I beam
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Transcript of I beam
![Page 1: I beam](https://reader036.fdocuments.in/reader036/viewer/2022082512/552515534a7959ce488b49b7/html5/thumbnails/1.jpg)
"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
![Page 2: I beam](https://reader036.fdocuments.in/reader036/viewer/2022082512/552515534a7959ce488b49b7/html5/thumbnails/2.jpg)
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.
![Page 3: I beam](https://reader036.fdocuments.in/reader036/viewer/2022082512/552515534a7959ce488b49b7/html5/thumbnails/3.jpg)
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 =