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Transformed Area of Partially Prestressed Members Formula

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The Transformed Area of Prestressed Member is the area of the member when steel is substituted by an equivalent area of concrete. Check FAQs

A t = A T + (\frac{E s}{E c}) \cdot A s + (\frac{E P}{E c}) \cdot As

A_t - Transformed Area of Prestressed Member?A_T - Transformed Area of Concrete?E_s - Modulus of Elasticity of Steel?E_c - Modulus of Elasticity of Concrete?A_s - Area of Reinforcement?E_P - Modulus of Elasticity of Prestressing Steel?As - Area of Prestressing Steel?

Transformed Area of Partially Prestressed Members Example

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Here is how the Transformed Area of Partially Prestressed Members equation looks like with Values.

Here is how the Transformed Area of Partially Prestressed Members equation looks like with Units.

Here is how the Transformed Area of Partially Prestressed Members equation looks like.

4500.1414 = 1000 + (\frac{210000}{30000}) \cdot 500 + (\frac{210}{30000}) \cdot 20.2

4500.1414mm² = 1000mm² + (\frac{210000MPa}{30000MPa}) \cdot 500mm² + (\frac{210MPa}{30000MPa}) \cdot 20.2mm²

4500.1414 = 1000 + (\frac{210000}{30000}) \cdot 500 + (\frac{210}{30000}) \cdot 20.2

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Home » Engineering » Civil » Structural Engineering » Transformed Area of Partially Prestressed Members

Transformed Area of Partially Prestressed Members Solution

Follow our step by step solution on how to calculate Transformed Area of Partially Prestressed Members?

FIRST Step Consider the formula

A t = A T + (\frac{E s}{E c}) \cdot A s + (\frac{E P}{E c}) \cdot As

Next Step Substitute values of Variables

∴

A t = 1000mm² + (\frac{210000MPa}{30000MPa}) \cdot 500mm² + (\frac{210MPa}{30000MPa}) \cdot 20.2mm²

Next Step Convert Units

∴

A t = 0.001m² + (\frac{2.1E+11Pa}{3E+10Pa}) \cdot 0.0005m² + (\frac{2.1E+8Pa}{3E+10Pa}) \cdot 2E-5m²

Next Step Prepare to Evaluate

∴

A t = 0.001 + (\frac{2.1E+11}{3E+10}) \cdot 0.0005 + (\frac{2.1E+8}{3E+10}) \cdot 2E-5

Next Step Evaluate

∴

A t = 0.0045001414m²

LAST Step Convert to Output's Unit

∴

A t = 4500.1414mm²

Transformed Area of Partially Prestressed Members Formula Elements

Variables

Transformed Area of Prestressed Member

The Transformed Area of Prestressed Member is the area of the member when steel is substituted by an equivalent area of concrete.

Symbol: A_t

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Transformed Area of Concrete

Transformed Area of Concrete is the modified or altered surface of a concrete structure resulting from changes or treatments.

Symbol: A_T

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Modulus of Elasticity of Steel

The Modulus of Elasticity of Steel is a characteristic that assesses steel's resistance to deformation under load. It is the ratio of stress to strain.

Symbol: E_s

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Modulus of Elasticity of Concrete

The modulus of elasticity of concrete is a characteristic that assesses concrete resistance to deformation under load. It is the ratio of stress to strain.

Symbol: E_c

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Area of Reinforcement

Area of Reinforcement is the area of steel, used in a prestressed section, which is not prestressed or prestressing force is not applied.

Symbol: A_s

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Modulus of Elasticity of Prestressing Steel

The modulus of elasticity of prestressing steel is a characteristic that assesses prestressing steel's resistance to deformation under load. It is the ratio of stress to strain.

Symbol: E_P

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Area of Prestressing Steel

Area of Prestressing Steel is the total cross sectional area of tendons.

Symbol: As

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Credits

Creator Image

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Formula and 500+ more formulas!

Verifier Image

Verified by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has verified this Formula and 900+ more formulas!

Other formulas in Geometrics Properties category

Go Area of Non-Prestressed Reinforcement in Partially Prestressed Members

A s = (A t - A T - (\frac{E P}{E c}) \cdot As) \cdot (\frac{E c}{E s})

Go Area of Prestressing Tendons about Non-Prestressed Reinforcements and Transformed Section

As = (A t - A T - (\frac{E s}{E c}) \cdot A s) \cdot (\frac{E c}{E P})

How to Evaluate Transformed Area of Partially Prestressed Members?

Transformed Area of Partially Prestressed Members evaluator uses Transformed Area of Prestressed Member = Transformed Area of Concrete+(Modulus of Elasticity of Steel/Modulus of Elasticity of Concrete)*Area of Reinforcement+(Modulus of Elasticity of Prestressing Steel/Modulus of Elasticity of Concrete)*Area of Prestressing Steel to evaluate the Transformed Area of Prestressed Member, The Transformed Area of Partially Prestressed Members is defined as the area of transformed section when the member is made by prestressing tendons, non-prestressed steel and concrete. Transformed Area of Prestressed Member is denoted by A_t symbol.

How to evaluate Transformed Area of Partially Prestressed Members using this online evaluator? To use this online evaluator for Transformed Area of Partially Prestressed Members, enter Transformed Area of Concrete (A_T), Modulus of Elasticity of Steel (E_s), Modulus of Elasticity of Concrete (E_c), Area of Reinforcement (A_s), Modulus of Elasticity of Prestressing Steel (E_P) & Area of Prestressing Steel (As) and hit the calculate button.

FAQs on Transformed Area of Partially Prestressed Members

What is the formula to find Transformed Area of Partially Prestressed Members?

The formula of Transformed Area of Partially Prestressed Members is expressed as Transformed Area of Prestressed Member = Transformed Area of Concrete+(Modulus of Elasticity of Steel/Modulus of Elasticity of Concrete)*Area of Reinforcement+(Modulus of Elasticity of Prestressing Steel/Modulus of Elasticity of Concrete)*Area of Prestressing Steel. Here is an example- 4.5E+9 = 0.001+(210000000000/30000000000)*0.0005+(210000000/30000000000)*2.02E-05.

How to calculate Transformed Area of Partially Prestressed Members?

With Transformed Area of Concrete (A_T), Modulus of Elasticity of Steel (E_s), Modulus of Elasticity of Concrete (E_c), Area of Reinforcement (A_s), Modulus of Elasticity of Prestressing Steel (E_P) & Area of Prestressing Steel (As) we can find Transformed Area of Partially Prestressed Members using the formula - Transformed Area of Prestressed Member = Transformed Area of Concrete+(Modulus of Elasticity of Steel/Modulus of Elasticity of Concrete)*Area of Reinforcement+(Modulus of Elasticity of Prestressing Steel/Modulus of Elasticity of Concrete)*Area of Prestressing Steel.

Can the Transformed Area of Partially Prestressed Members be negative?

No, the Transformed Area of Partially Prestressed Members, measured in Area cannot be negative.

Which unit is used to measure Transformed Area of Partially Prestressed Members?

Transformed Area of Partially Prestressed Members is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Transformed Area of Partially Prestressed Members can be measured.

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