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

✖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%
✖Axial Load is defined as applying a force on a structure directly along an axis of the structure.ⓘ Axial Load [P]			+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 X-Axis [I_x]			+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%

✖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 w.r.t axis XX given Total Stress where Load doesn't lie on Plane [e_y]

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

Formula

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

Example

`"0.745177"=(("14.8Pa"-("9.99kN"/"13m²")-(("4"*"9.99kN"*"15mm")/("50kg·m²")))*"51kg·m²")/("9.99kN"*"14mm")`

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
Axial Load - (Measured in Kilonewton) - Axial Load is defined as applying a force on a structure directly along an axis of the structure.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Total Stress: 14.8 Pascal --> 14.8 Pascal No Conversion Required
Axial Load: 9.99 Kilonewton --> 9.99 Kilonewton 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
Moment of Inertia about X-Axis: 51 Kilogram Square Meter --> 51 Kilogram Square Meter No Conversion Required
Distance from XX to Outermost Fiber: 14 Millimeter --> 14 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_y = ((σ_total-(P/A_cs)-((e_x*P*c_x)/(I_y)))*I_x)/(P*c_y) --> ((14.8-(9.99/13)-((4*9.99*15)/(50)))*51)/(9.99*14)

Evaluating ... ...

e_y = 0.745177045177045

STEP 3: Convert Result to Output's Unit

0.745177045177045 --> No Conversion Required

FINAL ANSWER

0.745177045177045 ≈ 0.745177 <-- Eccentricity with respect to Principal Axis XX

(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

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

Define Eccentricity

Any conic section 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. That ratio is called the eccentricity, commonly denoted as e. The eccentricity can also be defined in terms of the intersection of a plane and a double-napped cone associated with the conic section.

How to Calculate 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 calculator 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 calculate 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 calculate Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane using this online calculator? To use this online calculator 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. Here is how the Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane calculation can be explained with given input values -> 15.76877 = ((14.8-(9990/13)-((4*9990*0.015)/(50)))*51)/(9990*0.014).

FAQ

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

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

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

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 is calculated using 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 calculate Eccentricity w.r.t axis XX given Total Stress where Load doesn't lie on Plane, you need 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). With our tool, you need to enter the respective value for Total Stress, Axial Load, Cross-Sectional Area, Eccentricity with respect to Principal Axis YY, Distance from YY to Outermost Fiber, Moment of Inertia about Y-Axis, Moment of Inertia about X-Axis & Distance from XX to Outermost Fiber 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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