Length of Simply Supported Beam with Eccentric Point Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
L = (we*a^2*b^2)/(3*E*I*δ)
This formula uses 7 Variables
Variables Used
Length of beam - (Measured in Meter) - Length of beam between inflection points.
Eccentric point load - (Measured in Kilogram) - Eccentric point load is basically defined as the load whose line of action does not pass through the axis of the column.
Distance of load from one end - (Measured in Meter) - Distance of load from one end is a numerical measurement of how far apart objects or points are.
Distance of load from other end - (Measured in Meter) - Distance of load from other end is a numerical measurement of how far apart objects or points are.
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.
STEP 1: Convert Input(s) to Base Unit
Eccentric point load: 5.4 Kilogram --> 5.4 Kilogram No Conversion Required
Distance of load from one end: 4 Meter --> 4 Meter No Conversion Required
Distance of load from other end: 1.4 Meter --> 1.4 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
Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
L = (we*a^2*b^2)/(3*E*I*δ) --> (5.4*4^2*1.4^2)/(3*15*6*0.072)
Evaluating ... ...
L = 8.71111111111111
STEP 3: Convert Result to Output's Unit
8.71111111111111 Meter --> No Conversion Required
FINAL ANSWER
8.71111111111111 8.711111 Meter <-- Length of beam
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Indian Institute of Information Technology (IIIT), Guwahati
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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 Simply Supported Beam with Eccentric Point Load Formula

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)
L = (we*a^2*b^2)/(3*E*I*δ)

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 Simply Supported Beam with Eccentric Point Load?

Length of Simply Supported Beam with Eccentric Point Load calculator uses 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) to calculate the Length of beam, The Length of Simply Supported Beam with Eccentric Point Load formula is simply the total length of the member. Length of beam is denoted by L symbol.

How to calculate Length of Simply Supported Beam with Eccentric Point Load using this online calculator? To use this online calculator for Length of Simply Supported Beam with Eccentric Point Load, enter Eccentric point load (we), Distance of load from one end (a), Distance of load from other end (b), Young's Modulus (E), Moment of Inertia of Beam (I) & Static Deflection (δ) and hit the calculate button. Here is how the Length of Simply Supported Beam with Eccentric Point Load calculation can be explained with given input values -> 8.711111 = (5.4*4^2*1.4^2)/(3*15*6*0.072).

FAQ

What is Length of Simply Supported Beam with Eccentric Point Load?
The Length of Simply Supported Beam with Eccentric Point Load formula is simply the total length of the member and is represented as L = (we*a^2*b^2)/(3*E*I*δ) or 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). Eccentric point load is basically defined as the load whose line of action does not pass through the axis of the column, Distance of load from one end is a numerical measurement of how far apart objects or points are, Distance of load from other end is a numerical measurement of how far apart objects or points are, 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.
How to calculate Length of Simply Supported Beam with Eccentric Point Load?
The Length of Simply Supported Beam with Eccentric Point Load formula is simply the total length of the member is calculated using 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). To calculate Length of Simply Supported Beam with Eccentric Point Load, you need Eccentric point load (we), Distance of load from one end (a), Distance of load from other end (b), Young's Modulus (E), Moment of Inertia of Beam (I) & Static Deflection (δ). With our tool, you need to enter the respective value for Eccentric point load, Distance of load from one end, Distance of load from other end, Young's Modulus, Moment of Inertia of Beam & Static Deflection 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 Eccentric point load, Distance of load from one end, Distance of load from other end, Young's Modulus, Moment of Inertia of Beam & Static Deflection. 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 = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)
  • 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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