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Where does the T-beam come from? There's just a straight beam resting on two supports. And where do 10 and 80 come from? I am so confused.

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    $\begingroup$ 80 is width of top surface... $\endgroup$ – Solar Mike May 13 '19 at 18:36
  • $\begingroup$ The T-profile is the shape of the intersection, if you cut the beam at every arbitrary position and look at the intersection you'll see a T. $\endgroup$ – Sam Farjamirad May 13 '19 at 18:51
  • $\begingroup$ About 80, look at the comment of Solar Mike, and 10 is the half of the thickness of horizontal body, the centroid of the horizontal body lies at the center of of the horizontal rectangle $d_{zz}$ is the distance between the two centroids. $\endgroup$ – Sam Farjamirad May 13 '19 at 19:06
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To find the neutral axis of any section including the T section in your question, ( called T beam because its cross section is a T):

  • one picks a horizontal axis parallel to x axis (or the axis they need to find the beam's neutral axis).

  • break the section into simple geometric shapes.

  • find the area moment of each section by multiplying its area by the distance from its CG to the axis picked at the first step. (in your case they assumed the top surface's, Line Z, as that random reference axis, and 10 is the distances of the horizontal 80 by 20 flange and 60+20 is the vertical web CG from the top axis)

  • sum all the area moments and dived by total area of all the part, you get the neutral axis, which they did and got 52 mm from the top surface as the neutral axis of the T beam.

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