Distance from Centroidal Axis given Cracking Moment Calculator

✖The Modulus of Rupture of Concrete is a measure of the tensile strength of concrete beams or slabs.ⓘ Modulus of Rupture of Concrete [f_cr]			+10% -10%
✖Moment of Inertia of Gross Concrete Section is a term used to describe the capacity of a cross-section to resist bending.ⓘ Moment of Inertia of Gross Concrete Section [I_g]			+10% -10%
✖Cracking moment is defined as the moment, which when exceeded causes the cracking of concrete.ⓘ Cracking Moment [M_cr]			+10% -10%

✖Distance from Centroidal is a geometric center, to a point is the average of the distances from that point to all other points in the shape.ⓘ Distance from Centroidal Axis given Cracking Moment [y_t]

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Formula

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Distance from Centroidal Axis given Cracking Moment

Formula

`"y"_{"t"} = ("f"_{"cr"}*"I"_{"g"})/("M"_{"cr"})`

Example

`"150.075mm"=("3MPa"*"20.01m⁴")/("400kN*m")`

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Distance from Centroidal Axis given Cracking Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance from Centroidal = (Modulus of Rupture of Concrete*Moment of Inertia of Gross Concrete Section)/(Cracking Moment)
y_t = (f_cr*I_g)/(M_cr)
This formula uses 4 Variables

Variables Used

Distance from Centroidal - (Measured in Millimeter) - Distance from Centroidal is a geometric center, to a point is the average of the distances from that point to all other points in the shape.
Modulus of Rupture of Concrete - (Measured in Pascal) - The Modulus of Rupture of Concrete is a measure of the tensile strength of concrete beams or slabs.
Moment of Inertia of Gross Concrete Section - (Measured in Meter⁴) - Moment of Inertia of Gross Concrete Section is a term used to describe the capacity of a cross-section to resist bending.
Cracking Moment - (Measured in Newton Meter) - Cracking moment is defined as the moment, which when exceeded causes the cracking of concrete.

STEP 1: Convert Input(s) to Base Unit

Modulus of Rupture of Concrete: 3 Megapascal --> 3000000 Pascal (Check conversion here)
Moment of Inertia of Gross Concrete Section: 20.01 Meter⁴ --> 20.01 Meter⁴ No Conversion Required
Cracking Moment: 400 Kilonewton Meter --> 400000 Newton Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

y_t = (f_cr*I_g)/(M_cr) --> (3000000*20.01)/(400000)

Evaluating ... ...

y_t = 150.075

STEP 3: Convert Result to Output's Unit

0.150075 Meter -->150.075 Millimeter (Check conversion here)

FINAL ANSWER

150.075 Millimeter <-- Distance from Centroidal

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Concrete Formulas » Deflection Computations, Column Moments and Torsion » Deflection Computations and Concrete Beams Criteria » Distance from Centroidal Axis given Cracking Moment

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Birsa Institute of Technology (BIT), Sindri

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< 3 Deflection Computations and Concrete Beams Criteria Calculators

Moment of Inertia of Gross Concrete Section given Cracking Moment

Go Moment of Inertia of Gross Concrete Section = (Cracking Moment*Distance from Centroidal)/(Modulus of Rupture of Concrete)

Distance from Centroidal Axis given Cracking Moment

Go Distance from Centroidal = (Modulus of Rupture of Concrete*Moment of Inertia of Gross Concrete Section)/(Cracking Moment)

Cracking Moment for Reinforced Concrete Beams

Go Cracking Moment = (Modulus of Rupture of Concrete*Moment of Inertia of Gross Concrete Section)/(Distance from Centroidal)

Distance from Centroidal Axis given Cracking Moment Formula

Distance from Centroidal = (Modulus of Rupture of Concrete*Moment of Inertia of Gross Concrete Section)/(Cracking Moment)
y_t = (f_cr*I_g)/(M_cr)

What is Cracking Moment?

Cracking moment denoted as (Mcr ) is defined as the moment, which when exceeded causes the cracking of concrete. For the calculation of the deflection in the concrete at cracking moment, the moment is calculated at which point, the failure will occur in concrete.

How to Calculate Distance from Centroidal Axis given Cracking Moment?

Distance from Centroidal Axis given Cracking Moment calculator uses Distance from Centroidal = (Modulus of Rupture of Concrete*Moment of Inertia of Gross Concrete Section)/(Cracking Moment) to calculate the Distance from Centroidal, The Distance from Centroidal Axis given Cracking Moment formula is defined as ratio of product of the modulus of rupture and moment of inertia of gross concrete section to cracking moment. Distance from Centroidal is denoted by y_t symbol.

How to calculate Distance from Centroidal Axis given Cracking Moment using this online calculator? To use this online calculator for Distance from Centroidal Axis given Cracking Moment, enter Modulus of Rupture of Concrete (f_cr), Moment of Inertia of Gross Concrete Section (I_g) & Cracking Moment (M_cr) and hit the calculate button. Here is how the Distance from Centroidal Axis given Cracking Moment calculation can be explained with given input values -> 150000 = (3000000*20.01)/(400000).

FAQ

What is Distance from Centroidal Axis given Cracking Moment?

The Distance from Centroidal Axis given Cracking Moment formula is defined as ratio of product of the modulus of rupture and moment of inertia of gross concrete section to cracking moment and is represented as y_t = (f_cr*I_g)/(M_cr) or Distance from Centroidal = (Modulus of Rupture of Concrete*Moment of Inertia of Gross Concrete Section)/(Cracking Moment). The Modulus of Rupture of Concrete is a measure of the tensile strength of concrete beams or slabs, Moment of Inertia of Gross Concrete Section is a term used to describe the capacity of a cross-section to resist bending & Cracking moment is defined as the moment, which when exceeded causes the cracking of concrete.

How to calculate Distance from Centroidal Axis given Cracking Moment?

The Distance from Centroidal Axis given Cracking Moment formula is defined as ratio of product of the modulus of rupture and moment of inertia of gross concrete section to cracking moment is calculated using Distance from Centroidal = (Modulus of Rupture of Concrete*Moment of Inertia of Gross Concrete Section)/(Cracking Moment). To calculate Distance from Centroidal Axis given Cracking Moment, you need Modulus of Rupture of Concrete (f_cr), Moment of Inertia of Gross Concrete Section (I_g) & Cracking Moment (M_cr). With our tool, you need to enter the respective value for Modulus of Rupture of Concrete, Moment of Inertia of Gross Concrete Section & Cracking Moment 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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