Effective Length of Column given Maximum Stress for Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2)
Le = asech(((σmax-(P/Asectional))*S)/(P*e))/(sqrt(P/(εcolumn*I))/2)
This formula uses 3 Functions, 8 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
sech - The hyperbolic secant function is a hyperbolic function that is the reciprocal of the hyperbolic cosine function., sech(Number)
asech - The hyperbolic secant function is defined as sech(x) = 1/cosh(x), where cosh(x) is the hyperbolic cosine function., asech(Number)
Variables Used
Effective Column Length - (Measured in Meter) - Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip due to the applied nominal stress.
Eccentric load on column - (Measured in Newton) - Eccentric load on column is the load that causes direct stress as well as bending stress.
Column Cross Sectional Area - (Measured in Square Meter) - Column 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.
Section Modulus for Column - (Measured in Cubic Meter) - Section Modulus for Column is a geometric property for a given cross-section used in the design of beams or flexural members.
Eccentricity - (Measured in Meter) - Eccentricity is the distance from point of application of resultant to center of base.
Modulus of elasticity of column - (Measured in Pascal) - Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
STEP 1: Convert Input(s) to Base Unit
Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion ​here)
Eccentric load on column: 40 Newton --> 40 Newton No Conversion Required
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required
Section Modulus for Column: 13 Cubic Meter --> 13 Cubic Meter No Conversion Required
Eccentricity: 15000 Millimeter --> 15 Meter (Check conversion ​here)
Modulus of elasticity of column: 2 Megapascal --> 2000000 Pascal (Check conversion ​here)
Moment of Inertia: 0.000168 Kilogram Square Meter --> 0.000168 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Le = asech(((σmax-(P/Asectional))*S)/(P*e))/(sqrt(P/(εcolumn*I))/2) --> asech(((60-(40/1.4))*13)/(40*15))/(sqrt(40/(2000000*0.000168))/2)
Evaluating ... ...
Le = 5.41240687177984
STEP 3: Convert Result to Output's Unit
5.41240687177984 Meter -->5412.40687177984 Millimeter (Check conversion ​here)
FINAL ANSWER
5412.40687177984 5412.407 Millimeter <-- Effective Column Length
(Calculation completed in 00.004 seconds)

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16 Columns With Eccentric Load Calculators

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load
​ Go Column Cross Sectional Area = (Eccentric load on column)/(Maximum Stress at Crack Tip-(((Eccentric load on column*Eccentricity of Load*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)/Section Modulus for Column))
Effective Length of Column given Maximum Stress for Column with Eccentric Load
​ Go Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2)
Eccentricity given Maximum Stress for Column with Eccentric Load
​ Go Eccentricity = ((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/((Eccentric load on column*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)
Section Modulus given Maximum Stress for Column with Eccentric Load
​ Go Section Modulus for Column = ((Eccentric load on column*Eccentricity*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)/(Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))
Maximum Stress for Column with Eccentric Load
​ Go Maximum Stress at Crack Tip = (Eccentric load on column/Column Cross Sectional Area)+(((Eccentric load on column*Eccentricity*sec(Effective Column Length*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))))/2)/Section Modulus for Column)
Modulus of Elasticity given Maximum Stress for Column with Eccentric Load
​ Go Modulus of elasticity of column = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Moment of Inertia))
Moment of Inertia given Maximum Stress for Column with Eccentric Load
​ Go Moment of Inertia = ((asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(Effective Column Length))^2)/(Eccentric load on column/(Modulus of elasticity of column))
Eccentricity given Deflection at Section of Column with Eccentric load
​ Go Eccentricity = (Deflection of Column/(1-cos(Distance b/w fixed end and deflection point*sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia)))))-Deflection of Free End
Modulus of Elasticity given Deflection at Section of Column with Eccentric Load
​ Go Modulus of elasticity of column = (Eccentric load on column/(Moment of Inertia*(((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w fixed end and deflection point)^2)))
Moment of Inertia given Deflection at Section of Column with Eccentric Load
​ Go Moment of Inertia = (Eccentric load on column/(Modulus of elasticity of column*(((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w fixed end and deflection point)^2)))
Eccentric Load given Deflection at Section of Column with Eccentric Load
​ Go Eccentric load on column = (((acos(1-(Deflection of Column/(Deflection of Free End+Eccentricity of Load))))/Distance b/w fixed end and deflection point)^2)*(Modulus of elasticity of column*Moment of Inertia)
Eccentricity given Deflection at Free End of Column with Eccentric load
​ Go Eccentricity = Deflection of Free End/(sec(Column Length*sqrt(Eccentric load at column/(Modulus of elasticity of column*Moment of Inertia)))-1)
Modulus of Elasticity given Deflection at Free End of Column with Eccentric Load
​ Go Modulus of elasticity of column = Eccentric load on column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))
Moment of Inertia given Deflection at Free End of Column with Eccentric Load
​ Go Moment of Inertia = Eccentric load on column/(Modulus of elasticity of column*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))
Moment at Section of Column with Eccentric Load
​ Go Moment of force = Eccentric load on column*(Deflection of Free End+Eccentricity of Load-Deflection of Column)
Eccentricity given Moment at Section of Column with Eccentric Load
​ Go Eccentricity = (Moment of force/Eccentric load on column)-Deflection of Free End+Deflection of Column

Effective Length of Column given Maximum Stress for Column with Eccentric Load Formula

Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2)
Le = asech(((σmax-(P/Asectional))*S)/(P*e))/(sqrt(P/(εcolumn*I))/2)

What is buckling or crippling load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

How to Calculate Effective Length of Column given Maximum Stress for Column with Eccentric Load?

Effective Length of Column given Maximum Stress for Column with Eccentric Load calculator uses Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2) to calculate the Effective Column Length, The Effective length of column given maximum stress for column with eccentric load formula is defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration. Effective Column Length is denoted by Le symbol.

How to calculate Effective Length of Column given Maximum Stress for Column with Eccentric Load using this online calculator? To use this online calculator for Effective Length of Column given Maximum Stress for Column with Eccentric Load, enter Maximum Stress at Crack Tip max), Eccentric load on column (P), Column Cross Sectional Area (Asectional), Section Modulus for Column (S), Eccentricity (e), Modulus of elasticity of column column) & Moment of Inertia (I) and hit the calculate button. Here is how the Effective Length of Column given Maximum Stress for Column with Eccentric Load calculation can be explained with given input values -> 5.4E+6 = asech(((60-(40/1.4))*13)/(40*15))/(sqrt(40/(2000000*0.000168))/2).

FAQ

What is Effective Length of Column given Maximum Stress for Column with Eccentric Load?
The Effective length of column given maximum stress for column with eccentric load formula is defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration and is represented as Le = asech(((σmax-(P/Asectional))*S)/(P*e))/(sqrt(P/(εcolumn*I))/2) or Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2). Maximum stress at crack tip due to the applied nominal stress, Eccentric load on column is the load that causes direct stress as well as bending stress, Column 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, Section Modulus for Column is a geometric property for a given cross-section used in the design of beams or flexural members, Eccentricity is the distance from point of application of resultant to center of base, Modulus of elasticity of column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Effective Length of Column given Maximum Stress for Column with Eccentric Load?
The Effective length of column given maximum stress for column with eccentric load formula is defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration is calculated using Effective Column Length = asech(((Maximum Stress at Crack Tip-(Eccentric load on column/Column Cross Sectional Area))*Section Modulus for Column)/(Eccentric load on column*Eccentricity))/(sqrt(Eccentric load on column/(Modulus of elasticity of column*Moment of Inertia))/2). To calculate Effective Length of Column given Maximum Stress for Column with Eccentric Load, you need Maximum Stress at Crack Tip max), Eccentric load on column (P), Column Cross Sectional Area (Asectional), Section Modulus for Column (S), Eccentricity (e), Modulus of elasticity of column column) & Moment of Inertia (I). With our tool, you need to enter the respective value for Maximum Stress at Crack Tip, Eccentric load on column, Column Cross Sectional Area, Section Modulus for Column, Eccentricity, Modulus of elasticity of column & Moment of Inertia 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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