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Let's say we stretch a wire and it's cross-sectional area decreased.

When using the Young's modulus formula$$\frac{FL}{A\Delta L}$$

Where F is the force subjected on the body.

Should we take the cross sectional area after it stretches or before and why ?

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There are two type of stress. There is engineering stress and true stress. True stress is based on the actual cross-sectional area under load, whereas engineering stress is the load divided by the initial area.

There are several reasons for using engineering stress then true stress. For one, true stress is more difficult to measure. For another, the difference is generally not too much, given the use of a sufficient safety factor.

Hope this helps.

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