Problem: A beam of rectangular cross section 200mm deep and 100 mm wide. If the beam is 3 long, simply supported at either end and carries point loads as shown in figure.

(a) Calculate the maximum bending moment.

(b) Calculate the maximum stress in the beam.

(c) At the point of maximum stress sketch a graph of the stress distribution through the thickness of the beam, indicating which tensile and comprehensive stresses are.

(d) Determine the dimensions of the cross section which will minimize the maximum stress value if:

• The cross sectional area of the beam can be increased by 20%.
• The beam section is to remain a solid rectangle
• Either the breadth or depth of the beam section can be reduced below their original dimensions.

Show the dimensions of the proposed beam cross section with the aid of a sketch.

(e) Determine the percentage reduction of the maximum stress value when the new cross section is used.