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

✖Column Compressive Load is the load applied to a column that is compressive in nature.ⓘ Column Compressive Load [P_compressive]			+10% -10%
✖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.ⓘ Maximum Bending Stress [σb^max]			+10% -10%
✖Greatest Safe Load is the maximum safe point load allowable at the center of the beam.ⓘ Greatest Safe Load [W_p]			+10% -10%
✖Moment of Inertia in Column is the measure of the resistance of a column to angular acceleration about a given axis.ⓘ Moment of Inertia in Column [I]			+10% -10%
✖Modulus of Elasticity is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity [ε_column]			+10% -10%
✖Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.ⓘ Column Length [l_column]			+10% -10%
✖Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.ⓘ Distance from Neutral Axis to Extreme Point [c]			+10% -10%
✖Least Radius of Gyration of Column is a measure of the distribution of its cross-sectional area around its centroidal axis.ⓘ Least Radius of Gyration of Column [k]			+10% -10%

✖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.ⓘ Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load [A_sectional]

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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)))
A_sectional = (P_compressive/σb^max)+((W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(σb^max*(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

A_sectional = (P_compressive/σb^max)+((W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(σb^max*(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 ... ...

A_sectional = 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 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Strut With Lateral Load » Mechanical » Strut Subjected to Compressive Axial Thrust and a Transverse Point Load at the Centre » Cross-Sectional Area given Maximum Stress induced for Strut with Axial and Point Load

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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

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 A_sectional 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 (P_compressive), Maximum Bending Stress (σb^max), Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Length (l_column), 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 A_sectional = (P_compressive/σb^max)+((W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(σb^max*(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 (P_compressive), Maximum Bending Stress (σb^max), Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Length (l_column), 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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