3. Variation in τ for some representative cross-sections

Try these first

1. 1.

   Define shear stress and shear force.

   Hint

   Think of how forces act when bending a beam.

2. 2.

   What is the purpose of the moment of inertia in beam theory?

   Hint

   Consider how this impacts the shape and loading of a beam.

3. 3.

   What does shear stress (τ) depend on for beam cross-sections?

   • Material type
   • Shear force and geometry
   • Applied loads

   Hint

   Think about the factors that affect how beams bend and carry load.

4. 4.

   True or False: Shear stress in a circular beam is constant at all points.

   • True
   • False

   Hint

   Reflect on circular shapes and how loads are distributed.

5. 5.

   Given an I-beam with a total shear force of 500 N, width at the flanges = 150 mm, and height = 300 mm, calculate the shear stress at the neutral axis.

   Hint

   Carefully compute the moment of inertia based on A and b values.

6. 6.

   Analyze the shear stress variation for a circular beam of diameter 200 mm and total shear V = 600 N. How would you determine τ at different radial positions?

   Hint

   Focus on understanding shear at centroid vs. outer radius.