Moment of Inertia of Gross Concrete Section given Cracking Moment Calculator

✖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 [y_t]			+10% -10%
✖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 given Cracking Moment [I_g]

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Formula

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Moment of Inertia of Gross Concrete Section given Cracking Moment

Formula

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

Example

`"20m⁴"=("400kN*m"*"150mm")/("3MPa")`

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Moment of Inertia of Gross Concrete Section given Cracking Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Cracking Moment: 400 Kilonewton Meter --> 400000 Newton Meter (Check conversion here)
Distance from Centroidal: 150 Millimeter --> 150 Millimeter No Conversion Required
Modulus of Rupture of Concrete: 3 Megapascal --> 3000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_g = (M_cr*y_t)/(f_cr) --> (400000*150)/(3000000)

Evaluating ... ...

I_g = 20

STEP 3: Convert Result to Output's Unit

20 Meter⁴ --> No Conversion Required

FINAL ANSWER

20 Meter⁴ <-- Moment of Inertia of Gross Concrete Section

(Calculation completed in 00.004 seconds)

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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)

Moment of Inertia of Gross Concrete Section given Cracking Moment Formula

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

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

How to calculate Moment of Inertia of Gross Concrete Section given Cracking Moment using this online calculator? To use this online calculator for Moment of Inertia of Gross Concrete Section given Cracking Moment, enter Cracking Moment (M_cr), Distance from Centroidal (y_t) & Modulus of Rupture of Concrete (f_cr) and hit the calculate button. Here is how the Moment of Inertia of Gross Concrete Section given Cracking Moment calculation can be explained with given input values -> 20 = (400000*0.15)/(3000000).

FAQ

What is Moment of Inertia of Gross Concrete Section given Cracking Moment?

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

How to calculate Moment of Inertia of Gross Concrete Section given Cracking Moment?

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