**Strain Rosette Analysis on a Stainless Vessel**A strain rosette was attached to the outer surface of a stainless vessel in a stress-free state. The vessel was then subjected to complex loading, which included pressure, bending, and torsion. The strain readings from the three strain gauge elements in the rosette were recorded as follows, in microstrains:- \( \varepsilon_a = 210 \)- \( \varepsilon_b = 160 \)- \( \varepsilon_c = 330 \)The mechanical properties of the stainless steel material are provided:- Modulus of Elasticity, \( E = 193 \, \text{GPa} \)- Shear Modulus, \( G = 76 \, \text{GPa} \)- Poisson's Ratio, \( \nu = 0.27 \)- Yield Strength, \( \sigma_y = 205 \, \text{MPa} \)**Tasks:**1. Calculate the principal strains and in-plane maximum shear strain.2. Determine the principal stresses and absolute maximum shear stress.3. Assess the factor of safety based on the maximum shear stress failure theory.4. Evaluate the factor of safety based on the maximum distortion energy failure theory.**Diagram:**The diagram illustrates a 45° strain rosette with three gauges labeled as \( a \), \( b \), and \( c \). Each gauge is oriented at 45-degree angles relative to each other. - Gauge \( a \) is aligned along the \( x \)-axis.- Gauge \( b \) is rotated 45 degrees from gauge \( a \).- Gauge \( c \) is perpendicular to gauge \( a \).This arrangement enables the measurement of strains in multiple directions to calculate the principal strains and stresses.

A strain rosette was attached to the outer surface of stainless vessel when the vessel is in a stress-free state. The vessel was then put under a complex loading (pressure, bending and torsion) state. The train readings for the three strain gage elements in the strain rosette were recorded as: Ea=210, Eb=160, Ec-330, all in micro-strains. The mechanical properties of the stainless material are known: E=193 GPa, G=76 GPa, v=0.27, oy=205 MPa. Calculate the following: 1. Principal strains and in-plane maximum shear strain. 2. Principal stresses and absolute maximum shear stress. 3. The factor-of-safety based on the maximum shear stress failure theory. 4. The factor-of-safety based on the maximum distortion energy failure theory. 45° 45° b 45° strain rosette X

A strain rosette was attached to the outer surface of stainless vessel when the vessel is in a stress-free state. The vessel was then put under a complex loading (pressure, bending and torsion) state. The train readings for the three strain gage elements in the strain rosette were recorded as: Ea=210, Eb=160, Ec-330, all in micro-strains. The mechanical properties of the stainless material are known: E=193 GPa, G=76 GPa, v=0.27, oy=205 MPa. Calculate the following: 1. Principal strains and in-plane maximum shear strain. 2. Principal stresses and absolute maximum shear stress. 3. The factor-of-safety based on the maximum shear stress failure theory. 4. The factor-of-safety based on the maximum distortion energy failure theory. 45° 45° b 45° strain rosette X

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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**Strain Rosette Analysis on a Stainless Vessel**

A strain rosette was attached to the outer surface of a stainless vessel in a stress-free state. The vessel was then subjected to complex loading, which included pressure, bending, and torsion. The strain readings from the three strain gauge elements in the rosette were recorded as follows, in microstrains:

- \( \varepsilon_a = 210 \)
- \( \varepsilon_b = 160 \)
- \( \varepsilon_c = 330 \)

The mechanical properties of the stainless steel material are provided:

- Modulus of Elasticity, \( E = 193 \, \text{GPa} \)
- Shear Modulus, \( G = 76 \, \text{GPa} \)
- Poisson's Ratio, \( \nu = 0.27 \)
- Yield Strength, \( \sigma_y = 205 \, \text{MPa} \)

**Tasks:**

1. Calculate the principal strains and in-plane maximum shear strain.
2. Determine the principal stresses and absolute maximum shear stress.
3. Assess the factor of safety based on the maximum shear stress failure theory.
4. Evaluate the factor of safety based on the maximum distortion energy failure theory.

**Diagram:**

The diagram illustrates a 45° strain rosette with three gauges labeled as \( a \), \( b \), and \( c \). Each gauge is oriented at 45-degree angles relative to each other.

- Gauge \( a \) is aligned along the \( x \)-axis.
- Gauge \( b \) is rotated 45 degrees from gauge \( a \).
- Gauge \( c \) is perpendicular to gauge \( a \).

This arrangement enables the measurement of strains in multiple directions to calculate the principal strains and stresses.

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