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

✖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%
✖Central Point Load is the load applied at the midpoint of a beam, affecting its length under various load conditions and beam types.ⓘ Central Point Load [w_c]			+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 Beam for Simply Supported Beam with Central Point Load [L_SSB]

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

STEP 0: Pre-Calculation Summary

Formula Used

Length of Simply Supported Beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3)
L_SSB = ((48*E*I*δ)/(w_c))^(1/3)
This formula uses 5 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.
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.
Central Point Load - (Measured in Kilogram) - Central Point Load is the load applied at the midpoint of a beam, affecting its length under various load conditions and beam types.

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_SSB = ((48*E*I*δ)/(w_c))^(1/3) --> ((48*15*6*0.072)/(6.2))^(1/3)

Evaluating ... ...

L_SSB = 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 Simply Supported Beam

(Calculation completed in 00.004 seconds)

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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 Beam for Simply Supported Beam with Central Point Load Formula

LaTeX Go

Length of Simply Supported Beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3)
L_SSB = ((48*E*I*δ)/(w_c))^(1/3)

What is Simply Supported Beam?

A simply supported beam is a beam that rests on supports at both ends, allowing it to freely rotate but preventing vertical movement. One end is typically pinned, while the other end is supported by a roller or hinge. This beam type experiences bending under load and is commonly used in structures like bridges and buildings due to its simple design and ability to efficiently carry loads. The supports prevent excessive displacement, while the beam deflects to balance the applied loads.

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 Simply Supported Beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3) to calculate the Length of Simply Supported Beam, The Length of beam for simply supported beam with central 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 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 (w_c) 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_SSB = ((48*E*I*δ)/(w_c))^(1/3) or Length of Simply Supported Beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3). 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 & Central Point Load is the load applied at the midpoint of a beam, affecting its length under various load conditions and beam types.

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 Simply Supported 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 (w_c). 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 Simply Supported Beam?

In this formula, Length of Simply Supported Beam uses Young's Modulus, Moment of Inertia of Beam, Static Deflection & Central Point Load. 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 = (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)

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