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Transformed Area of Prestressed Member given Gross Area of Member Calculator

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Loss due to Anchorage Slip, Friction Loss and General Geometric Properties Loss due to Elastic Shortening

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✖The Gross Area of Cross-Section is defined as the total area of a section perpendicular to the direction of the load.ⓘ Gross Area of Cross-Section [A_g]			+10% -10%
✖The modular ratio 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.ⓘ Modular Ratio [m]			+10% -10%
✖Area of Prestressing Steel is the total cross sectional area of tendons.ⓘ Area of Prestressing Steel [As]			+10% -10%

✖The Transformed Area of Prestressed Member is the area of the member when steel is substituted by an equivalent area of concrete.ⓘ Transformed Area of Prestressed Member given Gross Area of Member [A_t]

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Transformed Area of Prestressed Member given Gross Area of Member Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transformed Area of Prestressed Member = Gross Area of Cross-Section+(Modular Ratio-1)*Area of Prestressing Steel
A_t = A_g+(m-1)*As
This formula uses 4 Variables

Variables Used

Transformed Area of Prestressed Member - (Measured in Square Meter) - The Transformed Area of Prestressed Member is the area of the member when steel is substituted by an equivalent area of concrete.
Gross Area of Cross-Section - (Measured in Square Meter) - The Gross Area of Cross-Section is defined as the total area of a section perpendicular to the direction of the load.
Modular Ratio - The modular ratio 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.
Area of Prestressing Steel - (Measured in Square Meter) - Area of Prestressing Steel is the total cross sectional area of tendons.

STEP 1: Convert Input(s) to Base Unit

Gross Area of Cross-Section: 1020 Square Millimeter --> 0.00102 Square Meter (Check conversion here)
Modular Ratio: 175 --> No Conversion Required
Area of Prestressing Steel: 20.2 Square Millimeter --> 2.02E-05 Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_t = A_g+(m-1)*As --> 0.00102+(175-1)*2.02E-05

Evaluating ... ...

A_t = 0.0045348

STEP 3: Convert Result to Output's Unit

0.0045348 Square Meter -->4534.8 Square Millimeter (Check conversion here)

FINAL ANSWER

4534.8 Square Millimeter <-- Transformed Area of Prestressed Member

(Calculation completed in 00.004 seconds)

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< General Geometric Properties Calculators

Transformed Area of Prestressed Member given Gross Area of Member

LaTeX Go Transformed Area of Prestressed Member = Gross Area of Cross-Section+(Modular Ratio-1)*Area of Prestressing Steel

Area of Concrete Section when Transformed Area is Calculated

LaTeX Go Transformed Area of Concrete = Transformed Area of Prestressed Member-(Modular Ratio*Area of Prestressing Steel)

Area of Prestressing Steel given Transformed Area

LaTeX Go Area of Prestressing Steel = (Transformed Area of Prestressed Member-Transformed Area of Concrete)/Modular Ratio

Transformed Area of Prestressed Member

LaTeX Go Transformed Area of Prestressed Member = Transformed Area of Concrete+(Modular Ratio*Area of Prestressing Steel)

Transformed Area of Prestressed Member given Gross Area of Member Formula

LaTeX Go

Transformed Area of Prestressed Member = Gross Area of Cross-Section+(Modular Ratio-1)*Area of Prestressing Steel
A_t = A_g+(m-1)*As

What is Loss of Prestress & What are the Losses in Prestressing Concrete?

A reduction in initial pre-stress resulting from the combined effect of creep, shrinkage or elastic shortening of the concrete, relaxation of the reinforcing steel, frictional losses resulting from the curvature of the draped tendons and slippage at the anchorage.
In a prestressed concrete beam, the loss is due to the following:
1. Elastic shortening
2. Shrinkage of concrete
3. Creep of concrete
4. Frictional loss
5. Relaxation of steel
6. Anchorage take-up

What are the Classification of Prestressing Losses?

The losses are broadly classified into two groups, immediate and time-dependent.
The losses due to elastic shortening of the member, friction at the tendon-concrete interface and slip of the anchorage are the immediate losses.
The time-dependent losses occur during the service life of the prestressed member. The losses due to the shrinkage and creep of the concrete and the relaxation of the steel are time-dependent losses.

How to Calculate Transformed Area of Prestressed Member given Gross Area of Member?

Transformed Area of Prestressed Member given Gross Area of Member calculator uses Transformed Area of Prestressed Member = Gross Area of Cross-Section+(Modular Ratio-1)*Area of Prestressing Steel to calculate the Transformed Area of Prestressed Member, The Transformed Area of Prestressed Member given Gross Area of Member is defined as the equation of area of transformed section when gross area(Ac+Ap) is used. Transformed Area of Prestressed Member is denoted by A_t symbol.

How to calculate Transformed Area of Prestressed Member given Gross Area of Member using this online calculator? To use this online calculator for Transformed Area of Prestressed Member given Gross Area of Member, enter Gross Area of Cross-Section (A_g), Modular Ratio (m) & Area of Prestressing Steel (As) and hit the calculate button. Here is how the Transformed Area of Prestressed Member given Gross Area of Member calculation can be explained with given input values -> 4.5E+9 = 0.00102+(175-1)*2.02E-05.

FAQ

What is Transformed Area of Prestressed Member given Gross Area of Member?

The Transformed Area of Prestressed Member given Gross Area of Member is defined as the equation of area of transformed section when gross area(Ac+Ap) is used and is represented as A_t = A_g+(m-1)*As or Transformed Area of Prestressed Member = Gross Area of Cross-Section+(Modular Ratio-1)*Area of Prestressing Steel. The Gross Area of Cross-Section is defined as the total area of a section perpendicular to the direction of the load, The modular ratio 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 & Area of Prestressing Steel is the total cross sectional area of tendons.

How to calculate Transformed Area of Prestressed Member given Gross Area of Member?

The Transformed Area of Prestressed Member given Gross Area of Member is defined as the equation of area of transformed section when gross area(Ac+Ap) is used is calculated using Transformed Area of Prestressed Member = Gross Area of Cross-Section+(Modular Ratio-1)*Area of Prestressing Steel. To calculate Transformed Area of Prestressed Member given Gross Area of Member, you need Gross Area of Cross-Section (A_g), Modular Ratio (m) & Area of Prestressing Steel (As). With our tool, you need to enter the respective value for Gross Area of Cross-Section, Modular Ratio & Area of Prestressing Steel 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 Transformed Area of Prestressed Member?

In this formula, Transformed Area of Prestressed Member uses Gross Area of Cross-Section, Modular Ratio & Area of Prestressing Steel. We can use 1 other way(s) to calculate the same, which is/are as follows -

Transformed Area of Prestressed Member = Transformed Area of Concrete+(Modular Ratio*Area of Prestressing Steel)

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