Tutorial

Bending Stresses Tutorial Questions

1. A beam has a rectangular cross section of breadth 60mm and depth 50mm and is bent in the vertical plane to the radius of curvature 100m.  Calculate the maximum tensile and compressive stresses and show by a diagram how the stresses vary over a transvers section.   E = 200 GN/m2.

2. A beam 4m long is simply supported at its ends and carries a central concentrated load on 10kN.  If the beam is to be of rectangular section with the depth being twice the width, determine its dimensions if the maximum stress in the material is to be 60MN/m2.

3. A circular steel bar is used as a cantilever beam to carry a transverse force of 20kN at a point 1.5m from the support.  Calculate the diameter of the bar required to limit the maximum bending stress to 170MN/m2.

4. A 3m long cantilever carries a vertical load (downward) of 10kN at its free end.  The beam has a square cross section of 75mm x 75mm.  Determine:
   a. The second moment of area of the beam cross‐section about its centroid axis;
   b. The magnitude of the maximum bending moment set up in the beam and where it acts.
   c. The maximum bending stress in the beam material and show the distribution of stress at the cross section where the maximum moment is acting.

5. A 5m long simply supported beam carries a point load of 12kN half way along its length.  The beam material has a maximum allowable stress of 280MN/m2. The beam has a hollow rectangular cross section, the outer dimensions are breadth = 80mm and depth = 120mm, the walls are 15mm thick.  Determine:
   a. The second moment of area of the beam cross section about the x‐x axis.
   b. The magnitude of the maximum bending moment set up in the beam.
   c. The maximum stress set up in the beam material due to bending.
   d. The factor of safety in the loaded beam.
   e. The factor of safety in the loaded beam if it has been loaded such that the bending takes place about the y‐y axis.