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Average Strain under Tension Formula

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Average Strain describes the response of a solid to the application of a normal force induced at the selected level. Check FAQs

ε m = ε 1 - \frac{W cr \cdot (h Crack - x) \cdot (D CC - x)}{3 \cdot E s \cdot A s \cdot (L eff - x)}

ε_m - Average Strain?ε₁ - Strain at Selected Level?W_cr - Crack Width?h_Crack - Height of Crack?x - Depth of Neutral Axis?D_CC - Distance from Compression to Crack Width?E_s - Modulus of Elasticity of Steel Reinforcement?A_s - Area of Reinforcement?L_eff - Effective Length?

Average Strain under Tension Example

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With units

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Here is how the Average Strain under Tension equation looks like with Values.

Here is how the Average Strain under Tension equation looks like with Units.

Here is how the Average Strain under Tension equation looks like.

0.0005 = 0.0005 - \frac{0.49 \cdot (12.01 - 50) \cdot (4.5 - 50)}{3 \cdot 200000 \cdot 500 \cdot (50.25 - 50)}

0.0005 = 0.0005 - \frac{0.49mm \cdot (12.01m - 50mm) \cdot (4.5m - 50mm)}{3 \cdot 200000MPa \cdot 500mm² \cdot (50.25m - 50mm)}

0.0005 = 0.0005 - \frac{0.49 \cdot (12.01 - 50) \cdot (4.5 - 50)}{3 \cdot 200000 \cdot 500 \cdot (50.25 - 50)}

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Average Strain under Tension Solution

Follow our step by step solution on how to calculate Average Strain under Tension?

FIRST Step Consider the formula

ε m = ε 1 - \frac{W cr \cdot (h Crack - x) \cdot (D CC - x)}{3 \cdot E s \cdot A s \cdot (L eff - x)}

Next Step Substitute values of Variables

∴

ε m = 0.0005 - \frac{0.49mm \cdot (12.01m - 50mm) \cdot (4.5m - 50mm)}{3 \cdot 200000MPa \cdot 500mm² \cdot (50.25m - 50mm)}

Next Step Convert Units

∴

ε m = 0.0005 - \frac{0.0005m \cdot (12.01m - 0.05m) \cdot (4.5m - 0.05m)}{3 \cdot 2E+11Pa \cdot 0.0005m² \cdot (50.25m - 0.05m)}

Next Step Prepare to Evaluate

∴

ε m = 0.0005 - \frac{0.0005 \cdot (12.01 - 0.05) \cdot (4.5 - 0.05)}{3 \cdot 2E+11 \cdot 0.0005 \cdot (50.25 - 0.05)}

Next Step Evaluate

∴

ε m = 0.000513999998268341

LAST Step Rounding Answer

∴

ε m = 0.0005

Average Strain under Tension Formula Elements

Variables

Average Strain

Average Strain describes the response of a solid to the application of a normal force induced at the selected level.

Symbol: ε_m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Average Strain

Open Variable

Strain at Selected Level

Strain at Selected Level is described as the strain induced in a rectangular zone which were selected.

Symbol: ε₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Strain at Selected Level

Open Variable

Crack Width

Crack Width describes the length of the crack in an element.

Symbol: W_cr

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Crack Width

Open Variable

Height of Crack

Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress.

Symbol: h_Crack

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Crack

Open Variable

Depth of Neutral Axis

Depth of Neutral Axis is defined as the distance from the top of the section to its neutral axis.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Neutral Axis

Open Variable

Distance from Compression to Crack Width

Distance from Compression to Crack Width can be described as the length from the compression level to the crack width.

Symbol: D_CC

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance from Compression to Crack Width

Open Variable

Modulus of Elasticity of Steel Reinforcement

Modulus of Elasticity of Steel Reinforcement is a measure of its stiffness.

Symbol: E_s

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Steel Reinforcement

Open Variable

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.

Formulas to find Area of Reinforcement

Open Variable

Effective Length

The Effective Length is the length which resists against buckling.

Symbol: L_eff

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Effective Length

Open Variable

Other formulas in Evaluation of Average Strain and Neutral Axis Depth category

Go Strain at Selected Level given Average Strain under Tension

ε 1 = ε m + \frac{W cr \cdot (h Crack - x) \cdot (D CC - x)}{3 \cdot E s \cdot A s \cdot (L eff - x)}

Go Height of Crack Width at Soffit given Average Strain

h Crack = (\frac{(ε 1 - ε m) \cdot (3 \cdot E s \cdot A s \cdot (d - x))}{W cr \cdot (D CC - x)}) + x

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How to Evaluate Average Strain under Tension?

Average Strain under Tension evaluator uses Average Strain = Strain at Selected Level-(Crack Width*(Height of Crack-Depth of Neutral Axis)*(Distance from Compression to Crack Width-Depth of Neutral Axis))/(3*Modulus of Elasticity of Steel Reinforcement*Area of Reinforcement*(Effective Length-Depth of Neutral Axis)) to evaluate the Average Strain, The Average Strain under Tension is defined as a relative displacement. Initial, The definition of strain is simple but at the same time is non-unique. Average Strain is denoted by ε_m symbol.

How to evaluate Average Strain under Tension using this online evaluator? To use this online evaluator for Average Strain under Tension, enter Strain at Selected Level (ε₁), Crack Width (W_cr), Height of Crack (h_Crack), Depth of Neutral Axis (x), Distance from Compression to Crack Width (D_CC), Modulus of Elasticity of Steel Reinforcement (E_s), Area of Reinforcement (A_s) & Effective Length (L_eff) and hit the calculate button.

FAQs on Average Strain under Tension

What is the formula to find Average Strain under Tension?

The formula of Average Strain under Tension is expressed as Average Strain = Strain at Selected Level-(Crack Width*(Height of Crack-Depth of Neutral Axis)*(Distance from Compression to Crack Width-Depth of Neutral Axis))/(3*Modulus of Elasticity of Steel Reinforcement*Area of Reinforcement*(Effective Length-Depth of Neutral Axis)). Here is an example- 0.000514 = 0.000514-(0.00049*(12.01-0.05)*(4.5-0.05))/(3*200000000000*0.0005*(50.25-0.05)).

How to calculate Average Strain under Tension?

With Strain at Selected Level (ε₁), Crack Width (W_cr), Height of Crack (h_Crack), Depth of Neutral Axis (x), Distance from Compression to Crack Width (D_CC), Modulus of Elasticity of Steel Reinforcement (E_s), Area of Reinforcement (A_s) & Effective Length (L_eff) we can find Average Strain under Tension using the formula - Average Strain = Strain at Selected Level-(Crack Width*(Height of Crack-Depth of Neutral Axis)*(Distance from Compression to Crack Width-Depth of Neutral Axis))/(3*Modulus of Elasticity of Steel Reinforcement*Area of Reinforcement*(Effective Length-Depth of Neutral Axis)).

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