Dear guests, as promised in the article on the calculation of wooden beams for deflection (link to article), in this material we will focus on the calculation of a steel metal beam for a span: channel and I-beam.
In this article, the calculation and selection of products are carried out in full accordance with the academic discipline on solid mechanics (section: resistance of materials).
I consider it necessary to warn that the article is completely technical, so do not scold me, I know that many Zen readers do not like this :)))
In the previous article on wooden beams - I received a lot of criticism in the comments that, they say, the 21st CENTURY in the yard is full of online calculators and ready-made tables on the Internet.
Of course, you can trust online calculators, but believe me, after spending 30-40 minutes and delving into it yourself, you can recheck any calculator and sleep more peacefully, because all calculations are done independently and the result on the face! As for the tables, any of them taken from the Internet is of unknown origin, and there is a high probability of taking inaccurate data ...
So, below are samples of hot-rolled steel products in accordance with the relevant GOSTs, according to which, depending on the final calculation, we will choose a suitable beam and its section (shape):
For example, in the calculation, the factory length of the steel product is taken - 6 m, and the spacing of the beams is also selected - 0.6 m (accordingly, these parameters will be different for each depending on the situation).
Having a drawing, project or a sketch of the dimensions of the rooms on paper, you need to decide on the estimated lengths. Clear distance (Lsv) is the length of the span to be covered. Knowing this length and the minimum support of the beam on the wall Lop = 120 mm., we get the length of the beam (in our example L = 6 m.).
For further calculation, you need to know the distance between the centers of the reference lengths (Lo) is the main quantity involved in the calculation (see picture above).
To begin with, before the calculation itself, you need to decide on the function of the room. For living quarters - according to the standard, the time load from the stay of people is 1.5 kPa or 150 kg / m2. (P1).
According to the rules of calculation, we lay a safety margin of 20%, therefore, further we use the coefficient K1 = 1.2
After determining the function of the room and the temporary load, we need to calculate the dead weight per square meter of the floor assembly (the whole pie), and namely: weight of beams, flooring, ceiling, sound insulation, etc. As an example, for the calculation we take the own weight - 150 kg / sq.m., Thus P2 = 150 kg / sq.m. But, according to the rules, it is already necessary to deliberately overestimate the reliability by 30%, respectively K2 = 1.3.
We determine the main parameters for the calculation
Payment
So, we consider the required moment of resistance W = M / (Yc * Ry),
W = 9.72 / (0.9 * 240) = 45 cc.
Having received the moment of resistance, we return to the tables of product characteristics (illustrations at the very beginning). In these tables, GOST has already determined the values of the moments for various sections, based on which we select the beam, rounding W upward:
For the obtained moment of 45 cm3, I-beam No. 12 with a value of W = 58.4 or channel No. 12 is suitable, where W = 50.6. For our example, we select an I-beam and then check for deflection.
It is important to make a reservation that if you are not satisfied with I-beams, there are wide-flange or column I-beams, which, at the same height, will have higher characteristics. Thus, due to the better bearing capacity, you can reduce the thickness of the entire slab:
After the choice of the steel beam is made, we write out all the characteristics of the selected product from the plate on the corresponding line:
- Static moment: S = 33.7 cm3;
- Moment of inertia: I = 350 cm4;
- Wall thickness: d = 4.8 mm.
We make a check for deflection. In the case of a large slack in the center of the structure, we need to take the I-beam next to No. 12.
Verification:
In the calculation, we need the main stiffness characteristic of the material - this is the elastic modulus, for steel it is equal to:
E = 206,000 MPa.
We determine the deflection according to the standard sopromat formula:
So, the calculated deflection in the center is 3.89 cm.
It must be compared with the aesthetic and psychological parameters according to SNiP (Table E.1)
Why aesthetic and psychological? The fact is that despite the reliability of the structure, the sag of the beam will "put pressure on the psyche", and therefore SNiP provides for permissible deflections.
Agree that we do not want to catch a glance at the curved ceiling in the house and it will seem that it is about to crack and fall on our heads.
According to the table, we have vertical deflections for beams: L / xxx. In order to compare the obtained value with this characteristic, it is required to calculate the parameter of the maximum permissible values:
When calculating, as an example - we took a beam of factory length - 6 m, so we are looking for the line L = 6m:
Based on the calculations and from the presented table, we compare the deflection parameters: L / 151> L / 200. Since the deflection is stronger than the standard, the selected steel beam does not satisfy the condition.
In other words, I-beam No. 12 will sag with a span of 5.8 m - by 3.9 cm, which is unacceptable according to SNiP. We have no choice but to select the next I-beam on the list and check again.
With I-beam # 14, the deflection is 2.4 cm. and the parameter of the maximum permissible values is Lo / f = 5.88 / 2.38 = 247.
L / 247
Please use it!
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The following topics planned for the channel: cost comparison when using steel and wooden beams, as well as a series of materials about options monolithic flooring devices along channels (I-beams) and organization of concreting in sections (grabs).
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