Strain at Selected Level given Average Strain under Tension Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
ε1 = εm+(Wcr*(hCrack-x)*(DCC-x))/(3*Es*As*(Leff-x))
This formula uses 9 Variables
Variables Used
Strain at Selected Level - Strain at Selected Level is described as the strain induced in a rectangular zone which were selected.
Average Strain - Average Strain describes the response of a solid to the application of a normal force induced at the selected level.
Crack Width - (Measured in Meter) - Crack Width describes the length of the crack in an element.
Height of Crack - (Measured in Meter) - Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress.
Depth of Neutral Axis - (Measured in Meter) - Depth of Neutral Axis is defined as the distance from the top of the section to its neutral axis.
Distance from Compression to Crack Width - (Measured in Meter) - Distance from Compression to Crack Width can be described as the length from the compression level to the crack width.
Modulus of Elasticity of Steel Reinforcement - (Measured in Pascal) - Modulus of Elasticity of Steel Reinforcement is a measure of its stiffness.
Area of Reinforcement - (Measured in Square Meter) - Area of Reinforcement is the area of steel, used in a prestressed section, which is not prestressed or prestressing force is not applied.
Effective Length - (Measured in Meter) - The Effective Length is the length which resists against buckling.
STEP 1: Convert Input(s) to Base Unit
Average Strain: 0.0005 --> No Conversion Required
Crack Width: 0.49 Millimeter --> 0.00049 Meter (Check conversion here)
Height of Crack: 12.01 Meter --> 12.01 Meter No Conversion Required
Depth of Neutral Axis: 50 Millimeter --> 0.05 Meter (Check conversion here)
Distance from Compression to Crack Width: 4.5 Meter --> 4.5 Meter No Conversion Required
Modulus of Elasticity of Steel Reinforcement: 200000 Megapascal --> 200000000000 Pascal (Check conversion here)
Area of Reinforcement: 500 Square Millimeter --> 0.0005 Square Meter (Check conversion here)
Effective Length: 50.25 Meter --> 50.25 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ε1 = εm+(Wcr*(hCrack-x)*(DCC-x))/(3*Es*As*(Leff-x)) --> 0.0005+(0.00049*(12.01-0.05)*(4.5-0.05))/(3*200000000000*0.0005*(50.25-0.05))
Evaluating ... ...
ε1 = 0.000500000001731659
STEP 3: Convert Result to Output's Unit
0.000500000001731659 --> No Conversion Required
FINAL ANSWER
0.000500000001731659 0.0005 <-- Strain at Selected Level
(Calculation completed in 00.020 seconds)

Credits

Created by M Naveen
National Institute of Technology (NIT), Warangal
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NSS College of Engineering (NSSCE), Palakkad
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13 Evaluation of Average Strain and Neutral Axis Depth Calculators

Height of Crack Width at Soffit given Average Strain
Go Height of Crack = (((Strain at Selected Level-Average Strain)*(3*Modulus of Elasticity of Steel Reinforcement*Area of Reinforcement*(Effective Depth of Reinforcement-Depth of Neutral Axis)))/(Crack Width*(Distance from Compression to Crack Width-Depth of Neutral Axis)))+Depth of Neutral Axis
Average Strain under Tension
Go 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))
Strain at Selected Level given Average Strain under Tension
Go 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))
Modulus of Elasticity of Concrete given Couple Force of Cross-Section
Go Modulus of Elasticity of Concrete = Couple Force/(0.5*Strain in Concrete*Depth of Neutral Axis*Crack Width)
Depth of Neutral Axis given Couple Force of Cross Section
Go Depth of Neutral Axis = Couple Force/(0.5*Modulus of Elasticity of Concrete*Strain in Concrete*Crack Width)
Strain given Couple Force of Cross Section
Go Strain in Concrete = Couple Force/(0.5*Modulus of Elasticity of Concrete*Depth of Neutral Axis*Crack Width)
Couple Force of Cross Section
Go Couple Force = 0.5*Modulus of Elasticity of Concrete*Strain in Concrete*Depth of Neutral Axis*Crack Width
Width of Section given Couple Force of Cross Section
Go Crack Width = Couple Force/(0.5*Modulus of Elasticity of Concrete*Strain*Depth of Neutral Axis)
Strain in Longitudinal Reinforcement given Tension Force
Go Strain in Longitudinal Reinforcement = Tension Force/(Area of Reinforcement*Modulus of Elasticity of Steel)
Modulus of Elasticity of Prestressed Steel given Compression Force
Go Prestressed Young's Modulus = Total Compression on Concrete/(Area of Prestressing Steel*Strain)
Compression Force for Prestressed Section
Go Total Compression on Concrete = Area of Prestressing Steel*Prestressed Young's Modulus*Strain
Strain in Prestressed Steel given Tension Force
Go Strain = Tension Force/(Area of Prestressing Steel*Prestressed Young's Modulus)
Area of Prestressing Steel given Tension Force
Go Area of Prestressing Steel = Tension Force/(Prestressed Young's Modulus*Strain)

Strain at Selected Level given Average Strain under Tension 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))
ε1 = εm+(Wcr*(hCrack-x)*(DCC-x))/(3*Es*As*(Leff-x))

What does Depth of Neutral Axis mean?

In engineering the line or plane through the section of a beam or plate which does not suffer extension or compression when the beam or plate bends. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression.

What is Tension force?

Tension Force (Ts) for a Prestressed Section is defined as the force that is transmitted through a rope, string or wire when pulled by forces acting from opposite sides. The tension force is directed over the length of the wire and pulls energy equally on the bodies at the ends.

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

Strain at Selected Level given Average Strain under Tension calculator 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 calculate 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 calculate Strain at Selected Level given Average Strain under Tension using this online calculator? To use this online calculator for Strain at Selected Level given Average Strain under Tension, enter Average Strain m), Crack Width (Wcr), Height of Crack (hCrack), Depth of Neutral Axis (x), Distance from Compression to Crack Width (DCC), Modulus of Elasticity of Steel Reinforcement (Es), Area of Reinforcement (As) & Effective Length (Leff) and hit the calculate button. Here is how the Strain at Selected Level given Average Strain under Tension calculation can be explained with given input values -> 0.0005 = 0.0005+(0.00049*(12.01-0.05)*(4.5-0.05))/(3*200000000000*0.0005*(50.25-0.05)).

FAQ

What is Strain at Selected Level given Average Strain under Tension?
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 and is represented as ε1 = εm+(Wcr*(hCrack-x)*(DCC-x))/(3*Es*As*(Leff-x)) or 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)). Average Strain describes the response of a solid to the application of a normal force induced at the selected level, Crack Width describes the length of the crack in an element, Height of Crack is the size of a flaw or crack in a material that can lead to catastrophic failure under a given stress, Depth of Neutral Axis is defined as the distance from the top of the section to its neutral axis, Distance from Compression to Crack Width can be described as the length from the compression level to the crack width, Modulus of Elasticity of Steel Reinforcement is a measure of its stiffness, Area of Reinforcement is the area of steel, used in a prestressed section, which is not prestressed or prestressing force is not applied & The Effective Length is the length which resists against buckling.
How to calculate Strain at Selected Level given Average Strain under Tension?
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 is calculated using 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 calculate Strain at Selected Level given Average Strain under Tension, you need Average Strain m), Crack Width (Wcr), Height of Crack (hCrack), Depth of Neutral Axis (x), Distance from Compression to Crack Width (DCC), Modulus of Elasticity of Steel Reinforcement (Es), Area of Reinforcement (As) & Effective Length (Leff). With our tool, you need to enter the respective value for Average Strain, Crack Width, Height of Crack, Depth of Neutral Axis, Distance from Compression to Crack Width, Modulus of Elasticity of Steel Reinforcement, Area of Reinforcement & Effective Length and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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