Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Column Cross Sectional Area = (Column Compressive Load/Maximum Bending Stress)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Maximum Bending Stress*(Least Radius of Gyration of Column^2)))
Asectional = (Pcompressive/σbmax)+((Wp*(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive))))))*(c)/(σbmax*(k^2)))
This formula uses 2 Functions, 9 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(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 column that is obtained when a column is sliced perpendicular to some specified axis at a point.
Column Compressive Load - (Measured in Newton) - Column Compressive Load is the load applied to a column that is compressive in nature.
Maximum Bending Stress - (Measured in Pascal) - Maximum Bending Stress is the highest stress experienced by a material when subjected to bending forces. It occurs at the point on a beam or structural element where the bending moment is greatest.
Greatest Safe Load - (Measured in Newton) - Greatest Safe Load is the maximum safe point load allowable at the center of the beam.
Moment of Inertia in Column - (Measured in Meter⁴) - Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis.
Modulus of Elasticity - (Measured in Pascal) - Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Column Length - (Measured in Meter) - Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
Distance from Neutral Axis to Extreme Point - (Measured in Meter) - Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.
Least Radius of Gyration of Column - (Measured in Meter) - Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis.
STEP 1: Convert Input(s) to Base Unit
Column Compressive Load: 0.4 Kilonewton --> 400 Newton (Check conversion ​here)
Maximum Bending Stress: 2 Megapascal --> 2000000 Pascal (Check conversion ​here)
Greatest Safe Load: 0.1 Kilonewton --> 100 Newton (Check conversion ​here)
Moment of Inertia in Column: 5600 Centimeter⁴ --> 5.6E-05 Meter⁴ (Check conversion ​here)
Modulus of Elasticity: 10.56 Megapascal --> 10560000 Pascal (Check conversion ​here)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion ​here)
Distance from Neutral Axis to Extreme Point: 10 Millimeter --> 0.01 Meter (Check conversion ​here)
Least Radius of Gyration of Column: 2.9277 Millimeter --> 0.0029277 Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Asectional = (Pcompressive/σbmax)+((Wp*(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive))))))*(c)/(σbmax*(k^2))) --> (400/2000000)+((100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))))*(0.01)/(2000000*(0.0029277^2)))
Evaluating ... ...
Asectional = 0.000225616850522253
STEP 3: Convert Result to Output's Unit
0.000225616850522253 Square Meter --> No Conversion Required
FINAL ANSWER
0.000225616850522253 0.000226 Square Meter <-- Column Cross Sectional Area
(Calculation completed in 00.020 seconds)

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Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre Calculators

Deflection at Section for Strut with Axial and Transverse Point Load at Center
​ LaTeX ​ Go Deflection at Column Section = Column Compressive Load-(Bending Moment in Column+(Greatest Safe Load*Distance of Deflection from end A/2))/(Column Compressive Load)
Compressive Axial Load for Strut with Axial and Transverse Point Load at Center
​ LaTeX ​ Go Column Compressive Load = -(Bending Moment in Column+(Greatest Safe Load*Distance of Deflection from end A/2))/(Deflection at Column Section)
Transverse Point Load for Strut with Axial and Transverse Point Load at Center
​ LaTeX ​ Go Greatest Safe Load = (-Bending Moment in Column-(Column Compressive Load*Deflection at Column Section))*2/(Distance of Deflection from end A)
Bending Moment at Section for Strut with Axial and Transverse Point Load at Center
​ LaTeX ​ Go Bending Moment in Column = -(Column Compressive Load*Deflection at Column Section)-(Greatest Safe Load*Distance of Deflection from end A/2)

Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load Formula

​LaTeX ​Go
Column Cross Sectional Area = (Column Compressive Load/Maximum Bending Stress)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Maximum Bending Stress*(Least Radius of Gyration of Column^2)))
Asectional = (Pcompressive/σbmax)+((Wp*(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive))))))*(c)/(σbmax*(k^2)))

What is Transverse Point Loading?

Transverse loading is a load applied vertically to the plane of the longitudinal axis of a configuration, such as a wind load. It causes the material to bend and rebound from its original position, with inner tensile and compressive straining associated with the change in curvature of the material.

How to Calculate Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load?

Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load calculator uses Column Cross Sectional Area = (Column Compressive Load/Maximum Bending Stress)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Maximum Bending Stress*(Least Radius of Gyration of Column^2))) to calculate the Column Cross Sectional Area, The Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load formula is defined as a measure of the minimum cross-sectional area required for a strut to withstand a given compressive axial thrust and a transverse point load at the center without failing due to induced stress. Column Cross Sectional Area is denoted by Asectional symbol.

How to calculate Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load using this online calculator? To use this online calculator for Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load, enter Column Compressive Load (Pcompressive), Maximum Bending Stress (σbmax), Greatest Safe Load (Wp), Moment of Inertia in Column (I), Modulus of Elasticity column), Column Length (lcolumn), Distance from Neutral Axis to Extreme Point (c) & Least Radius of Gyration of Column (k) and hit the calculate button. Here is how the Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load calculation can be explained with given input values -> 0.0002 = (400/2000000)+((100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))))*(0.01)/(2000000*(0.0029277^2))).

FAQ

What is Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load?
The Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load formula is defined as a measure of the minimum cross-sectional area required for a strut to withstand a given compressive axial thrust and a transverse point load at the center without failing due to induced stress and is represented as Asectional = (Pcompressive/σbmax)+((Wp*(((sqrt(I*εcolumn/Pcompressive))/(2*Pcompressive))*tan((lcolumn/2)*(sqrt(Pcompressive/(I*εcolumn/Pcompressive))))))*(c)/(σbmax*(k^2))) or Column Cross Sectional Area = (Column Compressive Load/Maximum Bending Stress)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Maximum Bending Stress*(Least Radius of Gyration of Column^2))). Column Compressive Load is the load applied to a column that is compressive in nature, Maximum Bending Stress is the highest stress experienced by a material when subjected to bending forces. It occurs at the point on a beam or structural element where the bending moment is greatest, Greatest Safe Load is the maximum safe point load allowable at the center of the beam, Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis, Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it, Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions, Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point & Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis.
How to calculate Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load?
The Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load formula is defined as a measure of the minimum cross-sectional area required for a strut to withstand a given compressive axial thrust and a transverse point load at the center without failing due to induced stress is calculated using Column Cross Sectional Area = (Column Compressive Load/Maximum Bending Stress)+((Greatest Safe Load*(((sqrt(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))/(2*Column Compressive Load))*tan((Column Length/2)*(sqrt(Column Compressive Load/(Moment of Inertia in Column*Modulus of Elasticity/Column Compressive Load))))))*(Distance from Neutral Axis to Extreme Point)/(Maximum Bending Stress*(Least Radius of Gyration of Column^2))). To calculate Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load, you need Column Compressive Load (Pcompressive), Maximum Bending Stress (σbmax), Greatest Safe Load (Wp), Moment of Inertia in Column (I), Modulus of Elasticity column), Column Length (lcolumn), Distance from Neutral Axis to Extreme Point (c) & Least Radius of Gyration of Column (k). With our tool, you need to enter the respective value for Column Compressive Load, Maximum Bending Stress, Greatest Safe Load, Moment of Inertia in Column, Modulus of Elasticity, Column Length, Distance from Neutral Axis to Extreme Point & Least Radius of Gyration of Column 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 Column Cross Sectional Area?
In this formula, Column Cross Sectional Area uses Column Compressive Load, Maximum Bending Stress, Greatest Safe Load, Moment of Inertia in Column, Modulus of Elasticity, Column Length, Distance from Neutral Axis to Extreme Point & Least Radius of Gyration of Column. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Column Cross Sectional Area = (Bending Moment in Column*Distance from Neutral Axis to Extreme Point)/(Bending Stress in Column*(Least Radius of Gyration of Column^2))
  • Column Cross Sectional Area = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/((Least Radius of Gyration of Column^2)*Maximum Bending Stress)
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