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))*(σUniform/γRod)
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))*(σUniformRod) --> (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 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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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))*(σUniform/γRod)

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 Uniform) & Specific Weight of Rod 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))*(σUniformRod) 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 Uniform) & Specific Weight of Rod 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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