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Strain at Selected Level given Average Strain under Tension Formula

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

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)}

ε₁ - Strain at Selected Level?ε_m - Average Strain?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?

Strain at Selected Level given Average Strain under Tension Example

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Here is how the Strain at Selected Level given Average Strain under Tension equation looks like with Values.

Here is how the Strain at Selected Level given Average Strain under Tension equation looks like with Units.

Here is how the Strain at Selected Level given 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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Strain at Selected Level given Average Strain under Tension Solution

Follow our step by step solution on how to calculate Strain at Selected Level given Average Strain under Tension?

FIRST Step Consider the formula

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)}

Next Step Substitute values of Variables

∴

ε 1 = 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 1 = 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 1 = 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 1 = 0.000500000001731659

LAST Step Rounding Answer

∴

ε 1 = 0.0005

Strain at Selected Level given Average Strain under Tension Formula Elements

Variables

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.

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.

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.

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.

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.

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.

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.

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.

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.

Credits

Created by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has created this Formula and 500+ more formulas!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Formula and 1700+ more formulas!

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

Go Average Strain under Tension

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)}

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

How to Evaluate Strain at Selected Level given Average Strain under Tension?

Strain at Selected Level given Average Strain under Tension evaluator uses Strain at Selected Level = Average Strain+(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 Strain at Selected Level, The Strain at Selected Level given Average Strain under Tension is defined as relative displacement. Initial, definition of strain is simple but at same time is non-unique. Strain at Selected Level is denoted by ε₁ symbol.

How to evaluate Strain at Selected Level given Average Strain under Tension using this online evaluator? To use this online evaluator for Strain at Selected Level given Average Strain under Tension, enter Average Strain (ε_m), 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 Strain at Selected Level given Average Strain under Tension

What is the formula to find Strain at Selected Level given Average Strain under Tension?

The formula of Strain at Selected Level given Average Strain under Tension is expressed as Strain at Selected Level = Average Strain+(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- 0.0005 = 0.0005+(0.00049*(12.01-0.05)*(4.5-0.05))/(3*200000000000*0.0005*(50.25-0.05)).

How to calculate Strain at Selected Level given Average Strain under Tension?

With Average Strain (ε_m), 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 Strain at Selected Level given Average Strain under Tension using the formula - Strain at Selected Level = Average Strain+(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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Strain at Selected Level given Average Strain under Tension Formula

Strain at Selected Level given Average Strain under Tension Example

Strain at Selected Level given Average Strain under Tension Solution

Strain at Selected Level given Average Strain under Tension Formula Elements

Credits

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

How to Evaluate Strain at Selected Level given Average Strain under Tension?

FAQs on Strain at Selected Level given Average Strain under Tension

Variable Name