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

✖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.ⓘ Eccentricity with respect to Principal Axis YY [e_x]			+10% -10%
✖Axial Load is defined as applying a force on a structure directly along an axis of the structure.ⓘ Axial Load [P]			+10% -10%
✖Distance from YY to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.ⓘ Distance from YY to Outermost Fiber [c_x]			+10% -10%
✖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.ⓘ Total Stress [σ_total]			+10% -10%
✖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.ⓘ Cross-Sectional Area [A_cs]			+10% -10%
✖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.ⓘ Eccentricity with respect to Principal Axis XX [e_y]			+10% -10%
✖Distance from XX to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.ⓘ Distance from XX to Outermost Fiber [c_y]			+10% -10%
✖Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX.ⓘ Moment of Inertia about X-Axis [I_x]			+10% -10%

✖Moment of Inertia about Y-Axis is defined as the moment of inertia of cross-section about YY.ⓘ Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane [I_y]

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Formula

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

Formula

`"I"_{"y"} = ("e"_{"x"}*"P"*"c"_{"x"})/("σ"_{"total"}-(("P"/"A"_{"cs"})+(("e"_{"y"}*"P"*"c"_{"y"})/"I"_{"x"})))`

Example

`"50.05523kg·m²"=("4"*"9.99kN"*"15mm")/("14.8Pa"-(("9.99kN"/"13m²")+(("0.75"*"9.99kN"*"14mm")/"51kg·m²")))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
I_y = (e_x*P*c_x)/(σ_total-((P/A_cs)+((e_y*P*c_y)/I_x)))
This formula uses 9 Variables

Variables Used

Moment of Inertia about Y-Axis - (Measured in Kilogram Square Meter) - Moment of Inertia about Y-Axis is defined as the moment of inertia of cross-section about YY.
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.
Axial Load - (Measured in Kilonewton) - Axial Load is defined as applying a force on a structure directly along an axis of the structure.
Distance from YY to Outermost Fiber - (Measured in Millimeter) - Distance from YY to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.
Total Stress - (Measured in Pascal) - 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.
Cross-Sectional Area - (Measured in Square Meter) - 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.
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.
Distance from XX to Outermost Fiber - (Measured in Millimeter) - Distance from XX to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber.
Moment of Inertia about X-Axis - (Measured in Kilogram Square Meter) - Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX.

STEP 1: Convert Input(s) to Base Unit

Eccentricity with respect to Principal Axis YY: 4 --> No Conversion Required
Axial Load: 9.99 Kilonewton --> 9.99 Kilonewton No Conversion Required
Distance from YY to Outermost Fiber: 15 Millimeter --> 15 Millimeter No Conversion Required
Total Stress: 14.8 Pascal --> 14.8 Pascal No Conversion Required
Cross-Sectional Area: 13 Square Meter --> 13 Square Meter No Conversion Required
Eccentricity with respect to Principal Axis XX: 0.75 --> No Conversion Required
Distance from XX to Outermost Fiber: 14 Millimeter --> 14 Millimeter No Conversion Required
Moment of Inertia about X-Axis: 51 Kilogram Square Meter --> 51 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_y = (e_x*P*c_x)/(σ_total-((P/A_cs)+((e_y*P*c_y)/I_x))) --> (4*9.99*15)/(14.8-((9.99/13)+((0.75*9.99*14)/51)))

Evaluating ... ...

I_y = 50.0552254456484

STEP 3: Convert Result to Output's Unit

50.0552254456484 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

50.0552254456484 ≈ 50.05523 Kilogram Square Meter <-- Moment of Inertia about Y-Axis

(Calculation completed in 00.004 seconds)

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< 18 Eccentric Loading Calculators

Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane

Go Cross-Sectional Area = Axial Load/(Total Stress-(((Eccentricity with respect to Principal Axis YY*Axial Load*Distance from YY to Outermost Fiber)/(Moment of Inertia about Y-Axis))+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))))

Distance from YY to outermost fiber given Total Stress where Load doesn't lie on Plane

Go 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))))*Moment of Inertia about Y-Axis/(Eccentricity with respect to Principal Axis YY*Axial Load)

Distance from XX to outermost fiber given Total Stress where Load doesn't lie on Plane

Go Distance from XX to Outermost Fiber = ((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*Eccentricity with respect to Principal Axis XX)

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

Go 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)

Total Stress in Eccentric Loading when Load doesn't lie on Plane

Go 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))+((Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(Moment of Inertia about X-Axis))

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

Go Moment of Inertia about X-Axis = (Eccentricity with respect to Principal Axis XX*Axial Load*Distance from XX to Outermost Fiber)/(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 YY given Total Stress where Load doesn't lie on Plane

Go 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)))

Eccentricity wrt axis YY given Total Stress where Load doesn't lie on Plane

Go Eccentricity with respect to Principal Axis YY = ((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))*Moment of Inertia about Y-Axis)/(Axial Load*Distance from YY to Outermost Fiber)

Moment of Inertia of Cross-Section given Total Unit Stress in Eccentric Loading

Go Moment of Inertia about Neutral Axis = (Axial Load*Outermost Fiber Distance*Distance from Load applied)/(Total Unit Stress-(Axial Load/Cross-Sectional Area))

Cross-Sectional Area given Total Unit Stress in Eccentric Loading

Go Cross-Sectional Area = Axial Load/(Total Unit Stress-((Axial Load*Outermost Fiber Distance*Distance from Load applied/Moment of Inertia about Neutral Axis)))

Total Unit Stress in Eccentric Loading

Go Total Unit Stress = (Axial Load/Cross-Sectional Area)+(Axial Load*Outermost Fiber Distance*Distance from Load applied/Moment of Inertia about Neutral Axis)

Critical Buckling Load given Deflection in Eccentric Loading

Go Critical Buckling Load = (Axial Load*(4*Eccentricity of Load+pi*Deflection in Eccentric Loading))/(Deflection in Eccentric Loading*pi)

Eccentricity given Deflection in Eccentric Loading

Go Eccentricity of Load = (pi*(1-Axial Load/Critical Buckling Load))*Deflection in Eccentric Loading/(4*Axial Load/Critical Buckling Load)

Deflection in Eccentric Loading

Go Deflection in Eccentric Loading = (4*Eccentricity of Load*Axial Load/Critical Buckling Load)/(pi*(1-Axial Load/Critical Buckling Load))

Load for Deflection in Eccentric Loading

Go Axial Load = (Critical Buckling Load*Deflection in Eccentric Loading*pi)/(4*Eccentricity of Load+pi*Deflection in Eccentric Loading)

Radius of Gyration in Eccentric Loading

Go Radius of Gyration = sqrt(Moment of Inertia/Cross-Sectional Area)

Cross-Sectional Area given Radius of Gyration in Eccentric Loading

Go Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2)

Moment of Inertia given Radius of Gyration in Eccentric Loading

Go Moment of Inertia = (Radius of Gyration^2)*Cross-Sectional Area

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

What is Area Moment of Inertia

The second moment of area, or second area moment and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an {\displaystyle I}I (for an axis that lies in the plane) or with a {\displaystyle J}J (for an axis perpendicular to the plane).

How to Calculate 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 calculator 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 calculate 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 calculate Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane using this online calculator? To use this online calculator 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. Here is how the Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane calculation can be explained with given input values -> 11.27226 = (4*9990*0.015)/(14.8-((9990/13)+((0.75*9990*0.014)/51))).

FAQ

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

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 and is represented as I_y = (e_x*P*c_x)/(σ_total-((P/A_cs)+((e_y*P*c_y)/I_x))) or 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))). 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, Axial Load is defined as applying a force on a structure directly along an axis of the structure, Distance from YY to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber, 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, 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, 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, Distance from XX to Outermost Fiber is defined as the distance in between the Neutral Axis and Outermost Fiber & Moment of Inertia about X-Axis is defined as the moment of inertia of cross-section about XX.

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

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 is calculated using 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 calculate Moment of Inertia about YY given Total Stress where Load doesn't lie on Plane, you need 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). With our tool, you need to enter the respective value for Eccentricity with respect to Principal Axis YY, Axial Load, Distance from YY to Outermost Fiber, Total Stress, Cross-Sectional Area, Eccentricity with respect to Principal Axis XX, Distance from XX to Outermost Fiber & Moment of Inertia about X-Axis and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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