Why does the strength of a sheet of material under strain increase with thickness? For instance, why is a thick plywood table able to bear heavier loads than a thin plywood table? 
I am aware of the concept of tensile strength but, seeing as that only says things about the strength of cross-sectional areas of material, I don’t see why greater thickness of materials tends to result in greater “practical” strength when the thickness of a sheet increases (after all, doesn’t cross-sectional area stay the same in that case)?
 A: In sheet or beam strength I assume you refer to the flexural strength, as the load is acting perpendicularly to the stress present in the material. This as opposed to yield strength where the load is acting parallel to the stress in the material. In the former case the "cross section" refers to the area looking at the edge of the table, not the surface area looking from the top. If you look up the formula for flexural strength you will find parameters referring to the "edge" cross section such as "height and width". Length is also a factor (distance between the two support points between which the load is applied)
A: in very simplified terms, a load imposed on a table top places it into a certain state of stress. that stress is supported by the particulars of the material from which the top is made, and the geometry of its cross-section. 
a thick cross-section will distribute the imposed load across a greater area of the material and in so doing it reduces the maximum value of the stress. this means a thicker table top can support a heavier load before it breaks. 
A detailed analysis of this problem can be found by searching under the topic "simply supported beam with point load".
