Eccentricity 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%
✖Critical Buckling Load is defined as the greatest load that will not cause lateral deflection.ⓘ Critical Buckling Load [P_c]			+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%

✖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 given Deflection in Eccentric Loading [e_load]

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Formula

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Eccentricity given Deflection in Eccentric Loading

Formula

e load = (π \cdot (1 - \frac{P}{P c})) \cdot \frac{δ}{4 \cdot \frac{P}{P c}}

Example

2.366965 mm = (π \cdot (1 - \frac{9.99 kN}{53 kN})) \cdot \frac{0.7 mm}{4 \cdot \frac{9.99 kN}{53 kN}}

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Eccentricity given Deflection in Eccentric Loading Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Axial Load - (Measured in Kilonewton) - Axial Load is defined as applying a force on a structure directly along an axis of the structure.
Critical Buckling Load - (Measured in Kilonewton) - Critical Buckling Load is defined as the greatest load that will not cause lateral deflection.
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
Critical Buckling Load: 53 Kilonewton --> 53 Kilonewton 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

e_load = (pi*(1-P/P_c))*δ/(4*P/P_c) --> (pi*(1-9.99/53))*0.7/(4*9.99/53)

Evaluating ... ...

e_load = 2.36696521575645

STEP 3: Convert Result to Output's Unit

0.00236696521575645 Meter -->2.36696521575645 Millimeter (Check conversion here)

FINAL ANSWER

2.36696521575645 ≈ 2.366965 Millimeter <-- Eccentricity of Load

(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

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)

Radius of Gyration in Eccentric Loading

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

Eccentricity given Deflection in Eccentric Loading Formula

Eccentricity of Load = (pi*(1-Axial Load/Critical Buckling Load))*Deflection in Eccentric Loading/(4*Axial Load/Critical Buckling Load)
e_load = (pi*(1-P/P_c))*δ/(4*P/P_c)

Define Eccentric loading

When the load acting on the column is offset from the centroid of the column, then it establishes the bending of column along with the axial stress. This offset loading of the column is referred as eccentric loading.

How to Calculate Eccentricity given Deflection in Eccentric Loading?

Eccentricity given Deflection in Eccentric Loading calculator uses Eccentricity of Load = (pi*(1-Axial Load/Critical Buckling Load))*Deflection in Eccentric Loading/(4*Axial Load/Critical Buckling Load) to calculate the Eccentricity of Load, The Eccentricity given Deflection in Eccentric Loading formula is defined as the distance in between the Neutral Axis and Outermost Fiber. Eccentricity of Load is denoted by e_load symbol.

How to calculate Eccentricity given Deflection in Eccentric Loading using this online calculator? To use this online calculator for Eccentricity given Deflection in Eccentric Loading, enter Axial Load (P), Critical Buckling Load (P_c) & Deflection in Eccentric Loading (δ) and hit the calculate button. Here is how the Eccentricity given Deflection in Eccentric Loading calculation can be explained with given input values -> 845.3447 = (pi*(1-9990/53000))*0.0007/(4*9990/53000).

FAQ

What is Eccentricity given Deflection in Eccentric Loading?

The Eccentricity given Deflection in Eccentric Loading formula is defined as the distance in between the Neutral Axis and Outermost Fiber and is represented as e_load = (pi*(1-P/P_c))*δ/(4*P/P_c) or Eccentricity of Load = (pi*(1-Axial Load/Critical Buckling Load))*Deflection in Eccentric Loading/(4*Axial Load/Critical Buckling Load). Axial Load is defined as applying a force on a structure directly along an axis of the structure, Critical Buckling Load is defined as the greatest load that will not cause lateral deflection & Deflection in Eccentric Loading the degree to which a structural element is displaced under a load (due to its deformation).

How to calculate Eccentricity given Deflection in Eccentric Loading?

The Eccentricity given Deflection in Eccentric Loading formula is defined as the distance in between the Neutral Axis and Outermost Fiber is calculated using Eccentricity of Load = (pi*(1-Axial Load/Critical Buckling Load))*Deflection in Eccentric Loading/(4*Axial Load/Critical Buckling Load). To calculate Eccentricity given Deflection in Eccentric Loading, you need Axial Load (P), Critical Buckling Load (P_c) & Deflection in Eccentric Loading (δ). With our tool, you need to enter the respective value for Axial Load, Critical Buckling 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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