H-beam and I-beam looks quite similar that makes it confusing to many who is not concered about the differences between h-beam and i beam. Lets discuss about these two structural members.
H-beam
H-beam is a structural beam made of rolled steel. It is incredibly strong. It gets its name because it looks like a capital H over its cross section. The H-beam has wider flanges than an I-beam, but the I-beam has tapered edges. The width is the flange, and the height is the Web. The difference between both H-beams and I-beams is the flange by web ratio. The H-beam tends to be heavier than the I-beam, and that is why some say that it is better than the I-beam, but that is subjective, as the H-beam is generally heavier.
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Related: RCC Beam Behavior
I-beam
I-beam has tapered edges where an H-beam does not. It gets its name from the fact that it looks like a capital I when you see it from its cross section. With an I-beam, the height of the cross section is higher than the width of its flange. The I-beam is lighter than the H-beam, which means a H-beam is not always ideal.
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The thickness of the center web is what is the most important, as that is what takes the force of the weight placed upon it, and that is why a lot of buildings require a H-beam over an I-beam. An I-beam is made by rolling or milling steel which means the I-beam is often limited by the capacity or size of the milling equipment. H-beams are built up; so they are able to be made at any size or width.
Related: RCC beam failure mode
Difference between I-beam and H-beam
It does seem that the H-beam is the better beam. But that is not always the case as it does depend on the use of the beam and the building/structure you are planning to put it into. Here is a closer h-beam vs i-beam comparison of the two beams.
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Heavier does not mean stronger. I find it crazy that inertia was not even mentioned once on this page. Any sophomore engineering student can tell you that a H beam will be stronger if you use it as an I beam. The inertia of an I is greater than the inertia of an H with the same dimensions.