2.1. Force on +z and −z Plane

Try these first

1. 1.

   Define the term 'traction vector'.

   Hint

   Think about forces acting on a surface.

2. 2.

   What does the integration of the area element represent?

   Hint

   Consider how small areas contribute to a total.

3. 3.

   What does the traction vector on the +z plane include?

   • Only normal stress
   • One shear stress component
   • Multiple stress components

   Hint

   Think about how many forces act on a surface.

4. 4.

   True or False: The integration for the total force on the -z plane uses positive traction components.

   • True
   • False

   Hint

   Remember the direction of the forces.

5. 5.

   A vertical cylindrical tank filled with water has a base area of 3 m². Calculate the force acting on the bottom (+z) plane if the water exerts a pressure of 100 kPa.

   Hint

   Use the basic formula for pressure force calculation.

6. 6.

   For a hollow cylinder with an inner radius of 1 m and outer radius of 1.5 m, derive the expression for the total force on the top surface if σ varies linearly from the center to the outer edge.

   Hint

   Set the limits for integration accordingly based on the radii.