8.1.1. Curvature Equation

Try these first

1. 1.

   What does curvature measure in a beam?

   Hint

   Think about how much the beam bends.

2. 2.

   What is the radius of curvature?

   Hint

   Connect it to the bending of the beam.

3. 3.

   What is the definition of curvature?

   • A measure of beam length
   • Rate of change of beam slope
   • Amount of material used

   Hint

   Think about what curvature provides information about in beams.

4. 4.

   True or False: The curvature increases with larger radii.

   • True
   • False

   Hint

   Consider the relationship between curvature and radius.

5. 5.

   Given a cantilever beam with a point load at its free end, derive the curvature equation and calculate deflection after applying the load.

   Hint

   Use principles of statics to solve?

6. 6.

   A beam with uniform loading has a total deflection of 0.03 m. Calculate its curvature if the moment of inertia is 1.5 m^4 and the modulus of elasticity is 200 GPa.

   Hint

   What formulas relate bending and curvature?