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Chapter: Civil - Mechanics Of Solids - Deflection Of Beams

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Deflection Of Beams - Introduction

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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