"I-beam" cross section

I-beam

The I-beam can be analyzed as either three pieces added together or as a large piece with two pieces removed from it. Either of these methods will require use of the formula for composite cross section. This section only covers doubly symmetric I-beams, meaning the shape has two planes of symmetry.

b = width (x-dimension), h = height (y-dimension) tw = width of central webbing h1 = inside distance between flanges (usually referred to as hw, the height of the web)

This formula uses the method of a block with two pieces removed. (While this may not be the easiest way to do this calculation, it is instructive in demonstrating how to subtract moments).

I-beam diagram, moment by subtraction

Since the I-beam is symmetrical with respect to the y-axis the Ix has no component for the centroid of the blocks removed being offset above or below the x axis.

When computing Iy it is necessary to allow for the fact that the pieces being removed are offset from the Y axis, this results in the Ax2 term.

A = Area contained within the middle of one of the 'C' shapes of created by two

flanges and the webbing on one side of the cross section = x = distance of the centroid of the area contained in the 'C' shape from the y-axis of

the beam =

Doing the same calculation by combining three pieces, the center webbing plus identical contributions for the top and bottom piece:

I-beam diagram, moment by addition

Since the centroids of all three pieces are on the y-axis Iy can be computed just by adding the moments together.

However, this time the law for composition with offsets must be used for Ix because the centroids of the top and bottom are offset from the centroid of the whole I-beam.

A = Area of the top or bottom piece = y = offset of the centroid of the top or bottom piece from the centroid of the whole I-

beam =