3.1. Rectangular cross-section

Try these first

1. 1.

   Define shear stress in the context of materials.

   Hint

   Think about forces acting parallel to the surface.

2. 2.

   What does the first moment of area (Q) represent?

   Hint

   Consider how areas contribute to stress distribution.

3. 3.

   What is shear stress typically measured in?

   • Pascals
   • Newtons
   • Joules

   Hint

   Consider the units of force divided by area.

4. 4.

   True or False: The first moment of area is independent of the location within the beam cross-section.

   • True
   • False

   Hint

   Think about how areas contribute to moments.

5. 5.

   A rectangular beam of height 12 cm and width 6 cm is subjected to a shear force of 2500 N. Calculate the shear stress at a point 3 cm from the neutral axis, given that the moment of inertia I is 640 cm^4.

   Hint

   Take care to set up the area calculations carefully for Q.

6. 6.

   You design a beam intended to carry a total shear force of 5000 N, with dimensions leading to a moment of inertia of 800 cm^4. Given the width remains constant at 8 cm, how does varying the height of the beam affect shear stress distribution?

   Hint

   Consider how both area and inertia interact in the equation.