Area of upper end of bar Calculator

✖The Area of the lower end of the rod s defined as an exponential function of the product of specific weight with the ratio of the length of rod and stress.ⓘ Area of the lower end [A₂]			+10% -10%
✖Weight per unit volume is the ratio of weight of a body to its volume.ⓘ Weight per unit volume [w]			+10% -10%
✖Length Of Bar is defined as the total length of the Bar.ⓘ Length of Bar [L_bar]			+10% -10%
✖Stress in Bar applied to a bar is the force per unit area applied to the barl. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress.ⓘ Stress in Bar [σ]			+10% -10%

✖The Area of Upper End is the area of the upper end of the rod.ⓘ Area of upper end of bar [A₁]

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Formula

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Area of upper end of bar

Formula

`"A"_{"1"} = "A"_{"2"}*e^("w"*"L"_{"bar"}/"σ")`

Example

`"3.005004m²"="3m²"*e^("10N/m³"*"2000mm"/"0.012MPa")`

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Area of upper end of bar Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Upper End = Area of the lower end*e^(Weight per unit volume*Length of Bar/Stress in Bar)
A₁ = A₂*e^(w*L_bar/σ)
This formula uses 1 Constants, 5 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Variables Used

Area of Upper End - (Measured in Square Meter) - The Area of Upper End is the area of the upper end of the rod.
Area of the lower end - (Measured in Square Meter) - The Area of the lower end of the rod s defined as an exponential function of the product of specific weight with the ratio of the length of rod and stress.
Weight per unit volume - (Measured in Newton per Cubic Meter) - Weight per unit volume is the ratio of weight of a body to its volume.
Length of Bar - (Measured in Meter) - Length Of Bar is defined as the total length of the Bar.
Stress in Bar - (Measured in Pascal) - Stress in Bar applied to a bar is the force per unit area applied to the barl. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress.

STEP 1: Convert Input(s) to Base Unit

Area of the lower end: 3 Square Meter --> 3 Square Meter No Conversion Required
Weight per unit volume: 10 Newton per Cubic Meter --> 10 Newton per Cubic Meter No Conversion Required
Length of Bar: 2000 Millimeter --> 2 Meter (Check conversion here)
Stress in Bar: 0.012 Megapascal --> 12000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A₁ = A₂*e^(w*L_bar/σ) --> 3*e^(10*2/12000)

Evaluating ... ...

A₁ = 3.00500416898245

STEP 3: Convert Result to Output's Unit

3.00500416898245 Square Meter --> No Conversion Required

FINAL ANSWER

3.00500416898245 ≈ 3.005004 Square Meter <-- Area of Upper End

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Stress and Strain » Analysis of Bar » Analysis of Bar of Uniform Strength » Area of upper end of bar

Credits

Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 2 Analysis of Bar of Uniform Strength Calculators

Area of upper end of bar

Go Area of Upper End = Area of the lower end*e^(Weight per unit volume*Length of Bar/Stress in Bar)

Area of lower end of bar

Go Area of the lower end = Area of Upper End/e^(Weight per unit volume*Length of Bar/Stress in Bar)

Area of upper end of bar Formula

Area of Upper End = Area of the lower end*e^(Weight per unit volume*Length of Bar/Stress in Bar)
A₁ = A₂*e^(w*L_bar/σ)

What is the curvature of a vertical bar kept in uniform tensile stress?

The curvature of a vertical bar kept at uniform tensile stress can be expressed as an exponential function that takes the least value at the lower end and maximum at the upper end.

How to Calculate Area of upper end of bar?

Area of upper end of bar calculator uses Area of Upper End = Area of the lower end*e^(Weight per unit volume*Length of Bar/Stress in Bar) to calculate the Area of Upper End, The Area of upper end of bar formula is defined as exponential function of the product of specific weight with the ratio of length of rod and stress. This exponential function is further multiplied by the area of the lower end. Area of Upper End is denoted by A₁ symbol.

How to calculate Area of upper end of bar using this online calculator? To use this online calculator for Area of upper end of bar, enter Area of the lower end (A₂), Weight per unit volume (w), Length of Bar (L_bar) & Stress in Bar (σ) and hit the calculate button. Here is how the Area of upper end of bar calculation can be explained with given input values -> 3.005004 = 3*e^(10*2/12000).

FAQ

What is Area of upper end of bar?

The Area of upper end of bar formula is defined as exponential function of the product of specific weight with the ratio of length of rod and stress. This exponential function is further multiplied by the area of the lower end and is represented as A₁ = A₂*e^(w*L_bar/σ) or Area of Upper End = Area of the lower end*e^(Weight per unit volume*Length of Bar/Stress in Bar). The Area of the lower end of the rod s defined as an exponential function of the product of specific weight with the ratio of the length of rod and stress, Weight per unit volume is the ratio of weight of a body to its volume, Length Of Bar is defined as the total length of the Bar & Stress in Bar applied to a bar is the force per unit area applied to the barl. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress.

How to calculate Area of upper end of bar?

The Area of upper end of bar formula is defined as exponential function of the product of specific weight with the ratio of length of rod and stress. This exponential function is further multiplied by the area of the lower end is calculated using Area of Upper End = Area of the lower end*e^(Weight per unit volume*Length of Bar/Stress in Bar). To calculate Area of upper end of bar, you need Area of the lower end (A₂), Weight per unit volume (w), Length of Bar (L_bar) & Stress in Bar (σ). With our tool, you need to enter the respective value for Area of the lower end, Weight per unit volume, Length of Bar & Stress in Bar and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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