1.2. Representation of displacement

Try these first

1. 1.

   What are the three components of the displacement vector in cylindrical coordinates?

   Hint

   Think about the directions related to a cylinder.

2. 2.

   Which component of displacement represents radial movement?

   Hint

   It relates to how far a point is from the center.

3. 3.

   What are the components of the displacement vector in cylindrical coordinates?

   • u_r
   • u_θ
   • u_z
   • x
   • y
   • z
   • r
   • θ
   • R

   Hint

   Recall the definitions laid out!

4. 4.

   True or False: The component u_θ affects only circumferential displacement.

   • True
   • False

   Hint

   Think about what happens to a circle if it rotates.

5. 5.

   A hollow cylinder of radius 5 m experiences a uniform radial displacement of 0.2 m. Calculate the new dimensions of the circumferential line. Discuss the resultant strain as well.

   Hint

   Use the basic strain formula for cylindrical shapes.

6. 6.

   Design a cylindrical container considering the effects of u_z under a load of 1000N. How should the material be selected to mitigate excessive vertical displacement?

   Hint

   Consider the principles of material science in your calculations.