21.3.2. Governing Moments

Try these first

1. 1.

   What equation is used to describe the moment in very short beams?

   Hint

   Think about the factors that affect moment in a plastic hinge.

2. 2.

   What is the significance of the section modulus?

   Hint

   Consider beam cross-section properties.

3. 3.

   What is the equation for moment capacity in a plastic hinge?

   • M_n = Z F_y
   • M_n = C_b (M_p - M_r)
   • M_{cr} = C_b C_w I + EI GJ C

   Hint

   Recall the conditions for very short beams.

4. 4.

   True or False: C_b increases moment capacity for unbraced beams.

   • True
   • False

   Hint

   Think about how external loads affect beams at different points.

5. 5.

   A steel beam with a section modulus of 30 in^3 and yield strength of 50 ksi is 10 feet long. Calculate the moment in the plastic hinge scenario.

   Hint

   Apply the principles of moment capacity based on Z and yield strength.

6. 6.

   Analyze a long steel beam under varying wind loads, using its properties to evaluate potential elastic lateral torsional buckling scenarios.

   Hint

   Think about how external forces can change the internal state of the beam.