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Moment of Inertia of Transformed Beam Section Calculator

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Check for Stress in Beams

✖Beam Width is defined as the shortest/least measurement of the beam.ⓘ Beam Width [b]			+10% -10%
✖Distance from Compression Fiber to NA is the distance from the extreme compression fiber or surface to the neutral axis.ⓘ Distance from Compression Fiber to NA [K_d]			+10% -10%
✖Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material.ⓘ Modular Ratio for Elastic Shortening [m_Elastic]			+10% -10%
✖Area of Compression Reinforcement is the amount of steel required in the compression zone.ⓘ Area of Compression Reinforcement [A_s']			+10% -10%
✖Distance Neutral to Compressive Reinforcing Steel is the length in between the neutral axis and the compressive reinforcing steel.ⓘ Distance Neutral to Compressive Reinforcing Steel [c_sc]			+10% -10%
✖Distance Neutral to Tensile Reinforcing Steel is the length in between the neutral axis and the tensile reinforcing steel.ⓘ Distance Neutral to Tensile Reinforcing Steel [c_s]			+10% -10%
✖Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength for the section.ⓘ Area of Tension Reinforcement [A]			+10% -10%

✖Moment of Inertia Transformed Beamis defined as the expressing a body's tendency to resist angular acceleration.ⓘ Moment of Inertia of Transformed Beam Section [I_TB]

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Moment of Inertia of Transformed Beam Section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia Transformed Beam = (0.5*Beam Width*(Distance from Compression Fiber to NA^2))+2*(Modular Ratio for Elastic Shortening-1)*Area of Compression Reinforcement*(Distance Neutral to Compressive Reinforcing Steel^2)+Modular Ratio for Elastic Shortening*(Distance Neutral to Tensile Reinforcing Steel^2)*Area of Tension Reinforcement
I_TB = (0.5*b*(K_d^2))+2*(m_Elastic-1)*A_s'*(c_sc^2)+m_Elastic*(c_s^2)*A
This formula uses 8 Variables

Variables Used

Moment of Inertia Transformed Beam - (Measured in Kilogram Square Meter) - Moment of Inertia Transformed Beamis defined as the expressing a body's tendency to resist angular acceleration.
Beam Width - (Measured in Meter) - Beam Width is defined as the shortest/least measurement of the beam.
Distance from Compression Fiber to NA - (Measured in Meter) - Distance from Compression Fiber to NA is the distance from the extreme compression fiber or surface to the neutral axis.
Modular Ratio for Elastic Shortening - Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material.
Area of Compression Reinforcement - (Measured in Square Meter) - Area of Compression Reinforcement is the amount of steel required in the compression zone.
Distance Neutral to Compressive Reinforcing Steel - (Measured in Meter) - Distance Neutral to Compressive Reinforcing Steel is the length in between the neutral axis and the compressive reinforcing steel.
Distance Neutral to Tensile Reinforcing Steel - (Measured in Meter) - Distance Neutral to Tensile Reinforcing Steel is the length in between the neutral axis and the tensile reinforcing steel.
Area of Tension Reinforcement - (Measured in Square Meter) - Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength for the section.

STEP 1: Convert Input(s) to Base Unit

Beam Width: 26.5 Millimeter --> 0.0265 Meter (Check conversion here)
Distance from Compression Fiber to NA: 100.2 Millimeter --> 0.1002 Meter (Check conversion here)
Modular Ratio for Elastic Shortening: 0.6 --> No Conversion Required
Area of Compression Reinforcement: 20 Square Millimeter --> 2E-05 Square Meter (Check conversion here)
Distance Neutral to Compressive Reinforcing Steel: 25.22 Millimeter --> 0.02522 Meter (Check conversion here)
Distance Neutral to Tensile Reinforcing Steel: 595 Millimeter --> 0.595 Meter (Check conversion here)
Area of Tension Reinforcement: 10 Square Meter --> 10 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_TB = (0.5*b*(K_d^2))+2*(m_Elastic-1)*A_s'*(c_sc^2)+m_Elastic*(c_s^2)*A --> (0.5*0.0265*(0.1002^2))+2*(0.6-1)*2E-05*(0.02522^2)+0.6*(0.595^2)*10

Evaluating ... ...

I_TB = 2.12428302035323

STEP 3: Convert Result to Output's Unit

2.12428302035323 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

2.12428302035323 ≈ 2.124283 Kilogram Square Meter <-- Moment of Inertia Transformed Beam

(Calculation completed in 00.020 seconds)

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Moment of Inertia of Transformed Beam Section

LaTeX Go Moment of Inertia Transformed Beam = (0.5*Beam Width*(Distance from Compression Fiber to NA^2))+2*(Modular Ratio for Elastic Shortening-1)*Area of Compression Reinforcement*(Distance Neutral to Compressive Reinforcing Steel^2)+Modular Ratio for Elastic Shortening*(Distance Neutral to Tensile Reinforcing Steel^2)*Area of Tension Reinforcement

Distance from Neutral Axis to Tensile Reinforcing Steel

LaTeX Go Distance Neutral to Tensile Reinforcing Steel = Unit Stress in Tensile Reinforcing Steel*Moment of Inertia of Beam/(Elasticity Ratio of Steel to Concrete*Bending Moment of Considered Section)

Unit Stress in Tensile Reinforcing Steel

LaTeX Go Unit Stress in Tensile Reinforcing Steel = Elasticity Ratio of Steel to Concrete*Bending Moment of Considered Section*Distance Neutral to Tensile Reinforcing Steel/Moment of Inertia of Beam

Total Bending Moment given Unit Stress in Tensile Reinforcing Steel

LaTeX Go Bending Moment = Unit Stress in Tensile Reinforcing Steel*Moment of Inertia of Beam/(Elasticity Ratio of Steel to Concrete*Distance Neutral to Tensile Reinforcing Steel)

Moment of Inertia of Transformed Beam Section Formula

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Define Moment of Inertia?

The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.

How to Calculate Moment of Inertia of Transformed Beam Section?

Moment of Inertia of Transformed Beam Section calculator uses Moment of Inertia Transformed Beam = (0.5*Beam Width*(Distance from Compression Fiber to NA^2))+2*(Modular Ratio for Elastic Shortening-1)*Area of Compression Reinforcement*(Distance Neutral to Compressive Reinforcing Steel^2)+Modular Ratio for Elastic Shortening*(Distance Neutral to Tensile Reinforcing Steel^2)*Area of Tension Reinforcement to calculate the Moment of Inertia Transformed Beam, The Moment of Inertia of Transformed Beam Section is defined as the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. Moment of Inertia Transformed Beam is denoted by I_TB symbol.

How to calculate Moment of Inertia of Transformed Beam Section using this online calculator? To use this online calculator for Moment of Inertia of Transformed Beam Section, enter Beam Width (b), Distance from Compression Fiber to NA (K_d), Modular Ratio for Elastic Shortening (m_Elastic), Area of Compression Reinforcement (A_s'), Distance Neutral to Compressive Reinforcing Steel (c_sc), Distance Neutral to Tensile Reinforcing Steel (c_s) & Area of Tension Reinforcement (A) and hit the calculate button. Here is how the Moment of Inertia of Transformed Beam Section calculation can be explained with given input values -> 2.124282 = (0.5*0.0265*(0.1002^2))+2*(0.6-1)*2E-05*(0.02522^2)+0.6*(0.595^2)*10.

FAQ

What is Moment of Inertia of Transformed Beam Section?

The Moment of Inertia of Transformed Beam Section is defined as the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation and is represented as I_TB = (0.5*b*(K_d^2))+2*(m_Elastic-1)*A_s'*(c_sc^2)+m_Elastic*(c_s^2)*A or Moment of Inertia Transformed Beam = (0.5*Beam Width*(Distance from Compression Fiber to NA^2))+2*(Modular Ratio for Elastic Shortening-1)*Area of Compression Reinforcement*(Distance Neutral to Compressive Reinforcing Steel^2)+Modular Ratio for Elastic Shortening*(Distance Neutral to Tensile Reinforcing Steel^2)*Area of Tension Reinforcement. Beam Width is defined as the shortest/least measurement of the beam, Distance from Compression Fiber to NA is the distance from the extreme compression fiber or surface to the neutral axis, Modular Ratio for Elastic Shortening is the ratio of the elastic modulus of a particular material in a cross-section to the elastic modulus of the “base” or the reference material, Area of Compression Reinforcement is the amount of steel required in the compression zone, Distance Neutral to Compressive Reinforcing Steel is the length in between the neutral axis and the compressive reinforcing steel, Distance Neutral to Tensile Reinforcing Steel is the length in between the neutral axis and the tensile reinforcing steel & Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength for the section.

How to calculate Moment of Inertia of Transformed Beam Section?

The Moment of Inertia of Transformed Beam Section is defined as the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation is calculated using Moment of Inertia Transformed Beam = (0.5*Beam Width*(Distance from Compression Fiber to NA^2))+2*(Modular Ratio for Elastic Shortening-1)*Area of Compression Reinforcement*(Distance Neutral to Compressive Reinforcing Steel^2)+Modular Ratio for Elastic Shortening*(Distance Neutral to Tensile Reinforcing Steel^2)*Area of Tension Reinforcement. To calculate Moment of Inertia of Transformed Beam Section, you need Beam Width (b), Distance from Compression Fiber to NA (K_d), Modular Ratio for Elastic Shortening (m_Elastic), Area of Compression Reinforcement (A_s'), Distance Neutral to Compressive Reinforcing Steel (c_sc), Distance Neutral to Tensile Reinforcing Steel (c_s) & Area of Tension Reinforcement (A). With our tool, you need to enter the respective value for Beam Width, Distance from Compression Fiber to NA, Modular Ratio for Elastic Shortening, Area of Compression Reinforcement, Distance Neutral to Compressive Reinforcing Steel, Distance Neutral to Tensile Reinforcing Steel & Area of Tension Reinforcement 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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