5.6 BEAMS OF UNIFORM STRENGTH
In general, beams have uniform cross section throughout their length. When they are loaded, there is a variation in bending moment from section to section along the length. The stress in extreme outer fibre (top and bottom) also vary from section to section along their length. The extreme fibres can be loaded to the maximum capacity of permissible stress (say pmax), but they are loaded to less capacity. Hence, in beams of uniform cross section there is a considerable waste of materials.
When a beam is suitably designed such that the extreme fibres are loaded to the maximum permissble stress pmax by varying the cross section it will be known as a beam of uniform strength.
If at every point of the extreme fibre, ...