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Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Formula

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

I y = \frac{e x \cdot P \cdot c x}{σ total - ((\frac{P}{A cs}) + (\frac{e y \cdot P \cdot c y}{I x}))}

I_y - Moment of Inertia about Y-Axis?e_x - Eccentricity with respect to Principal Axis YY?P - Axial Load?c_x - Distance from YY to Outermost Fiber?σ_total - Total Stress?A_cs - Cross-Sectional Area?e_y - Eccentricity with respect to Principal Axis XX?c_y - Distance from XX to Outermost Fiber?I_x - Moment of Inertia about X-Axis?

Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Example

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Here is how the Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane equation looks like with Values.

Here is how the Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane equation looks like with Units.

Here is how the Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane equation looks like.

50.0552 = \frac{4 \cdot 9.99 \cdot 15}{14.8 - ((\frac{9.99}{13}) + (\frac{0.75 \cdot 9.99 \cdot 14}{51}))}

50.0552kg·m² = \frac{4 \cdot 9.99kN \cdot 15mm}{14.8Pa - ((\frac{9.99kN}{13m²}) + (\frac{0.75 \cdot 9.99kN \cdot 14mm}{51kg·m²}))}

50.0552 = \frac{4 \cdot 9.99 \cdot 15}{14.8 - ((\frac{9.99}{13}) + (\frac{0.75 \cdot 9.99 \cdot 14}{51}))}

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Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Solution

Follow our step by step solution on how to calculate Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane?

FIRST Step Consider the formula

I y = \frac{e x \cdot P \cdot c x}{σ total - ((\frac{P}{A cs}) + (\frac{e y \cdot P \cdot c y}{I x}))}

Next Step Substitute values of Variables

∴

I y = \frac{4 \cdot 9.99kN \cdot 15mm}{14.8Pa - ((\frac{9.99kN}{13m²}) + (\frac{0.75 \cdot 9.99kN \cdot 14mm}{51kg·m²}))}

Next Step Prepare to Evaluate

∴

I y = \frac{4 \cdot 9.99 \cdot 15}{14.8 - ((\frac{9.99}{13}) + (\frac{0.75 \cdot 9.99 \cdot 14}{51}))}

Next Step Evaluate

∴

I y = 50.0552254456484kg·m²

LAST Step Rounding Answer

∴

I y = 50.0552kg·m²

Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Formula Elements

Variables

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.

Formulas to find Moment of Inertia about Y-Axis

Eccentricity with respect to Principal Axis YY

Eccentricity with respect to Principal Axis YY can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio.

Symbol: e_x

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Eccentricity with respect to Principal Axis YY

Axial Load

Axial Load is defined as applying a force on a structure directly along an axis of the structure.

Symbol: P

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Axial Load

Distance from YY to Outermost Fiber

Distance from YY to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.

Symbol: c_x

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from YY to Outermost Fiber

Total Stress

Total Stress is defined as the force acting on the unit area of a material. The effect of stress on a body is named strain.

Symbol: σ_total

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Total Stress

Cross-Sectional Area

Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point.

Symbol: A_cs

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross-Sectional Area

Eccentricity with respect to Principal Axis XX

Eccentricity with respect to Principal Axis XX can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio.

Symbol: e_y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Eccentricity with respect to Principal Axis XX

Distance from XX to Outermost Fiber

Distance from XX to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.

Symbol: c_y

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from XX to Outermost Fiber

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.

Formulas to find Moment of Inertia about X-Axis

Other formulas in Eccentric Loading category

Go Total Unit Stress in Eccentric Loading

f = (\frac{P}{A cs}) + (P \cdot c \cdot \frac{e}{I neutral})

Go Cross-Sectional Area given Total Unit Stress in Eccentric Loading

A cs = \frac{P}{f - ((P \cdot c \cdot \frac{e}{I neutral}))}

How to Evaluate Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane?

Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane evaluator uses Moment of Inertia about Y-Axis = (Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/Moment of Inertia about X-Axis))) to evaluate the Moment of Inertia about Y-Axis, The Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane formula is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation. Moment of Inertia about Y-Axis is denoted by I_y symbol.

How to evaluate Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane using this online evaluator? To use this online evaluator for Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane, enter Eccentricity with respect to Principal Axis YY (e_x), Axial Load (P), Distance from YY to Outermost Fiber (c_x), Total Stress (σ_total), Cross-Sectional Area (A_cs), Eccentricity with respect to Principal Axis XX (e_y), Distance from XX to Outermost Fiber (c_y) & Moment of Inertia about X-Axis (I_x) and hit the calculate button.

FAQs on Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane

What is the formula to find Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane?

The formula of Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane is expressed as Moment of Inertia about Y-Axis = (Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/Moment of Inertia about X-Axis))). Here is an example- 11.27226 = (4*9990*0.015)/(14.8-((9990/13)+((0.75*9990*0.014)/51))).

How to calculate Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane?

With Eccentricity with respect to Principal Axis YY (e_x), Axial Load (P), Distance from YY to Outermost Fiber (c_x), Total Stress (σ_total), Cross-Sectional Area (A_cs), Eccentricity with respect to Principal Axis XX (e_y), Distance from XX to Outermost Fiber (c_y) & Moment of Inertia about X-Axis (I_x) we can find Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane using the formula - Moment of Inertia about Y-Axis = (Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Total Stress-((Axial Load/Cross-Sectional Area)+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/Moment of Inertia about X-Axis))).

Can the Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane be negative?

No, the Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane?

Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane 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 YY given Total Stress where Load doesn't lie on Plane can be measured.

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Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Formula

Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Example

Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Solution

Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane Formula Elements

Other formulas in Eccentric Loading category

How to Evaluate Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane?

FAQs on Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane

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