Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center Calculator

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

✖Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads.ⓘ Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center [M_max]

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Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Bending Moment In Column = 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)))))
M_max = W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive)))))
This formula uses 2 Functions, 6 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 Moment In Column - (Measured in Newton Meter) - Maximum Bending Moment In Column is the highest moment of force that causes the column to bend or deform under applied loads.
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 Compressive Load - (Measured in Newton) - Column Compressive Load is the load applied to a column that is compressive in nature.
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.

STEP 1: Convert Input(s) to Base Unit

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 Compressive Load: 0.4 Kilonewton --> 400 Newton (Check conversion here)
Column Length: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_max = W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))) --> 100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))

Evaluating ... ...

M_max = 0.0439145943300586

STEP 3: Convert Result to Output's Unit

0.0439145943300586 Newton Meter --> No Conversion Required

FINAL ANSWER

0.0439145943300586 ≈ 0.043915 Newton Meter <-- Maximum Bending Moment In Column

(Calculation completed in 00.020 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 Bending Moment for Strut with Axial and Transverse Point Load at Center

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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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 Bending Moment for Strut with Axial and Transverse Point Load at Center Formula

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What is Bending Moment?

A Bending Moment is a measure of the bending effect due to forces acting on a structural element, such as a beam, that causes it to bend. It is defined as the product of a force and the perpendicular distance from the point of interest to the line of action of the force. The bending moment reflects how much a beam or other structural member is likely to bend or rotate due to external forces applied to it.

How to Calculate Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center?

Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center calculator uses Maximum Bending Moment In Column = 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))))) to calculate the Maximum Bending Moment In Column, The Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center formula is defined as a measure of the maximum bending stress that occurs in a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, providing critical information for structural engineers to design safe and stable structures. Maximum Bending Moment In Column is denoted by M_max symbol.

How to calculate Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center using this online calculator? To use this online calculator for Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center, enter Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Compressive Load (P_compressive) & Column Length (l_column) and hit the calculate button. Here is how the Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center calculation can be explained with given input values -> 0.043915 = 100*(((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400))))).

FAQ

What is Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center?

The Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center formula is defined as a measure of the maximum bending stress that occurs in a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, providing critical information for structural engineers to design safe and stable structures and is represented as M_max = W_p*(((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive))))) or Maximum Bending Moment In Column = 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))))). 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 Compressive Load is the load applied to a column that is compressive in nature & Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

How to calculate Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center?

The Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center formula is defined as a measure of the maximum bending stress that occurs in a strut when it is subjected to both compressive axial thrust and a transverse point load at its center, providing critical information for structural engineers to design safe and stable structures is calculated using Maximum Bending Moment In Column = 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))))). To calculate Maximum Bending Moment for Strut with Axial and Transverse Point Load at Center, you need Greatest Safe Load (W_p), Moment of Inertia in Column (I), Modulus of Elasticity (ε_column), Column Compressive Load (P_compressive) & Column Length (l_column). With our tool, you need to enter the respective value for Greatest Safe Load, Moment of Inertia in Column, Modulus of Elasticity, Column Compressive Load & Column Length 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 Moment In Column?

In this formula, Maximum Bending Moment In Column uses Greatest Safe Load, Moment of Inertia in Column, Modulus of Elasticity, Column Compressive Load & Column Length. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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