Stress in Unsymmetrical Bending - Unsymmetrical Bending - Structural analysis 1 | Summary and Q&A

TL;DR

This video discusses the theory of stresses in unsymmetrical bending, including finding resultant stress at any point, determining the neutral axis, and understanding the nature of stress on either side of the neutral axis.

Key Insights

• 😁 Unsymmetrical bending occurs when the bending moment is not perpendicular to the beam's cross-section.
• 😥 The resultant stress at any point in unsymmetrical bending can be found by resolving the bending moment into components and using the appropriate formula.
• 😁 The neutral axis in unsymmetrical bending is a straight line passing through the centroid of the beam's cross-section.

Transcript

hello students so we are starting with our theory topic stress in unsymmetrical bending so here let's see a cross section of a beam where bending moment m is in the plane of y is as shown in the figure so let me take you to the diagram so this is a figure so cross section of a beam subjected to a bending moment m in the plane y y so bending moment ... Read More

Questions & Answers

Q: What is unsymmetrical bending and why is it important to analyze the stresses in it?

Unsymmetrical bending occurs when a bending moment acts in a plane that is not perpendicular to the beam's cross-section. It is important to analyze the stresses in unsymmetrical bending to ensure the structural integrity of the beam and understand its behavior under different loading conditions.

Q: How do you find the resultant stress at any point in unsymmetrical bending?

To find the resultant stress at any point, you need to resolve the bending moment into components in the principal axes. Then, use the formula sigma_b = (m * sin(theta)) / (I_vb) * u + (m * cos(theta)) / (I_u) * v, where sigma_b is the resultant bending stress, m is the bending moment, u and v are the coordinates of the point, theta is the angle of inclination of the principal axes, and I_vb and I_u are the moments of inertia about the principal axes.

Q: How can you determine the neutral axis in unsymmetrical bending?

The neutral axis is the axis through which no bending stress is present. To determine the equation of the neutral axis, set the resultant bending stress (sigma_b) equal to zero and solve the equation m * (u * sin(theta) / (I_vb) + v * cos(theta) / (I_u)) = 0. This equation represents a straight line passing through the centroid of the beam's cross-section.

Q: What is the nature of stress on either side of the neutral axis in unsymmetrical bending?

The nature of stress on one side of the neutral axis is the same, meaning it is either tensile or compressive. On the other side of the neutral axis, the stress is of the opposite nature. The stress is maximum at a point that is farthest from the neutral axis.

Summary & Key Takeaways

• This video explains the concept of stresses in unsymmetrical bending of a beam and how to find the resultant stress at any point.

• The video shows how to resolve the bending moment into components and calculate the bending stress in different planes.

• It also discusses the formula to determine the coordinates of a point with respect to the principal axes and the equation of the neutral axis.