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Moment of Inertia of Transformed Beam Section Formula

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Moment of Inertia Transformed Beamis defined as the expressing a body's tendency to resist angular acceleration. Check FAQs

I TB = (0.5 \cdot b \cdot ({K d}^{2})) + 2 \cdot (m Elastic - 1) \cdot A s' \cdot ({c sc}^{2}) + m Elastic \cdot ({c s}^{2}) \cdot A

I_TB - Moment of Inertia Transformed Beam?b - Beam Width?K_d - Distance from Compression Fiber to NA?m_Elastic - Modular Ratio for Elastic Shortening?A_s' - Area of Compression Reinforcement?c_sc - Distance Neutral to Compressive Reinforcing Steel?c_s - Distance Neutral to Tensile Reinforcing Steel?A - Area of Tension Reinforcement?

Moment of Inertia of Transformed Beam Section Example

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Here is how the Moment of Inertia of Transformed Beam Section equation looks like with Values.

Here is how the Moment of Inertia of Transformed Beam Section equation looks like with Units.

Here is how the Moment of Inertia of Transformed Beam Section equation looks like.

2.1243 = (0.5 \cdot 26.5 \cdot ({100.2}^{2})) + 2 \cdot (0.6 - 1) \cdot 20 \cdot ({25.22}^{2}) + 0.6 \cdot (595^{2}) \cdot 10

2.1243kg·m² = (0.5 \cdot 26.5mm \cdot ({100.2mm}^{2})) + 2 \cdot (0.6 - 1) \cdot 20mm² \cdot ({25.22mm}^{2}) + 0.6 \cdot ({595mm}^{2}) \cdot 10m²

2.1243 = (0.5 \cdot 26.5 \cdot ({100.2}^{2})) + 2 \cdot (0.6 - 1) \cdot 20 \cdot ({25.22}^{2}) + 0.6 \cdot (595^{2}) \cdot 10

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Moment of Inertia of Transformed Beam Section Solution

Follow our step by step solution on how to calculate Moment of Inertia of Transformed Beam Section?

FIRST Step Consider the formula

I TB = (0.5 \cdot b \cdot ({K d}^{2})) + 2 \cdot (m Elastic - 1) \cdot A s' \cdot ({c sc}^{2}) + m Elastic \cdot ({c s}^{2}) \cdot A

Next Step Substitute values of Variables

∴

I TB = (0.5 \cdot 26.5mm \cdot ({100.2mm}^{2})) + 2 \cdot (0.6 - 1) \cdot 20mm² \cdot ({25.22mm}^{2}) + 0.6 \cdot ({595mm}^{2}) \cdot 10m²

Next Step Convert Units

∴

I TB = (0.5 \cdot 0.0265m \cdot ({0.1002m}^{2})) + 2 \cdot (0.6 - 1) \cdot 2E-5m² \cdot ({0.0252m}^{2}) + 0.6 \cdot ({0.595m}^{2}) \cdot 10m²

Next Step Prepare to Evaluate

∴

I TB = (0.5 \cdot 0.0265 \cdot ({0.1002}^{2})) + 2 \cdot (0.6 - 1) \cdot 2E-5 \cdot ({0.0252}^{2}) + 0.6 \cdot ({0.595}^{2}) \cdot 10

Next Step Evaluate

∴

I TB = 2.12428302035323kg·m²

LAST Step Rounding Answer

∴

I TB = 2.1243kg·m²

Moment of Inertia of Transformed Beam Section Formula Elements

Variables

Moment of Inertia Transformed Beam

Moment of Inertia Transformed Beamis defined as the expressing a body's tendency to resist angular acceleration.

Symbol: I_TB

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Beam Width

Beam Width is defined as the shortest/least measurement of the beam.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Distance from Compression Fiber to NA

Distance from Compression Fiber to NA is the distance from the extreme compression fiber or surface to the neutral axis.

Symbol: K_d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

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.

Symbol: m_Elastic

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Area of Compression Reinforcement

Area of Compression Reinforcement is the amount of steel required in the compression zone.

Symbol: A_s'

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Distance Neutral to Compressive Reinforcing Steel

Distance Neutral to Compressive Reinforcing Steel is the length in between the neutral axis and the compressive reinforcing steel.

Symbol: c_sc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Distance Neutral to Tensile Reinforcing Steel

Distance Neutral to Tensile Reinforcing Steel is the length in between the neutral axis and the tensile reinforcing steel.

Symbol: c_s

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Area of Tension Reinforcement

Area of Tension Reinforcement is the space occupied by the steel in order to impart tensile strength for the section.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Credits

Creator Image

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Formula and 1000+ more formulas!

Verifier Image

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has verified this Formula and 1700+ more formulas!

Other formulas in Check for Stress in Beams category

Go Distance from Neutral Axis to Tensile Reinforcing Steel

c s = f unit stress \cdot \frac{I A}{n \cdot B M}

Go Unit Stress in Tensile Reinforcing Steel

f unit stress = n \cdot B M \cdot \frac{c s}{I A}

See More

How to Evaluate Moment of Inertia of Transformed Beam Section?

Moment of Inertia of Transformed Beam Section evaluator 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 evaluate 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 evaluate Moment of Inertia of Transformed Beam Section using this online evaluator? To use this online evaluator 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.

FAQs on Moment of Inertia of Transformed Beam Section

What is the formula to find Moment of Inertia of Transformed Beam Section?

The formula of Moment of Inertia of Transformed Beam Section is expressed as 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. Here is an example- 2.124282 = (0.5*0.0265*(0.1002^2))+2*(0.6-1)*2E-05*(0.02522^2)+0.6*(0.595^2)*10.

How to calculate Moment of Inertia of Transformed Beam Section?

With 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) we can find Moment of Inertia of Transformed Beam Section using the formula - 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.

Can the Moment of Inertia of Transformed Beam Section be negative?

Yes, the Moment of Inertia of Transformed Beam Section, measured in Moment of Inertia can be negative.

Which unit is used to measure Moment of Inertia of Transformed Beam Section?

Moment of Inertia of Transformed Beam Section is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Moment of Inertia of Transformed Beam Section can be measured.

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