Normal Stress in Two Mutually Perpendicular Directions: Problem 5 - Principal Stresses and Planes | Summary and Q&A

TL;DR

This video discusses a problem where a body is subjected to principal stresses and determines normal and tangential stresses, resultant stress, angle of obliquity, and normal stress on the plane of maximum shear stress.

Key Insights

• 😀 The problem involves a strained material with principal stresses of 200 N/mm² (tensile) and 30 N/mm² (compressive).
• ✈️ The calculation of normal stress on an inclined plane requires using the formula σₙ = (σₓ + σᵧ)/2 + (σₓ - σᵧ)/2 * cos(2θ).
• ✈️ The tangential stress on the inclined plane can be calculated using the formula σₜ = (σₓ - σᵧ)/2 * sin(2θ).
• ❓ The resultant stress is determined using the formula σᵣ = √(σₙ² + σₜ²).
• 🔺 The angle of obliquity is obtained using the formula φ = tan⁻¹(σₜ/σₙ).

Transcript

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Questions & Answers

Q: What are the principal stresses in the given problem?

The principal stresses in the problem are 200 N/mm² (tensile) and -30 N/mm² (compressive).

Q: How do you calculate the normal stress on the inclined plane?

The normal stress can be calculated using the formula σₙ = (σₓ + σᵧ)/2 + (σₓ - σᵧ)/2 * cos(2θ), where σₙ is the normal stress, σₓ and σᵧ are the principal stresses, and θ is the angle of inclination. In this case, the normal stress is 27.5 N/mm².

Q: How do you calculate the tangential stress on the inclined plane?

The tangential stress can be calculated using the formula σₜ = (σₓ - σᵧ)/2 * sin(2θ), where σₜ is the tangential stress, σₓ and σᵧ are the principal stresses, and θ is the angle of inclination. In this case, the tangential stress is 99.59 N/mm².

Q: How can you find the resultant stress?

The resultant stress can be calculated using the formula σᵣ = √(σₙ² + σₜ²), where σᵣ is the resultant stress, σₙ is the normal stress, and σₜ is the tangential stress. The calculated resultant stress in this problem is 103.3 N/mm².

Q: How do you determine the angle of obliquity?

The angle of obliquity can be calculated using the formula φ = tan⁻¹(σₜ/σₙ), where φ is the angle of obliquity, σₜ is the tangential stress, and σₙ is the normal stress. In this problem, the angle of obliquity is 74.56 degrees.

Q: What is the normal stress on the plane of maximum shear stress?

The normal stress on the plane of maximum shear stress can be calculated as σₙ = (σₓ + σᵧ)/2. In this case, the normal stress on the plane of maximum shear stress is 85 N/mm².

Summary & Key Takeaways

• The video discusses a problem involving a strained material with principal stresses of 200 N/mm² (tensile) and 30 N/mm² (compressive).

• It explores how to calculate the normal and tangential stresses on a plane inclined at 60 degrees to the major principal plane.

• The video also covers the calculation of the resultant stress, angle of obliquity, and normal stress on the plane of maximum shear stress.