Transverse Point Load given Maximum Deflection for Strut Calculator

✖Deflection at Column Section is the lateral displacement at the section of the column.ⓘ Deflection at Column Section [δ]			+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%

✖Greatest Safe Load is the maximum safe point load allowable at the center of the beam.ⓘ Transverse Point Load given Maximum Deflection for Strut [W_p]

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Transverse Point Load given Maximum Deflection for Strut Solution

STEP 0: Pre-Calculation Summary

Formula Used

Greatest Safe Load = Deflection at Column Section/((((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)))
W_p = δ/((((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

Greatest Safe Load - (Measured in Newton) - Greatest Safe Load is the maximum safe point load allowable at the center of the beam.
Deflection at Column Section - (Measured in Meter) - Deflection at Column Section is the lateral displacement at the section of the column.
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

Deflection at Column Section: 12 Millimeter --> 0.012 Meter (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

W_p = δ/((((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))) --> 0.012/((((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))-(5/(4*400)))

Evaluating ... ...

W_p = -4.46785258866468

STEP 3: Convert Result to Output's Unit

-4.46785258866468 Newton -->-0.00446785258866468 Kilonewton (Check conversion here)

FINAL ANSWER

-0.00446785258866468 ≈ -0.004468 Kilonewton <-- Greatest Safe Load

(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 » Transverse Point Load given Maximum Deflection for Strut

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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)

Transverse Point Load given Maximum Deflection for Strut 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 Transverse Point Load given Maximum Deflection for Strut?

Transverse Point Load given Maximum Deflection for Strut calculator uses Greatest Safe Load = Deflection at Column Section/((((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 Greatest Safe Load, The Transverse Point Load given Maximum Deflection for Strut formula is defined as a measure of the load applied perpendicularly to the axis of a strut at its midpoint, considering the maximum deflection of the strut under compressive axial thrust and a transverse point load, providing insights into the strut's behavior under combined loading conditions. Greatest Safe Load is denoted by W_p symbol.

How to calculate Transverse Point Load given Maximum Deflection for Strut using this online calculator? To use this online calculator for Transverse Point Load given Maximum Deflection for Strut, enter Deflection at Column Section (δ), 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 Transverse Point Load given Maximum Deflection for Strut calculation can be explained with given input values -> -4.5E-6 = 0.012/((((sqrt(5.6E-05*10560000/400))/(2*400))*tan((5/2)*(sqrt(400/(5.6E-05*10560000/400)))))-(5/(4*400))).

FAQ

What is Transverse Point Load given Maximum Deflection for Strut?

The Transverse Point Load given Maximum Deflection for Strut formula is defined as a measure of the load applied perpendicularly to the axis of a strut at its midpoint, considering the maximum deflection of the strut under compressive axial thrust and a transverse point load, providing insights into the strut's behavior under combined loading conditions and is represented as W_p = δ/((((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 Greatest Safe Load = Deflection at Column Section/((((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))). Deflection at Column Section is the lateral displacement at the section of the column, 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 Transverse Point Load given Maximum Deflection for Strut?

The Transverse Point Load given Maximum Deflection for Strut formula is defined as a measure of the load applied perpendicularly to the axis of a strut at its midpoint, considering the maximum deflection of the strut under compressive axial thrust and a transverse point load, providing insights into the strut's behavior under combined loading conditions is calculated using Greatest Safe Load = Deflection at Column Section/((((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 Transverse Point Load given Maximum Deflection for Strut, you need Deflection at Column Section (δ), 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 Deflection at Column Section, 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 Greatest Safe Load?

In this formula, Greatest Safe Load uses Deflection at Column Section, Moment of Inertia in Column, Modulus of Elasticity, Column Compressive Load & Column Length. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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