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Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Formula

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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. Check FAQs

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

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

Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Example

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Here is how the Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane equation looks like with Values.

Here is how the Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane equation looks like with Units.

Here is how the Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane equation looks like.

0.7452 = \frac{(14.8 - (\frac{9.99}{13}) - (\frac{4 \cdot 9.99 \cdot 15}{50})) \cdot 51}{9.99 \cdot 14}

0.7452 = \frac{(14.8Pa - (\frac{9.99kN}{13m²}) - (\frac{4 \cdot 9.99kN \cdot 15mm}{50kg·m²})) \cdot 51kg·m²}{9.99kN \cdot 14mm}

0.7452 = \frac{(14.8 - (\frac{9.99}{13}) - (\frac{4 \cdot 9.99 \cdot 15}{50})) \cdot 51}{9.99 \cdot 14}

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Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Solution

Follow our step by step solution on how to calculate Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

e y = \frac{(14.8Pa - (\frac{9.99kN}{13m²}) - (\frac{4 \cdot 9.99kN \cdot 15mm}{50kg·m²})) \cdot 51kg·m²}{9.99kN \cdot 14mm}

Next Step Prepare to Evaluate

∴

e y = \frac{(14.8 - (\frac{9.99}{13}) - (\frac{4 \cdot 9.99 \cdot 15}{50})) \cdot 51}{9.99 \cdot 14}

Next Step Evaluate

∴

e y = 0.745177045177045

LAST Step Rounding Answer

∴

e y = 0.7452

Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Formula Elements

Variables

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

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

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

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 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

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

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

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

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

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 Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane?

Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane evaluator uses Eccentricity with respect to Principal Axis XX = ((Total Stress-(Axial Load/Cross-Sectional Area)-((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Moment of Inertia about Y-Axis)))*Moment of Inertia about X-Axis)/(Axial Load*Distance from XX to Outermost Fiber) to evaluate the Eccentricity with respect to Principal Axis XX, The Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane formula is defined as the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. Eccentricity with respect to Principal Axis XX is denoted by e_y symbol.

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

FAQs on Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane

What is the formula to find Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane?

The formula of Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane is expressed as Eccentricity with respect to Principal Axis XX = ((Total Stress-(Axial Load/Cross-Sectional Area)-((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Moment of Inertia about Y-Axis)))*Moment of Inertia about X-Axis)/(Axial Load*Distance from XX to Outermost Fiber). Here is an example- 15.76877 = ((14.8-(9990/13)-((4*9990*0.015)/(50)))*51)/(9990*0.014).

How to calculate Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane?

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

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Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Formula

Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Example

Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Solution

Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane Formula Elements

Other formulas in Eccentric Loading category

How to Evaluate Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane?

FAQs on Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane

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