Bars of Uniform Strength:

If we calculate the stresses induced in the various segments of the bar shown in Figure (a), we get the following results:

σ1 =160 × 1000/800= 200 N/mm²

σ2 = 100 × 1000/200= 500 N/mm²

σ3 = 140 × 1000/600= 233.33 N/mm²

σ4 =60 × 1000/150= 400 N/mm²

The results show that the bar should be made of a material with permissible stress not less than 500 N/mm². Such a material (should be specially manufactured, if required) is wasted in segments where the stress induced is much less. For instance, in segment 1, the stress induced is only 200 N/mm². If we reduce the cross sectional area of segment 1, 3 and 4 to 320 mm², 280 mm² and 120 mm² respectively, the stress in all segments will be uniformly 500 N/mm², the bar would be safe and we would have effected considerably economy of material. Such a bar is called a bar of uniform strength. A designer will strive to achieve a bar of uniform strength, whenever possible. However, because of other constraints and variations in loadings, it might not always be possible to provide a bar of uniform strength. Therefore, the concept of bar of uniform strength is a design ideal aiming to effect maximum saving in the material.