Maximum deflection for strut subjected to compressive axial and uniformly distributed load Calculator

✖Load Intensity is defined as load applied per unit area.ⓘ Load Intensity [q_f]			+10% -10%
✖Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity Column [ε_column]			+10% -10%
✖Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia Column [I]			+10% -10%
✖The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material.ⓘ Axial Thrust [P_axial]			+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 initial deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum deflection for strut subjected to compressive axial and uniformly distributed load [C]

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Formula

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Maximum deflection for strut subjected to compressive axial and uniformly distributed load

Formula

`"C" = ("q"_{"f"}*("ε"_{"column"}*"I"/("P"_{"axial"}^2))*((sec(("l"_{"column"}/2)*("P"_{"axial"}/("ε"_{"column"}*"I"))))-1))-("q"_{"f"}*("l"_{"column"}^2)/(8*"P"_{"axial"}))`

Example

`"-10414.443273mm"=("0.005MPa"*("10.56MPa"*"5600cm⁴"/(("1500N")^2))*((sec(("5000mm"/2)*("1500N"/("10.56MPa"*"5600cm⁴"))))-1))-("0.005MPa"*(("5000mm")^2)/(8*"1500N"))`

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Maximum deflection for strut subjected to compressive axial and uniformly distributed load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum initial deflection = (Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust))
C = (q_f*(ε_column*I/(P_axial^2))*((sec((l_column/2)*(P_axial/(ε_column*I))))-1))-(q_f*(l_column^2)/(8*P_axial))
This formula uses 1 Functions, 6 Variables

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)

Variables Used

Maximum initial deflection - (Measured in Meter) - Maximum initial deflection is the degree to which a structural element is displaced under a load.
Load Intensity - (Measured in Pascal) - Load Intensity is defined as load applied per unit area.
Modulus of Elasticity Column - (Measured in Pascal) - Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Moment of Inertia Column - (Measured in Meter⁴) - Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.
Axial Thrust - (Measured in Newton) - The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material.
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

Load Intensity: 0.005 Megapascal --> 5000 Pascal (Check conversion here)
Modulus of Elasticity Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Moment of Inertia Column: 5600 Centimeter⁴ --> 5.6E-05 Meter⁴ (Check conversion here)
Axial Thrust: 1500 Newton --> 1500 Newton No Conversion Required
Column Length: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C = (q_f*(ε_column*I/(P_axial^2))*((sec((l_column/2)*(P_axial/(ε_column*I))))-1))-(q_f*(l_column^2)/(8*P_axial)) --> (5000*(10560000*5.6E-05/(1500^2))*((sec((5/2)*(1500/(10560000*5.6E-05))))-1))-(5000*(5^2)/(8*1500))

Evaluating ... ...

C = -10.4144432728591

STEP 3: Convert Result to Output's Unit

-10.4144432728591 Meter -->-10414.4432728591 Millimeter (Check conversion here)

FINAL ANSWER

-10414.4432728591 ≈ -10414.443273 Millimeter <-- Maximum initial deflection

(Calculation completed in 00.014 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Strut With lateral load » Strut Subjected To Compressive Axial Thrust And A Transverse Uniformly Distributed Load » Maximum deflection for strut subjected to compressive axial and uniformly distributed load

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National Institute Of Technology (NIT), Hamirpur

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< 25 Strut Subjected To Compressive Axial Thrust And A Transverse Uniformly Distributed Load Calculators

Maximum deflection for strut subjected to compressive axial and uniformly distributed load

Go Maximum initial deflection = (Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust))

Load intensity given max deflection for strut subjected to uniformly distributed load

Go Load Intensity = Maximum initial deflection/((1*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(1*(Column Length^2)/(8*Axial Thrust)))

Maximum bending moment for strut subjected to compressive axial and uniformly distributed load

Go Maximum Bending Moment In Column = -Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/Axial Thrust)*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1)

Load intensity given max bending moment for strut subjected to uniformly distributed load

Go Load Intensity = Maximum Bending Moment In Column/(Modulus of Elasticity Column*Moment of Inertia Column/Axial Thrust)*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1)

Bending moment at section for strut subjected to compressive axial and uniformly distributed load

Go Bending Moment in Column = -(Axial Thrust*Deflection at Section)+(Load Intensity*(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2)))

Deflection at section for strut subjected to compressive axial and uniformly distributed load

Go Deflection at Section = (-Bending Moment in Column+(Load Intensity*(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2))))/Axial Thrust

Axial thrust for strut subjected to compressive axial and uniformly distributed load

Go Axial Thrust = (-Bending Moment in Column+(Load Intensity*(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2))))/Deflection at Section

Length of column for strut subjected to compressive axial and uniformly distributed load

Go Column Length = (((Distance of deflection from end A^2)/2)-((Bending Moment in Column+(Axial Thrust*Deflection at Section))/Load Intensity))*2/Distance of deflection from end A

Load intensity for strut subjected to compressive axial and uniformly distributed load

Go Load Intensity = (Bending Moment in Column+(Axial Thrust*Deflection at Section))/(((Distance of deflection from end A^2)/2)-(Column Length*Distance of deflection from end A/2))

Moment of inertia given maximum stress for strut subjected to uniformly distributed load

Go Moment of Inertia Column = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))))

Distance of extreme layer from NA given max stress for strut under uniformly distributed load

Go Distance from Neutral Axis to Extreme Point = (Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))*Moment of Inertia Column/(Maximum Bending Moment In Column)

Maximum bending moment given max stress for strut subjected to uniformly distributed load

Go Maximum Bending Moment In Column = (Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))*Moment of Inertia Column/(Distance from Neutral Axis to Extreme Point)

Cross-sectional area given maximum stress for strut subjected to uniformly distributed load

Go Column Cross Sectional Area = Axial Thrust/(Maximum bending stress-(Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/Moment of Inertia Column))

Maximum stress for strut subjected to compressive axial and uniformly distributed load

Go Maximum bending stress = (Axial Thrust/Column Cross Sectional Area)+(Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/Moment of Inertia Column)

Axial thrust given maximum stress for strut subjected to uniformly distributed load

Go Axial Thrust = (Maximum bending stress-(Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/Moment of Inertia Column))*Column Cross Sectional Area

Length of column given max bending moment for strut subjected to uniformly distributed load

Go Column Length = sqrt(((Axial Thrust*Maximum initial deflection)-Maximum Bending Moment In Column)*8/(Load Intensity))

Maximum bending moment given elastic modulus for strut subjected to uniformly distributed load

Go Maximum Bending Moment In Column = (Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))*Modulus of Elasticity Column

Cross-sectional area given elastic modulus for strut subjected to uniformly distributed load

Go Column Cross Sectional Area = Axial Thrust/(Maximum bending stress-(Maximum Bending Moment In Column/Modulus of Elasticity Column))

Maximum stress given elastic modulus for strut subjected to uniformly distributed load

Go Maximum bending stress = (Axial Thrust/Column Cross Sectional Area)+(Maximum Bending Moment In Column/Modulus of Elasticity Column)

Elastic modulus given maximum stress for strut subjected to uniformly distributed load

Go Modulus of Elasticity Column = Maximum Bending Moment In Column/(Maximum bending stress-(Axial Thrust/Column Cross Sectional Area))

Axial thrust given elastic modulus for strut subjected to uniformly distributed load

Go Axial Thrust = (Maximum bending stress-(Maximum Bending Moment In Column/Modulus of Elasticity Column))*Column Cross Sectional Area

Load intensity given maximum bending moment for strut subjected to uniformly distributed load

Go Load Intensity = (-(Axial Thrust*Maximum initial deflection)-Maximum Bending Moment In Column)*8/((Column Length^2))

Maximum deflection given max bending moment for strut subjected to uniformly distributed load

Go Maximum initial deflection = (-Maximum Bending Moment In Column-(Load Intensity*(Column Length^2)/8))/(Axial Thrust)

Axial thrust given maximum bending moment for strut subjected to uniformly distributed load

Go Axial Thrust = (-Maximum Bending Moment In Column-(Load Intensity*(Column Length^2)/8))/(Maximum initial deflection)

Maximum bending moment given max deflection for strut subjected to uniformly distributed load

Go Maximum Bending Moment In Column = -(Axial Thrust*Maximum initial deflection)-(Load Intensity*(Column Length^2)/8)

Maximum deflection for strut subjected to compressive axial and uniformly distributed load Formula

What is axial thrust?

Axial thrust refers to a propelling force applied along the axis (also called axial direction) of an object in order to push the object against a platform in a particular direction.

How to Calculate Maximum deflection for strut subjected to compressive axial and uniformly distributed load?

Maximum deflection for strut subjected to compressive axial and uniformly distributed load calculator uses Maximum initial deflection = (Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust)) to calculate the Maximum initial deflection, The Maximum deflection for strut subjected to compressive axial and uniformly distributed load formula is defined as the vertical displacement of a point on a loaded beam. Maximum initial deflection is denoted by C symbol.

How to calculate Maximum deflection for strut subjected to compressive axial and uniformly distributed load using this online calculator? To use this online calculator for Maximum deflection for strut subjected to compressive axial and uniformly distributed load, enter Load Intensity (q_f), Modulus of Elasticity Column (ε_column), Moment of Inertia Column (I), Axial Thrust (P_axial) & Column Length (l_column) and hit the calculate button. Here is how the Maximum deflection for strut subjected to compressive axial and uniformly distributed load calculation can be explained with given input values -> -10414443.272859 = (5000*(10560000*5.6E-05/(1500^2))*((sec((5/2)*(1500/(10560000*5.6E-05))))-1))-(5000*(5^2)/(8*1500)).

FAQ

What is Maximum deflection for strut subjected to compressive axial and uniformly distributed load?

The Maximum deflection for strut subjected to compressive axial and uniformly distributed load formula is defined as the vertical displacement of a point on a loaded beam and is represented as C = (q_f*(ε_column*I/(P_axial^2))*((sec((l_column/2)*(P_axial/(ε_column*I))))-1))-(q_f*(l_column^2)/(8*P_axial)) or Maximum initial deflection = (Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust)). Load Intensity is defined as load applied per unit area, Modulus of Elasticity Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it, Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis, The Axial Thrust is the resultant force of all the axial forces (F) acting on the object or material & 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 subjected to compressive axial and uniformly distributed load?

The Maximum deflection for strut subjected to compressive axial and uniformly distributed load formula is defined as the vertical displacement of a point on a loaded beam is calculated using Maximum initial deflection = (Load Intensity*(Modulus of Elasticity Column*Moment of Inertia Column/(Axial Thrust^2))*((sec((Column Length/2)*(Axial Thrust/(Modulus of Elasticity Column*Moment of Inertia Column))))-1))-(Load Intensity*(Column Length^2)/(8*Axial Thrust)). To calculate Maximum deflection for strut subjected to compressive axial and uniformly distributed load, you need Load Intensity (q_f), Modulus of Elasticity Column (ε_column), Moment of Inertia Column (I), Axial Thrust (P_axial) & Column Length (l_column). With our tool, you need to enter the respective value for Load Intensity, Modulus of Elasticity Column, Moment of Inertia Column, Axial Thrust & 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 initial deflection?

In this formula, Maximum initial deflection uses Load Intensity, Modulus of Elasticity Column, Moment of Inertia Column, Axial Thrust & Column Length. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum initial deflection = (-Maximum Bending Moment In Column-(Load Intensity*(Column Length^2)/8))/(Axial Thrust)

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