Length of Bar using its Uniform Strength Calculator

✖Area 1 is the cross-sectional area at one end of a bar/shaft.ⓘ Area 1 [A₁]			+10% -10%
✖Area 2 is the cross-sectional area at the second end of the bar/section.ⓘ Area 2 [A₂]			+10% -10%
✖Uniform Stress is one in which stress developed at every cross-section of the bar remains the same along the longitudinal axis.ⓘ Uniform Stress [σ_Uniform]			+10% -10%
✖Specific Weight of Rod is defined as weight per unit volume of the rod.ⓘ Specific Weight of Rod [γ_Rod]			+10% -10%

✖Length is the measurement or extent of something from end to end.ⓘ Length of Bar using its Uniform Strength [L]

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Length of Bar using its Uniform Strength Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length = (2.303*log10(Area 1/Area 2))*(Uniform Stress/Specific Weight of Rod)
L = (2.303*log10(A₁/A₂))*(σ_Uniform/γ_Rod)
This formula uses 1 Functions, 5 Variables

Functions Used

log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)

Variables Used

Length - (Measured in Meter) - Length is the measurement or extent of something from end to end.
Area 1 - (Measured in Square Meter) - Area 1 is the cross-sectional area at one end of a bar/shaft.
Area 2 - (Measured in Square Meter) - Area 2 is the cross-sectional area at the second end of the bar/section.
Uniform Stress - (Measured in Pascal) - Uniform Stress is one in which stress developed at every cross-section of the bar remains the same along the longitudinal axis.
Specific Weight of Rod - (Measured in Newton per Cubic Meter) - Specific Weight of Rod is defined as weight per unit volume of the rod.

STEP 1: Convert Input(s) to Base Unit

Area 1: 0.001256 Square Meter --> 0.001256 Square Meter No Conversion Required
Area 2: 0.00125 Square Meter --> 0.00125 Square Meter No Conversion Required
Uniform Stress: 27 Megapascal --> 27000000 Pascal (Check conversion here)
Specific Weight of Rod: 4930.96 Kilonewton per Cubic Meter --> 4930960 Newton per Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = (2.303*log10(A₁/A₂))*(σ_Uniform/γ_Rod) --> (2.303*log10(0.001256/0.00125))*(27000000/4930960)

Evaluating ... ...

L = 0.0262247612535184

STEP 3: Convert Result to Output's Unit

0.0262247612535184 Meter --> No Conversion Required

FINAL ANSWER

0.0262247612535184 ≈ 0.026225 Meter <-- Length

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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NSS College of Engineering (NSSCE), Palakkad

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< Elongation due to Self weight Calculators

Length of Rod of Truncated Conical Section

LaTeX Go Length of Tapered Bar = sqrt(Elongation/(((Specific Weight of Rod)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2))))

Specific weight of Truncated Conical Rod using its elongation due to Self Weight

LaTeX Go Specific Weight of Rod = Elongation/(((Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2)))

Modulus of Elasticity of Rod using Extension of Truncated Conical Rod due to Self Weight

LaTeX Go Young's Modulus = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Elongation*(Diameter1-Diameter2))

Elongation of Truncated Conical Rod due to Self Weight

LaTeX Go Elongation = ((Specific Weight of Rod*Length of Tapered Bar^2)*(Diameter1+Diameter2))/(6*Young's Modulus*(Diameter1-Diameter2))

Length of Bar using its Uniform Strength Formula

LaTeX Go

Length = (2.303*log10(Area 1/Area 2))*(Uniform Stress/Specific Weight of Rod)
L = (2.303*log10(A₁/A₂))*(σ_Uniform/γ_Rod)

What is Uniform Strength of Bar?

The extreme fibres can be loaded to the maximum capacity of permissible stress (say p max), but they are loaded to less capacity. When a beam is suitably designed such that the extreme fibres are loaded to the maximum permissible stress p max by varying the cross section it will be known as a beam of uniform strength.

How to Calculate Length of Bar using its Uniform Strength?

Length of Bar using its Uniform Strength calculator uses Length = (2.303*log10(Area 1/Area 2))*(Uniform Stress/Specific Weight of Rod) to calculate the Length, The Length of Bar using its Uniform Strength formula is defined as the length where the pull is experienced on the bars when strength is uniform throughout. Length is denoted by L symbol.

How to calculate Length of Bar using its Uniform Strength using this online calculator? To use this online calculator for Length of Bar using its Uniform Strength, enter Area 1 (A₁), Area 2 (A₂), Uniform Stress (σ_Uniform) & Specific Weight of Rod (γ_Rod) and hit the calculate button. Here is how the Length of Bar using its Uniform Strength calculation can be explained with given input values -> 0.026225 = (2.303*log10(0.001256/0.00125))*(27000000/4930960).

FAQ

What is Length of Bar using its Uniform Strength?

The Length of Bar using its Uniform Strength formula is defined as the length where the pull is experienced on the bars when strength is uniform throughout and is represented as L = (2.303*log10(A₁/A₂))*(σ_Uniform/γ_Rod) or Length = (2.303*log10(Area 1/Area 2))*(Uniform Stress/Specific Weight of Rod). Area 1 is the cross-sectional area at one end of a bar/shaft, Area 2 is the cross-sectional area at the second end of the bar/section, Uniform Stress is one in which stress developed at every cross-section of the bar remains the same along the longitudinal axis & Specific Weight of Rod is defined as weight per unit volume of the rod.

How to calculate Length of Bar using its Uniform Strength?

The Length of Bar using its Uniform Strength formula is defined as the length where the pull is experienced on the bars when strength is uniform throughout is calculated using Length = (2.303*log10(Area 1/Area 2))*(Uniform Stress/Specific Weight of Rod). To calculate Length of Bar using its Uniform Strength, you need Area 1 (A₁), Area 2 (A₂), Uniform Stress (σ_Uniform) & Specific Weight of Rod (γ_Rod). With our tool, you need to enter the respective value for Area 1, Area 2, Uniform Stress & Specific Weight of Rod 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?

In this formula, Length uses Area 1, Area 2, Uniform Stress & Specific Weight of Rod. We can use 1 other way(s) to calculate the same, which is/are as follows -

Length = sqrt(Elongation/(Specific Weight of Rod/(Young's Modulus*2)))

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