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Resulting Stress due to Moment and Prestress and Eccentric Strands Formula

GoUniform Compressive Stress due to Prestress Formula

GoResulting Stress due to Moment and Prestressing Force Formula

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Compressive Stress in Prestress is the force that is responsible for the deformation of the material such that the volume of the material reduces. Check FAQs

σ c = \frac{F}{A} + (M \cdot \frac{y}{I a}) + (F \cdot e \cdot \frac{y}{I a})

σ_c - Compressive Stress in Prestress?F - Prestressing Force?A - Area of Beam Section?M - External Moment?y - Distance from Centroidal Axis?I_a - Moment of Inertia of Section?e - Distance from Centroidal Geometric Axis?

Resulting Stress due to Moment and Prestress and Eccentric Strands Example

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Here is how the Resulting Stress due to Moment and Prestress and Eccentric Strands equation looks like with Values.

Here is how the Resulting Stress due to Moment and Prestress and Eccentric Strands equation looks like with Units.

Here is how the Resulting Stress due to Moment and Prestress and Eccentric Strands equation looks like.

2.0008 = \frac{400}{200} + (20 \cdot \frac{30}{720000}) + (400 \cdot 5.01 \cdot \frac{30}{720000})

2.0008Pa = \frac{400kN}{200mm²} + (20kN*m \cdot \frac{30mm}{720000mm⁴}) + (400kN \cdot 5.01mm \cdot \frac{30mm}{720000mm⁴})

2.0008 = \frac{400}{200} + (20 \cdot \frac{30}{720000}) + (400 \cdot 5.01 \cdot \frac{30}{720000})

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Resulting Stress due to Moment and Prestress and Eccentric Strands Solution

Follow our step by step solution on how to calculate Resulting Stress due to Moment and Prestress and Eccentric Strands?

FIRST Step Consider the formula

σ c = \frac{F}{A} + (M \cdot \frac{y}{I a}) + (F \cdot e \cdot \frac{y}{I a})

Next Step Substitute values of Variables

∴

σ c = \frac{400kN}{200mm²} + (20kN*m \cdot \frac{30mm}{720000mm⁴}) + (400kN \cdot 5.01mm \cdot \frac{30mm}{720000mm⁴})

Next Step Convert Units

∴

σ c = \frac{400kN}{200mm²} + (20000N*m \cdot \frac{0.03m}{720000mm⁴}) + (400kN \cdot 0.005m \cdot \frac{0.03m}{720000mm⁴})

Next Step Prepare to Evaluate

∴

σ c = \frac{400}{200} + (20000 \cdot \frac{0.03}{720000}) + (400 \cdot 0.005 \cdot \frac{0.03}{720000})

Next Step Evaluate

∴

σ c = 2.00083341683333Pa

LAST Step Rounding Answer

∴

σ c = 2.0008Pa

Resulting Stress due to Moment and Prestress and Eccentric Strands Formula Elements

Variables

Compressive Stress in Prestress

Compressive Stress in Prestress is the force that is responsible for the deformation of the material such that the volume of the material reduces.

Symbol: σ_c

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Compressive Stress in Prestress

Prestressing Force

Prestressing Force is the force internally applied to the prestressed concrete section.

Symbol: F

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Prestressing Force

Area of Beam Section

Area of Beam Section here refers to the area of cross section of the concrete section where the prestressing force was applied.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Area of Beam Section

External Moment

External Moment is the moment applied externally on the concrete section.

Symbol: M

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find External Moment

Distance from Centroidal Axis

Distance from Centroidal Axis defines the distance from the extreme fiber of the concrete section to centroidal axis of the section.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Centroidal Axis

Moment of Inertia of Section

Moment of Inertia of section is defined as a property of a two-dimensional plane shape that characterizes its deflection under loading.

Symbol: I_a

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Section

Distance from Centroidal Geometric Axis

Distance from Centroidal Geometric Axis is the distance at which the prestressing force is acted on section when the tendons are placed in some other point above or below the centroidal axis.

Symbol: e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Centroidal Geometric Axis

Other Formulas to find Compressive Stress in Prestress

Go Uniform Compressive Stress due to Prestress

σ c = \frac{F}{A}

Go Resulting Stress due to Moment and Prestressing Force

σ c = \frac{F}{A} + (M b \cdot \frac{y}{I a})

Other formulas in General Principles of Prestressed Concrete category

Go Prestressing Force given Compressive Stress

F = A \cdot σ c

Go Cross Sectional Area given Compressive Stress

A = \frac{F}{σ c}

How to Evaluate Resulting Stress due to Moment and Prestress and Eccentric Strands?

Resulting Stress due to Moment and Prestress and Eccentric Strands evaluator uses Compressive Stress in Prestress = Prestressing Force/Area of Beam Section+(External Moment*Distance from Centroidal Axis/Moment of Inertia of Section)+(Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section) to evaluate the Compressive Stress in Prestress, The Resulting Stress due to Moment and Prestress and Eccentric Strands is defined as the overall stress caused on the prestressed section due to all three effects, say, axial, flexural and eccentric loads. Since the moment can be compressive and tensile, the sign conventions need to be used. Compressive Stress in Prestress is denoted by σ_c symbol.

How to evaluate Resulting Stress due to Moment and Prestress and Eccentric Strands using this online evaluator? To use this online evaluator for Resulting Stress due to Moment and Prestress and Eccentric Strands, enter Prestressing Force (F), Area of Beam Section (A), External Moment (M), Distance from Centroidal Axis (y), Moment of Inertia of Section (I_a) & Distance from Centroidal Geometric Axis (e) and hit the calculate button.

FAQs on Resulting Stress due to Moment and Prestress and Eccentric Strands

What is the formula to find Resulting Stress due to Moment and Prestress and Eccentric Strands?

The formula of Resulting Stress due to Moment and Prestress and Eccentric Strands is expressed as Compressive Stress in Prestress = Prestressing Force/Area of Beam Section+(External Moment*Distance from Centroidal Axis/Moment of Inertia of Section)+(Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section). Here is an example- 2.000833 = 400000/0.0002+(20000*0.03/7.2E-07)+(400000*0.00501*0.03/7.2E-07).

How to calculate Resulting Stress due to Moment and Prestress and Eccentric Strands?

With Prestressing Force (F), Area of Beam Section (A), External Moment (M), Distance from Centroidal Axis (y), Moment of Inertia of Section (I_a) & Distance from Centroidal Geometric Axis (e) we can find Resulting Stress due to Moment and Prestress and Eccentric Strands using the formula - Compressive Stress in Prestress = Prestressing Force/Area of Beam Section+(External Moment*Distance from Centroidal Axis/Moment of Inertia of Section)+(Prestressing Force*Distance from Centroidal Geometric Axis*Distance from Centroidal Axis/Moment of Inertia of Section).

What are the other ways to Calculate Compressive Stress in Prestress?

Here are the different ways to Calculate Compressive Stress in Prestress-

Compressive Stress in Prestress=Prestressing Force/Area of Beam Section
Compressive Stress in Prestress=Prestressing Force/Area of Beam Section+(Bending Moment in Prestress*Distance from Centroidal Axis/Moment of Inertia of Section)

Can the Resulting Stress due to Moment and Prestress and Eccentric Strands be negative?

No, the Resulting Stress due to Moment and Prestress and Eccentric Strands, measured in Pressure cannot be negative.

Which unit is used to measure Resulting Stress due to Moment and Prestress and Eccentric Strands?

Resulting Stress due to Moment and Prestress and Eccentric Strands is usually measured using the Pascal[Pa] for Pressure. Kilopascal[Pa], Bar[Pa], Pound Per Square Inch[Pa] are the few other units in which Resulting Stress due to Moment and Prestress and Eccentric Strands can be measured.

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Resulting Stress due to Moment and Prestress and Eccentric Strands Formula

​GoUniform Compressive Stress due to Prestress Formula

​GoResulting Stress due to Moment and Prestressing Force Formula

Resulting Stress due to Moment and Prestress and Eccentric Strands Example

Resulting Stress due to Moment and Prestress and Eccentric Strands Solution

Resulting Stress due to Moment and Prestress and Eccentric Strands Formula Elements

Other Formulas to find Compressive Stress in Prestress

Other formulas in General Principles of Prestressed Concrete category

How to Evaluate Resulting Stress due to Moment and Prestress and Eccentric Strands?

FAQs on Resulting Stress due to Moment and Prestress and Eccentric Strands

Variable Name

GoUniform Compressive Stress due to Prestress Formula

GoResulting Stress due to Moment and Prestressing Force Formula