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

STEP 0: Pre-Calculation Summary
Formula Used
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))
σtotal = (P/Acs)+((ex*P*cx)/(Iy))+((ey*P*cy)/(Ix))
This formula uses 9 Variables
Variables Used
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.
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
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
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
σtotal = (P/Acs)+((ex*P*cx)/(Iy))+((ey*P*cy)/(Ix)) --> (9.99/13)+((4*9.99*15)/(50))+((0.75*9.99*14)/(51))
Evaluating ... ...
σtotal = 14.8132262443439
STEP 3: Convert Result to Output's Unit
14.8132262443439 Pascal --> No Conversion Required
FINAL ANSWER
14.8132262443439 14.81323 Pascal <-- Total Stress
(Calculation completed in 00.004 seconds)

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Osmania University (OU), Hyderabad
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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

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

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))
σtotal = (P/Acs)+((ex*P*cx)/(Iy))+((ey*P*cy)/(Ix))

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

Total Stress in Eccentric Loading when Load doesn't lie on Plane calculator uses 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)) to calculate the Total Stress, The Total Stress in Eccentric Loading when Load doesn't lie on Plane formula is defined as the total force per unit area acting within a mass of soil. It is the sum of neutral and effective stresses. Total Stress is denoted by σtotal symbol.

How to calculate Total Stress in Eccentric Loading when Load doesn't lie on Plane using this online calculator? To use this online calculator for Total Stress in Eccentric Loading when Load doesn't lie on Plane, enter Axial Load (P), Cross-Sectional Area (Acs), Eccentricity with respect to Principal Axis YY (ex), Distance from YY to Outermost Fiber (cx), Moment of Inertia about Y-Axis (Iy), Eccentricity with respect to Principal Axis XX (ey), Distance from XX to Outermost Fiber (cy) & Moment of Inertia about X-Axis (Ix) and hit the calculate button. Here is how the Total Stress in Eccentric Loading when Load doesn't lie on Plane calculation can be explained with given input values -> 14.81323 = (9990/13)+((4*9990*0.015)/(50))+((0.75*9990*0.014)/(51)).

FAQ

What is Total Stress in Eccentric Loading when Load doesn't lie on Plane?
The Total Stress in Eccentric Loading when Load doesn't lie on Plane formula is defined as the total force per unit area acting within a mass of soil. It is the sum of neutral and effective stresses and is represented as σtotal = (P/Acs)+((ex*P*cx)/(Iy))+((ey*P*cy)/(Ix)) or 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)). 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, 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 Total Stress in Eccentric Loading when Load doesn't lie on Plane?
The Total Stress in Eccentric Loading when Load doesn't lie on Plane formula is defined as the total force per unit area acting within a mass of soil. It is the sum of neutral and effective stresses is calculated using 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)). To calculate Total Stress in Eccentric Loading when Load doesn't lie on Plane, you need Axial Load (P), Cross-Sectional Area (Acs), Eccentricity with respect to Principal Axis YY (ex), Distance from YY to Outermost Fiber (cx), Moment of Inertia about Y-Axis (Iy), Eccentricity with respect to Principal Axis XX (ey), Distance from XX to Outermost Fiber (cy) & Moment of Inertia about X-Axis (Ix). With our tool, you need to enter the respective value for Axial Load, Cross-Sectional Area, 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.
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