Modulus of Elasticity given Maximum Stress for Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
εcolumn = ((asech(((σmax-(P/Asectional))*S)/(P*e))/(Le))^2)/(P/(I))
This formula uses 2 Functions, 8 Variables
Functions Used
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
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.
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.
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.
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)
Effective Column Length: 200 Millimeter --> 0.2 Meter (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
εcolumn = ((asech(((σmax-(P/Asectional))*S)/(P*e))/(Le))^2)/(P/(I)) --> ((asech(((60-(40/1.4))*13)/(40*15))/(0.2))^2)/(40/(0.000168))
Evaluating ... ...
εcolumn = 9.15442129552802E-05
STEP 3: Convert Result to Output's Unit
9.15442129552802E-05 Pascal -->9.15442129552802E-11 Megapascal (Check conversion here)
FINAL ANSWER
9.15442129552802E-11 9.2E-11 Megapascal <-- Modulus of elasticity of column
(Calculation completed in 00.020 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

Modulus of Elasticity given Maximum Stress for Column with Eccentric Load Formula

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))
εcolumn = ((asech(((σmax-(P/Asectional))*S)/(P*e))/(Le))^2)/(P/(I))

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 Modulus of Elasticity given Maximum Stress for Column with Eccentric Load?

Modulus of Elasticity given Maximum Stress for Column with Eccentric Load calculator uses 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)) to calculate the Modulus of elasticity of column, The Modulus of elasticity given maximum stress for column with eccentric load formula is defined as a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it. Modulus of elasticity of column is denoted by εcolumn symbol.

How to calculate Modulus of Elasticity given Maximum Stress for Column with Eccentric Load using this online calculator? To use this online calculator for Modulus of Elasticity 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), Effective Column Length (Le) & Moment of Inertia (I) and hit the calculate button. Here is how the Modulus of Elasticity given Maximum Stress for Column with Eccentric Load calculation can be explained with given input values -> 9.2E-17 = ((asech(((60-(40/1.4))*13)/(40*15))/(0.2))^2)/(40/(0.000168)).

FAQ

What is Modulus of Elasticity given Maximum Stress for Column with Eccentric Load?
The Modulus of elasticity given maximum stress for column with eccentric load formula is defined as a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it and is represented as εcolumn = ((asech(((σmax-(P/Asectional))*S)/(P*e))/(Le))^2)/(P/(I)) or 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)). 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, 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 & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Modulus of Elasticity given Maximum Stress for Column with Eccentric Load?
The Modulus of elasticity given maximum stress for column with eccentric load formula is defined as a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when stress is applied to it is calculated using 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)). To calculate Modulus of Elasticity 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), Effective Column Length (Le) & 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, Effective Column Length & Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Modulus of elasticity of column?
In this formula, Modulus of elasticity of column uses Maximum Stress at Crack Tip, Eccentric load on column, Column Cross Sectional Area, Section Modulus for Column, Eccentricity, Effective Column Length & Moment of Inertia. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • 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)))
  • Modulus of elasticity of column = Eccentric load on column/(Moment of Inertia*(((arcsec((Deflection of Free End/Eccentricity of Load)+1))/Column Length)^2))
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