Maximum Deflection 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%

✖Deflection at Column Section is the lateral displacement at the section of the column.ⓘ Maximum Deflection for Strut with Axial and Transverse Point Load at Center [δ]

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

STEP 0: Pre-Calculation Summary

Formula Used

Deflection at Column Section = 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)))))-(Column Length/(4*Column Compressive Load)))
δ = W_p*((((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive)))))-(l_column/(4*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

Deflection at Column Section - (Measured in Meter) - Deflection at Column Section is the lateral displacement at the section of the column.
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

δ = W_p*((((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive)))))-(l_column/(4*P_compressive))) --> 100*((((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))-(5/(4*400)))

Evaluating ... ...

δ = -0.268585405669941

STEP 3: Convert Result to Output's Unit

-0.268585405669941 Meter -->-268.585405669941 Millimeter (Check conversion here)

FINAL ANSWER

-268.585405669941 ≈ -268.585406 Millimeter <-- Deflection at Column Section

(Calculation completed in 00.022 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 Deflection 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 Deflection for Strut with Axial and Transverse Point Load at Center Formula

LaTeX Go

What is Deflection?

Deflection refers to the displacement or deformation of a structural element, such as a beam, column, or cantilever, under an applied load. It is the distance by which a point on the element moves from its original, unloaded position due to the forces or moments acting on it.

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

Maximum Deflection for Strut with Axial and Transverse Point Load at Center calculator uses Deflection at Column Section = 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)))))-(Column Length/(4*Column Compressive Load))) to calculate the Deflection at Column Section, The Maximum Deflection for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum displacement of a strut subjected to both compressive axial thrust and a transverse point load at its center, which affects its stability and structural integrity. Deflection at Column Section is denoted by δ symbol.

How to calculate Maximum Deflection for Strut with Axial and Transverse Point Load at Center using this online calculator? To use this online calculator for Maximum Deflection 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 Deflection for Strut with Axial and Transverse Point Load at Center calculation can be explained with given input values -> -268585.40567 = 100*((((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))-(5/(4*400))).

FAQ

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

The Maximum Deflection for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum displacement of a strut subjected to both compressive axial thrust and a transverse point load at its center, which affects its stability and structural integrity and is represented as δ = W_p*((((sqrt(I*ε_column/P_compressive))/(2*P_compressive))*tan((l_column/2)*(sqrt(P_compressive/(I*ε_column/P_compressive)))))-(l_column/(4*P_compressive))) or Deflection at Column Section = 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)))))-(Column Length/(4*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 Deflection for Strut with Axial and Transverse Point Load at Center?

The Maximum Deflection for Strut with Axial and Transverse Point Load at Center formula is defined as the maximum displacement of a strut subjected to both compressive axial thrust and a transverse point load at its center, which affects its stability and structural integrity is calculated using Deflection at Column Section = 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)))))-(Column Length/(4*Column Compressive Load))). To calculate Maximum Deflection 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 Deflection at Column Section?

In this formula, Deflection at Column Section 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 -

Deflection at Column Section = Column Compressive Load-(Bending Moment in Column+(Greatest Safe Load*Distance of Deflection from end A/2))/(Column Compressive Load)

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