1.2. Variation of σ in the cross-section

Try these first

1. 1.

   What is the formula for calculating σ in the context of non-uniform bending?

   Hint

   Think about how bending moments relate to stress.

2. 2.

   What does τ represent in mechanical systems?

   Hint

   Consider forces acting parallel to a cross-section.

3. 3.

   What is the primary factor that causes variation in σ across the beam's cross-section?

   • Constant load
   • Variable bending moments
   • Shear forces

   Hint

   Think about which forces cause bending.

4. 4.

   True or False: The shear stress τ is assumed to be a function of both y and z in the analysis.

   • True
   • False

   Hint

   Reflect on the simplifications made in calculations.

5. 5.

   A steel beam with a rectangular cross-section experiences a non-uniform load giving rise to varying bending moments. Analyze the stress distribution and calculate σ at three key points of the beam.

   Hint

   Break down the stress at each location with the formula provided.

6. 6.

   For an I-beam under loading, derive the shear stress distribution analytically and graphically depict how τ varies from the neutral axis to the edges.

   Hint

   Pay attention to how I-beams have distinct width regions and adjust calculations accordingly.