Static Deflection for Cantilever Beam with Point Load at Free End Solution

STEP 0: Pre-Calculation Summary
Formula Used
Static Deflection = (Load Attached to Free End of Constraint*Length of beam^3)/(3*Young's Modulus*Moment of Inertia of Beam)
δ = (Wattached*L^3)/(3*E*I)
This formula uses 5 Variables
Variables Used
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.
Length of beam - (Measured in Meter) - Length of beam between inflection points.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of Inertia of Beam - (Measured in Meter⁴ per Meter) - Moment of Inertia of Beam is a quantitative measure of the rotational inertia of a body.
STEP 1: Convert Input(s) to Base Unit
Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required
Length of 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 = (Wattached*L^3)/(3*E*I) --> (0.52*5^3)/(3*15*6)
Evaluating ... ...
δ = 0.240740740740741
STEP 3: Convert Result to Output's Unit
0.240740740740741 Meter --> No Conversion Required
FINAL ANSWER
0.240740740740741 0.240741 Meter <-- Static Deflection
(Calculation completed in 00.019 seconds)

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National Institute Of Technology (NIT), Hamirpur
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8 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
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 beam)
Static Deflection in Fixed Beam with Eccentric Point Load
Go Static Deflection = (Eccentric point load*Distance of load from one end^3*Distance of load from other end^3)/(3*Young's Modulus*Moment of Inertia of Beam*Length of beam)
Static Deflection for Cantilever Beam with Point Load at Free End
Go Static Deflection = (Load Attached to Free End of Constraint*Length of beam^3)/(3*Young's Modulus*Moment of Inertia of Beam)
Static Deflection for Simply Supported Beam with Uniformly Distributed Load
Go Static Deflection = (5*Load per unit length*Length of beam^4)/(384*Young's Modulus*Polar Moment of Inertia)
Static Deflection for Fixed Beam with Uniformly Distributed Point Load
Go Static Deflection = (Load per unit length*Length of beam^4)/(384*Young's Modulus*Moment of Inertia of Beam)
Static Deflection for Cantilever Beam with Uniformly Distributed Load
Go Static Deflection = (Load per unit length*Length of beam^4)/(8*Young's Modulus*Moment of Inertia of Beam)
Static Deflection for Fixed Beam with Central Point Load
Go Static Deflection = (Central point load*Length of beam^3)/(192*Young's Modulus*Moment of Inertia of Beam)
Static Deflection for Simply Supported Beam with Central Point Load
Go Static Deflection = (Central point load*Length of beam^3)/(48*Young's Modulus*Moment of Inertia of Beam)

Static Deflection for Cantilever Beam with Point Load at Free End Formula

Static Deflection = (Load Attached to Free End of Constraint*Length of beam^3)/(3*Young's Modulus*Moment of Inertia of Beam)
δ = (Wattached*L^3)/(3*E*I)

What is the difference between bending and deflection?

With "bending" you really mean the bending moment. The bending moment in an inner stress within a member (usually beam) that allows it to carry a load. Deflection measures the actual change in a material you could call "bending." It measures the physical displacement of a member under a load.

How to Calculate Static Deflection for Cantilever Beam with Point Load at Free End?

Static Deflection for Cantilever Beam with Point Load at Free End calculator uses Static Deflection = (Load Attached to Free End of Constraint*Length of beam^3)/(3*Young's Modulus*Moment of Inertia of Beam) to calculate the Static Deflection, The Static deflection for cantilever beam with point load at free end formula is defined as deflection resulting from an applied load which remains after the removal of the load. Static Deflection is denoted by δ symbol.

How to calculate Static Deflection for Cantilever Beam with Point Load at Free End using this online calculator? To use this online calculator for Static Deflection for Cantilever Beam with Point Load at Free End, enter Load Attached to Free End of Constraint (Wattached), Length of beam (L), 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 Point Load at Free End calculation can be explained with given input values -> 0.240741 = (0.52*5^3)/(3*15*6).

FAQ

What is Static Deflection for Cantilever Beam with Point Load at Free End?
The Static deflection for cantilever beam with point load at free end formula is defined as deflection resulting from an applied load which remains after the removal of the load and is represented as δ = (Wattached*L^3)/(3*E*I) or Static Deflection = (Load Attached to Free End of Constraint*Length of beam^3)/(3*Young's Modulus*Moment of Inertia of Beam). Load attached to free end of constraint is a weight or source of pressure, Length of beam between inflection points, Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain & Moment of Inertia of Beam is a quantitative measure of the rotational inertia of a body.
How to calculate Static Deflection for Cantilever Beam with Point Load at Free End?
The Static deflection for cantilever beam with point load at free end formula is defined as deflection resulting from an applied load which remains after the removal of the load is calculated using Static Deflection = (Load Attached to Free End of Constraint*Length of beam^3)/(3*Young's Modulus*Moment of Inertia of Beam). To calculate Static Deflection for Cantilever Beam with Point Load at Free End, you need Load Attached to Free End of Constraint (Wattached), Length of beam (L), Young's Modulus (E) & Moment of Inertia of Beam (I). With our tool, you need to enter the respective value for Load Attached to Free End of Constraint, Length of 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 Attached to Free End of Constraint, Length of beam, Young's Modulus & Moment of Inertia of Beam. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Static Deflection = (Load per unit length*Length of beam^4)/(8*Young's Modulus*Moment of Inertia of Beam)
  • Static Deflection = (Central point load*Length of 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 beam)
  • Static Deflection = (5*Load per unit length*Length of beam^4)/(384*Young's Modulus*Polar Moment of Inertia)
  • Static Deflection = (Eccentric point load*Distance of load from one end^3*Distance of load from other end^3)/(3*Young's Modulus*Moment of Inertia of Beam*Length of beam)
  • Static Deflection = (Central point load*Length of beam^3)/(192*Young's Modulus*Moment of Inertia of Beam)
  • Static Deflection = (Load per unit length*Length of beam^4)/(384*Young's Modulus*Moment of Inertia of Beam)
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