Length of Simply Supported Beam with Eccentric Point Load Calculator

✖Eccentric Point Load for Simply Supported Beam is the load applied at a point on a simply supported beam, affecting its length under various load conditions.ⓘ Eccentric Point Load for Simply Supported Beam [w_{e SSB}]			+10% -10%
✖Distance of Load from One End is the length of a beam measured from one end, considering various types of beams and load conditions.ⓘ Distance of Load from One End [a]			+10% -10%
✖Distance of Load from Other End is the length of a beam measured from the point of load application to the other end of the beam under various load conditions.ⓘ Distance of Load from Other End [b]			+10% -10%
✖Young's Modulus is a measure of the stiffness of a solid material, used to calculate the length of a beam under various load conditions and beam types.ⓘ 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, depending on its length and type.ⓘ 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, providing values for different types of beams.ⓘ Static Deflection [δ]			+10% -10%

✖Length of Simply Supported Beam is the distance of a beam between its supports, varying with types of beams and load conditions.ⓘ Length of Simply Supported Beam with Eccentric Point Load [L_SSB]

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Length of Simply Supported Beam with Eccentric Point Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Simply Supported Beam = (Eccentric Point Load for Simply Supported Beam*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_SSB = (w_{e SSB}*a^2*b^2)/(3*E*I*δ)
This formula uses 7 Variables

Variables Used

Length of Simply Supported Beam - (Measured in Meter) - Length of Simply Supported Beam is the distance of a beam between its supports, varying with types of beams and load conditions.
Eccentric Point Load for Simply Supported Beam - (Measured in Kilogram) - Eccentric Point Load for Simply Supported Beam is the load applied at a point on a simply supported beam, affecting its length under various load conditions.
Distance of Load from One End - (Measured in Meter) - Distance of Load from One End is the length of a beam measured from one end, considering various types of beams and load conditions.
Distance of Load from Other End - (Measured in Meter) - Distance of Load from Other End is the length of a beam measured from the point of load application to the other end of the beam under various load conditions.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a measure of the stiffness of a solid material, used to calculate the length of a beam under various load conditions and beam types.
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, depending on its length and type.
Static Deflection - (Measured in Meter) - Static Deflection is the maximum displacement of a beam from its original position under various load conditions, providing values for different types of beams.

STEP 1: Convert Input(s) to Base Unit

Eccentric Point Load for Simply Supported Beam: 2.25 Kilogram --> 2.25 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_SSB = (w_{e SSB}*a^2*b^2)/(3*E*I*δ) --> (2.25*4^2*1.4^2)/(3*15*6*0.072)

Evaluating ... ...

L_SSB = 3.62962962962963

STEP 3: Convert Result to Output's Unit

3.62962962962963 Meter --> No Conversion Required

FINAL ANSWER

3.62962962962963 ≈ 3.62963 Meter <-- Length of Simply Supported Beam

(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Values of length of beam for the various types of beams and under various load conditions Calculators

Length of Fixed Beam with Eccentric Point Load

LaTeX Go Length of Fixed Beam = (Eccentric Point Load for Fixed Beam*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 Simply Supported Beam with Uniformly Distributed Load

LaTeX Go Length of Simply Supported Beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(5*Load in Simply Supported Beam))^(1/4)

Length of Beam for Fixed Beam with Uniformly Distributed Load

LaTeX Go Length of Fixed Beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load in Fixed Beam))^(1/4)

Length of Beam for Fixed Beam with Central Point Load

LaTeX Go Length of Fixed Beam = ((192*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

LaTeX Go

What is Cantilever Beam?

A cantilever beam is a structural element that is fixed at one end and free at the other. The fixed end supports the entire load, allowing the free end to extend without additional support. Cantilever beams are commonly used in structures like balconies, overhangs, and bridges where one end must remain unsupported. They resist both bending and shear forces, making them effective for carrying loads that are far from the point of support. Cantilever beams offer flexibility in design but require careful analysis to ensure stability.

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 Simply Supported Beam = (Eccentric Point Load for Simply Supported Beam*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 Simply Supported Beam, The Length of Simply Supported Beam with Eccentric Point Load formula is simply the total length of the member. Length of Simply Supported Beam is denoted by L_SSB 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 for Simply Supported Beam (w_{e SSB}), 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 -> 3.548971 = (2.25*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_SSB = (w_{e SSB}*a^2*b^2)/(3*E*I*δ) or Length of Simply Supported Beam = (Eccentric Point Load for Simply Supported Beam*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 for Simply Supported Beam is the load applied at a point on a simply supported beam, affecting its length under various load conditions, Distance of Load from One End is the length of a beam measured from one end, considering various types of beams and load conditions, Distance of Load from Other End is the length of a beam measured from the point of load application to the other end of the beam under various load conditions, Young's Modulus is a measure of the stiffness of a solid material, used to calculate the length of a beam under various load conditions and beam types, Moment of Inertia of Beam is a measure of the beam's resistance to bending under various load conditions, depending on its length and type & Static Deflection is the maximum displacement of a beam from its original position under various load conditions, providing values for different types of beams.

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 Simply Supported Beam = (Eccentric Point Load for Simply Supported Beam*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 for Simply Supported Beam (w_{e SSB}), 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 for Simply Supported Beam, 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 Simply Supported Beam?

In this formula, Length of Simply Supported Beam uses Eccentric Point Load for Simply Supported Beam, 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 2 other way(s) to calculate the same, which is/are as follows -

Length of Simply Supported Beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(5*Load in Simply Supported Beam))^(1/4)
Length of Simply Supported Beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3)

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