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

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

✖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 given Total Stress is where Load doesn't lie on Plane [A_cs]

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

Formula

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

Example

`"13.22767m²"="9.99kN"/("14.8Pa"-((("4"*"9.99kN"*"15mm")/("50kg·m²"))+(("0.75"*"9.99kN"*"14mm")/("51kg·m²"))))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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

Axial Load: 9.99 Kilonewton --> 9.99 Kilonewton No Conversion Required
Total Stress: 14.8 Pascal --> 14.8 Pascal 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
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

A_cs = P/(σ_total-(((e_x*P*c_x)/(I_y))+((e_y*P*c_y)/(I_x)))) --> 9.99/(14.8-(((4*9.99*15)/(50))+((0.75*9.99*14)/(51))))

Evaluating ... ...

A_cs = 13.2276657060519

STEP 3: Convert Result to Output's Unit

13.2276657060519 Square Meter --> No Conversion Required

FINAL ANSWER

13.2276657060519 ≈ 13.22767 Square Meter <-- Cross-Sectional Area

(Calculation completed in 00.011 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

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

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

Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane calculator uses 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)))) to calculate the Cross-Sectional Area, The Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane formula is defined as the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point. Cross-Sectional Area is denoted by A_cs symbol.

How to calculate Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane using this online calculator? To use this online calculator for Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane, enter Axial Load (P), Total Stress (σ_total), 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), 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 Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane calculation can be explained with given input values -> 0.238111 = 9990/(14.8-(((4*9990*0.015)/(50))+((0.75*9990*0.014)/(51)))).

FAQ

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

The Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane formula is defined as the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point and is represented as A_cs = P/(σ_total-(((e_x*P*c_x)/(I_y))+((e_y*P*c_y)/(I_x)))) or 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)))). Axial Load is defined as applying a force on a structure directly along an axis of the structure, 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, 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, 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 Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane?

The Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane formula is defined as the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point is calculated using 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)))). To calculate Cross-Sectional Area given Total Stress is where Load doesn't lie on Plane, you need Axial Load (P), Total Stress (σ_total), 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), 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 Axial Load, Total Stress, Eccentricity with respect to Principal Axis YY, Distance from YY to Outermost Fiber, Moment of Inertia about Y-Axis, 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.

How many ways are there to calculate Cross-Sectional Area?

In this formula, Cross-Sectional Area uses Axial Load, Total Stress, Eccentricity with respect to Principal Axis YY, Distance from YY to Outermost Fiber, Moment of Inertia about Y-Axis, Eccentricity with respect to Principal Axis XX, Distance from XX to Outermost Fiber & Moment of Inertia about X-Axis. We can use 2 other way(s) to calculate the same, which is/are as follows -

Cross-Sectional Area = Axial Load/(Total Unit Stress-((Axial Load*Outermost Fiber Distance*Distance from Load applied/Moment of Inertia about Neutral Axis)))
Cross-Sectional Area = Moment of Inertia/(Radius of Gyration^2)

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