How to Calculate an Elastic Axis

Written by james t wood | 13/05/2017
How to Calculate an Elastic Axis
Finding the elastic axis, or neutral axis, of something like an I-beam involves calculating the centre of gravity for the whole piece. (large steel girders image by Yali Shi from

Elastic bending theory defines an axis that, when bent, does not change in length. This is known as the neutral axis and it is the line formed by the intersection of the two neutral faces of the elastic material. Imagine a steel I-beam which bends under a load - the neutral axis is the line through the relative centre that is the same length whether the steel is bent or straight. This neutral axis corresponds to the centre of gravity of the entire piece.

Draw a cross section of the material for which you are wanting to find the neutral axis. Include the measurements for each surface of the piece.

Divide the cross section into shapes for which the centre of gravity is easily defined. Look for circles, triangles, trapezoids, squares, or any other common shapes.

Find the centre of gravity for each segment. The centre of gravity of a circle is the middle point. The centre of gravity for a parallelogram or a square is the intersection of lines drawn from opposite corners. The centre of gravity for a triangle is found when you draw a line from the centre of two of the sides to the opposite points.

Plot a line that intersects all of the centres of gravity and you have found the neutral axis.

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