15.6. Mode Shapes of Typical Structures

Try these first

1. 1.

   What defines a mode shape?

   Hint

   Think about how structures respond to vibrations.

2. 2.

   What structure type has floors modeled as lumped masses?

   Hint

   Consider what stiffens them laterally.

3. 3.

   What is the first mode shape of a shear building mainly characterized by?

   • Lateral deflection
   • Torsion
   • Vertical displacement

   Hint

   Consider how a building sways during an earthquake.

4. 4.

   T/F: Cantilever beams only exhibit single curvature in their first mode.

   • True
   • False

   Hint

   Think about how their shapes evolve.

5. 5.

   Design a shear building taking into account the mode shapes discussed. How will you mitigate the effects of resonance?

   Hint

   Think about alterations to the geometry and stiffness.

6. 6.

   A cantilever beam is subjected to a load resulting in its first and second mode shapes. What are critical design considerations we need to account for?

   Hint

   Remember how higher modes increase curvatures.