Maximum Value of Normal Stress Calculator

✖Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.ⓘ Stress Along x Direction [σ_x]			+10% -10%
✖Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.ⓘ Stress Along y Direction [σ_y]			+10% -10%
✖Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress in Mpa [τ]			+10% -10%

✖Maximum Normal Stress is defined as stress acting on a plane normally.ⓘ Maximum Value of Normal Stress [σ_n,max]

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Maximum Value of Normal Stress

Formula

`"σ"_{"n,max"} = ("σ"_{"x"}+"σ"_{"y"})/2+sqrt((("σ"_{"x"}-"σ"_{"y"})/2)^2+"τ"^2)`

Example

`"113.7675MPa"=("95MPa"+"22MPa")/2+sqrt((("95MPa"-"22MPa")/2)^2+("41.5MPa")^2)`

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Maximum Value of Normal Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
σ_n,max = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/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

Maximum Normal Stress - (Measured in Pascal) - Maximum Normal Stress is defined as stress acting on a plane normally.
Stress Along x Direction - (Measured in Pascal) - Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.
Stress Along y Direction - (Measured in Pascal) - Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.
Shear Stress in Mpa - (Measured in Pascal) - Shear Stress in Mpa, 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

Stress Along x Direction: 95 Megapascal --> 95000000 Pascal (Check conversion here)
Stress Along y Direction: 22 Megapascal --> 22000000 Pascal (Check conversion here)
Shear Stress in Mpa: 41.5 Megapascal --> 41500000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_n,max = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+τ^2) --> (95000000+22000000)/2+sqrt(((95000000-22000000)/2)^2+41500000^2)

Evaluating ... ...

σ_n,max = 113767531.155281

STEP 3: Convert Result to Output's Unit

113767531.155281 Pascal -->113.767531155281 Megapascal (Check conversion here)

FINAL ANSWER

113.767531155281 ≈ 113.7675 Megapascal <-- Maximum Normal Stress

(Calculation completed in 00.004 seconds)

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National Institute of Technology (NIT), Tiruchirapalli

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< 7 Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress Calculators

Maximum Value of Normal Stress

Go Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)

Minimum Value of Normal Stress

Go Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)

Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses

Go Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)

Maximum Value of Shear Stress

Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress

Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)

Condition for Maximum Value of Normal Stress

Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Condition for Minimum Normal Stress

Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

< 7 When a Body is subjected to two Mutual Perpendicular Principal Tensile stresses along with Simple Shear Stress Calculators

Maximum Value of Normal Stress

Go Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)

Minimum Value of Normal Stress

Go Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)

Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses

Go Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)

Maximum Value of Shear Stress

Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress

Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)

Condition for Maximum Value of Normal Stress

Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Condition for Minimum Normal Stress

Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Maximum Value of Normal Stress Formula

What is Normal Stress?

The intensity of net force acting per unit area normal to the cross-section under consideration is called normal stress.

What is Shear Stress?

When an external force acts on an object, It undergoes deformation. If the direction of the force is parallel to the plane of the object. The deformation will be along that plane. The stress experienced by the object here is shear stress or tangential stress.

It arises when the force vector components are parallel to the cross-sectional area of the material. In the case of normal/longitudinal stress, the force vectors will be perpendicular to the cross-sectional area on which it acts.

How to Calculate Maximum Value of Normal Stress?

Maximum Value of Normal Stress calculator uses Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2) to calculate the Maximum Normal Stress, The Maximum Value of Normal Stress formula is defined as equal to the major principal stress value or maximum principal stress value. Maximum Normal Stress is denoted by σ_n,max symbol.

How to calculate Maximum Value of Normal Stress using this online calculator? To use this online calculator for Maximum Value of Normal Stress, enter Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ) and hit the calculate button. Here is how the Maximum Value of Normal Stress calculation can be explained with given input values -> 0.000114 = (95000000+22000000)/2+sqrt(((95000000-22000000)/2)^2+41500000^2).

FAQ

What is Maximum Value of Normal Stress?

The Maximum Value of Normal Stress formula is defined as equal to the major principal stress value or maximum principal stress value and is represented as σ_n,max = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+τ^2) or Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation, Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure & Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

How to calculate Maximum Value of Normal Stress?

The Maximum Value of Normal Stress formula is defined as equal to the major principal stress value or maximum principal stress value is calculated using Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). To calculate Maximum Value of Normal Stress, you need Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ). With our tool, you need to enter the respective value for Stress Along x Direction, Stress Along y Direction & Shear Stress in Mpa 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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