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Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending Formula

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Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX. Check FAQs

I x = \frac{M x \cdot y}{f Max - (\frac{M y \cdot x}{I y})}

I_x - Moment of Inertia about X-Axis?M_x - Bending Moment about X-Axis?y - Distance from Point to XX Axis?f_Max - Maximum Stress?M_y - Bending Moment about Y-Axis?x - Distance from Point to YY Axis?I_y - Moment of Inertia about Y-Axis?

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending Example

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Here is how the Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending equation looks like with Values.

Here is how the Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending equation looks like with Units.

Here is how the Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending equation looks like.

51.0348 = \frac{239 \cdot 169}{1430 - (\frac{307 \cdot 104}{50})}

51.0348kg·m² = \frac{239N*m \cdot 169mm}{1430N/m² - (\frac{307N*m \cdot 104mm}{50kg·m²})}

51.0348 = \frac{239 \cdot 169}{1430 - (\frac{307 \cdot 104}{50})}

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Home » Engineering » Civil » Structural Engineering » Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending Solution

Follow our step by step solution on how to calculate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

FIRST Step Consider the formula

I x = \frac{M x \cdot y}{f Max - (\frac{M y \cdot x}{I y})}

Next Step Substitute values of Variables

∴

I x = \frac{239N*m \cdot 169mm}{1430N/m² - (\frac{307N*m \cdot 104mm}{50kg·m²})}

Next Step Convert Units

∴

I x = \frac{239N*m \cdot 169mm}{1430Pa - (\frac{307N*m \cdot 104mm}{50kg·m²})}

Next Step Prepare to Evaluate

∴

I x = \frac{239 \cdot 169}{1430 - (\frac{307 \cdot 104}{50})}

Next Step Evaluate

∴

I x = 51.0348226018397kg·m²

LAST Step Rounding Answer

∴

I x = 51.0348kg·m²

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending Formula Elements

Variables

Moment of Inertia about X-Axis

Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX.

Symbol: I_x

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Bending Moment about X-Axis

Bending Moment about X-Axis is defined as the bending moment about principal axis XX.

Symbol: M_x

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Distance from Point to XX Axis

Distance from Point to XX Axis is the distance of the point to XX axis where stress is to be computed.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Maximum Stress

Maximum Stress is defined as force per unit area that the force acts upon.

Symbol: f_Max

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Bending Moment about Y-Axis

Bending Moment about Y-Axis is defined as the bending moment about principal axis YY.

Symbol: M_y

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Distance from Point to YY Axis

Distance from Point to YY Axis is the distance from the point to the YY axis where stress is to be computed.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Moment of Inertia about Y-Axis

Moment of Inertia about Y-Axis is defined as the moment of inertia of cross-section about YY.

Symbol: I_y

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Credits

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Created by Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

Alithea Fernandes has created this Formula and 100+ more formulas!

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Verified by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

Rudrani Tidke has verified this Formula and 50+ more formulas!

Other formulas in Unsymmetrical Bending category

Go Maximum Stress in Unsymmetrical Bending

f Max = (\frac{M x \cdot y}{I x}) + (\frac{M y \cdot x}{I y})

Go Bending Moment about Axis XX given Maximum Stress in Unsymmetrical Bending

M x = (f Max - (\frac{M y \cdot x}{I y})) \cdot \frac{I x}{y}

See More

How to Evaluate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending evaluator uses Moment of Inertia about X-Axis = (Bending Moment about X-Axis*Distance from Point to XX Axis)/(Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/(Moment of Inertia about Y-Axis))) to evaluate the Moment of Inertia about X-Axis, Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending formula is defined as the second moment of the area distribution with respect to the bending axis, crucial for calculating maximum stress in the asymmetrically loaded structure. Moment of Inertia about X-Axis is denoted by I_x symbol.

How to evaluate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending using this online evaluator? To use this online evaluator for Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending, enter Bending Moment about X-Axis (M_x), Distance from Point to XX Axis (y), Maximum Stress (f_Max), Bending Moment about Y-Axis (M_y), Distance from Point to YY Axis (x) & Moment of Inertia about Y-Axis (I_y) and hit the calculate button.

FAQs on Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending

What is the formula to find Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

The formula of Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending is expressed as Moment of Inertia about X-Axis = (Bending Moment about X-Axis*Distance from Point to XX Axis)/(Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/(Moment of Inertia about Y-Axis))). Here is an example- -63.402191 = (239*0.169)/(1430-((307*0.104)/(50))).

How to calculate Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

With Bending Moment about X-Axis (M_x), Distance from Point to XX Axis (y), Maximum Stress (f_Max), Bending Moment about Y-Axis (M_y), Distance from Point to YY Axis (x) & Moment of Inertia about Y-Axis (I_y) we can find Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending using the formula - Moment of Inertia about X-Axis = (Bending Moment about X-Axis*Distance from Point to XX Axis)/(Maximum Stress-((Bending Moment about Y-Axis*Distance from Point to YY Axis)/(Moment of Inertia about Y-Axis))).

Can the Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending be negative?

No, the Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending?

Moment of Inertia about XX given Maximum Stress in Unsymmetrical Bending 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 about XX given Maximum Stress in Unsymmetrical Bending can be measured.

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