# 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

## 1 Answer

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.

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

I assume your loads are distributed loads and you forgot to mention that.

$$M= \frac{1.2 *2.2kN*9^2}{8}+\frac{1.6* 11kN*9^2}{ 8}=26.73 kNm+178.2 kNm=205 kNm$$ $$assuming \ \phi=0.85, \ 205/0.85=241 kNm$$

As a first test size, we pick $$\text{ h = L/20 = 45cm and b=25 cm.}$$

The stress triangle is a 45cm height by 25 cm base and with 350kg/cm^2 on top of the beam and zero at the bottom.

$$C=T= 350 *45/2 *2/3*45*25= 5906250kgcm *9.8/100= 578.8kNm$$ So we are over designing by a factor of roughly 2.5.

We can now iterate down to find the right size, albeit with an eye on controlling the deflection.

This is a very basic first rough step to get an idea for the size of the beam, we need to know a lot more as to the type of strand or concrete before we can start the formal design.