Normal Stress 1 Calculator

✖Principal stress along x is stress along x-axis.ⓘ Principal Stress along x [σ_x]			+10% -10%
✖Principal stress along y is stress along y-axis.ⓘ Principal Stress along y [σ_y]			+10% -10%
✖Shear stress on upper surface refers to the amount of shear force that acts on a small element of the surface parallel to a given fluid particle. .ⓘ Shear Stress on Upper Surface [τ]			+10% -10%

✖A normal stress 1 is a stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress 1 [σ₁]

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Formula

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Normal Stress 1

Formula

`"σ"_{"1"} = ("σ"_{"x"}+"σ"_{"y"})/2+sqrt((("σ"_{"x"}-"σ"_{"y"})/2)^2+"τ"^2)`

Example

`"100.7188"=("100N/m²"+"0.2N/m²")/2+sqrt((("100N/m²"-"0.2N/m²")/2)^2+("8.5N/m²")^2)`

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Normal Stress 1 Solution

STEP 0: Pre-Calculation Summary

Formula Used

Normal Stress 1 = (Principal Stress along x+Principal Stress along y)/2+sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2)
σ₁ = (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

Normal Stress 1 - A normal stress 1 is a stress that occurs when a member is loaded by an axial force.
Principal Stress along x - (Measured in Pascal) - Principal stress along x is stress along x-axis.
Principal Stress along y - (Measured in Pascal) - Principal stress along y is stress along y-axis.
Shear Stress on Upper Surface - (Measured in Pascal) - Shear stress on upper surface refers to the amount of shear force that acts on a small element of the surface parallel to a given fluid particle. .

STEP 1: Convert Input(s) to Base Unit

Principal Stress along x: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Principal Stress along y: 0.2 Newton per Square Meter --> 0.2 Pascal (Check conversion here)
Shear Stress on Upper Surface: 8.5 Newton per Square Meter --> 8.5 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ₁ = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+τ^2) --> (100+0.2)/2+sqrt(((100-0.2)/2)^2+8.5^2)

Evaluating ... ...

σ₁ = 100.718771221751

STEP 3: Convert Result to Output's Unit

100.718771221751 --> No Conversion Required

FINAL ANSWER

100.718771221751 ≈ 100.7188 <-- Normal Stress 1

(Calculation completed in 00.004 seconds)

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Verified by Himanshi Sharma

Bhilai Institute of Technology (BIT), Raipur

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< 21 Stress and Strain Calculators

Normal Stress 1

Go Normal Stress 1 = (Principal Stress along x+Principal Stress along y)/2+sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2)

Normal Stress 2

Go Normal Stress 2 = (Principal Stress along x+Principal Stress along y)/2-sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2)

Elongation Circular Tapered Bar

Go Elongation = (4*Load*Length of Bar)/(pi*Diameter of Bigger End*Diameter of Smaller End*Elastic Modulus)

Total Angle of Twist

Go Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)

Moment of Inertia for Hollow Circular Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4))

Equivalent Bending Moment

Go Equivalent Bending Moment = Bending Moment+sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Deflection of Fixed Beam with Uniformly Distributed Load

Go Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)

Deflection of Fixed Beam with Load at Center

Go Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)

Elongation of Prismatic Bar due to its Own Weight

Go Elongation = (2*Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Axial Elongation of Prismatic Bar due to External Load

Go Elongation = (Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Hooke's Law

Go Young's Modulus = (Load*Elongation)/(Area of Base*Initial Length)

Equivalent Torsional Moment

Go Equivalent Torsion Moment = sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Rankine's Formula for Columns

Go Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns)

Slenderness Ratio

Go Slenderness Ratio = Effective Length/Least Radius of Gyration

Moment of Inertia about Polar Axis

Go Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32

Torque on Shaft

Go Torque Exerted on Shaft = Force*Shaft Diameter/2

Bulk Modulus given Volume Stress and Strain

Go Bulk Modulus = Volume Stress/Volumetric Strain

Shear Modulus

Go Shear Modulus = Shear Stress/Shear Strain

Bulk Modulus given Bulk Stress and Strain

Go Bulk Modulus = Bulk Stress/Bulk Strain

Young's Modulus

Go Young's Modulus = Stress/Strain

Elastic Modulus

Go Young's Modulus = Stress/Strain

Normal Stress 1 Formula

What is mohr's circle?

The Mohr circle is used to find the stress components and, i.e., coordinates of any point on the circle, acting on any other plane passing through making an angle with the plane.

How to Calculate Normal Stress 1?

Normal Stress 1 calculator uses Normal Stress 1 = (Principal Stress along x+Principal Stress along y)/2+sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2) to calculate the Normal Stress 1, A normal stress 1 is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area. Normal Stress 1 is denoted by σ₁ symbol.

How to calculate Normal Stress 1 using this online calculator? To use this online calculator for Normal Stress 1, enter Principal Stress along x (σ_x), Principal Stress along y (σ_y) & Shear Stress on Upper Surface (τ) and hit the calculate button. Here is how the Normal Stress 1 calculation can be explained with given input values -> 100.7188 = (100+0.2)/2+sqrt(((100-0.2)/2)^2+8.5^2).

FAQ

What is Normal Stress 1?

A normal stress 1 is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area and is represented as σ₁ = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+τ^2) or Normal Stress 1 = (Principal Stress along x+Principal Stress along y)/2+sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2). Principal stress along x is stress along x-axis, Principal stress along y is stress along y-axis & Shear stress on upper surface refers to the amount of shear force that acts on a small element of the surface parallel to a given fluid particle. .

How to calculate Normal Stress 1?

A normal stress 1 is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area is calculated using Normal Stress 1 = (Principal Stress along x+Principal Stress along y)/2+sqrt(((Principal Stress along x-Principal Stress along y)/2)^2+Shear Stress on Upper Surface^2). To calculate Normal Stress 1, you need Principal Stress along x (σ_x), Principal Stress along y (σ_y) & Shear Stress on Upper Surface (τ). With our tool, you need to enter the respective value for Principal Stress along x, Principal Stress along y & Shear Stress on Upper Surface 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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