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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.

Formulas to find Moment of Inertia Transformed Beam

Beam Width

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

Symbol: b

Measurement: LengthUnit: mm