In reply to Hooo:
To improve the effectiveness of structural elements in bending, there are two basic things you have to do.
1. Choose a shape where sufficient material is significantly displaced from the axis of bending.
2. Ensure that the shape also has sufficient stability in the axis of banding.
So at (1), the section modulus increases in proportion to the square of that distance displaced and in proportion to its width. This means reducing the height is a bad thing to do and you very quickly lose strength in bending by doing that. You do not lose or gain as much by changing width.
At (2), one would typically find that by choosing a shape will too much of the material displaced from the bending axis, there is no longer sufficient material in the webs or sides of the shape to hold its shape when under stress. In such a case, the shape is unstable and collapses.
These are the reasons that an I-shaped beam or column is so popular in important structures. A hollow section, such as the rectangle you describe, is also a structurally effective shape but can be more difficult to join to other elements.
https://en.wikipedia.org/wiki/Section_modulus
Post edited at 16:27