Depth of Neutral Axis given Couple Force of Cross Section Calculator

✖Couple Force is a system of forces with a resultant moment but no resultant force.ⓘ Couple Force [C]			+10% -10%
✖Modulus of Elasticity of Concrete is defined as the ratio of the applied stress to the corresponding strain.ⓘ Modulus of Elasticity of Concrete [E_c]			+10% -10%
✖Strain in Concrete is the reduction in volume of concrete after the application of loading then change in volume with respect to volume of concrete before applied loading.ⓘ Strain in Concrete [ε_c]			+10% -10%
✖Crack Width describes the length of the crack in an element.ⓘ Crack Width [W_cr]			+10% -10%

✖Depth of Neutral Axis is defined as the distance from the top of the section to its neutral axis.ⓘ Depth of Neutral Axis given Couple Force of Cross Section [x]

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Formula

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Depth of Neutral Axis given Couple Force of Cross Section

Formula

`"x" = "C"/(0.5*"E"_{"c"}*"ε"_{"c"}*"W"_{"cr"})`

Example

`"430.7305mm"="0.028kN"/(0.5*"0.157MPa"*"1.69"*"0.49mm")`

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Download Crack Width and Deflection of Prestress Concrete Members Formulas PDF

Depth of Neutral Axis given Couple Force of Cross Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Neutral Axis = Couple Force/(0.5*Modulus of Elasticity of Concrete*Strain in Concrete*Crack Width)
x = C/(0.5*E_c*ε_c*W_cr)
This formula uses 5 Variables

Variables Used

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.
Couple Force - (Measured in Newton) - Couple Force is a system of forces with a resultant moment but no resultant force.
Modulus of Elasticity of Concrete - (Measured in Pascal) - Modulus of Elasticity of Concrete is defined as the ratio of the applied stress to the corresponding strain.
Strain in Concrete - Strain in Concrete is the reduction in volume of concrete after the application of loading then change in volume with respect to volume of concrete before applied loading.
Crack Width - (Measured in Meter) - Crack Width describes the length of the crack in an element.

STEP 1: Convert Input(s) to Base Unit

Couple Force: 0.028 Kilonewton --> 28 Newton (Check conversion here)
Modulus of Elasticity of Concrete: 0.157 Megapascal --> 157000 Pascal (Check conversion here)
Strain in Concrete: 1.69 --> No Conversion Required
Crack Width: 0.49 Millimeter --> 0.00049 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = C/(0.5*E_c*ε_c*W_cr) --> 28/(0.5*157000*1.69*0.00049)

Evaluating ... ...

x = 0.430730465027378

STEP 3: Convert Result to Output's Unit

0.430730465027378 Meter -->430.730465027378 Millimeter (Check conversion here)

FINAL ANSWER

430.730465027378 ≈ 430.7305 Millimeter <-- Depth of Neutral Axis

(Calculation completed in 00.004 seconds)

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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

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))

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))

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)

Depth of Neutral Axis given Couple Force of Cross Section Formula

Depth of Neutral Axis = Couple Force/(0.5*Modulus of Elasticity of Concrete*Strain in Concrete*Crack Width)
x = C/(0.5*E_c*ε_c*W_cr)

What does Modulus of Elasticity of Concrete mean?

Modulus of elasticity of concrete (Ec) is defined as the ratio of the applied stress to the corresponding strain. Not only does it demonstrate the ability of concrete to withstand deformation due to applied stress but also its stiffness.

What are Prestressed Members?

In a prestressed concrete member, the internal stresses are introduced in a planned manner so that the stresses resulting from the superimposed loads are counteracted to the desired degree.
The principle behind prestressed concrete is that compressive stresses induced by high-strength steel tendons in a concrete member before loads are applied will balance the tensile stresses imposed in the member during service.

How to Calculate Depth of Neutral Axis given Couple Force of Cross Section?

Depth of Neutral Axis given Couple Force of Cross Section calculator uses Depth of Neutral Axis = Couple Force/(0.5*Modulus of Elasticity of Concrete*Strain in Concrete*Crack Width) to calculate the Depth of Neutral Axis, The Depth of Neutral Axis given Couple Force of Cross Section is defined as the axis through beam where stress is zero, that is there is neither compression nor tension. Depth of Neutral Axis is denoted by x symbol.

How to calculate Depth of Neutral Axis given Couple Force of Cross Section using this online calculator? To use this online calculator for Depth of Neutral Axis given Couple Force of Cross Section, enter Couple Force (C), Modulus of Elasticity of Concrete (E_c), Strain in Concrete (ε_c) & Crack Width (W_cr) and hit the calculate button. Here is how the Depth of Neutral Axis given Couple Force of Cross Section calculation can be explained with given input values -> 3.1E+8 = 28/(0.5*157000*1.69*0.00049).

FAQ

What is Depth of Neutral Axis given Couple Force of Cross Section?

The Depth of Neutral Axis given Couple Force of Cross Section is defined as the axis through beam where stress is zero, that is there is neither compression nor tension and is represented as x = C/(0.5*E_c*ε_c*W_cr) or Depth of Neutral Axis = Couple Force/(0.5*Modulus of Elasticity of Concrete*Strain in Concrete*Crack Width). Couple Force is a system of forces with a resultant moment but no resultant force, Modulus of Elasticity of Concrete is defined as the ratio of the applied stress to the corresponding strain, Strain in Concrete is the reduction in volume of concrete after the application of loading then change in volume with respect to volume of concrete before applied loading & Crack Width describes the length of the crack in an element.

How to calculate Depth of Neutral Axis given Couple Force of Cross Section?

The Depth of Neutral Axis given Couple Force of Cross Section is defined as the axis through beam where stress is zero, that is there is neither compression nor tension is calculated using Depth of Neutral Axis = Couple Force/(0.5*Modulus of Elasticity of Concrete*Strain in Concrete*Crack Width). To calculate Depth of Neutral Axis given Couple Force of Cross Section, you need Couple Force (C), Modulus of Elasticity of Concrete (E_c), Strain in Concrete (ε_c) & Crack Width (W_cr). With our tool, you need to enter the respective value for Couple Force, Modulus of Elasticity of Concrete, Strain in Concrete & Crack Width 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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