Static Deflection for Cantilever Beam with Uniformly Distributed Load Calculator

✖Load per unit length is the amount of load applied per unit length of a beam, used to calculate static deflection under various load conditions.ⓘ Load per unit Length [w]			+10% -10%
✖Length of Cantilever Beam is the maximum downward displacement of a cantilever beam under various load conditions, affecting its structural integrity and stability.ⓘ Length of Cantilever Beam [L_cant]			+10% -10%
✖Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the static deflection of beams under various load conditions.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of Inertia of Beam is a measure of the beam's resistance to bending under various load conditions, providing insight into its structural behavior.ⓘ Moment of Inertia of Beam [I]			+10% -10%

✖Static Deflection is the maximum displacement of a beam from its original position under various load conditions and types of beams.ⓘ Static Deflection for Cantilever Beam with Uniformly Distributed Load [δ]

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Static Deflection for Cantilever Beam with Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam)
δ = (w*L_cant^4)/(8*E*I)
This formula uses 5 Variables

Variables Used

Static Deflection - (Measured in Meter) - Static Deflection is the maximum displacement of a beam from its original position under various load conditions and types of beams.
Load per unit Length - Load per unit length is the amount of load applied per unit length of a beam, used to calculate static deflection under various load conditions.
Length of Cantilever Beam - (Measured in Meter) - Length of Cantilever Beam is the maximum downward displacement of a cantilever beam under various load conditions, affecting its structural integrity and stability.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the static deflection of beams under various load conditions.
Moment of Inertia of Beam - (Measured in Meter⁴ per Meter) - Moment of Inertia of Beam is a measure of the beam's resistance to bending under various load conditions, providing insight into its structural behavior.

STEP 1: Convert Input(s) to Base Unit

Load per unit Length: 0.81 --> No Conversion Required
Length of Cantilever Beam: 5 Meter --> 5 Meter No Conversion Required
Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of Inertia of Beam: 6 Meter⁴ per Meter --> 6 Meter⁴ per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (w*L_cant^4)/(8*E*I) --> (0.81*5^4)/(8*15*6)

Evaluating ... ...

δ = 0.703125

STEP 3: Convert Result to Output's Unit

0.703125 Meter --> No Conversion Required

FINAL ANSWER

0.703125 Meter <-- Static Deflection

(Calculation completed in 00.020 seconds)

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< Values of static deflection for the various types of beams and under various load conditions Calculators

Static Deflection for Simply Supported Beam with Eccentric Point Load

LaTeX Go Static Deflection = (Eccentric Point Load*Distance of Load from One End^2*Distance of Load from Other End^2)/(3*Young's Modulus*Moment of Inertia of Beam*Length of Simply Supported Beam)

Static Deflection for Cantilever Beam with Point Load at Free End

LaTeX Go Static Deflection = (Load Attached to Free End of Constraint*Length of Cantilever Beam^3)/(3*Young's Modulus*Moment of Inertia of Beam)

Static Deflection for Simply Supported Beam with Central Point Load

LaTeX Go Static Deflection = (Central Point Load*Length of Simply Supported Beam^3)/(48*Young's Modulus*Moment of Inertia of Beam)

Static Deflection for Cantilever Beam with Uniformly Distributed Load

LaTeX Go Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam)

Static Deflection for Cantilever Beam with Uniformly Distributed Load Formula

LaTeX Go

Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam)
δ = (w*L_cant^4)/(8*E*I)

What is Cantilever Beam?

A cantilever beam is a structural element that is fixed at one end and free at the other. It is commonly used in construction, bridges, and mechanical structures. The fixed end supports all loads, while the free end allows the beam to extend without support. It can bear bending and shear forces, making it ideal for overhanging structures.

How to Calculate Static Deflection for Cantilever Beam with Uniformly Distributed Load?

Static Deflection for Cantilever Beam with Uniformly Distributed Load calculator uses Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam) to calculate the Static Deflection, Static Deflection for Cantilever Beam with Uniformly Distributed Load formula is defined as a measure of the maximum displacement of a cantilever beam under a uniformly distributed load, providing insight into the beam's structural integrity and ability to withstand external forces. Static Deflection is denoted by δ symbol.

How to calculate Static Deflection for Cantilever Beam with Uniformly Distributed Load using this online calculator? To use this online calculator for Static Deflection for Cantilever Beam with Uniformly Distributed Load, enter Load per unit Length (w), Length of Cantilever Beam (L_cant), Young's Modulus (E) & Moment of Inertia of Beam (I) and hit the calculate button. Here is how the Static Deflection for Cantilever Beam with Uniformly Distributed Load calculation can be explained with given input values -> 0.703125 = (0.81*5^4)/(8*15*6).

FAQ

What is Static Deflection for Cantilever Beam with Uniformly Distributed Load?

Static Deflection for Cantilever Beam with Uniformly Distributed Load formula is defined as a measure of the maximum displacement of a cantilever beam under a uniformly distributed load, providing insight into the beam's structural integrity and ability to withstand external forces and is represented as δ = (w*L_cant^4)/(8*E*I) or Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam). Load per unit length is the amount of load applied per unit length of a beam, used to calculate static deflection under various load conditions, Length of Cantilever Beam is the maximum downward displacement of a cantilever beam under various load conditions, affecting its structural integrity and stability, Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the static deflection of beams under various load conditions & Moment of Inertia of Beam is a measure of the beam's resistance to bending under various load conditions, providing insight into its structural behavior.

How to calculate Static Deflection for Cantilever Beam with Uniformly Distributed Load?

Static Deflection for Cantilever Beam with Uniformly Distributed Load formula is defined as a measure of the maximum displacement of a cantilever beam under a uniformly distributed load, providing insight into the beam's structural integrity and ability to withstand external forces is calculated using Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam). To calculate Static Deflection for Cantilever Beam with Uniformly Distributed Load, you need Load per unit Length (w), Length of Cantilever Beam (L_cant), Young's Modulus (E) & Moment of Inertia of Beam (I). With our tool, you need to enter the respective value for Load per unit Length, Length of Cantilever Beam, Young's Modulus & Moment of Inertia of Beam 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 Static Deflection?

In this formula, Static Deflection uses Load per unit Length, Length of Cantilever Beam, Young's Modulus & Moment of Inertia of Beam. We can use 3 other way(s) to calculate the same, which is/are as follows -

Static Deflection = (Load Attached to Free End of Constraint*Length of Cantilever Beam^3)/(3*Young's Modulus*Moment of Inertia of Beam)
Static Deflection = (Central Point Load*Length of Simply Supported Beam^3)/(48*Young's Modulus*Moment of Inertia of Beam)
Static Deflection = (Eccentric Point Load*Distance of Load from One End^2*Distance of Load from Other End^2)/(3*Young's Modulus*Moment of Inertia of Beam*Length of Simply Supported Beam)

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