Wooden beams on the floor for a large span. Calculation of the bearing capacity and deflection of wooden beams Permissible load on the timber 150x150
It is possible to make a reliable overlap only with the correct size of the beams. To determine this most accurate size, you will need to make a calculation. This can be done with online programs which is a kind of calculator.
Why count?
The whole load on interfloor overlap, rests on wooden beams, so they are load-bearing. The integrity of the building and the safety of the people in it depend on the strength of the floor beams.
Calculate wooden elements it is necessary to find out the permissible vertical load acting on it. The construction of a new or reconstruction of an old building without a preliminary calculation of the section carries a huge risk.
A ceiling built at random from weak wooden beams can collapse at any time, which will lead to high financial costs, and even worse, to injury to people. Stocked beams large section will create unnecessary stress on the walls and base of the building.
In addition to determining the strength, there is a calculation of the deflection of wooden elements. It more defines the aesthetic side of the structure. Even if a strong floor beam can withstand the weight falling on it, it can bend. Except tainted appearance, a bowed ceiling will create the discomfort of being in such a room. According to the norms, the deflection should not exceed 1/250 of the beam length.
- The entrance of wooden beams made of timber in concrete or brick building must be at least 150 mm. If a board is used instead of a timber, its minimum lead is 100 mm. By wooden houses the indicator is slightly different. The minimum run of an element made from a bar or board is 70 mm;
- When using metal fasteners, the span should be equal to the length of the floor structure. The weight of the ceiling and other elements will fall on the metal parts;
- The standard layout of the house has a span of 2.5–4 m. It can be covered with a six-meter element. Large spans overlap with glued beams or build additional partition walls.
Using a conventional calculator to calculate, these recommendations will help you make a strong overlap.
Determination of load
The overlap, together with the objects on it, creates a certain load on the wooden beams. It can be calculated accurately only in design organizations. An approximate calculation is done with a calculator, using the following recommendations:
- Attics insulated with mineral wool and lined with planks have a minimum load, approximately 50 kg / m2. The calculation of the load is performed according to the formula: the value of the safety factor is 1.3 multiplied by the maximum load indicator - 70.
- If instead of mineral wool, a heavier heat insulator and a massive boarding board are used, the load increases to an average of 150 kg / m2. The total load can be determined as follows: the safety factor value is multiplied by average load and the size of the required load is added to everything.
- When calculating for the attic, the load is allowed up to 350 kg / m2. This is due to the fact that the weight of the floor, furniture, etc. is added.
We figured out this definition, now we go further.
Determination of the section and the pitch of installation of floor elements
This process requires adherence to the following rules: 
- The ratio of the width to the height of the structure is equal to 1.4 / 1. Consequently, the width of the floor elements depends on this indicator and can vary from 40 to 200 mm. The thickness and height of the timber elements depends on the thickness of the thermal insulation approximately 100–3000 mm;
- The distance between the elements, that is, their step, can be from 300 to 1200 mm. Here it is necessary to take into account the dimensions of the thermal insulation with the filing material. V frame building the distance between the beams is equated to the pitch of the frame racks;
- Wooden beams are allowed a slight bend, which is 1/200 for the attic overlap, and 1/350 for the interfloor;
- With a load of 400 kg / m2, the pitch to section ratio is 75/100 mm. In general, the larger the cross-section of the beams, the greater the distance between them.
When using a cross section calculator, you need to use reference materials for more accurate results.
In addition to the accurate results obtained, the strength of the structure depends on the quality of the material.
The workpieces are used from conifers wood, humidity up to 14%. The wood must be free from fungus and insects. Well, in order to increase the service life of a wooden structure, the workpieces must be treated with an antiseptic before installation.
V next video you can see an example of work in the program for calculating floors.
In private housing construction, there are 3 types of structures that must be selected by calculation. These are the foundation, floor and roof. Of course, you can do this without calculation, relying on your own experience or from the experience of your friends and acquaintances. But then you risk your safety or your "wallet". In other words, structures may not be able to withstand the loads that fall on them, or they are being erected with greater reliability than required, and extra money is spent on this.
The calculation of the beams should take place in the following sequence:
1. Collecting loads on the beam.
For those who need to calculate the beam of an interfloor or attic floor and who do not want to deal with the collection of loads, there is a universal method. It lies in the fact that for the interfloor overlap, you can take the design load equal to 400 kg / m2, and for the attic floor - 200 kg / m2.
But sometimes these loads can be greatly overestimated. For example, when a small country house, on the second floor of which there will be two beds and a wardrobe, the load can be taken up to 150 kg / m2. Only this is entirely at your discretion.
2. The choice of the design scheme.
The design scheme is selected depending on the support method (rigid termination, hinged support), the type of loads (concentrated or widespread) and the number of spans.
3. Determination of the required moment of resistance.
This is the so-called calculation for the first group of limiting states - on bearing capacity (strength and stability). Here the minimum allowable cross-section is determined wooden beams, in which the operation of structures will take place without the risk of their complete unsuitability for operation.
Note : calculated loads are used.
4. Determination of the maximum permissible deflection of the beam.
This is a calculation for the second group of limit states - by deformations(deflection and displacement). According to this calculation, the cross-section of a wooden beam is determined depending on the limiting deflection, if exceeded, their normal operation will be disrupted.
Note : normative loads are used in the calculation.
Now more specifically. In order to calculate a wooden floor beam, you can use a special calculator or the example below.
An example of calculating a wooden floor beam.
The calculation is carried out in accordance with SNiP II-25-80 (SP 64.13330.2011) " Wooden structures"and the use of tables.
Initial data.
Material - 2 grade oak.
The service life of the structures is from 50 to 100 years.
The composition of the beam is solid rock (not glued).
Beam pitch - 800 mm;
Span length - 5 m (5000 mm);
Pressure impregnation with flame retardants - not provided.
Estimated floor load - 400 kg / m2; per beam - q p = 400 0.8 = 320 kg / m.
The standard floor load is 400 / 1.1 = 364 kg / m2; on the beam - q n = 364 0.8 = 292 kg / m.
Payment.
1) Selection of the design scheme.
Since the beam rests on two walls, i.e. it is hingedly supported and loaded with a uniformly distributed load, then the design scheme will look like this:
2) Strength calculation.
Determine the maximum bending moment for this design scheme:
M max = q p L 2/8 = 320 5 2/8 = 1000 kg m = 100000 kg cm,
L is the span length.
Determine the required moment of resistance of a wooden beam:
W required = γ n / o M max / R = 1.05 100000 / 121.68 = 862.92 cm 3,
where: R = R and m p m d m in m t γ s c = 130 1.3 0.8 1.1 0.9 = 121.68 kg / cm 2 - calculated resistance of wood, selected depending on the calculated values for pine, spruce and larch at a moisture content of 12% according to SNiP - table 1 and correction factors:
m p = 1.3 is the transition coefficient for other types of wood, in this case taken for oak (table 7).
m d = 0.8 - the correction factor adopted in accordance with clause 5.2. , is introduced in the case when permanent and temporary long-term loads exceed 80% of the total voltage from all loads.
m in = 1 - coefficient of working conditions (table 2).
m t = 1 - temperature coefficient, taken as 1, provided that the room temperature does not exceed +35 ° C.
γ cc = 0.9 - the coefficient of the service life of wood, is selected depending on how long you are going to operate the structure (table 8).
γ n / a = 1.05 - coefficient of the class of responsibility. It is taken according to table 6, taking into account that the building responsibility class I.
In the case of deep impregnation of wood with fire retardants, one more factor would be added to these coefficients: m a = 0.9.
You can familiarize yourself with the rest of the less important coefficients in clause 5.2 of SP 64.13330.2011.
Note: the listed tables can be found here.
Determination of the minimum allowable section of the beam:
Since most often wooden floor beams are 5 cm wide, we will find the minimum allowable beam height using the following formula:
h = √ (6W req / b) = √ (6 862.92 / 5) = 32.2 cm.
The formula is selected from the condition W beams = b · h 2/6. We are not satisfied with the result, since an overlap with a thickness of more than 32 cm is useless. Therefore, we increase the width of the beam to 10 cm.
h = √ (6W req / b) = √ (6 862.92 / 10) = 22.8 cm.
Accepted section of the beam: bxh = 10x25 cm.
3) Calculation by deflection.
Here we find the deflection of the beam and compare it with the maximum allowable.
We determine the deflection of the adopted beam according to the formula corresponding to the accepted design scheme:
f = (5 q n L 4) / (384 E J) = (5 2.92 500 4) / (384 100000 13020.83) = 1.83 cm
where: q n = 2.92 kg / cm - standard load on the beam;
L = 5 m - span length;
E = 100000 kg / cm2 - elastic modulus. It is taken equal in accordance with clause 5.3 of SP 64.13330.2011 along the fibers 100000 kg / cm2 and 4000 kg / cm2 across the fibers regardless of the rocks when calculating according to the second group of limiting states. But in fairness, it should be noted that the modulus of elasticity, depending on humidity, the presence of impregnations and the duration of loads, only in pine can range from 60,000 to 110,000 kg / cm2. Therefore, if you want to play it safe, you can take the minimum modulus of elasticity.
J = b h 3/12 = 10 25 3/12 = 13020.83 cm 4 - moment of inertia for the board rectangular section.
Determine the maximum deflection of the beam:
f max = L 1/250 = 500/250 = 2.0 cm.
The ultimate deflection is determined according to table 9, as for intermediate floors.
Compare deflections:
f beams = 1.83 cm< f max = 2,0 см - условие выполняется, поэтому увеличения сечения не требуется.
Output: a beam with a section bxh = 10x25 cm fully meets the conditions for strength and deflection.
You just need to calculate the wooden floor beams. The online calculator that we present in this review will help you cope with this task quickly and easily.
Under the action of a load, wooden beams can receive rather large deflections, as a result of which their normal operation is disrupted. Therefore, in addition to calculations for the first group of limiting states (strength), it is necessary to perform the calculation of wooden beams and for the second group, i.e.
by deflections. The calculation of timber beams for deflection is performed for the action of standard loads. The standard load is obtained by dividing the design load by the load safety factor.
Calculation of the standard load will be performed in the service of calculation of wooden beams automatically. Normal operation of beams is possible if the calculated deflection of a wooden beam does not exceed the deflection, statutory. Regulatory documents established constructive and aesthetic and psychological requirements.
Presented in SP64.13330.2011 “WOODEN CONSTRUCTIONS” Table 19 Structural elements Limit deflections in span fractions, no more than 1 Interfloor beams 2 Beams attic floors 3 Coverings (except for valleys): a) purlins, rafter legs b) cantilever beams c) trusses, glued beams (except cantilever beams) d) slabs e) battens, floorings 4 Load-bearing elements valleys 5 Panels and half-timbered elements
1. Aesthetic and psychological requirements for the deflections of wooden beams.
Presented in SP20.13330.2011 “LOADS AND IMPACTS” Appendix E.2
Structural elements Vertical limiting deflections 2 Beams, girders, girders, purlins, slabs, decks (including transverse ribs of slabs and decks): a) coverings and ceilings open for viewing, with a span l, m: l<1 l<3 l<6 l<12 l<24 1/1201/150 1/2001/2501/300В случае если балка скрыта (к примеру, под подшивным потолком) то соблюдение эстетико-психологических требований не является обязательным. В данном случае необходимо выполнить расчет прогибов балкина соблюдение только конструктивных требований по прогибам.
To build a wooden house, it is necessary to calculate the bearing capacity of a wooden beam. The definition of deflection is also of particular importance in construction terminology.
Without a qualitative mathematical analysis of all parameters, it is simply impossible to build a house from a bar. That is why, before starting construction, it is extremely important to correctly calculate the deflection of wooden beams. These calculations will serve as a guarantee of your confidence in the quality and reliability of the building.
What is needed in order to make the correct calculation
Calculating the bearing capacity and deflection of wooden beams is not as easy as it might seem at first glance. To determine how many boards you need, as well as what size they should be, you need to spend a lot of time, or you can simply use our calculator.
First, you need to measure the span that you are going to cover with wooden beams.
Secondly, pay extra attention to the fastening method. It is extremely important how deep the fixing elements will go into the wall. Only then will you be able to calculate the bearing capacity together with the deflection and a number of other equally important parameters.
Length
This parameter is determined by the span length. However, this is not all. You have to make the calculation with some margin.
Important! If wooden beams are embedded in the walls, this directly affects their length and all further calculations.
When calculating, the material from which the house is made is of particular importance. If it is brick, the boards will be mounted inside the nests. Approximate depth approx. 100-150 mm.
When it comes to wooden buildings, the parameters according to SNiPs vary greatly. Now a depth of 70-90 mm is enough. Naturally, this will also change the final bearing capacity.
If clamps or brackets are used during installation, the length of the logs or boards corresponds to the opening. Simply put, calculate the distance from wall to wall and, as a result, you can find out the bearing capacity of the entire structure.
Important! When the roof slope is formed, the logs are carried out beyond the walls by 30-50 centimeters. This must be taken into account when calculating the ability of a structure to withstand loads.
Unfortunately, not everything depends on the architect's imagination when it comes to mathematics only. For edged boards, the maximum length is six meters. Otherwise, the bearing capacity decreases and the deflection becomes greater.
It goes without saying that now it is not uncommon for houses with a span of 10-12 meters. In this case, glued laminated timber is used.
It can be I-beam or rectangular. Also, for greater reliability, you can use supports. Additional walls or columns are ideal for them.
Advice! Many builders use trusses to cover a long span.
General information on the calculation methodology
In most cases, single-span beams are used in low-rise construction.
They can be in the form of logs, planks or beams. The length of the elements can vary over a wide range. In most cases, it directly depends on the parameters of the building that you are going to build.
Attention! The calculator for calculating beams for deflection presented at the end of the page will allow you to calculate all the values with a minimum amount of time. To use the program, you just need to enter basic data.
The role of load-bearing elements in the structure is played by wooden blocks, the cross-sectional height of which is from 140 to 250 mm, the thickness is in the range of 55-155 mm. These are the most commonly used parameters when calculating the bearing capacity of timber beams.
Very often, professional builders use a cross-beam mounting scheme to strengthen the structure. It is this technique that gives the best result with the minimum investment of time and materials.
If we consider the length of the optimal span when calculating the bearing capacity of wooden beams, then it is best to limit the architect's imagination in the range from two and a half to four meters.
Attention! The best cross-section for wooden beams is considered to be an area in which the height and width are correlated as 1.5 to 1.
How to calculate bearing capacity and deflection
It is worth recognizing that over many years of practice in the construction craft, a certain canon has been developed, which is most often used in order to calculate the bearing capacity:
Let's decipher the value of each variable in the formula:
- The letter M at the beginning of the formula indicates the bending moment. It is calculated in kgf * m. W denotes the moment of resistance. Units of measurement cm3.
The calculation of the deflection of a wooden beam is part of the above formula. The letter Mouches us at this indicator. To find out the parameter, the following formula is applied:
There are only two variables in the deflection calculation formula, but they are the ones that determine to the greatest extent what the bearing capacity of a wooden beam will ultimately be:
- The q symbol indicates the load that the board can withstand, while the l is the length of one wooden beam.
Attention! The result of the calculation of the bearing capacity and deflection depends on the material from which the beam is made, as well as on the method of processing it.
How important is it to calculate the deflection correctly?
This parameter is extremely important for the strength of the entire structure. The fact is that the durability of the timber alone is not enough for a long and reliable service, because over time, its deflection under load can increase.
The deflection does not just spoil the aesthetic appearance of the floor. If this parameter exceeds 1/250 of the total length of the floor element, then the likelihood of an emergency will increase tenfold.
So why do you need a calculator
The calculator below will allow you to instantly calculate the deflection, bearing capacity and many other parameters without using formulas and calculations. In just a few seconds, the data for your future home will be ready.
In modern individual construction, timber beams are used in almost every project. Finding a building that does not use hardwood floors is almost impossible. Wooden beams are used both for flooring, and as load-bearing elements, as supports for interfloor and attic floors.
It is known that wooden beams, like any other, can bend under the influence of various loads.
This value - the deflection arrow - depends on the material, the nature of the load and the geometric characteristics of the structure. A slight deflection is perfectly acceptable. When we walk, for example, on a wooden flooring, we feel that the floor is slightly springy, but if such deformations are insignificant, then this does not bother us much.
How much deflection can be tolerated is determined by two factors:
- The deflection should not exceed the calculated permissible values. The deflection should not interfere with the operation of the building.
To find out how much the wooden elements will deform in a particular case, you need to make calculations for strength and stiffness. Detailed and detailed calculations of this kind are the work of civil engineers, however, having the skill of mathematical calculations and knowing several formulas from the course of strength of materials, it is quite possible to independently calculate a wooden beam.
Any building must be solid.
That is why floor beams are checked first of all for strength, so that the structure can withstand all the necessary loads without collapsing. In addition to strength, the structure must have rigidity and stability. The deflection is an element of the stiffness calculation.
Strength and rigidity are inextricably linked. First, strength calculations are made, and then, using the results obtained, you can calculate the deflection.
To properly design your own country house, you do not need to know the full course of resistance of materials. But it is not worth delving into too detailed calculations, as well as calculating various design options.
In order not to be mistaken, it is better to use aggregated calculations, using simple schemes, and when calculating the load on the supporting elements, always make a small margin upwards.
Algorithm for calculating the deflection
Let us consider a simplified calculation scheme, omitting some technical terms, and formulas for calculating the two main load cases adopted in construction.
You need to do the following:
- Draw up a design scheme and determine the geometric characteristics of the beam. Determine the maximum load on this supporting element. If necessary, check the beam for bending moment strength. Calculate the maximum deflection.
Design diagram of a beam and moment of inertia
The design scheme is quite simple to make. You need to know the size and shape of the cross-section of the structural element, the method of support, as well as the span, that is, the distance between the supports. For example, if you are laying the support beams of the floor on the load-bearing walls of the house, and the distance between the walls is 4 m, then the span will be l = 4 m.
Timber beams are calculated as freely supported. If this is a floor beam, then a scheme with a uniformly distributed load q is adopted. If it is necessary to determine the bending from a concentrated load (for example, from a small stove laid directly on the floor), a scheme with a concentrated load F is adopted, equal to the weight that will press on the structure.
To determine the value of the deflection f, such a geometric characteristic as the moment of inertia of the section J.
For a rectangular section, the moment of inertia is calculated by the formula:
J = b * h ^ 3/12, where:
b - section width;
h is the height of the beam section.
For example, for a section measuring 15x20 cm, the moment of inertia will be:
J = 15 * 20 ^ 3/12 = 10,000 cm ^ 4 = 0.0001 m ^ 4.
Here you need to pay attention to the fact that the moment of inertia of a rectangular section depends on how it is oriented in space. If the beam is put on the support with its wide side, then the moment of inertia will be much less, and the deflection will be greater.
Everyone can feel this effect in practice. Everyone knows that a board laid down in the usual way bends much more than the same board laid on its edge. This property is very well reflected in the very formula for calculating the moment of inertia.
Determination of the maximum load
To determine the maximum load on the beam, you need to add up all its components: the weight of the beam itself, the weight of the ceiling, the weight of the situation along with the people there, the weight of the partitions.
All this must be done in terms of 1 running meter. m beams. Thus, the load q will consist of the following indicators:
weight 1 linear
m beams; weight 1 sq. m of floor; live load on the floor; load from partitions per 1 sq. m overlap.
In addition, you need to take into account the coefficient k, which is equal to the distance between the beams, measured in meters.
To simplify the calculations, you can take the average floor weight of 60 kg / m², the standard temporary floor load adopted in construction, equal to 250 kg / m², the load from partitions according to the same standards 75 kg / m², the weight of a wooden beam can be calculated knowing the volume and density wood.
For a section of 0.15x0.2 m, this weight will be 18 kg / r. m. If the distance between the floor beams is 600 mm, then the coefficient k is 0.6.
We calculate: q = (60 + 250 + 75) * 0.6 + 18 = 249 kg / m.
Let's move on to calculating the value of the maximum deflection.
Maximum deflection calculations
For the case under consideration with a uniformly distributed load, the maximum deflection is calculated by the formula:
f = -5 * q * l ^ 4/384 * E * J.
In this formula, the value E is the modulus of elasticity of the material. For wood E = 100,000 kgf / m².
Substituting the previously obtained values, we find that the maximum deflection of a wooden beam with a section of 0.15x0.2 m and a length of 4 m will be 0.83 cm.
If we accept the design scheme with a concentrated load, then the formula for calculating the deflection will be different:
f = -F * l ^ 3/48 * E * J, where:
F is the force of pressure on the timber, for example, the weight of a furnace or other heavy equipment.
The modulus of elasticity E is different for different types of wood, this characteristic depends not only on the type of wood, but also on the type of timber - solid beams, glued beams or rounded logs have different elastic moduli.
Such calculations can be performed for various purposes. If you just need to find out in what limits the deformations of structural elements will be, then after defining the deflection arrow, the case can be considered complete. But if you are interested in how the results obtained correspond to building codes, then it is necessary to compare the results obtained with the figures given in the relevant regulatory documents.
The beam is the main element of the supporting structure of the structure.
During construction, it is important to calculate the deflection of the beam. In real construction, this element is affected by wind force, loading and vibration. However, when calculating, it is customary to take into account only the lateral load or the conducted load, which is equivalent to the lateral load.
In the calculation, the beam is perceived as a rigidly fixed bar, which is installed on two supports.
If it is installed on three or more supports, the calculation of its deflection is more complicated, and it is almost impossible to carry it out independently. The main load is calculated as the sum of forces that act in the direction of the perpendicular section of the structure. The design model is required to determine the maximum deformation, which should not exceed the limit values. This will allow you to determine the optimal material of the required size, section, flexibility and other indicators.
Types of beams
For the construction of various structures, beams made of strong and durable materials are used. Such designs may differ in length, shape and cross-section.
Most often, wooden and metal structures are used. For the design model of the deflection, the material of the element is of great importance. The peculiarity of calculating the deflection of the beam in this case will depend on the homogeneity and structure of its material.
Wooden
For the construction of private houses, summer cottages and other individual construction, wooden beams are most often used. Bending timber can be used for ceilings and floors.
To calculate the maximum deflection, consider:
- Material. Different types of wood have different indicators of strength, hardness and flexibility. Cross-sectional shape and other geometric characteristics. Different types of load on the material.
The permissible deflection of the beam takes into account the maximum actual deflection as well as possible additional operational loads.
Coniferous wood structures
Steel
Metal beams are characterized by a complex or even composite section and are most often made of several types of metal. When calculating such structures, it is necessary to take into account not only their rigidity, but also the strength of the joints.
Metal structures are made by connecting several types of rolled metal, using the following types of connections:
- electric welding; rivets; bolts, screws and other types of threaded connections.
Steel beams are most often used for multi-storey buildings and other types of construction where high structural strength is required. In this case, when using high-quality joints, an evenly distributed load on the beam is guaranteed.
To calculate the deflection of a beam, a video can help:
Beam strength and rigidity
To ensure the strength, durability and safety of the structure, it is necessary to calculate the deflection of the beams at the design stage of the structure. Therefore, it is extremely important to know the maximum deflection of the beam, the formula of which will help to draw a conclusion about the likelihood of using a certain building structure.
Using the design stiffness scheme allows you to determine the maximum changes in the geometry of the part.
The calculation of the structure according to the experimental formulas is not always effective. It is recommended to use additional factors to add the required safety factor. Not leaving an additional margin of safety is one of the main construction mistakes, which leads to the impossibility of operating the building or even serious consequences.
There are two main methods for calculating strength and stiffness:
- Simple. This method applies a magnification factor. This method includes the use of not only the factors for the safety factor, but also additional calculations of the boundary state.
The last method is the most accurate and reliable, because it is he who helps to determine what kind of load the beam can withstand.
Stiffness calculation
To calculate the bending strength of a beam, the formula is used:
M is the maximum moment that occurs in the beam;
Wn, min - the moment of resistance of the section, which is a tabular value or is determined separately for each type of profile.
Ry is the design bending resistance of the steel. Depends on the type of steel.
γc is the operating condition factor, which is a tabular value.
Calculation of the stiffness or deflection of a beam is quite simple, so even an inexperienced builder can perform the calculations. However, to accurately determine the maximum deflection, the following steps must be taken:
- Drawing up a design model of an object Calculation of the dimensions of a beam and its section Calculation of the maximum load that acts on the beam Determination of the point of application of the maximum load. In addition, the beam can be checked for strength by the maximum bending moment. Calculation of the stiffness value or maximum deflection of the beam.
To draw up a design scheme, you will need the following data:
- the dimensions of the beam, the length of the cantilevers and the span between them; the size and shape of the cross-section; the peculiarities of the load on the structure and precisely its application; the material and its properties.
If a two-support beam is calculated, then one support is considered rigid, and the second is hinged.
Calculation of moments of inertia and cross-section resistance
To perform stiffness calculations, you need the value of the moment of inertia of the section (J) and the moment of resistance (W). To calculate the moment of resistance of a section, it is best to use the formula:
An important characteristic in determining the moment of inertia and resistance of a section is the orientation of the section in the plane of the section. With an increase in the moment of inertia, the stiffness index also increases.
Determination of maximum load and deflection
To accurately determine the deflection of a beam, it is best to use this formula:
q is an evenly distributed load;
E is the modulus of elasticity, which is a tabular value;
l - length;
I is the moment of inertia of the section.
To calculate the maximum load, static and intermittent loads must be taken into account. For example, if we are talking about a two-story structure, then a load from its weight, equipment, people will constantly act on a wooden beam.
Features of the calculation for deflection
Calculation of the deflection is required for any slabs.
It is extremely important to accurately calculate this indicator under significant external loads. It is not necessary to use complex formulas in this case. If you use the appropriate coefficients, then the calculations can be reduced to simple schemes:
- A rod, which rests on one rigid and one pivotal support, and perceives a concentrated load; A rod, which rests on a rigid and articulated support, and at the same time a distributed load acts on it; Loading options for a cantilever bar, which is rigidly fixed.Action on a structure of a complex load ...
By using this method of calculating the deflection, material is not taken into account. Therefore, the calculations are not affected by the values of its main characteristics.
Deflection calculation example
To understand the process of calculating the stiffness of a beam and its maximum deflection, a simple calculation example can be used. This calculation is carried out for a beam with the following characteristics:
- production material - wood; density is 600 kg / m3; length is 4 m; material cross-section is 150 * 200 mm; the mass of the overlapping elements is 60 kg / m2; the maximum load of the structure is 249 kg / m; the elasticity of the material is 100,000 kgf / m²; J is equal to 10 kg * m².
To calculate the maximum permissible load, the weight of the beam, floors and supports is taken into account. It is also recommended to take into account the weight of furniture, appliances, decoration, people and other heavy things, which will also affect the structure. For the calculation, you will need the following data:
- weight of one meter of the beam; weight m2 of the floor; the distance that is left between the beams; live load; load from partitions on the floor.
To simplify the calculation of this example, we can take the mass of the floor as 60 kg / m², the load on each floor as 250 kg / m², the load on the partitions 75 kg / m², and the weight of a meter of the beam equal to 18 kg. With a distance between the beams of 60 cm, the coefficient k will be 0.6.
If you substitute all these values into the formula, you get:
q = (60 + 250 + 75) * 0.6 + 18 = 249 kg / m.
To calculate the bending moment, use the formula f = (5/384) * [(qn * L4) / (E * J)] £ [¦].
Substituting data into it, it turns out f = (5/384) * [(qn * L4) / (E * J)] = (5/384) * [(249 * 44) / (100 000 * 10)] = 0 , 13020833 * [(249 * 256) / (100,000 * 10)] = 0.13020833 * (6 3744 / 10,000,000) = 0.13020833 * 0.0000063744 = 0.00083 m = 0.83 cm.
This is exactly what is an indicator of the deflection when the maximum load is applied to the beam. These calculations show that when the maximum load is applied to it, it will bend by 0.83 cm. If this indicator is less than 1, then its use under the specified loads is allowed.
The use of such calculations is a universal way of calculating the stiffness of a structure and the amount of their deflection. It is quite easy to independently calculate these values. It is enough to know the necessary formulas, as well as calculate the values.
Some data must be taken in the table. When making calculations, it is extremely important to pay attention to the units of measurement. If the value in the formula is in meters, then it must be converted to this form.
Such simple mistakes can render calculations useless. To calculate the stiffness and maximum deflection of a beam, it is enough to know the basic characteristics and dimensions of the material. This data should be plugged into a few simple formulas.
Sources:
- rascheta.net
- bouw.ru
- 1poderevu.ru
- viascio.ru
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Floor beams or ceiling beams are the supporting structure of the house, therefore, before you start to independently mount the floor beams in the log cabin of a house or bathhouse, we strongly recommend that you be especially careful approach the choice of material and calculate correctly floor structure.
For the manufacture of floor slabs, it is best to use a dry, first-grade material impregnated with a fire-retardant composition.
Beams are most often embedded in:
How to ensure the strength of the floors and convenient installation
Having previously marked the places where the beams are cut in, cuts are made in the log and tightly beams are inserted into them at a distance of about 600 mm from each other. This distance between the beams provides the necessary strength of the floors. Most types of insulation are produced with a width of exactly 600 mm, which ensures convenient installation of thermal and noise insulation. With this method of mounting the lags, there is no need to attach them additionally to the wall.
Floor joists can also be mounted after assembling the log house, fixing them to the wall using special brackets and self-tapping screws. The construction market now hasa huge variety of fasteners. But more correct and reliable installation method is the first!
Questions arising during the construction process
During construction log house, log baths Naturally, questions arise: What section should the floor beams (floor, ceiling) be embedded in? What kind of load can wooden logs (beams) withstand? What is the maximum length of the beam possible for which section of the board, timber, log? 
Based on the table below, it is easy to calculate the cross-section of the log, depending on its length. The data are given for standard spans with a width of 2 to 6 meters, with a frequency of logging through 600 mm (distance between logs 600 mm) Design load 300 kg per 1 sq. meter. The table shows the breaking loads for these lags in kg per square meter.
Simply put, the numbers on a colored background are the load in kilograms per 1 m2, at which the overlap will simply break. But in order for the floor not to "spring" there is also an indicator of the bending of the beam. Blue background - the floor will not "spring", yellow - the maximum allowable, and the red background of the floor will bend under a load of 300 kg more than the allowable norm.
Table for calculating the breaking load (kg / m2) on the logs (beams) of the floors of a log house.
| log length m | 2,0 | 2,5 | 3,0 | 3,5 | 4,0 | 4,5 | 5,0 | 5,5 | 6,0 |
| lag section mm | |||||||||
| Board 100x50 | 733 | 587 | 489 | 419 | 367 | 326 | 293 | 267 | 244 |
| Board 150x50 | 1650 | 1320 | 1100 | 943 | 825 | 733 | 660 | 600 | 500 |
| Board 200x50 | 2933 | 2347 | 1956 | 1676 | 1467 | 1304 | 1173 | 1067 | 978 |
| Beam 200x100 | 5867 | 4693 | 3911 | 3352 | 2933 | 2607 | 2347 | 2133 | 1956 |
| Beam 200x200 | 11733 | 9387 | 7822 | 6705 | 5867 | 5215 | 4693 | 4267 | 3911 |
| Log 200 | 6912 | 5529 | 4608 | 3949 | 3456 | 3072 | 2765 | 2513 | 2304 |
| Log 220 | 9199 | 7359 | 6133 | 5257 | 4600 | 4089 | 3680 | 3345 | 3066 |
In blue highlighted in the table safety values
In yellow the values in the table are highlighted maximum allowable for beams deflection for these conditions
In red highlighted values inadmissible in deflection(more than twice the permissible norm) of beams for these conditions.
Note: Additional rigidity to the beam can also be made by splicing two or more thick boards together. 