are i-beams considered more efficient than rectangular hollow sections of the same cross sectional areas?

Question

I'm talking about bending here, i.e. used as a horizontal beam, not as a column. and assume no torsion either.

I tried to compare i-beams with rectangular hollow sections of similar dimensions and same cross section areas.

what i mean by similar dimensions: by cutting off the two vertical sides of the cross section area of a rectangular hollow sections and moving them to the middle and 'stick together', the shape can be transformed to an i-beam cross-section, and this is the i-beam which the rectangular cross-section is compared with. under such conditions, the two shapes should also have the same area.

what i have problems with: I calculated the i values (second moment of area) of the two aforementioned shapes and I seem to get the same values. with this being the case, why do people say i-beams are the best shapes to withstand bending?

Answer 1

If you take the center portion of an I-Beam and move it to the outside of the I beam, you are going to get the exact same moment of inertia. The same could be said for a C channel of the same dimensions or an I beam that is not symmetric.



For rectangular sections, I = (1/2) b h^3



I beams are the best shape to resist bending because you are putting the most amount of material away from the neutral axis in the easiest way to manufacture and use. A hollow section is harder to extrude and a C channel is asymmetric which provides its own difficulties in use.

Answer 2

The typical 'universal beam' (UB) has quite a lot more metal in the 'flanges' (the flat top and bottom) than in the 'web' (the connecting bit down the middle). This compares with rolled hollow sections such as rectangular hollow section (RHS), which is normally the same thickness throughout. So you really need to compare typical sections that you can actually buy; you will then see that UB gives higher second moment of area than RHS for bending, so it's stronger per area.

Answer 3

In order for the I beam and the rectangular hollow section to have the same resistance to bending (Section Modulus), the thickness of the sides of the RHS would be half the thickness of the web of the beam.

Since in practise the flanges are much thicker than the web on a rolled section and the walls of a Hollow Section are consistent the I Beam or WF section will be more efficient in pure bending.

Answer 4

Yes it will affecvt the crossectional area. Since wire is same only redrawn therefore volume in both cases will be same. Let original area = A New Area = A' original length= L New Length = 2L Original volume = New Volume (original area)*(Original length)=(new area)*(new length) A*L = A' * (2L) A=2A' A' = A/2 Thur area is reduced to half of original area