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

✖Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment.ⓘ Maximum Bending Moment In Column [M]			+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%

✖Load Intensity is defined as load applied per unit area.ⓘ Load intensity given max bending moment for strut subjected to uniformly distributed load [q_f]

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Formula

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

Formula

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

Example

`"6.9E^-8MPa"="16N*m"/("10.56MPa"*"5600cm⁴"/"1500N")*((sec(("5000mm"/2)*("1500N"/("10.56MPa"*"5600cm⁴"))))-1)`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
q_f = M/(ε_column*I/P_axial)*((sec((l_column/2)*(P_axial/(ε_column*I))))-1)
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

Load Intensity - (Measured in Pascal) - Load Intensity is defined as load applied per unit area.
Maximum Bending Moment In Column - (Measured in Newton Meter) - Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment.
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

Maximum Bending Moment In Column: 16 Newton Meter --> 16 Newton Meter No Conversion Required
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

q_f = M/(ε_column*I/P_axial)*((sec((l_column/2)*(P_axial/(ε_column*I))))-1) --> 16/(10560000*5.6E-05/1500)*((sec((5/2)*(1500/(10560000*5.6E-05))))-1)

Evaluating ... ...

q_f = 0.0686651316157676

STEP 3: Convert Result to Output's Unit

0.0686651316157676 Pascal -->6.86651316157676E-08 Megapascal (Check conversion here)

FINAL ANSWER

6.86651316157676E-08 ≈ 6.9E-8 Megapascal <-- Load Intensity

(Calculation completed in 00.004 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 » Load intensity given max bending moment for strut subjected to uniformly distributed load

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National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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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)

Load intensity given max bending moment for strut subjected to 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 to push the object against a platform in a particular direction.

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

Load intensity given max bending moment for strut subjected to uniformly distributed load calculator uses 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) to calculate the Load Intensity, The Load intensity given max bending moment for strut subjected to uniformly distributed load formula is defined as the intensity of loading is equal to the rate of change of bending moment concerning x. Load Intensity is denoted by q_f symbol.

How to calculate Load intensity given max bending moment for strut subjected to uniformly distributed load using this online calculator? To use this online calculator for Load intensity given max bending moment for strut subjected to uniformly distributed load, enter Maximum Bending Moment In Column (M), 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 Load intensity given max bending moment for strut subjected to uniformly distributed load calculation can be explained with given input values -> 6.9E-14 = 16/(10560000*5.6E-05/1500)*((sec((5/2)*(1500/(10560000*5.6E-05))))-1).

FAQ

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

The Load intensity given max bending moment for strut subjected to uniformly distributed load formula is defined as the intensity of loading is equal to the rate of change of bending moment concerning x and is represented as q_f = M/(ε_column*I/P_axial)*((sec((l_column/2)*(P_axial/(ε_column*I))))-1) or 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). Maximum Bending Moment In Column is the absolute value of the maximum moment in the unbraced beam segment, 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 Load intensity given max bending moment for strut subjected to uniformly distributed load?

The Load intensity given max bending moment for strut subjected to uniformly distributed load formula is defined as the intensity of loading is equal to the rate of change of bending moment concerning x is calculated using 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). To calculate Load intensity given max bending moment for strut subjected to uniformly distributed load, you need Maximum Bending Moment In Column (M), 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 Maximum Bending Moment In Column, 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 Load Intensity?

In this formula, Load Intensity uses Maximum Bending Moment In Column, Modulus of Elasticity Column, Moment of Inertia Column, Axial Thrust & Column Length. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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