Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Calculator

✖Column Compressive Load is the load applied to a column that is compressive in nature.ⓘ Column Compressive Load [P_compressive]			+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.ⓘ Column Cross Sectional Area [A_sectional]			+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%

✖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 Stress Induced for Strut with Axial and Transverse Point Load at Center [σb^max]

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Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Bending Stress = (Column Compressive Load/Column Cross Sectional Area)+((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)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2)))
σb^max = (P_compressive/A_sectional)+((W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(A_sectional*(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

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.
Column Compressive Load - (Measured in Newton) - Column Compressive Load is the load applied to a column that is compressive in nature.
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.
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)
Column Cross Sectional Area: 1.4 Square Meter --> 1.4 Square Meter No Conversion Required
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

σb^max = (P_compressive/A_sectional)+((W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(A_sectional*(k^2))) --> (400/1.4)+((100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))))*(0.01)/(1.4*(0.0029277^2)))

Evaluating ... ...

σb^max = 322.309786460362

STEP 3: Convert Result to Output's Unit

322.309786460362 Pascal -->0.000322309786460362 Megapascal (Check conversion here)

FINAL ANSWER

0.000322309786460362 ≈ 0.000322 Megapascal <-- Maximum Bending Stress

(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 » Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center

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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)

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center 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 Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center calculator uses Maximum Bending Stress = (Column Compressive Load/Column Cross Sectional Area)+((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)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))) to calculate the Maximum Bending Stress, The Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum stress experienced by a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, taking into account the strut's geometric and material properties. Maximum Bending Stress is denoted by σb^max symbol.

How to calculate Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center using this online calculator? To use this online calculator for Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center, enter Column Compressive Load (P_compressive), Column Cross Sectional Area (A_sectional), 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 Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center calculation can be explained with given input values -> 2.9E-10 = (400/1.4)+((100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))))*(0.01)/(1.4*(0.0029277^2))).

FAQ

What is Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

The Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum stress experienced by a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, taking into account the strut's geometric and material properties and is represented as σb^max = (P_compressive/A_sectional)+((W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))))*(c)/(A_sectional*(k^2))) or Maximum Bending Stress = (Column Compressive Load/Column Cross Sectional Area)+((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)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))). Column Compressive Load is the load applied to a column that is compressive in nature, 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, 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 Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center?

The Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum stress experienced by a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, taking into account the strut's geometric and material properties is calculated using Maximum Bending Stress = (Column Compressive Load/Column Cross Sectional Area)+((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)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))). To calculate Maximum Stress Induced for Strut with Axial and Transverse Point Load at Center, you need Column Compressive Load (P_compressive), Column Cross Sectional Area (A_sectional), 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, Column Cross Sectional Area, 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 Maximum Bending Stress?

In this formula, Maximum Bending Stress uses Column Compressive Load, Column Cross Sectional Area, 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 1 other way(s) to calculate the same, which is/are as follows -

Maximum Bending Stress = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point)/(Column Cross Sectional Area*(Least Radius of Gyration of Column^2))

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