Increase In Radius Of Disc Given Stresses Calculator

Formula Used:

\[ \text{Increase in radius} = \frac{\text{Circumferential Stress} - (\text{Poisson's Ratio} \times \text{Radial Stress})}{\text{Modulus Of Elasticity Of Disc}} \times \text{Disc Radius} \] \[ R_i = \frac{\sigma_c - (\mu \times \sigma_r)}{E} \times r_{\text{disc}} \]

Circumferential Stress (σc):

Pascal

Poisson's Ratio (μ):

(unitless)

Radial Stress (σr):

Pascal

Modulus Of Elasticity Of Disc (E):

Pascal

Disc Radius (r_disc):

Meter

Increase In Radius (R_i):

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1. What Is The Increase In Radius Of Disc Given Stresses Formula?

The formula calculates the increase in radius of a disc when subjected to circumferential and radial stresses, taking into account material properties including Poisson's ratio and modulus of elasticity.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ R_i = \frac{\sigma_c - (\mu \times \sigma_r)}{E} \times r_{\text{disc}} \]

Where:

\( R_i \) — Increase in radius (Meter)
\( \sigma_c \) — Circumferential Stress (Pascal)
\( \mu \) — Poisson's Ratio (unitless)
\( \sigma_r \) — Radial Stress (Pascal)
\( E \) — Modulus Of Elasticity Of Disc (Pascal)
\( r_{\text{disc}} \) — Disc Radius (Meter)

Explanation: The formula calculates the radial deformation of a disc under stress conditions, accounting for material elasticity and Poisson's effect.

3. Importance Of Radius Increase Calculation

Details: Calculating radial deformation is crucial in mechanical engineering for designing rotating discs, flywheels, and other circular components to ensure they operate within safe deformation limits.

4. Using The Calculator

Tips: Enter all stress values in Pascal, Poisson's ratio as a dimensionless value between 0.1-0.5, modulus of elasticity in Pascal, and disc radius in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is circumferential stress?
A: Circumferential stress (hoop stress) is the stress acting tangentially to the circumference of a cylindrical or disc-shaped object.

Q2: What is Poisson's ratio?
A: Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain when a material is stretched.

Q3: What is radial stress?
A: Radial stress is the stress acting in the radial direction (perpendicular to the axis of rotation) in a disc or cylinder.

Q4: What is modulus of elasticity?
A: Modulus of elasticity (Young's modulus) is a measure of a material's stiffness, defined as the ratio of stress to strain.

Q5: When is this calculation important?
A: This calculation is important in designing rotating machinery, pressure vessels, and any application where circular components are subjected to mechanical stresses.