Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
Asectional = (P)/(σmax-(((P*eload*sec(Le*sqrt(P/(εcolumn*I))))/2)/S))
This formula uses 2 Functions, 8 Variables
Functions Used
sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
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)
Variables Used
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.
Eccentric load on column - (Measured in Newton) - Eccentric load on column is the load that causes direct stress as well as bending stress.
Maximum Stress at Crack Tip - (Measured in Pascal) - Maximum stress at crack tip due to the applied nominal stress.
Eccentricity of Load - (Measured in Meter) - Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load.
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Eccentric load on column: 40 Newton --> 40 Newton No Conversion Required
Maximum Stress at Crack Tip: 6E-05 Megapascal --> 60 Pascal (Check conversion here)
Eccentricity of Load: 2.5 Millimeter --> 0.0025 Meter (Check conversion here)
Effective Column Length: 200 Millimeter --> 0.2 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
Section Modulus for Column: 13 Cubic Meter --> 13 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Asectional = (P)/(σmax-(((P*eload*sec(Le*sqrt(P/(εcolumn*I))))/2)/S)) --> (40)/(60-(((40*0.0025*sec(0.2*sqrt(40/(2000000*0.000168))))/2)/13))
Evaluating ... ...
Asectional = 0.666709506414469
STEP 3: Convert Result to Output's Unit
0.666709506414469 Square Meter --> No Conversion Required
FINAL ANSWER
0.666709506414469 0.66671 Square Meter <-- Column Cross Sectional Area
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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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

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load Formula

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))
Asectional = (P)/(σmax-(((P*eload*sec(Le*sqrt(P/(εcolumn*I))))/2)/S))

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 Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?

Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load calculator uses 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)) to calculate the Column Cross Sectional Area, Cross sectional area of Column given Maximum stress for Column with Eccentric loadis defined as the area of a two-dimensional shape that is obtained when a three-dimensional object - such as a cylinder - is sliced perpendicular to some specified axis at a point. Column Cross Sectional Area is denoted by Asectional symbol.

How to calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load using this online calculator? To use this online calculator for Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load, enter Eccentric load on column (P), Maximum Stress at Crack Tip max), Eccentricity of Load (eload), Effective Column Length (Le), Modulus of elasticity of column column), Moment of Inertia (I) & Section Modulus for Column (S) and hit the calculate button. Here is how the Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load calculation can be explained with given input values -> 0.66671 = (40)/(60-(((40*0.0025*sec(0.2*sqrt(40/(2000000*0.000168))))/2)/13)).

FAQ

What is Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?
Cross sectional area of Column given Maximum stress for Column with Eccentric loadis defined as the area of a two-dimensional shape that is obtained when a three-dimensional object - such as a cylinder - is sliced perpendicular to some specified axis at a point and is represented as Asectional = (P)/(σmax-(((P*eload*sec(Le*sqrt(P/(εcolumn*I))))/2)/S)) or 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)). Eccentric load on column is the load that causes direct stress as well as bending stress, Maximum stress at crack tip due to the applied nominal stress, Eccentricity of Load is the distance from the center of gravity of the column section to the center of gravity of the applied load, 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, 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 & Section Modulus for Column is a geometric property for a given cross-section used in the design of beams or flexural members.
How to calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load?
Cross sectional area of Column given Maximum stress for Column with Eccentric loadis defined as the area of a two-dimensional shape that is obtained when a three-dimensional object - such as a cylinder - is sliced perpendicular to some specified axis at a point is calculated using 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)). To calculate Cross Sectional Area of Column given Maximum Stress for Column with Eccentric Load, you need Eccentric load on column (P), Maximum Stress at Crack Tip max), Eccentricity of Load (eload), Effective Column Length (Le), Modulus of elasticity of column column), Moment of Inertia (I) & Section Modulus for Column (S). With our tool, you need to enter the respective value for Eccentric load on column, Maximum Stress at Crack Tip, Eccentricity of Load, Effective Column Length, Modulus of elasticity of column, Moment of Inertia & Section Modulus for Column 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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