Length of Beam for Simply Supported Beam with Central Point Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)
L = ((48*E*I*δ)/(wc))^(1/3)
This formula uses 5 Variables
Variables Used
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.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
Central point load - (Measured in Kilogram) - Central point load is defined when load is applied at the center of beam.
STEP 1: Convert Input(s) to Base Unit
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
Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required
Central point load: 6.2 Kilogram --> 6.2 Kilogram No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
L = ((48*E*I*δ)/(wc))^(1/3) --> ((48*15*6*0.072)/(6.2))^(1/3)
Evaluating ... ...
L = 3.68814667730501
STEP 3: Convert Result to Output's Unit
3.68814667730501 Meter --> No Conversion Required
FINAL ANSWER
3.68814667730501 3.688147 Meter <-- Length of beam
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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8 Values of length of beam for the various types of beams and under various load conditions Calculators

Length of Simply Supported Beam with Eccentric Point Load
Go Length of beam = (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*Static Deflection)
Length of Fixed Beam with Eccentric Point Load
Go Length of beam = (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*Static Deflection)
Length of Beam for Cantilever Beam with Point Load at Free End
Go Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3)
Length of Beam for Simply Supported Beam with Uniformly Distributed Load
Go Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(5*Load per unit length))^(1/4)
Length of Beam for Fixed Beam with Uniformly Distributed Load
Go Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)
Length of Beam for Cantilever Beam with Uniformly Distributed Load
Go Length of beam = ((8*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)
Length of Beam for Fixed Beam with Central Point Load
Go Length of beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)
Length of Beam for Simply Supported Beam with Central Point Load
Go Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)

Length of Beam for Simply Supported Beam with Central Point Load Formula

Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)
L = ((48*E*I*δ)/(wc))^(1/3)

What is beam and column?

Communally a horizontal member of a structure that resists transverse load is called a beam. Communally a vertical member of a structure that resists axial/eccentric load is called a column. Beam is basically carried or resists bending and shear force. Column is basically carried or resists compression load.

How to Calculate Length of Beam for Simply Supported Beam with Central Point Load?

Length of Beam for Simply Supported Beam with Central Point Load calculator uses Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3) to calculate the Length of beam, The Length of beam for simply supported beam with central point load formula is simply the total length of the member. Length of beam is denoted by L symbol.

How to calculate Length of Beam for Simply Supported Beam with Central Point Load using this online calculator? To use this online calculator for Length of Beam for Simply Supported Beam with Central Point Load, enter Young's Modulus (E), Moment of Inertia of Beam (I), Static Deflection (δ) & Central point load (wc) and hit the calculate button. Here is how the Length of Beam for Simply Supported Beam with Central Point Load calculation can be explained with given input values -> 3.688147 = ((48*15*6*0.072)/(6.2))^(1/3).

FAQ

What is Length of Beam for Simply Supported Beam with Central Point Load?
The Length of beam for simply supported beam with central point load formula is simply the total length of the member and is represented as L = ((48*E*I*δ)/(wc))^(1/3) or Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3). 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, Static deflection is the extension or compression of the constraint & Central point load is defined when load is applied at the center of beam.
How to calculate Length of Beam for Simply Supported Beam with Central Point Load?
The Length of beam for simply supported beam with central point load formula is simply the total length of the member is calculated using Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3). To calculate Length of Beam for Simply Supported Beam with Central Point Load, you need Young's Modulus (E), Moment of Inertia of Beam (I), Static Deflection (δ) & Central point load (wc). With our tool, you need to enter the respective value for Young's Modulus, Moment of Inertia of Beam, Static Deflection & Central point load 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 Length of beam?
In this formula, Length of beam uses Young's Modulus, Moment of Inertia of Beam, Static Deflection & Central point load. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)
  • Length of beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)
  • Length of beam = (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*Static Deflection)
  • Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(5*Load per unit length))^(1/4)
  • Length of beam = (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*Static Deflection)
  • Length of beam = ((8*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)
  • Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3)
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