Stress-Strain Curves:

From the results of such a study the subsequent observations might be made.

(a)        While the loading is completed inside the proportional limit of the solid, the strain (deformation) caused is fully recovered while the stress is erased. (If the load is partially erased, a proportional amount of strain gets relieved.)

(b)       Whenever the solid is loaded beyond yield limit and then unloaded; only a part of the strain is relieved and a considerable element of strain still persist therefore effecting permanent changes in the geometry of the solid. The strain remaining unrelieved is called as permanent set.

(c)        When we reload a solid that is already subjected to permanent set, the stress-strain curve for reloading is linear up to the maximum stage to that it was subjected to previously.

By these observations, what does a designer learn? If a structure or any elements is loaded beyond proportional limit, the geometry gets permanently modified and if repeatedly loaded beyond proportional limit, it will go fully out of shape after a few repetitions. Instead, you can load it within their proportional limit any number of times and the original geometry recover on the removal of the load. Therefore, in any design, one has to be careful to prevent loading the component beyond the proportional limit. Within this limit the solid is said to be elastic. The property known as elasticity consists of two aspects, generally complete removal of strains on unloading and linearity of stress-strain relationship. Therefore, the part of stress-strain curve up to yield point is also known as elastic limit. To ensure in which the solid is always inside this elastic limit, designers allow stresses in solid much lower than the elastic limit. The ratio of the maximum stress a material could withstand to the maximum stress that a designer chooses to permit is called the factor of safety. In summary,

Factor of Safety = Maximum stress the material can withstand/Maximum stress permissible

If the numerator is yield point stress, a factor of safety is 2 commonly permitted and if it is ultimate stress, factor of safety might be 3 or more.