Strain due to Compression+Strain due to Bending)
Area of Concrete Section given Prestress Drop
Go Concrete Occupied Area = Modular Ratio for Elastic Shortening*Prestress Force/(Prestress Drop)
Average Stress for Parabolic Tendons
Go Average Stress = Stress at End+2/3*(Stress at Midspan-Stress at End)
Change in Eccentricity of Tendon A due to Parabolic Shape
Go Change in Eccentricity at A = Eccentricity at Midspan for A-Eccentricity at End for A
Stress in Concrete given Prestress Drop
Go Stress in Concrete Section = Prestress Drop/Modular Ratio for Elastic Shortening
Prestress Drop given Modular Ratio
Go Prestress Drop = Modular Ratio for Elastic Shortening*Stress in Concrete Section
Component of Strain at Level of First Tendon due to Bending
Go Strain due to Bending = Change in Length Dimension/Length of Beam in Prestress
Change in Eccentricity of Tendon B due to Parabolic Shape
Go Change in Eccentricity B = Eccentricity at Midspan B-Eccentricity at End for B
Prestress Drop
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*Change in Strain
Prestress Drop when Two parabolic Tendons are Incorporated
Go Prestress Drop = Modulus of Elasticity of Steel Reinforcement*Concrete Strain

Area of Concrete Section given Prestress Drop Formula

Concrete Occupied Area = Modular Ratio for Elastic Shortening*Prestress Force/(Prestress Drop)
Ac = mElastic*PB/(Δfp)

What is Concrete Shrinkage?

The volumetric contraction of concrete specimen due to the loss of free water through
evaporation, carbonation or continued cement hydration, in the absence of load is called shrinkage.

How to Calculate Area of Concrete Section given Prestress Drop?

Area of Concrete Section given Prestress Drop calculator uses Concrete Occupied Area = Modular Ratio for Elastic Shortening*Prestress Force/(Prestress Drop) to calculate the Concrete Occupied Area, The Area of Concrete Section given Prestress Drop is defined as area of concrete section affected by prestress reduction due to relaxation or other factors, impacting structural performance. Concrete Occupied Area is denoted by Ac symbol.

How to calculate Area of Concrete Section given Prestress Drop using this online calculator? To use this online calculator for Area of Concrete Section given Prestress Drop, enter Modular Ratio for Elastic Shortening (mElastic), Prestress Force (PB) & Prestress Drop (Δfp) and hit the calculate button. Here is how the Area of Concrete Section given Prestress Drop calculation can be explained with given input values -> 12 = 0.6*200000/(10000000).

FAQ

What is Area of Concrete Section given Prestress Drop?
The Area of Concrete Section given Prestress Drop is defined as area of concrete section affected by prestress reduction due to relaxation or other factors, impacting structural performance and is represented as Ac = mElastic*PB/(Δfp) or Concrete Occupied Area = Modular Ratio for Elastic Shortening*Prestress Force/(Prestress Drop). Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material, Prestress Force is the force acted on the tendon B if multiple tendons are used in a section & Prestress Drop is the drop in applied prestress force due to strain in tendons.
How to calculate Area of Concrete Section given Prestress Drop?
The Area of Concrete Section given Prestress Drop is defined as area of concrete section affected by prestress reduction due to relaxation or other factors, impacting structural performance is calculated using Concrete Occupied Area = Modular Ratio for Elastic Shortening*Prestress Force/(Prestress Drop). To calculate Area of Concrete Section given Prestress Drop, you need Modular Ratio for Elastic Shortening (mElastic), Prestress Force (PB) & Prestress Drop (Δfp). With our tool, you need to enter the respective value for Modular Ratio for Elastic Shortening, Prestress Force & Prestress Drop 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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