Rankine's Formula for Columns Calculator

✖The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend.ⓘ Euler’s Buckling Load [P_E]			+10% -10%
✖The Ultimate Crushing Load for Columns is the ultimate load that column can bear before failure.ⓘ Ultimate Crushing Load for Columns [P_cs]			+10% -10%

✖The Rankine’s critical load is the axial load at which a perfectly straight column or structural member starts to bend.ⓘ Rankine's Formula for Columns [P_r]

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Rankine's Formula for Columns

Formula

`"P"_{"r"} = 1/(1/"P"_{"E"}+1/"P"_{"cs"})`

Example

`"385.5667kN"=1/(1/"1491.407kN"+1/"520kN")`

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Rankine's Formula for Columns Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns)
P_r = 1/(1/P_E+1/P_cs)
This formula uses 3 Variables

Variables Used

Rankine’s Critical Load - (Measured in Newton) - The Rankine’s critical load is the axial load at which a perfectly straight column or structural member starts to bend.
Euler’s Buckling Load - (Measured in Newton) - The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend.
Ultimate Crushing Load for Columns - (Measured in Newton) - The Ultimate Crushing Load for Columns is the ultimate load that column can bear before failure.

STEP 1: Convert Input(s) to Base Unit

Euler’s Buckling Load: 1491.407 Kilonewton --> 1491407 Newton (Check conversion here)
Ultimate Crushing Load for Columns: 520 Kilonewton --> 520000 Newton (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_r = 1/(1/P_E+1/P_cs) --> 1/(1/1491407+1/520000)

Evaluating ... ...

P_r = 385566.740097852

STEP 3: Convert Result to Output's Unit

385566.740097852 Newton -->385.566740097852 Kilonewton (Check conversion here)

FINAL ANSWER

385.566740097852 ≈ 385.5667 Kilonewton <-- Rankine’s Critical Load

(Calculation completed in 00.004 seconds)

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Home » Engineering » Mechanical » Strength of Materials » Stress and Strain » Rankine's Formula for Columns

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Created by Pragati Jaju

College Of Engineering (COEP), Pune

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Osmania University (OU), Hyderabad

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< 18 Stress and Strain Calculators

Elongation Circular Tapered Bar

Go Elongation = (4*Load*Length of Bar)/(pi*Diameter of Bigger End*Diameter of Smaller End*Elastic Modulus)

Total Angle of Twist

Go Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)

Moment of Inertia for Hollow Circular Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4))

Equivalent Bending Moment

Go Equivalent Bending Moment = Bending Moment+sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Deflection of Fixed Beam with Uniformly Distributed Load

Go Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)

Deflection of Fixed Beam with Load at Center

Go Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)

Elongation of Prismatic Bar due to its Own Weight

Go Elongation = (2*Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Axial Elongation of Prismatic Bar due to External Load

Go Elongation = (Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Hooke's Law

Go Young's Modulus = (Load*Elongation)/(Area of Base*Initial Length)

Equivalent Torsional Moment

Go Equivalent Torsion Moment = sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Rankine's Formula for Columns

Go Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns)

Slenderness Ratio

Go Slenderness Ratio = Effective Length/Least Radius of Gyration

Moment of Inertia about Polar Axis

Go Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32

Bulk Modulus given Volume Stress and Strain

Go Bulk Modulus = Volume Stress/Volumetric Strain

Shear Modulus

Go Shear Modulus = Shear Stress/Shear Strain

Bulk Modulus given Bulk Stress and Strain

Go Bulk Modulus = Bulk Stress/Bulk Strain

Young's Modulus

Go Young's Modulus = Stress/Strain

Elastic Modulus

Go Young's Modulus = Stress/Strain

Rankine's Formula for Columns Formula

Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns)
P_r = 1/(1/P_E+1/P_cs)

What is Crippling Load?

The crippling load, or more frequently called load, is the load over which a column prefers to deform laterally rather than compressing itself. Buckling is not about going over the maximum compressive stress, it is rather about the structure finding a geometrically stable alternative to being compressed.

How to Calculate Rankine's Formula for Columns?

Rankine's Formula for Columns calculator uses Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns) to calculate the Rankine’s Critical Load, The Rankine's Formula for Columns is inverse of sum of reciprocal of crippling load by euler's formula and reciprocal of ultinate crushing load for columns. Rankine’s Critical Load is denoted by P_r symbol.

How to calculate Rankine's Formula for Columns using this online calculator? To use this online calculator for Rankine's Formula for Columns, enter Euler’s Buckling Load (P_E) & Ultimate Crushing Load for Columns (P_cs) and hit the calculate button. Here is how the Rankine's Formula for Columns calculation can be explained with given input values -> 0.385567 = 1/(1/1491407+1/520000).

FAQ

What is Rankine's Formula for Columns?

The Rankine's Formula for Columns is inverse of sum of reciprocal of crippling load by euler's formula and reciprocal of ultinate crushing load for columns and is represented as P_r = 1/(1/P_E+1/P_cs) or Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns). The Euler’s Buckling Load is the axial load at which a perfectly straight column or structural member starts to bend & The Ultimate Crushing Load for Columns is the ultimate load that column can bear before failure.

How to calculate Rankine's Formula for Columns?

The Rankine's Formula for Columns is inverse of sum of reciprocal of crippling load by euler's formula and reciprocal of ultinate crushing load for columns is calculated using Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns). To calculate Rankine's Formula for Columns, you need Euler’s Buckling Load (P_E) & Ultimate Crushing Load for Columns (P_cs). With our tool, you need to enter the respective value for Euler’s Buckling Load & Ultimate Crushing Load for Columns 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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