Elastic curve of neutral axis

**Deflection Of Beams - Introduction**

Elastic
curve of neutral axis

Assuming that the I-beam is symmetric, the neutral axis will
be situated at the midsection of the beam. The neutral axis is defined as the
point in a beam where there is neither tension nor compression forces. So if
the beam is loaded uniformly from above, any point above the neutral axis will
be in compression, whereas any point below it will be in tension . However, if
the beam is NOT symmetric, then you will have to use the following methodology
to calculate the position of the neutral axis. .

1. Calculate the total cross-sectional area of the beam (we
shall call this A). Let x denote the position of the neutral axis from the
topmost edge of the top flange of the beam . .

2. Divide the I-beam into rectangles and find the area of
these rectangles (we shall denote these areas as A1, A2, and A3 for the top
flange, web and bottom flange respectively). Additionally, find the distance
from the edge of the top flange to the midsection of these 3 rectangles (these
distances will be denoted as x1, x2 and x3) . .

3. Now,
to find the position of the neutral axis, the following general formula must be
used:

A*x = A1*x1 + A2*x2 + A3*x3

We know all the variables in the above formula, except for x
(the position of the neutral axis from the top edge of the top flange). So it
is just a case of rearranging the formula to find x.

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