Length of Beam for Fixed 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 Fixed Beam is the distance of a fixed beam under various load conditions, used to determine the beam's stability and structural integrity.ⓘ Length of Beam for Fixed Beam with Central Point Load [L_FB]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Longitudinal and Transverse Vibrations Formula PDF PDF Image

Length of Beam for Fixed Beam with Central Point Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Fixed Beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3)
L_FB = ((192*E*I*δ)/(w_c))^(1/3)
This formula uses 5 Variables

Variables Used

Length of Fixed Beam - (Measured in Meter) - Length of Fixed Beam is the distance of a fixed beam under various load conditions, used to determine the beam's stability and structural integrity.
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_FB = ((192*E*I*δ)/(w_c))^(1/3) --> ((192*15*6*0.072)/(6.2))^(1/3)

Evaluating ... ...

L_FB = 5.85456791536699

STEP 3: Convert Result to Output's Unit

5.85456791536699 Meter --> No Conversion Required

FINAL ANSWER

5.85456791536699 ≈ 5.854568 Meter <-- Length of Fixed Beam

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Mechanical » Values of length of beam for the various types of beams and under various load conditions » Length of Beam for Fixed Beam with Central Point Load

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has verified this Calculator and 400+ more calculators!

< 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 Fixed Beam with Central Point Load Formula

LaTeX Go

Length of Fixed Beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3)
L_FB = ((192*E*I*δ)/(w_c))^(1/3)

What is Fixed Beam?

A fixed beam is a type of beam that is rigidly supported at both ends, preventing any movement or rotation. This beam is capable of carrying larger loads compared to simply supported beams because both ends resist bending and deflection. Fixed beams are often used in construction where strength and stability are critical, such as in buildings and bridges. The rigid supports create internal moments, reducing deflection and distributing stresses more evenly along the beam.

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

Length of Beam for Fixed Beam with Central Point Load calculator uses Length of Fixed Beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3) to calculate the Length of Fixed Beam, The Length of beam for fixed beam with central point load formula is simply the total length of the member. Length of Fixed Beam is denoted by L_FB symbol.

How to calculate Length of Beam for Fixed Beam with Central Point Load using this online calculator? To use this online calculator for Length of Beam for Fixed 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 Fixed Beam with Central Point Load calculation can be explained with given input values -> 5.854568 = ((192*15*6*0.072)/(6.2))^(1/3).

FAQ

What is Length of Beam for Fixed Beam with Central Point Load?

The Length of beam for fixed beam with central point load formula is simply the total length of the member and is represented as L_FB = ((192*E*I*δ)/(w_c))^(1/3) or Length of Fixed Beam = ((192*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 Fixed Beam with Central Point Load?

The Length of beam for fixed beam with central point load formula is simply the total length of the member is calculated using Length of Fixed Beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central Point Load))^(1/3). To calculate Length of Beam for Fixed 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 Fixed Beam?

In this formula, Length of Fixed 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 Fixed Beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load in Fixed Beam))^(1/4)
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)

Home

FREE PDFs

🔍 Search