Critical Buckling Load given Deflection in Eccentric Loading Calculator

✖Axial Load is defined as applying a force on a structure directly along an axis of the structure.ⓘ Axial Load [P]			+10% -10%
✖Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.ⓘ Eccentricity of Load [e_load]			+10% -10%
✖Deflection in Eccentric Loading the degree to which a structural element is displaced under a load (due to its deformation).ⓘ Deflection in Eccentric Loading [δ]			+10% -10%

✖Critical Buckling Load is defined as the greatest load that will not cause lateral deflection.ⓘ Critical Buckling Load given Deflection in Eccentric Loading [P_c]

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Formula

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Critical Buckling Load given Deflection in Eccentric Loading

Formula

`"P"_{"c"} = ("P"*(4*"e"_{"load"}+pi*"δ"))/("δ"*pi)`

Example

`"55.41737kN"=("9.99kN"*(4*"2.5mm"+pi*"0.7mm"))/("0.7mm"*pi)`

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Critical Buckling Load given Deflection in Eccentric Loading Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Buckling Load = (Axial Load*(4*Eccentricity of Load+pi*Deflection in Eccentric Loading))/(Deflection in Eccentric Loading*pi)
P_c = (P*(4*e_load+pi*δ))/(δ*pi)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Critical Buckling Load - (Measured in Kilonewton) - Critical Buckling Load is defined as the greatest load that will not cause lateral deflection.
Axial Load - (Measured in Kilonewton) - Axial Load is defined as applying a force on a structure directly along an axis of the structure.
Eccentricity of Load - (Measured in Millimeter) - Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.
Deflection in Eccentric Loading - (Measured in Millimeter) - Deflection in Eccentric Loading the degree to which a structural element is displaced under a load (due to its deformation).

STEP 1: Convert Input(s) to Base Unit

Axial Load: 9.99 Kilonewton --> 9.99 Kilonewton No Conversion Required
Eccentricity of Load: 2.5 Millimeter --> 2.5 Millimeter No Conversion Required
Deflection in Eccentric Loading: 0.7 Millimeter --> 0.7 Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_c = (P*(4*e_load+pi*δ))/(δ*pi) --> (9.99*(4*2.5+pi*0.7))/(0.7*pi)

Evaluating ... ...

P_c = 55.4173680425153

STEP 3: Convert Result to Output's Unit

55417.3680425153 Newton -->55.4173680425153 Kilonewton (Check conversion here)

FINAL ANSWER

55.4173680425153 ≈ 55.41737 Kilonewton <-- Critical Buckling Load

(Calculation completed in 00.005 seconds)

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Created by Kethavath Srinath

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

Critical Buckling Load given Deflection in Eccentric Loading Formula

Critical Buckling Load = (Axial Load*(4*Eccentricity of Load+pi*Deflection in Eccentric Loading))/(Deflection in Eccentric Loading*pi)
P_c = (P*(4*e_load+pi*δ))/(δ*pi)

Define Buckling Load

The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. The critical load puts the column in a state of unstable equilibrium. A load beyond the critical load causes the column to fail by buckling.

How to Calculate Critical Buckling Load given Deflection in Eccentric Loading?

Critical Buckling Load given Deflection in Eccentric Loading calculator uses Critical Buckling Load = (Axial Load*(4*Eccentricity of Load+pi*Deflection in Eccentric Loading))/(Deflection in Eccentric Loading*pi) to calculate the Critical Buckling Load, The Critical Buckling Load given Deflection in Eccentric Loading formula is defined as the greatest load that will not cause lateral deflection (buckling). Critical Buckling Load is denoted by P_c symbol.

How to calculate Critical Buckling Load given Deflection in Eccentric Loading using this online calculator? To use this online calculator for Critical Buckling Load given Deflection in Eccentric Loading, enter Axial Load (P), Eccentricity of Load (e_load) & Deflection in Eccentric Loading (δ) and hit the calculate button. Here is how the Critical Buckling Load given Deflection in Eccentric Loading calculation can be explained with given input values -> 0.055417 = (9990*(4*0.0025+pi*0.0007))/(0.0007*pi).

FAQ

What is Critical Buckling Load given Deflection in Eccentric Loading?

The Critical Buckling Load given Deflection in Eccentric Loading formula is defined as the greatest load that will not cause lateral deflection (buckling) and is represented as P_c = (P*(4*e_load+pi*δ))/(δ*pi) or Critical Buckling Load = (Axial Load*(4*Eccentricity of Load+pi*Deflection in Eccentric Loading))/(Deflection in Eccentric Loading*pi). Axial Load is defined as applying a force on a structure directly along an axis of the structure, Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load & Deflection in Eccentric Loading the degree to which a structural element is displaced under a load (due to its deformation).

How to calculate Critical Buckling Load given Deflection in Eccentric Loading?

The Critical Buckling Load given Deflection in Eccentric Loading formula is defined as the greatest load that will not cause lateral deflection (buckling) is calculated using Critical Buckling Load = (Axial Load*(4*Eccentricity of Load+pi*Deflection in Eccentric Loading))/(Deflection in Eccentric Loading*pi). To calculate Critical Buckling Load given Deflection in Eccentric Loading, you need Axial Load (P), Eccentricity of Load (e_load) & Deflection in Eccentric Loading (δ). With our tool, you need to enter the respective value for Axial Load, Eccentricity of Load & Deflection in Eccentric Loading 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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