Calculation of permissible spans of plywood (step of transverse beams a). Calculation of a wooden floor Calculate a plywood sheet for strength

So there is a cell with clear dimensions of 50x50 cm, which is planned to be sewn up with plywood with a thickness of h = 1 cm (actually, according to GOST 3916.1-96, the plywood thickness can be 0.9 cm, but to simplify further calculations, we will assume that we have plywood with a thickness of 1 cm), a flat load of 300 kg / m 2 (0.03 kg / cm 2) will act on the plywood sheet. Will stick on plywood ceramic tile, and therefore it is very desirable to know the deflection of the plywood sheet (the calculation of plywood for strength is not considered in this article).

The ratio h/l = 1/50, i.e. such a plate is thin. Since we are technically unable to provide such fastening on supports so that the logs perceive the horizontal component of the support reaction that occurs in the membranes, it makes no sense to consider a plywood sheet as a membrane, even if its deflection is large enough.

As already noted, to determine the deflection of the plate, you can use the appropriate design coefficients. So for square slab with hinged support along the contour, the calculated coefficient k 1 \u003d 0.0443, and the formula for determining the deflection will be as follows

f = k 1 ql 4 /(Eh 3)

The formula seems to be not complicated and we have almost all the data for the calculation, only the value of the modulus of elasticity of wood is missing. But wood is an anisotropic material and the value of the modulus of elasticity for wood depends on the direction of normal stresses.

Yes, if you believe regulatory documents, in particular SP 64.13330.2011, then the modulus of elasticity of wood along the fibers E = 100000 kgf / cm 2, and across the fibers E 90 = 4000 kg / cm 2, i.e. 25 times less. However, for plywood, the values ​​of the moduli of elasticity are taken not simply, as for wood, but taking into account the direction of the fibers of the outer layers according to the following table:

Table 475.1. Moduli of elasticity, shear and Poisson's ratios for plywood in the sheet plane

It can be assumed that for further calculations it is enough to determine a certain average value of the wood elasticity modulus, especially since the plywood layers have a perpendicular direction. However, this assumption would not be correct.

It is more correct to consider the ratio of elastic moduli as an aspect ratio, for example, for birch plywood b/l = 90000/60000 = 1.5, then the calculated coefficient will be equal to k 1 = 0.0843, and the deflection will be:

f \u003d k 1 ql 4 / (Eh 3) \u003d 0.0843 0.03 50 4 / (0.9 10 5 1 3) \u003d 0.176 cm

If we did not take into account the presence of support along the contour, but calculated the sheet as a simple beam with a width b = 50 cm, a length l = 50 cm and a height h = 1 cm on the action of a uniformly distributed load, then the deflection of such a beam would be (according to the calculated scheme 2.1 of table 1):

f = 5ql 4 / (384EI) = 5 0.03 50 50 4 / (384 0.9 10 5 4.167) = 0.326 cm

where the moment of inertia I \u003d bh 3 /12 \u003d 50 1 3 /12 \u003d 4.167 cm 4, 0.03 50 - bringing the flat load to a linear one, acting across the entire width of the beam.

Thus, support along the contour makes it possible to reduce the deflection by almost 2 times.

For plates that have one or more rigid supports along the contour, the influence of additional supports creating the contour will be less.

For example, if a plywood sheet will be laid on 2 adjacent cells, and we will consider it as a two-span beam with equal spans and three hinged supports, not taking into account the support along the contour, then the maximum deflection of such a beam will be (according to the design scheme 2.1 of Table 2):

f \u003d ql 4 / (185EI) \u003d 0.03 50 50 4 / (185 0.9 10 5 4.167) \u003d 0.135 cm

Thus, laying plywood sheets over at least 2 spans makes it possible to reduce the maximum deflection by almost 2 times even without increasing the thickness of the plywood and without taking into account the support along the contour.

If we take into account the support along the contour, then we have, as it were, a plate with rigid clamping on one side and hinged support on the other three. In this case, the aspect ratio l / b = 0.667 and then the calculated coefficient will be equal to k 1 = 0.046, and the maximum deflection will be:

f \u003d k 1 ql 4 / (Eh 3) \u003d 0.046 0.03 50 4 / (0.9 10 5 1 3) \u003d 0.096 cm

As you can see, the difference is not as significant as with hinged support along the contour, but in any case, an almost twofold decrease in deflection in the presence of a hard jam on one of the sides can be very useful.

Well, now I would like to say a few words about why the elasticity moduli for plywood differ depending on the direction of the fibers, because plywood is such a tricky material in which the directions of the fibers in adjacent layers are perpendicular.

Determination of the modulus of elasticity of a plywood sheet. Theoretical background

If we assume that the modulus of elasticity of each individual layer of plywood depends only on the direction of the fibers and corresponds to the modulus of elasticity of wood, i.e. impregnation, pressing during manufacture and the presence of glue do not affect the value of the elastic modulus, then the moments of inertia for each of the considered sections should first be determined.

In 10 mm plywood, there are usually 7 layers of veneer. Accordingly, each layer of veneer will have a thickness of approximately t = 1.43 mm. In general, the given sections with respect to perpendicular axes will look something like this:

Figure 475.1. The given sections are for a plywood sheet with a thickness of 10 mm.

Then, taking the width b = 1 and b" = 1/24, we get the following results:

I z = t(2(3t) 2 + t(2t 2) + 4 t 3 /12 + 2t(2t 2)/24 + 3t 3 /(24 12) = t 3 (18 + 2 + 1/ 3 + 1/3 + 1/96) = 1985t 3 /96 = 20.67t 3

I x \u003d t (2 (3t) 2 / 24 + t (2t 2) / 24 + 4 t 3 / (12 24) + 2t (2t 2) + 3t 3 / 12 \u003d t 3 (18/24 + 2/24 + 1/72 + 8 + 6/24) = 655t 3 /72 = 9.1t 3

If the moduli of elasticity were the same in all directions, then the moment of inertia about any of the axes would be:

I" x \u003d t (2 (3t) 2 + t (2t 2) + 4 t 3 / 12 + 2t (2t 2) + 3t 3 / 12 \u003d t 3 (18 + 2 + 1/3 + 8 + 1 /4 =43 3 /12 = 28.58t ​​3

Thus, if we do not take into account the presence of glue and other factors listed above, the ratio of the moduli of elasticity would be 20.67/9.1 = 2.27, and when considering the plywood sheet as a beam, the modulus of elasticity along the fibers of the outer layers would be (20.67/28.58)10 5 = 72300 kgf /cm 2 . As you can see, the technologies used in the manufacture of plywood make it possible to increase the calculated value of the elastic moduli, especially when the sheet is deflected across the fibers.

Meanwhile, the ratio of the calculated resistances during bending along and across the fibers of the outer layers (which can also be considered as the ratio of the moments of inertia) is much closer to that determined by us and is approximately 2.3-2.4.

Sometimes clients ask us: "Do you have OSB plywood for sale?". And then we politely explain that this is not quite the correct term. There are two different wood-based board materials: plywood and OSB board. Their characteristics are somewhat similar, but somewhat different, and our task is to choose suitable material depending on the requirements that apply to it. Before answering the question "which is better: plywood or OSB?", You need to decide on a large number parameters that influence the choice of one or the second material. It should be noted that there are four types OSB boards, which differ in their parameters, scope and cost. We will compare with plywood, which is the most common Russian market building materials.

We will try to objectively evaluate and compare different indicators so that the buyer can choose the most suitable of the two materials.

Strength.

Many companies selling OSB are a little cunning in their advertising, stating that OSB boards have the same strength indicators as plywood. To put it mildly, this is not entirely true. If we look at GOST 3916.1-96 for plywood, we will see that the ultimate strength in static bending along the fibers of the outer layers of plywood must be at least:

FSF birch plywood - 60 MPa (or N/mm2), FK birch plywood - 55 MPa, FSF softwood plywood - 40 MPa, FK softwood plywood - 35 MPa.

Most great importance the flexural strength of OSB along the fibers of the outer layer is 22MPa.

Thus, even coniferous plywood is superior to OSB-3 in terms of strength.

Moisture resistance.

We will compare moisture resistance by such an indicator as swelling in thickness after immersion in water.

Price.

The idea behind launching OSB boards on the market was to find a cheaper and not too inferior alternative to construction plywood. In the USA, Canada and European countries, this idea is embodied. In Russia, the production of OSB boards has not yet been established, and imported products often cost more than plywood due to customs and logistics costs. Logically, having a lower cost OSB should cost less than plywood, but in Russia this principle is still being violated.

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Features of the calculation of glued elements from plywood with wood

4.23. The calculation of glued elements made of plywood with wood should be carried out according to the reduced cross-section method.

4.24. The strength of the stretched plywood sheathing of slabs (Fig. 3) and panels should be checked using the formula

where M- calculated bending moment;

R f.r - design tensile strength of plywood;

mφ - coefficient taking into account the reduction in design resistance at the joints of plywood sheathing, taken equal to with a miter joint or with double-sided overlays: m f = 0.6 for plain plywood and m f = 0.8 for bakelized plywood. In the absence of joints m f = 1;

W pr is the moment of section modulus reduced to plywood, which should be determined in accordance with the instructions of clause 4.25.

4.25. The reduced modulus of the cross section of glued elements made of plywood with wood should be determined by the formula

where y o - distance from the center of gravity of the reduced section to the lower edge of the skin;

I pr - moment of inertia of the section reduced to plywood:

, (40)

where I f is the moment of inertia of the cross section of plywood sheathing;

I e - moment of inertia of the cross section of the wooden frame ribs;

E d / E f - the ratio of the moduli of elasticity of wood and plywood.

When determining the reduced moments of inertia and the reduced moments of resistance, the calculated width of plywood sheathing should be taken equal to b races = 0.9 b at l³ 6 a and b races = 0.15 b,

at l< 6a (b- full width of the slab section, l- slab span, a- the distance between the longitudinal ribs along the axes).

4.26. The stability of the compressed sheathing of slabs and panels should be checked using the formula

where at ³ 50;

at > 50

(a- distance between the ribs in the light; d - plywood thickness).

The upper skin of the slabs should additionally be checked for local bending from a concentrated load. R= 1 kN (100 kgf) (with overload factor n\u003d 1.2) as a plate embedded in the places of gluing to the ribs.

4.27. Checking for chipping of the ribs of the frame of slabs and panels or sheathing along the seam at its junction with the ribs should be carried out according to the formula

where Q- design transverse force;

S pr - static moment of the shifted part of the reduced section relative to the neutral axis;

R cn - design chipping resistance of wood along the fibers or plywood along the fibers of the outer layers;

b ras - the calculated width of the section, which should be taken equal to the total width of the frame ribs.

4.28. The strength calculation of the chords of bent elements of I-section and box sections with plywood walls (Fig. 4) should be carried out according to formula (17), taking W races = W pr, while the stresses in the stretched belt should not exceed R p, and in compressed -j R c (j is the coefficient of buckling from the plane of the bend).

4.29. When checking the wall for a shear along the neutral axis in formula (42), the value R ck is taken equal to R f.sr, and the estimated width b races

b race = åd st, (43)

where åd st is the total wall thickness.

When checking chipping at the seams between the chords and the wall in the formula (42) R sk = R f.sk, and the calculated section width should be taken equal to

b races = nh n, (44)

where h n - the height of the belts;

n- number of vertical seams.

4.30. The strength of the wall in the dangerous section to the action of the main tensile stresses in the bending elements of the I-section and box sections should be checked by the formula

, (45)

where R f.r. a - calculated tensile strength of plywood at angle a determined from the graph in fig. 17 app. 5;

s st - normal stress in the wall from bending at the level of the inner edge of the belts;

t st - shear stresses in the wall at the level of the inner edge of the belts;

a - angle determined from dependence

The stability of a wall with an arrangement of fibers of the outer layers longitudinal with respect to the element axis should be checked for the action of shear and normal stresses under the condition

where h st - wall height between the inner edges of the shelves;

d is the wall thickness.

The calculation should be made according to the formula

, (48)

where k and and k t - coefficients determined from the graphs of fig. 18, 19 app. 5;

h race - the estimated height of the wall, which should be taken equal to h st at the distance between the ribs a ³ h st and equal a at a <h Art.

When the outer fibers of the plywood wall are transverse to the element axis, the stability check should be carried out according to formula (48) for the action of only tangential stresses in cases where

B. Calculation of elements of wooden structures according to the limit states of the second group

4.31. Deformations of wooden structures or their individual elements should be determined taking into account the shear and compliance of the joints. The magnitude of the deformations of a pliable connection with the full use of its bearing capacity should be taken from Table. 15, and in case of incomplete - proportional to the force acting on the joint.

Table 15

4.32. Deflections of elements of buildings and structures should not exceed the values ​​given in Table. sixteen

Table 16

Notes: 1. In the presence of plaster, the deflection of the floor elements only from a long-term temporary load should not exceed 1/350 of the span.

2. In the presence of a building lift, the maximum deflection of glued beams can be increased up to 1/200 of the span.

4.33. The deflection of bending elements should be determined from the moment of inertia of the gross cross section. For composite sections, the moment of inertia is multiplied by the coefficient k Well taking into account the shift of pliable joints, given in table. thirteen.

The greatest deflection of hinged and cantilever bending elements of constant and variable sections f should be determined by the formula

, (50)

where f o - deflection of a beam of constant section with a height h without taking into account shear deformations;

h- the greatest height of the section;

l- beam span;

k- coefficient taking into account the influence of the variability of the section height, taken equal to 1 for beams of a constant section;

with- coefficient taking into account the influence of shear deformations from the transverse force.

Coefficient values k and with for the main design schemes of beams are given in table. 3 app. 4.

4.34. The deflection of glued elements made of plywood with wood should be determined, taking the section stiffness equal to 0.7 EI etc. The calculated width of the skins of slabs and panels when determining the deflection is taken in accordance with the instructions in clause 4.25.

4.35. The deflection of compressively-bent hinged-supported symmetrically loaded elements and cantilever elements should be determined by the formula

where f- deflection determined by formula (50);

x - coefficient determined by formula (30).

Plywood is a durable, multi-layer material made from natural wood. The physical and mechanical properties and technical characteristics of plywood are determined by the very process of its production. Namely, an odd number of sheets of thin wood veneer are glued together with glue.

Veneer sheets are arranged in such a way that the direction of the wood fibers is perpendicular to each other. This makes the plywood very resistant to breaking, stretching and chipping (see table below).

Due to such parameters and affordable cost, plywood flooring is often used in construction.

Bending strength of plywood

Specification for plywood - table

Birch, coniferous, laminated and combined
(TU 5512-001-44769167-02 and TU 5512-002-44769167-98).

It should be noted that due to the fact that plywood for a long time remained almost the only material available to our compatriots, it was used everywhere. This, in turn, led to the emergence of various types and types of plywood.

Varieties of plywood

Types of plywood are determined by the scope of its purpose:

• construction;
• furniture;
• structural;
• industrial;
• packaging.

Types of plywood depend on the glue used in the production:

• FC- waterproof plywood. In its manufacture, kabamide glue is used;

• FSF- plywood of the increased moisture resistance. Here, veneer sheets are glued together using phenol-formaldehyde glue;

• FBA- plywood is waterproof. In this case, albumin-casein glue was used to glue the veneer. FBA plywood has a slight moisture resistance, but is very much appreciated by those who bring the environmental friendliness of the material to the fore;

• FB- plywood, which, thanks to the use of bakelite varnish, can be used in especially humid conditions and in water.

And these are just the main types of plywood. There are many more levels of classification, depending on the thickness of the sheet, the number of layers, the type of wood, the grade, the degree of finish and the type of additional processing.

1. Using plywood for flooring "+" and "-"

Advantages of plywood:

• plywood, unlike OSB and fiberboard, refers to natural materials, and not recycled production waste. Therefore, it is more environmentally friendly;

• plywood moisture indicators are in the range of 12-15%;

• plywood takes the brunt of variable loads. Thus, the screed retains its integrity, and the wood gets microcracks. However, they do not affect the quality of the floor;

• Due to the fact that plywood is made from wood, it is in better contact with floor coverings. As a result, the service life of the latter increases;

• plywood makes it possible to obtain a floor that will meet the specified characteristics (flatness, surface quality) with less time and resource;

• laying plywood on the floor does not require special preparation and can be done in several stages;

• plywood plays the role of a kind of insulation, allowing you to reduce heat loss through a concrete screed and floor slabs;

• with a significant difference in height across the floor, the use of a screed is not recommended due to the large weight and cost. But plywood, on the contrary, would be ideal;

• depending on the grade and quality of polishing, plywood can be used for sub-flooring and finishing.

But:

• plywood is not suitable for rooms with a significant temperature difference (for example, for cottages or houses of non-permanent residence), as well as for high humidity levels (in a bathroom, bath, sauna, swimming pool).

2. What kind of plywood to lay on the floor

To begin with, it is worth clarifying two important factors.

• First moment - What type of floor is plywood for?. After all, the floor, in fact, is a two-layer structure, which consists of a draft (lining) and a finishing (front) coating layers.

• Second moment - in which room to lay plywood. So, for example, in a residential area, and even more so in a bedroom or a children's room, it is permissible to use only FK brand plywood. It does not contain formaldehyde. Therefore, its use is absolutely safe, with satisfactory indicators of moisture resistance. In a production room with good ventilation, it is permissible to use FSF plywood. But only 1 emission class. The class means that the formaldehyde content does not exceed 100 mg. per 1 kg. plywood sheet.

Depending on the above points, the question of which plywood is better for the floor (which one to use for the floor) will be decided.

3. What kind of plywood to choose for the floor

When choosing plywood for the floor, you should pay attention to the following parameters:

• brand of plywood. As already noted, for residential premises it is better to purchase plywood of the FC brand. Its moisture resistance indicators fully meet the operating conditions in residential premises;

• plywood class(emission class). Only class E-1 is suitable for the floor;

• type of plywood for the floor. Plywood is divided into 4 grades. In this case, the sides of the sheet may have a different grade. It is marked like this 1/1, 1/2, 2/2, etc. Plywood of 3 and 4 grades is suitable for the subfloor. For finishing - 1 or 2 grade;

• plywood moisture. A sheet with a moisture index of 12-15% is of high quality;

• number of layers of plywood. The thickness of the veneer in a plywood sheet is from 1.7 to 1.9 mm. Therefore, their number determines the thickness of the sheet. The more layers a sheet has, the more durable it is. However, the thickness of plywood is selected taking into account its purpose. So for the subfloor you need plywood 12-18 mm thick, for finishing 10-12 mm. When using plywood in production - at least 25 mm. Please note that if the plywood is to be laid in two layers, then the thickness of the sheet must be divided by two;

• plywood manufacturer. European or domestic manufacturers offer good quality material. But Chinese-made plywood causes criticism from users and often does not meet the stated characteristics.

4. Laying plywood on the floor

4.1 Subfloor plywood

Laying a plywood subfloor is the fastest, most affordable and easiest way, which also has several varieties.

.
Sheet thickness 10-12 mm. glued to the base. It is used in the presence of a smooth concrete screed of normal quality. The main thing is not to forget about expansion joints when laying. The gap is 3-4 mm. between the sheets, as well as between the sheet and the wall, will allow the plywood to play and adapt to the surrounding conditions.

This method of installation can be applied with a height difference. It is enough to use special fasteners.

Adjustable floors from plywood do not require the installation of a log, and the height difference is leveled by fasteners located under the plywood.

The material was prepared for the site www.site

Laying plywood on logs or floor beams.

Plywood, thickness over 12 mm. attached to the prepared base. The method is laborious, usually used when it is necessary to insulate the floor or raise it to a certain height.

allow you to install a sheet of plywood so that it can compensate for the difference in height across the floor.

Quite common is the situation when they have partially lost their appearance, but nevertheless do not cause any complaints. Then the floor covering is laid on top of them.

But, so that the finish coating does not become unusable, an intermediate floor (in this case, plywood) should be laid on the boards, which will level the surface.

Laying plywood on a wooden floor is carried out using hardware and is characterized by simplicity and high speed of work.

In order for plywood laid under laminate, under linoleum or to perform its functions for a long period, you must adhere to the following installation rules:

• securely fasten all sheets, taking into account deformation gaps;

• caps of hardware "drown" in the sheet;

• remove irregularities with a grinder;

• to putty grooves and cracks;

• lay the underlay.

But laying plywood under a wooden floor is absolutely not required. Due to the massiveness of the floorboard, it can be laid on logs or on a flat concrete screed.

4.3 Finished plywood floor

Craftsmen can create a real palace parquet from plywood. In this case, special requirements are put forward for the quality of plywood. It is allowed to use only the first grade, the surface of the front side of the sheet must be polished. To create a beautiful pattern, plywood is stained, and the laid plywood parquet is sanded and opened with several layers of parquet varnish.

5. Floor plywood - protection, operation and storage

In order for the plywood floor to serve you faithfully for a long time, you need to provide protection for the sheets even at the installation stage. When working with plywood, you need to consider:

• plywood needs acclimatization. Only purchased material should not be used immediately. He needs to be given time to lie down in the conditions in which he will be operated.

  The exposure period depends on where, how, in what position, at what temperature and humidity levels the plywood was stored. The acclimatization period can be:

• day. If the difference in temperature and humidity in the place of sale and installation is minimal, and the sheets were stored in a dry room, on a flat surface in a horizontal position;

• 3-5 days. If the difference exceeds 5-8°C and 10% (temperature and humidity, respectively);

• over a week. If the deviations are significant or the sheets are slightly deformed. The latter is eliminated by pressing down the stack with sheets with weights and using more hardware per 1 sq.m. sheet.

• dampness destroys plywood. Humidity fluctuations can cause serious damage to the wood from which plywood is made. At the same time, constant humidity in the room cannot be higher than 70%, and short-term - 80%. Laying plywood on a wet base is unacceptable. To check the moisture level of a wooden base, use a special device. And the concrete is covered with a film for a day. The presence of condensate under the film indicates that it is worth delaying the installation of plywood;

• plywood sheets are laid at a temperature of 20-30 ° C. In this case, the sheet is in optimal conditions for itself;

• additional processing improves the performance of plywood. So, for example, an antibacterial primer will protect the sheet from the effects of fungi and microorganisms. Impregnation with PVA-based putty will increase its moisture resistance. And the application of acrylic varnish will increase the strength of the surface layer.

Conclusion

Having familiarized yourself with the types and types of plywood for the floor, as well as with the nuances of its selection, storage and laying rules, you can say with confidence which plywood is best suited for flooring.