1.2. Governing equations

Try these first

1. 1.

   What are the two independent variables in Timoshenko Beam Theory?

   Hint

   Think about what differentiates Timoshenko from Euler-Bernoulli.

2. 2.

   Write down the formula for average shear stress.

   Hint

   It's about force distribution over an area!

3. 3.

   What is the main distinction of Timoshenko Beam Theory from Euler-Bernoulli?

   • It ignores shear deformation
   • It accounts for shear deformation
   • It uses only bending stress

   Hint

   Consider what effects shear has compared to bending.

4. 4.

   True or False: In Timoshenko Beam Theory, deflection and rotation are treated independently.

   • True
   • False

   Hint

   Think about their relationship in equations.

5. 5.

   A cantilever beam with a length of 5m is subjected to a point load of 1000N at its free end. Calculate the shear force and bending moment profile along the beam first using Timoshenko Beam Theory.

   Hint

   Identify shear and bending effects distinctly throughout the beam.

6. 6.

   A Timoshenko beam with a rectangular cross-section experiences a shear force of 200 N and has a width of 0.1 m and height of 0.2 m. Calculate the average shear stress and compare it to calculated shear strain using the governing equations.

   Hint

   Remember to apply TBT's unique equations for shear strain!