Why don't we consider the reduce cross-sectional area while calculating stress in a metallic wire? Consider a wire which is being pulled by a force (within elastic limit) then the reaction force will be equal to the applied force then we say that the stress will be equal to applied force/cross-sectional area but at the same time we also know that there will be a decrease in the cross sectional area then why don't we consider it while calculating stress ?
 A: The change in cross sectional area can be considered by differentiating between  Engineering Stress/Strain and True Stress/Strain.
Engineering stress is the load divided by the original cross sectional area. Engineering strain is the change in length divided by the original length. These are convenient and useful approximations when dealing with small deformations and linear elastic behavior following Hooke’s Law.
True stress is the load divided by the instantaneous cross sectional area and true strain is the incremental change in length divided by the instantaneous length, I.e. the length at the start of each incremental change, not the original length. These may be used for accurate description of plastic behavior.
The two types of stress/strain are generally the same in the region of linear elastic behavior.
Hope this helps.
A: My dear friend, let us take an example of steel rod of length 100m and diameter 5m. If we apply tangential forces until the rod breaks. We observe that the change in the cross sectional area is 0.15% that is very small and can be neglected. Your point is right
