2.1. Hoop (Circumferential) Stress

Try these first

1. 1.

   Define hoop stress in your own words.

   Hint

   Think about how pressure affects the walls of a cylinder.

2. 2.

   What is the formula for calculating hoop stress in thin-walled cylinders?

   Hint

   Remember P.R.T. - Pressure, Radius, Thickness.

3. 3.

   What is the formula for calculating hoop stress in thin-walled cylinders?

   • σh = p * r / (2 * t)
   • σh = pr/t
   • σh = p/(r * t)

   Hint

   Think about how the radius and thickness are involved in the calculation.

4. 4.

   True or False: In thick-walled cylinders, the hoop stress is constant throughout the thickness.

   • True
   • False

   Hint

   Consider what happens to stress as you move from the inner to the outer wall.

5. 5.

   A steel cylinder is designed to withstand an internal pressure of 800 kPa with an internal radius of 20 cm and a wall thickness of 3 cm. Calculate the hoop stress and determine if the design meets a safety factor of 2.

   Hint

   Remember to consider the safety margin when calculating.

6. 6.

   A cylindrical tank has a radial temperature gradient causing uneven thermal expansion. If the inside temperature is 200°C and the outside is 20°C, calculate the thermal stress given E=200 GPa and α=12 x 10^-6 /°C.

   Hint

   Use the coefficients correctly to express temperature differences.