7.1. Common shapes

Try these first

1. 1.

   What is the formula for the moment of inertia of a rectangle?

   Hint

   Remember the standard formula used for rectangles.

2. 2.

   How does height affect the moment of inertia of a rectangular beam?

   Hint

   Think about how the formula changes as the height increases.

3. 3.

   What is the moment of inertia of a rectangle with a width of 100 mm and a height of 200 mm?

   Hint

   You need to use the rectangle's formula.

4. 4.

   True or False: Hollow sections can support the same loads as solid sections while using less material.

   • True
   • False

   Hint

   Think about strength-to-weight ratios.

5. 5.

   A rectangular beam has a breadth of 150 mm and height of 600 mm. Calculate its moment of inertia and compare it to a circular beam with a diameter of 150 mm.

   Hint

   Use the respective formulas for both shapes.

6. 6.

   Design a hollow beam structure and calculate its moment of inertia using hypothetical dimensions of outer 400 mm width/height and inner wall thickness of 50 mm.

   Hint

   Perform the step-by-step calculations for clarity.