Major principal stress in thin cylindrical stress Calculator

✖Hoop Stress in Thin shell is the circumferential stress in a cylinder.ⓘ Hoop Stress in Thin shell [σ_θ]			+10% -10%
✖Longitudinal Stress is defined as the stress produced when a pipe is subjected to internal pressure.ⓘ Longitudinal Stress [σ_l]			+10% -10%
✖Shear Stress in Cylindrical Shell is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress in Cylindrical Shell [𝜏]			+10% -10%

✖The Major Principal Stress Value.ⓘ Major principal stress in thin cylindrical stress [σ_max]

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Formula

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Major principal stress in thin cylindrical stress

Formula

`"σ"_{"max"} = (("σ"_{"θ"}+"σ"_{"l"})/2)+(sqrt(((("σ"_{"θ"}+"σ"_{"l"})/2)^2)+("𝜏"^2)))`

Example

`"25.12995MPa"=(("25.03MPa"+"0.09MPa")/2)+(sqrt(((("25.03MPa"+"0.09MPa")/2)^2)+(("0.5MPa")^2)))`

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Major principal stress in thin cylindrical stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2)))
σ_max = ((σ_θ+σ_l)/2)+(sqrt((((σ_θ+σ_l)/2)^2)+(𝜏^2)))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Major Principal Stress - (Measured in Pascal) - The Major Principal Stress Value.
Hoop Stress in Thin shell - (Measured in Pascal) - Hoop Stress in Thin shell is the circumferential stress in a cylinder.
Longitudinal Stress - (Measured in Pascal) - Longitudinal Stress is defined as the stress produced when a pipe is subjected to internal pressure.
Shear Stress in Cylindrical Shell - (Measured in Pascal) - Shear Stress in Cylindrical Shell is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

STEP 1: Convert Input(s) to Base Unit

Hoop Stress in Thin shell: 25.03 Megapascal --> 25030000 Pascal (Check conversion here)
Longitudinal Stress: 0.09 Megapascal --> 90000 Pascal (Check conversion here)
Shear Stress in Cylindrical Shell: 0.5 Megapascal --> 500000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_max = ((σ_θ+σ_l)/2)+(sqrt((((σ_θ+σ_l)/2)^2)+(𝜏^2))) --> ((25030000+90000)/2)+(sqrt((((25030000+90000)/2)^2)+(500000^2)))

Evaluating ... ...

σ_max = 25129948.289472

STEP 3: Convert Result to Output's Unit

25129948.289472 Pascal -->25.129948289472 Megapascal (Check conversion here)

FINAL ANSWER

25.129948289472 ≈ 25.12995 Megapascal <-- Major Principal Stress

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< 5 Thin Cylindrical Vessel Subjected to Internal Fluid Pressure and Torque Calculators

Major principal stress in thin cylindrical stress

Go Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2)))

Minor principal stress in thin cylindrical stress

Go Minor Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)-(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2)))

Maximum shear stress in thin cylindrical stress

Go Maximum shear stress = (1/2)*(Major Principal Stress-Minor Principal Stress)

Major principal stress in thin cylindrical stress given maximum shear stress

Go Major Principal Stress = (2*Maximum shear stress)+Minor Principal Stress

Minor principal stress in thin cylindrical stress given maximum shear stress

Go Minor Principal Stress = Major Principal Stress-(2*Maximum shear stress)

Major principal stress in thin cylindrical stress Formula

What is tensile strength with example?

Tensile strength is a measurement of the force required to pull something such as rope, wire, or a structural beam to the point where it breaks. The tensile strength of a material is the maximum amount of tensile stress that it can take before failure, for example, breaking.

How to Calculate Major principal stress in thin cylindrical stress?

Major principal stress in thin cylindrical stress calculator uses Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2))) to calculate the Major Principal Stress, Major principal stress in thin cylindrical stress is the major normal stress acting on the principle plane. Major Principal Stress is denoted by σ_max symbol.

How to calculate Major principal stress in thin cylindrical stress using this online calculator? To use this online calculator for Major principal stress in thin cylindrical stress, enter Hoop Stress in Thin shell (σ_θ), Longitudinal Stress (σ_l) & Shear Stress in Cylindrical Shell (𝜏) and hit the calculate button. Here is how the Major principal stress in thin cylindrical stress calculation can be explained with given input values -> 2.9E-5 = ((25030000+90000)/2)+(sqrt((((25030000+90000)/2)^2)+(500000^2))).

FAQ

What is Major principal stress in thin cylindrical stress?

Major principal stress in thin cylindrical stress is the major normal stress acting on the principle plane and is represented as σ_max = ((σ_θ+σ_l)/2)+(sqrt((((σ_θ+σ_l)/2)^2)+(𝜏^2))) or Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2))). Hoop Stress in Thin shell is the circumferential stress in a cylinder, Longitudinal Stress is defined as the stress produced when a pipe is subjected to internal pressure & Shear Stress in Cylindrical Shell is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

How to calculate Major principal stress in thin cylindrical stress?

Major principal stress in thin cylindrical stress is the major normal stress acting on the principle plane is calculated using Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2))). To calculate Major principal stress in thin cylindrical stress, you need Hoop Stress in Thin shell (σ_θ), Longitudinal Stress (σ_l) & Shear Stress in Cylindrical Shell (𝜏). With our tool, you need to enter the respective value for Hoop Stress in Thin shell, Longitudinal Stress & Shear Stress in Cylindrical Shell 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 Major Principal Stress?

In this formula, Major Principal Stress uses Hoop Stress in Thin shell, Longitudinal Stress & Shear Stress in Cylindrical Shell. We can use 1 other way(s) to calculate the same, which is/are as follows -

Major Principal Stress = (2*Maximum shear stress)+Minor Principal Stress

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