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

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

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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 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.
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 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Eccentricity with respect to Principal Axis XX: 0.75 --> No Conversion Required
Axial Load: 9.99 Kilonewton --> 9.99 Kilonewton No Conversion Required
Distance from XX to Outermost Fiber: 14 Millimeter --> 14 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 YY: 4 --> No Conversion Required
Distance from YY to Outermost Fiber: 15 Millimeter --> 15 Millimeter No Conversion Required
Moment of Inertia about Y-Axis: 50 Kilogram Square Meter --> 50 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_x = (e_y*P*c_y)/(σ_total-((P/A_cs)+((e_x*P*c_x)/I_y))) --> (0.75*9.99*14)/(14.8-((9.99/13)+((4*9.99*15)/50)))

Evaluating ... ...

I_x = 51.3300835654596

STEP 3: Convert Result to Output's Unit

51.3300835654596 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

51.3300835654596 ≈ 51.33008 Kilogram Square Meter <-- Moment of Inertia about X-Axis

(Calculation completed in 00.020 seconds)

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< Eccentric Loading Calculators

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

LaTeX 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

LaTeX 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

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

Radius of Gyration in Eccentric Loading

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

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

LaTeX Go

Define Total Stress

In physics, stress is the force acting on the unit area of a material. The effect of stress on a body is named as strain. Stress can deform the body. How much force material experience can be measured using stress units. Stress can be categorized into three categories depending upon the direction of the deforming forces acting on the body.

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

Moment of Inertia about XX given Total Stress where Load doesn't lie on Plane calculator uses 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))) to calculate the Moment of Inertia about X-Axis, The Moment of Inertia about XX 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 X-Axis is denoted by I_x symbol.

How to calculate Moment of Inertia about XX given Total Stress where Load doesn't lie on Plane using this online calculator? To use this online calculator for Moment of Inertia about XX given Total Stress where Load doesn't lie on Plane, enter Eccentricity with respect to Principal Axis XX (e_y), Axial Load (P), Distance from XX to Outermost Fiber (c_y), Total Stress (σ_total), 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) and hit the calculate button. Here is how the Moment of Inertia about XX given Total Stress where Load doesn't lie on Plane calculation can be explained with given input values -> 2.42568 = (0.75*9990*0.014)/(14.8-((9990/13)+((4*9990*0.015)/50))).

FAQ

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

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

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

The Moment of Inertia about XX 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 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))). To calculate Moment of Inertia about XX given Total Stress where Load doesn't lie on Plane, you need Eccentricity with respect to Principal Axis XX (e_y), Axial Load (P), Distance from XX to Outermost Fiber (c_y), Total Stress (σ_total), 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). With our tool, you need to enter the respective value for Eccentricity with respect to Principal Axis XX, Axial Load, Distance from XX to Outermost Fiber, Total Stress, Cross-Sectional Area, Eccentricity with respect to Principal Axis YY, Distance from YY to Outermost Fiber & Moment of Inertia about Y-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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