# How to choose the dimensions for a prestressed I-beam?

I need to design a simply supported symmetric I-beam (for a school problem). However, I can't find much information about the selection of the section or if there exist any standards for that. the only thing I could find is AASHTO I-beams of which there appears to only 5 types (sizes) and all of them are too large for my needs (since they are used in bridges I guess). the beam I need to design has a span of 9m and carries DL 2.2 kN and LL 11 kN.

• A quick Google for "i-beam sizes" gave me multiple pages with standard I-beam specs. – Wasabi Jul 16 '20 at 13:57
• @Wasabi most of these are for "steel" I-beams and I need prestressed concrete beams – MaxSmith060 Jul 16 '20 at 14:02
• Ah, of course, missed the tags! In that case, you'll have a lot more trouble finding standards. (Though I did find this, which has 10 sizes). Concrete's advantage of being easily poured into any shape also means it is much less standardized. – Wasabi Jul 16 '20 at 14:11
• Have a look at Eurocode steel specs for indepth design specs. You ought to find them in there. – Rhodie Jul 26 '20 at 23:30

Let's assume we have prestressed the beam enough so the concrete under the load has zero stress at the bottom and the and maximum at the top. and let's assume it is a 350kg/cm^2 concrete which is a lower range of prestress concrete strength.

$$M= 1.2\cdot M_{deadload}+1.6\cdot M_{live load}$$

$$M= \frac{1.2 *2.2kN*9^2}{8}+\frac{1.6* 11kN*9^2}{ 8}=26.73 kNm+178.2 kNm=205 kNm$$ $$assuming \ \phi=0.85, \ 205/0.85=241 kNm$$
As a first test size, we pick $$\text{ h = L/20 = 45cm and b=25 cm.}$$
$$C=T= 350 *45/2 *2/3*45*25= 5906250kgcm *9.8/100= 578.8kNm$$ So we are over designing by a factor of roughly 2.5.