21.2. Background

Try these first

1. 1.

   What is torsion in the context of beams?

   Hint

   Think about how twists affect the structure.

2. 2.

   Define Saint-Venant's torsion.

   Hint

   Consider the absence of lateral displacements.

3. 3.

   What type of torsion remains constant along the length of a beam?

   • Warping Torsion
   • Saint-Venant’s Torsion
   • Both

   Hint

   Think about how each type behaves over the length of the beam.

4. 4.

   True or False: Warping torsion leads to lateral displacements of the beam’s flanges.

   • True
   • False

   Hint

   Consider the definition of warping torsion.

5. 5.

   Consider a steel beam subjected to a load that induces torsion. Calculate the shear stress and angle of twist at different points along the beam, providing both mathematical derivations and a diagram to illustrate your findings.

   Hint

   Use the formula τ = T*r/J, where τ is shear stress, T is torque, r is the distance from the center, and J is the polar moment of inertia.

6. 6.

   Design a simple structure incorporating a beam subjected to known torsional loads, ensuring to analyze and modify the design for both Saint-Venant's and warping torsion effects.

   Hint

   Think about how to support the beam and what materials will prevent failure.