Wooden beam calculator. Wooden beams on floors for a large span

Calculation of logs for roofs, floors, coverings of wooden structures.

To calculate, you need to know the snow load in the region. Snow load for Udmurtia is 320 kg/m.

The most advanced wooden floor beam calculator...

Manual calculation of floor beams

The main load-bearing structures of a wooden floor are beams. They perceive the load of their own weight, filling, as well as operational loads, transferring them to runs or poles.

Beams (logs), usually made of pine, spruce, larch, for interfloor and attic floors must be dry (permissible humidity is not more than 14%; at proper storage wood acquires such moisture in a year). The drier the beam, the stronger it is and the less it sags from the load.

Beams should not have defects that affect their strength characteristics ( big number knots, slanting, curl, etc.). Beams are subject to mandatory antiseptic and fire impregnation.

If the floor beams of the first floor rest on columns set quite often, then the beams of interfloor and attic floors rest on the walls only at their ends and rarely when supports are placed under them. So that the interfloor beams do not sag, they should be carefully calculated and laid at a distance of 1 m from each other, or even closer.

The most durable beam in bending is a beam with an aspect ratio of 7: 5, i.e., the height of the beam should be equal to seven of some measures, and the width should be only five of the same measures. A round log can withstand a greater load than a hewn beam, but it is less bending strong.

Typically, beams sag from the pressure on them from the weight of the backfill, floor, furniture, people, etc. The deflection mainly depends on the height of the beam, not on its width. If, for example, two identical beams are fastened with bolts and dowels, then such a beam will withstand a load that is already twice as large as both of these beams laid side by side. Therefore, it is more profitable to increase the height of the beam than its width. However, there is a limit to reducing the width. If the beam is too thin, it may bend to the side.

Let's assume that the deflection of the beams of interfloor floors is considered to be no more than 1/300 of the length of the overlapped span, attic - no more than 1/250. If the attic is covered with a span of 9 m (900 cm), then the deflection should not be more than 3.5 cm (900:250 = 3.5 cm). Visually, it is almost imperceptible, but the deflection is still there.

Any overlap, even under load, will be completely even if the so-called building rise is pre-cut out in the beams being laid. In this case, the bottom side of each beam is shaped into a smooth curve with a rise in the middle (Fig. 1).

Rice. 1 Structural lifting beam (dimensions in cm)

At first, the ceiling with such beams will be slightly raised in the middle, but gradually it will level out from the load and become almost horizontal. For the same purpose, logs bent to one side can be used for beams, respectively hemming them.

The thickness of beams for interfloor and attic floors should be at least 1/24 of its length. For example, a beam with a length of 6 m (600 cm) is installed. This means that its thickness should be: 600:24 \u003d 25 cm. If it is necessary to carve out a rectangular beam with an aspect ratio of 7:5, they take a log with a diameter of 30 cm.

The beam can be replaced by two boards with a total cross section equal to the beam. Such boards are usually knocked down with nails, staggering them every 20 cm.

With more frequent laying, instead of logs (beams), you can use ordinary thick boards placed on edge.

Let's consider such an example. To span a 5 m span with a load of 1259 kg, two beams are required rectangular section 200X140 mm, laid every 1000 mm. However, they can be replaced with three boards with a section of 200X70 mm, placed every 500 mm, or four boards with a section of 200X50 mm, laid every 330 mm (Fig. 2).

Rice. 2 Arrangement of block and plank beams

The fact is that a board with a section of 200X70 mm can withstand a load of 650 kg, a section of 200X50 mm - 420 kg. In sum, they will withstand the expected load.

To select the cross section of round or rectangular beams for a load of 400 kg per 1 m2 of flooring, you can use the data in the table or the above calculations.

Permissible sections of beams of interfloor and attic floors, depending on the span at a load of 400 kg

Span (m)	Distance between beams (m)	Log diameter (cm)	Section of bars (height to width, cm)
2	1	13	12×8
	0,6	11	10x7
2,5	1	15	14x10
	0,6	13	12×8
3	1	17	16x11
	0,6	14	14×9
3,5	1	19	18×12
	0,6	16	15x10
4	1	21	20×12
	0,6	17	16×12
4,5	1	22	22×14
	0,6	19	18×12
5	1	24	22×16
	0,6	20	18×14
5,5	1	25	24×16
	0,6	21	20×14
6	1	27	25×18
	0,6	23	22×14
6,5	1	29	25×20
	0,6	25	23x15
7	1	31	27×20
	0,6	27	26x15
7,5	1	33	30×27
	0,6	29	28×16

The ends of the beams of interfloor and attic floors of wooden buildings are cut with a frying pan into the upper crowns for the entire thickness of the wall.

To select beams, you can also use the table developed by I. Stoyanov.

Selection of wooden floor beams

Loads, kg/rm	Cross-section of beams with span length, m
Loads, kg/rm	3,0	3,5	4,0	4,5	5,0	5,5	6,0
150	5x14	5x16	6×18	8×18	8×20	10×20	10×22
200	5x16	5x18	7x18	7×20	10×20	12×22	14×22
250	6×16	6×18	7×20	10×20	12×20	14×22	16×22
350	7×16	7x18	8×20	10×22	12×22	16×22	20×00

The loads on the floors are made up of their own mass and temporary loads that arise during the operation of the house. Own weight of interfloor wooden floors depends on the design of the ceiling, the insulation used and is usually 220-230 kg / m2, attic - depending on the mass of the insulation - 250-300 kg / m2. Temporary loads on the attic floor are taken as 100 kg / m2, on the interfloor - 200 kg / m2. In order to determine the total load per one square meter overlappings during the operation of the house, add up the temporary and own loads, and their sum is the desired value.

The most economical in terms of wood consumption are beams with a thickness of 5 and a height of 15-18 cm with a distance between them of 40-60 cm and mineral wool insulation.

Here is a table for calculating a cold attic.

Maximum spans of attic floor beams. Unused attic.

The program for the calculation of wooden floor beams- a small and handy tool that will simplify the basic calculations for determining the cross section of the beam and the step of its installation when constructing interfloor floors.

Instructions for working with the program

The considered program is small and does not require additional installation.

Program interface

To make it clearer, consider each item of the program:

Material- select the required material of timber or logs.
beam type- beam or log.
Dimensions- length height width.
Beam spacing- the distance between the beams. By changing this parameter (as well as the dimensions), you can achieve the optimal ratio.

SNiP 2.01.07-85

With relative deflection. Destruction wooden beam usually comes from transverse bending, at which compressive and tensile stresses occur in the beam section. At first, the wood works elastically, then plastic deformations occur, while in the compressed zone, the extreme fibers (folds) are crushed, the neutral axis falls below the center of gravity. With a further increase in the bending moment, plastic deformations increase and destruction occurs as a result of rupture of the extreme stretched fibers. The maximum relative deflection of beams and girders of roofing should not exceed 1/200.

Instructions for working with the program

The considered program is small and does not require additional installation.

To make it clearer, consider each item of the program:

Material- select the required material of timber or logs.
beam type- beam or log.
Dimensions- length height width.
Beam spacing- the distance between the beams. By changing this parameter (as well as the dimensions), you can achieve the optimal ratio.

SNiP 2.01.07-85

With relative deflection. The destruction of a wooden beam usually occurs from transverse bending, in which compressive and tensile stresses occur in the cross section of the beam. At first, the wood works elastically, then plastic deformations occur, while in the compressed zone, the extreme fibers (folds) are crushed, the neutral axis falls below the center of gravity. With a further increase in the bending moment, plastic deformations increase and destruction occurs as a result of rupture of the extreme stretched fibers. The maximum relative deflection of beams and girders of roofing should not exceed 1/200.

When designing the roofing system of a small building (private house, garage, barn, etc.), load-bearing elements such as single-span wooden beams are used. They are designed to cover the spans and act as the basis for laying the flooring on the roof. At the stage of planning and creating a project for a future building, it is mandatory to calculate the bearing capacity of wooden beams.

Wooden beams are designed to cover the spans and act as the basis for laying the flooring on the roof.

Basic rules for the selection and installation of single-span beams

The process of calculating, selecting and laying load-bearing elements should be approached with all responsibility, since the reliability and durability of the entire floor will depend on this. Over the many centuries of the existence of the construction industry, some rules for the design of a roofing system have been developed, among which the following are worth noting:

The length of single-span beams, their dimensions and number are determined after measuring the span to be covered. It is important to consider how they are attached to the walls of the building.
In walls built from blocks or bricks, load-bearing elements should be deepened by at least 15 cm if they are made of timber, and by at least 10 cm if boards are used. Beams should be deepened at least 7 cm into the walls from the log house.
The optimal span width suitable for overlapping with wooden beams is in the range of 250-400 cm. In this case, the maximum length of the beams is 6 m. If longer bearing elements are required, then it is recommended to install intermediate supports.

Calculation of loads acting on the floor

The roof transfers the load to the load-bearing elements, which consists of its own weight, including the weight of the used thermal insulation material, operating weight (objects, furniture, people who can walk on it in the process of performing certain work), as well as seasonal loads (for example, snow). You are unlikely to be able to perform an exact calculation at home. To do this, you need to contact the design organization for help. More simple calculations you can do it yourself like this:

Figure 1. Table of the minimum allowable distance between beams.

For attic floors, which were insulated with light materials (for example, mineral wool), which are not affected by large operational loads, we can say that on average 1 m 2 of roof has a weight of 50 kg. According to GOST, for such a case, the load will be equal to: 70 * 1.3 \u003d 90 kg / m 2, where 1.3 is the margin of safety, and 70 (kg / m 2) is the normalized value for the above example. The total load will be equal to: 50 + 90 \u003d 140 kg / m 2.
If more than heavy material, then the normalized value according to GOST will be equal to 150 kg / m 2. Then the total load: 150 * 1.3 + 50 \u003d 245 kg / m 2.
For the attic given value will be equal to 350 kg / m 2, and for interfloor overlapping - 400 kg / m 2.

Having learned the load, you can begin to calculate the dimensions of single-span wooden beams.

Calculation of the section of wooden beams and laying step

The bearing capacity of the beams depends on their cross section and the laying step.. These quantities are interrelated, so they are calculated simultaneously. The optimal shape for floor beams is rectangular with an aspect ratio of 1.4: 1, that is, the height should be 1.4 times greater than the width.

The distance between adjacent elements should be at least 0.3 m and not more than 1.2 m. In the case of installing rolled insulation, they try to take a step that will be equal to its width.

If designed frame house, then the width is taken equal to the step between the racks of the frame.

To determine the minimum allowable dimensions of beams with a laying step of 0.5 and 1.0 m, you can use a special table (Fig. 1).

All calculations must be made in strict accordance with existing rules and regulations. If there is some doubt about the accuracy of the calculations, it is recommended that the obtained values be rounded up.

To select the cross section of the beam, you must first determine the maximum bending moment in it ( M ) and on it for specific dimensions of the beam section (width and height) the maximum stress is determined (  ). The cross section is chosen so that this stress (  ) did not exceed the calculated resistance of the beam material (in this case, wood) R u . To ensure the economy of the choice of section, it is necessary that the difference between  And R u was as small as possible. Such a calculation refers to “calculations for bearing capacity” (otherwise “calculations for group I of limit states”).

After selection of the section according to the bearing capacity, “calculation by deformations” is carried out (in other words, “calculation by group II of limit states”), i.e. the deflection of the beam is determined and its admissibility is evaluated. If, with a beam section selected according to the bearing capacity, the deflection is greater than the permissible one, the section is additionally increased, if less, it is left unchanged.

2.5. Bearing capacity calculation

Maximum bending moment M in the beam is determined according to the rules of mechanics (strength of materials) by the formula

where q)

l - beam span ( m).

Stress in the beam  is determined by the formula

, (2)

where M - bending moment ( kNm) determined by formula (1),

W– section modulus ( m 3 ).

, (3)

where b, h- respectively, the width and height of the beam section.

Example. Beam span l = 3.6 I = 2.56 kN/m. Check beam section 0.10.2 m(large side - height).

= 4.15 kNm

= 0.00056 m 3

= 6 200 kN/m 2 (kPa) =6.2 MPa R u =13 MPa

Thus, the cross section is 0.10.14 m satisfies the strength (load-bearing capacity) requirements, however, the maximum stress obtained  about half the design resistance of wood R u, i.e. "margin of safety" is unreasonably large. Reduce the cross section to 0.10.14 m and check the possibility of its acceptance.

= 0.000327m 3

= 12 691kPa = 12.7 MPa MPa

"Margin" at a section of 0.1 0.14 m less than 5%, which fully satisfies the requirements of economy. Thus, we accept (on this stage) section 0.1 0.14 m.

2.6. Deformation calculation

beam deflection f determined by the formula (resistance of materials)

, (4)

where) in relation to deformation calculations (see table 4);

l - beam span ( m);

E is the modulus of elasticity of the beam material, i.e. wood (kPa);

I – moment of inertia of the beam section ( m 4)

, (5)

where the designations are the same as in formula (2).

II =1.8 kN/m, E = 10 000 MPa = 10 7 kPa (see section 3.1), beam span l = 3.6m. Check beam section 0.10.14 m.

= 0.0000228 m 4 = 2.28 10 -5 m 4

= 0.0173m= 1.73 cm

Relative beam deflection, i.e. deflection ratio f to the span l, is in this case

The resulting relative deflection is less than the allowable one (1/200). In this regard, we accept the cross section of the beam 0.10.14 m as the final, satisfying the requirements of not only bearing capacity, but also deformability.

Obviously, any other building structure must also meet the requirements for both load-bearing capacity and deformability. Verification of the compliance of its parameters with both requirements is not carried out only in cases where it is clear without calculation that one of the requirements is certainly satisfied.

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 limit states (strength), it is necessary to perform the calculation of wooden beams for the second group, i.e.

by bends. The calculation of wooden beams for deflection is performed on the action of standard loads. The standard load is obtained by dividing the calculated load by the load safety factor.

Calculation normative load the calculation of wooden beams will be performed automatically in the service. Normal operation of the beams is possible if the calculated deflection of the wooden beam does not exceed the deflection, statutory. Regulatory documents constructive and aesthetic-psychological requirements are established.

Presented in SP64.13330.2011 "WOODEN STRUCTURES" Table 19 Structural elements Limit deflections in span fractions, not more than 1 rafter legs b) cantilever beams c) trusses, glued beams (except cantilever beams) d) slabs e) battens, flooring 4 Bearing elements of valleys 5 Panels and half-top elements1/2501/2001/2001/1501/3001/250 1/1501/4001/250

1. Aesthetic and psychological requirements for deflections of wooden beams.

Presented in SP20.13330.2011 “LOADS AND IMPACTS” Appendix E.2

Structural elements Vertical limit deflections 2 Beams, trusses, crossbars, girders, slabs, floorings (including transverse ribs of slabs and floorings):<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. Also of particular importance in construction terminology is the definition of deflection.

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 simple a task 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 special attention to the method of fastening. It is extremely important how deep the fixing elements will go into the wall. Only after that you will be able to calculate the bearing capacity along 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 must carry out the calculation with some margin.

Important! If wooden beams are embedded in 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 a brick, the boards will be mounted inside the nests. Approximate depth is about 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, then the length of the logs or boards corresponds to the opening. Simply put, calculate the distance from wall to wall and in the end you can find out the bearing capacity of the entire structure.

Important! When forming a roof slope, logs are carried out of the walls by 30-50 centimeters. This must be taken into account when calculating the ability of the structure to withstand loads.

Unfortunately, not everything depends on the imagination of the architect when it comes to mathematics only. For edged boards, the maximum length is six meters. Otherwise, the bearing capacity decreases and the deflection becomes larger.

It goes without saying that now it is not uncommon for houses with a span of 10-12 meters. In this case, glued timber is used.

It can be I-beam or rectangular. Also, for greater reliability, you can use supports. In their quality, additional walls or columns are ideal.

Advice! Many builders, if necessary, use trusses to block 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, boards or beams. The length of the elements can vary over a wide range. In most cases, it directly depends on the parameters of the structure that you are going to build.

Attention! The deflection calculator presented at the end of the page will allow you to calculate all the values with minimal time. To use the program, it is enough to enter basic data.

The role of load-bearing elements in the structure is played by wooden bars, the section height of which is from 140 to 250 mm, the thickness lies in the range of 55-155 mm. These are the most commonly used parameters when calculating the bearing capacity of wooden beams.

Very often, professional builders use a cross beam installation scheme to strengthen the structure. It is this technique that gives the best result with minimal 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 section for wooden beams is the area in which the height and width are related as 1.5 to 1.

How to Calculate Bearing Capacity and Deflection

It is worth recognizing that over many years of practice in the building trade, 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 cm3.

The calculation of the deflection of a wooden beam is part of the above formula. The letter Mu shows us this indicator. To find out the parameter, the following formula is used:

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 symbol q shows the load that the board can withstand. In turn, the letter l is the length of one wooden beam.

Attention! The result of calculating the bearing capacity and deflection depends on the material from which the beam is made, as well as on the method of its processing.

How important is it to correctly calculate the deflection

This parameter is extremely important for the strength of the entire structure. The fact is that the stability of the beam 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 probability of an emergency will increase tenfold.

So why do you need a calculator

The calculator presented below will allow you to instantly calculate the deflection, bearing capacity and many other parameters without the use of formulas and calculations. Just a few seconds and the data on your future home will be ready.

In modern individual construction, wooden beams are used in almost every project. It is almost impossible to find a building that does not use wooden floors. 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 sag 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 wooden flooring, we feel how 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 must not exceed the calculated allowable values. The deflection must 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 rigidity. Detailed and detailed calculations of this kind are the work of civil engineers, however, having the skill of mathematical calculations and knowing a few 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 the floor beams are first of all checked 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 amount of 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, the deflection can be calculated.

To properly design your own country house, it is not necessary to know the full course of the strength 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 enlarged calculations, using simple schemes, and when calculating the loads on the load-bearing elements, always make a small margin up.

Deflection Calculation Algorithm

Let's consider a simplified calculation scheme, omitting some special terms, and formulas for calculating the two main loading 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 bearing element. If necessary, check the beam for strength in terms of bending moment. Calculate the maximum deflection.

Calculation scheme of the beam and moment of inertia

The calculation scheme is quite simple to make. Need to know the size and shape cross section structural element, the method of support, as well as the span, that is, the distance between the supports. For example, if you lay the floor support beams 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.

Wooden 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 out directly on the floor), a scheme with a concentrated load F equal to the weight that will put pressure on the structure is adopted.

To determine the amount of deflection f, such a geometric characteristic as the moment of inertia of the section J is necessary.

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 equal to:

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 placed on the supports with the 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 in the usual way bends much more than the same board laid on its edge. This property is very well reflected in the formula itself for calculating the moment of inertia.

Determining 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 who are there, the weight of the partitions.

All this must be done in terms of 1 running. m beams. Thus, the load q will consist of the following indicators:

weight 1 rm.

m beams; weight 1 sq. m of overlap; temporary load on the ceiling; load from partitions per 1 sq. m of overlap.

In addition, you need to take into account the coefficient k, equal to the distance between the beams, measured in meters.

To simplify the calculations, we can take the average floor weight of 60 kg / m², the normative temporary load on the floor adopted in construction, equal to 250 kg / m², the load from partitions according to the same standards is 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 equal to 18 kg / linear meter. m. If the distance between the floor beams is 600 mm, then the coefficient k is 0.6.

We calculate: q \u003d (60 + 250 + 75) * 0.6 + 18 \u003d 249 kg / m.

Let's proceed to the calculation of the maximum deflection.

Maximum Deflection Calculations

For the considered case 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 of E is the modulus of elasticity of the material. For wood E=100,000 kgf/m².

Substituting the values obtained earlier, we obtain that the maximum deflection of a wooden beam with a section of 0.15x0.2 m and a length of 4 m will be equal to 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 pressure force on the beam, for example, the weight of the furnace or other heavy equipment.

The modulus of elasticity E for different types of wood is different, this characteristic depends not only on the type of wood, but also on the type of timber - solid beams, glued laminated timber or round logs have different moduli of elasticity.

Such calculations can be made for various purposes. If you just need to find out within what limits the deformations of the structural elements will be, then after determining the deflection arrow, the matter can be considered completed. 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 performing calculations, it is customary to take into account only the transverse load or the conducted load, which is equivalent to the transverse one.

In the calculation, the beam is perceived as a rigidly fixed rod, 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 practically impossible to carry it out independently. The main loading is calculated as the sum of the forces that act in the direction of the perpendicular section of the structure. The calculation scheme is required to determine the maximum deformation, which should not be higher than the limit values. This will 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 structures may differ in length, shape and cross section.

The most commonly used wooden and metal structures. For the calculation scheme of the deflection, the material of the element is of great importance. The peculiarity of calculating the beam deflection in this case will depend on the homogeneity and structure of its material.

Wooden

For the construction of private houses, cottages and other individual construction, wooden beams are most often used. Wooden structures working in bending can be used for ceiling and floor ceilings.

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 allowable beam deflection takes into account the maximum actual deflection, as well as possible additional operating loads.

Coniferous wood structures

Steel

Metal beams are distinguished by a complex or even composite section and are most often made of several types of metal. When calculating such structures, it is required 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 high-rise buildings and other types of construction where high structural strength is required. In this case, when using high-quality connections, a uniformly distributed load on the beam is guaranteed.

To calculate the beam for deflection, a video can help:

Strength and stiffness of the beam

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 particular building structure.

Using the calculation scheme of stiffness allows you to determine the maximum changes in the geometry of the part.

Calculation of the structure according to experimental formulas is not always effective. It is recommended to use additional coefficients to add the necessary margin of safety. Not leaving an additional margin of safety is one of the main construction errors, which leads to the impossibility of building operation or even serious consequences.

There are two main methods for calculating strength and stiffness:

Simple. When using this method, a magnifying factor is applied. Accurate. This method includes not only the use of coefficients for the factor of safety, but also additional calculations of the boundary state.

The latter 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 - section modulus, 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 service factor, which is a tabular value.

The calculation of the stiffness or deflection of a beam is quite simple, so even an inexperienced builder can perform calculations. However, to accurately determine the maximum deflection, the following steps must be taken:

Drawing up the design scheme of the object. Calculating the dimensions of the beam and its section. Calculating the maximum load that acts on the beam. Determining the point of application of the maximum load. Additionally, the beam can be checked for strength by the maximum bending moment. Calculating the stiffness value or the maximum deflection of the beam.

To draw up a calculation scheme, you will need the following data:

dimensions of the beam, the length of the consoles and the span between them; the size and shape of the cross section; features of the load on the structure and exactly its application; 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 sectional resistance

To perform stiffness calculations, you will need the value of the moment of inertia of the section (J) and the moment of resistance (W). To calculate the section modulus, 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 cut. As the moment of inertia increases, 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 a uniformly distributed load;

E is the modulus of elasticity, which is a tabular value;

l is the length;

I is the moment of inertia of the section.

To calculate the maximum load, static and periodic loads must be taken into account. For example, if we are talking about a two-story structure, then a load from its weight, equipment, and people will constantly act on a wooden beam.

Features of the calculation for deflection

Deflection calculation is mandatory for any floors.

It is extremely important to accurately calculate this indicator under significant external loads. Complex formulas in this case are optional. If you use the appropriate coefficients, then the calculations can be reduced to simple schemes:

A bar that rests on one rigid and one hinged support and perceives a concentrated load. A bar that rests on a rigid and hinged support, and at the same time it is subject to a distributed load. Loading options for a cantilever bar that is rigidly fixed. Action on the structure of a complex load .

Using this method of deflection calculation allows you to ignore the material. 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, you can use a simple calculation example. This calculation is carried out for a beam with the following characteristics:

production material - wood; density is 600 kg / m3; length is 4 m; cross-section of the material is 150 * 200 mm; mass of overlapping elements is 60 kg / m²; maximum load of the structure is 249 kg / m; material elasticity is 100,000 kgf / m²; J is equal to 10 kg*m².

To calculate the maximum allowable 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, finishes, people and other heavy things, which will also affect the structure. The following information is required for the calculation:

weight of one meter of the beam; weight m2 of the floor; the distance left between the beams; live load; load from the 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 loads on the partitions 75 kg / m², and the weight of the beam meter is 18 kg. With a distance between the beams of 60 cm, the coefficient k will be equal to 0.6.

If we substitute all these values into the formula, we get:

q \u003d (60 + 250 + 75) * 0.6 + 18 \u003d 249 kg / m.

To calculate the bending moment, use the formula f = (5 / 384) * [(qn * L4) / (E * J)] £ [¦].

Substituting the data into it, we get 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 precisely the indicator of deflection when exposed to the maximum load on 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 to calculate the stiffness of the structure and the amount of their deflection. It is quite easy to calculate these values on your own. It is enough to know the necessary formulas, as well as calculate the values.

Some data needs to be taken in the table. When making calculations, it is extremely important to pay attention to units of measure. If the value in the formula is in meters, then it must be converted to this form.

Such simple errors can render calculations useless. To calculate the stiffness and maximum deflection of the beam, it is enough to know the main characteristics and dimensions of the material. This data should be substituted into a few simple formulas.

Sources:

rascheta.net
bouw.ru
1poderevu.ru
www.viascio.ru

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It is possible to make a reliable overlap only with the right size of the beams. To determine this most accurate size, you will need to make a calculation. This can be done using an online program that is a kind of calculator.

Why do you need to count?

The entire load on the interfloor overlap falls on the 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.
It is necessary to calculate the wooden elements to determine the allowable 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 randomly built ceiling of weak wooden beams can collapse at any time, which will lead to large financial costs, and even worse, to injury to people. Large-section beams taken with a margin will create an extra load on the walls and the base of the building.

In addition to determining the strength, there is a calculation of the deflection of wooden elements. It determines the aesthetic side of the building more. Even if a strong floor beam can withstand the weight falling on it, it can bend. In addition to a spoiled appearance, a sagging ceiling will create discomfort in such a room. According to the norms, the deflection should not exceed 1/250 of the beam length.

The entry of wooden beams made of timber in a concrete or brick building must be at least 150 mm. If a board is used instead of a beam, its minimum entry is 100 mm. For wooden houses, the figure is slightly different. The minimum entry of an element made from a bar or a 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 are covered with glued beams or additional partition walls are built.

Using a regular calculator to calculate, these recommendations will help to make a strong overlap.

Load definition

The overlap, together with the objects on it, creates a certain load on the wooden beams. It can be accurately calculated only in design organizations. An approximate calculation is made with a calculator, using the following recommendations:

Attics insulated with mineral wool and hemmed with boards are distinguished by a minimum load, approximately 50 kg / m2. The calculation of the load is performed according to the formula: the value of the safety margin - 1.3 is multiplied by the maximum load indicator - 70.
If instead of mineral wool a heavier heat insulator and a massive hemmed board are used, the load increases to an average of 150 kg / m2. You can determine the total load as follows: the value of the safety factor is multiplied by the average load indicator and the size of the required load is added to everything.
When making a calculation 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.

With this definition sorted out, now we go further.

Determination of the section and the installation step of the 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. Therefore, the width of the floor elements depends on this indicator and can vary from 40 to 200 mm. The thickness and height of the wooden elements depends on the thickness of the thermal insulation, approximately 100–3000 mm;
The distance between the elements, that is, their pitch, can be from 300 to 1200 mm. Here it is necessary to take into account the dimensions of the thermal insulation with the hemming material. In a frame building, the distance between the beams is equated to the step of the frame racks;
A slight bend is allowed for wooden beams, which is 1/200 for the attic floor, 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 section of the beams, the greater the distance between them.

When using a calculator to determine the cross section, it is necessary 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.

Blanks are used from coniferous wood, with a moisture content of up to 14%. Wood should not be affected by fungus and insects. Well, in order to increase the life of a wooden structure, the workpieces must be treated with an antiseptic before installation.
In the following video, you can watch an example of working in the program for calculating floors.

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Wooden beam calculator. Wooden beams on floors for a large span

Manual calculation of floor beams

Instructions for working with the program

Instructions for working with the program

Basic rules for the selection and installation of single-span beams

Calculation of loads acting on the floor

Calculation of the section of wooden beams and laying step

2.5. Bearing capacity calculation

1. Aesthetic and psychological requirements for deflections of wooden beams.

What is needed in order to make the correct calculation

Length

General information on the calculation methodology

How to Calculate Bearing Capacity and Deflection

How important is it to correctly calculate the deflection

So why do you need a calculator

Deflection Calculation Algorithm

Calculation scheme of the beam and moment of inertia

Determining the maximum load

Maximum Deflection Calculations

Types of beams

Wooden

Steel

Strength and stiffness of the beam

Stiffness calculation

Calculation of moments of inertia and sectional resistance

Determination of maximum load and deflection

Features of the calculation for deflection

Deflection calculation example

Why do you need to count?

Load definition

Determination of the section and the installation step of the floor elements

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