Calculation of the beam for the deflection of the p-shaped form. Methodology for calculating load-bearing structures made of various materials
And the collapse of buildings is necessary to perform the calculation of the data load-bearing structures. Beams are made of wooden beams, rolled metal and reinforced concrete. Below are the simplest calculation methods and recommendations for choosing beams from these materials.
Calculation of wooden beams
For calculation wooden beams it is necessary to know the distributed load on, the length of the beams and the distance between them. The beams are laid parallel to the short side of the building, the distributed load is chosen to be 400 kg/sq. meter for interfloor and 200 kg / sq. meter for attic floors. For example, we calculate the beams for a room with dimensions of 6x4.5 meters, while the length of the beam will be about five meters, but the calculation is based on the distance between the walls - 4.5 meters. The distance between the beams is chosen equal to 0.8 meters.
Calculate the maximum bending moment:
M \u003d (q x hxl2) / 8 \u003d 400 x 0.8 x 4.52 / 8 \u003d 810 kgm \u003d 81000 kgcm;
where q is the distributed load, h is the distance between the beams; l is the span length.
The required modulus of the beam is:
W \u003d M / R \u003d 81000 / 142.71 \u003d 567.6 cu. cm;
where R is the design resistance of wood, for pine equal to 14 MPa or 142.71 kgf / sq. cm.
By setting the width of the beam section (10 cm), we determine the height of the beam:
h \u003d √ (6W / b) \u003d √ (6 x 567.6 / 10) \u003d 18.5 cm;
where h is the height, b is the width of the beam. The calculation results show that a 10x20 cm beam can be used.
The optimal ratio of the width and height of the beam is 1:1.4. Substituting into formulas different meanings distances between the beams and their width, we calculate the consumption of materials and choose the most economical option with the optimal section.
To select wooden beams, you can use the Romanov online calculator or tables that show the most typical options based on the results of the calculations. Similar materials can be easily found on the Internet.
The deflection of a wooden beam must be less than 1/250 of its length, in our case 450/250 = 1.8 cm. It is calculated by the formula:
f \u003d (5ql4) / (384EI) \u003d 5 x 400 x 4.5 x 4.5 x 4.5 x 4.5 / 384 x 109 x 6666.6667 x 10 - 8 \u003d 3.2 cm;
where E is the modulus of elasticity, for wood equal to 109 kgf/m2; I - moment of inertia, for a rectangular beam equal to:
I \u003d b x h3 / 12 \u003d 10 x 203 / 12 \u003d 6666.6667 cm4.
In this case, the deflection is greater than the allowable one, so you should choose a beam with a larger section or reduce the distance between the beams and repeat the calculations.
The methodology for determining the maximum bending moment and the moment of resistance is the same for beams of any material. Metal beams are most often made of I-beams. The value of the permissible moment of resistance for the selected profile can be found in the rolled metal reference or calculated on online calculator by geometric dimensions. Calculations are greatly facilitated by using programs available on the Internet. The table shows the recommended numbers of I-beams with a distributed load of 400 kgf / sq. m.
Calculation of reinforced concrete beams
Factory beams are selected according to the allowable moment of resistance, which is indicated in the documentation. The choice of the design of monolithic beams is complicated by the fact that reinforced concrete is a material consisting of several components and it is quite difficult to foresee the influence of all factors on the bearing capacity of the beam. The calculation methodology can be mastered only by specialists who have studied strength of materials and have practical experience.- Concrete can withstand significant compressive loads, and reinforcement can withstand tension, so it is installed in the tension zone - the bottom of the beam.
- The height of the beam section is chosen greater than 1/20 of the span length, the ratio of the height to the width of the section is equal to 7:5.
- The diameter of the reinforcement should be 12 mm or more, the number of bars should be at least 4, thicker reinforcement is laid in the lower part of the section (the reinforcement in the upper part is needed if the beam is made on the ground and is installed in place by a crane).
- Concreting should be carried out in one step, the next portion of concrete is laid before the previous one sets.
- The choice of beams is simplified when using programs that determine their cross section and the amount of reinforcement.
Conclusion
The above formulas and recommendations give an idea of the calculation methodology and, in most cases, are suitable for choosing floor beams. More sophisticated techniques take into account all operating conditions, while checking for resistance to loads acting in different directions.
Wooden floor beams
Timber beams are often the most economical option. Wooden beams are easy to manufacture and install, have low thermal conductivity compared to steel or reinforced concrete beams. The disadvantages of wooden beams are lower mechanical strength, requiring large sections, low fire resistance and resistance to damage by microorganisms and termites (if they are found in your area). Therefore, wooden floor beams must be carefully treated with antiseptics and flame retardants, for example, XM-11 or HMBB manufactured by Antiseptic (St. Petersburg).
How to calculate the required cross-section of a wooden floor beam?
The optimal span for wooden beams is 2.5-4 meters. The best section for a wooden beam is rectangular with a height to width ratio of 1.4:1. The beams are led into the wall by at least 12 cm and waterproofed in a circle, except for the end. It is advisable to fix the beam with an anchor embedded in the wall.
When choosing a section of a floor beam, the load of its own weight is taken into account, which for beams of interfloor floors, as a rule, is 190-220 kg / m2, and the temporary (operational) load, its value is taken equal to 200 kg / m2. Floor beams are laid along a short section of the span. It is recommended to choose the installation step of wooden beams equal to the installation step of the frame racks.
To calculate the minimum and optimal cross-section of a wooden floor beam, you can use the Romanov online calculator for wooden floor beams
Below are several tables, with the values of the minimum sections of wooden beams for various loads and span lengths:
Table of sections of wooden floor beams depending on the span and installation step, with a load of 400 kg / m2. - it is recommended to rely on this load
If you do not use insulation or do not plan to load floors (for example, an uninhabited attic floor), then you can use the table for lower load values of wooden floor beams:
Table of minimum sections of wooden floor beams depending on the span and load, with loads from 150 to 350 kg / m2.
If you use round logs instead of rectangular beams, you can use the following table:
The minimum allowable diameter of round logs used as floor beams depending on the span at a load of 400 kg per 1 m2
If you want to block large runs, we recommend using the experience from the Okolotok website.
Steel (metal) I-beams
An I-beam metal floor beam has a number of undeniable advantages, with only one drawback - high cost. metal I-beam it is possible to block large spans with a significant load, the metal steel beam is non-combustible and resistant to biological influences. However, a metal beam can corrode in the absence of a protective coating and the presence of aggressive environments in the room.
To calculate the parameters of an I-beam metal beam you can use good
In most cases, in amateur construction, when calculating in the above program or others similar to it, it should be assumed that the metal beam has articulated supports(that is, the ends are not rigidly fixed - for example, since in the frame steel structure). The load on the floor with steel I-beams, taking into account their own weight, should be calculated as 350 (without screed) -500 (with screed) kg / m2
The step between the I-beams is recommended to be equal to 1 meter. In case of economy, it is possible to increase the step between metal beams up to 1200 mm.
Table for selecting the number of an I-beam metal beam with different pitches and lengths of runs
Reinforced concrete floor beams
When constructing reinforced concrete beams, the following rules must be used (according to Vladimir Romanov):
- Height reinforced concrete beam must be at least 1/20 of the length of the opening. Divide the length of the opening by 20 and get the minimum height of the beam. For example, with an opening of 4 m, the height of the beam should be at least 0.2 m.
- The width of the beam is calculated based on the ratio of 5 to 7 (5 - width, 7 - height).
- The beam should be reinforced with at least 4 bars of reinforcement d12-14 (it can be thicker from below) - two at the top and bottom. Tables of the ratio of the length and mass of reinforcement of various sections.
- Concrete at one time, without interruptions, so that the previously laid portion of the mortar does not have time to grab before laying a new portion. Concreting beams with a concrete mixer is more convenient than ordering a mixer. The mixer is good for quickly pouring large volumes.
The weight of building reinforcement or how many meters of reinforcement in a ton. Weight of rebar 11.75 m long. Weight of rebar with a diameter of 5.5 to 32 mm.
I-beam weight and number of meters per ton of I-beam
During the construction of private residential buildings, outbuildings and other buildings, it is important to correctly calculate the parameters of each structural element. One of the key elements of any wood structure is the floor.
About floor materials
Properly selected material, choice of length, section and installation scheme determines its durability and the loads that it can withstand. The selection and calculation of wooden beams for floors between floors is one of the most important decisions in private construction. Since wood is an environmentally friendly material and quite durable.
The only supposed minus of wood when compared with concrete is its combustibility, the indicator of which, if necessary, can be reduced if the wood is treated with special compounds.
It is generally accepted that concrete is refractory, although this is not entirely true: it cracks at temperatures above 250 and crumbles at a temperature of 550 degrees, that is, it is completely destroyed in a fire. Therefore, wood is a good alternative to concrete.
But, in order to calculate how much wood is needed for construction, so that there is no excess of it, so that the maximum bearing capacity of this wooden beam is ensured, a calculator for automatically calculating floor parameters is often used. The calculator for calculating wood floor beams will help you quickly and fairly accurately determine the safety margin indicators when using different materials and, accordingly, choose one of them. The best materials, section parameters, design features, high-quality floor beams allow you to optimally distribute the load without exceeding the permissible one, as well as walls made of brick or made of other material.
What determines the strength of the coating?
The main parameters that affect the quality of the overlap depend on the properties of the material, technical parameters and operating conditions.
Properties of wood materials:
- Type of tree. Pine, spruce, larch are considered popular species for use in residential construction. Sometimes oak, birch, aspen, as well as combined materials are used.
- Sort. Three types of wood are determined, which are numbered 1 (the best), 2 and 3. The grade is determined by the maximum number of knots on the wood, the bending of the beams, including healthy and rotten ones, the number, depth and length of cracks, and other wood defects. Detailed requirements for wood are determined by standards, norms, rules (SNiP II-25-80, SP 64.13330.2011 and others).
Each material has its own strength and deflection characteristics, which depend on the technical parameters described below. Some breeds are lighter, others more resistant to moisture.
For example, softwoods have better resistance to moisture. The first grade of wood is of the best quality, lack of flaws, but it is correspondingly more expensive.
Technical indicators:
- Beam type. Defines types such as rectangular beams, round logs, beams,. glued from boards or LVL veneer.
- Span length. Typically, a beam span for private residential buildings is no more than 6 meters. It is important to remember that this indicator is different from the length of the beam itself, which must also capture the supporting sections on the walls or other supports.
- Beam height and width. For a beam, another rectangular beam, these indicators may be the same or different. The greater their height, the greater the rigidity and the less they flex. In the case of logs, the diameter or average diameter of the log is taken into account. When choosing these parameters, the features and ease of manufacture, transportation, and installation of beams are also taken into account.
- Beam step. This is the distance between two adjacent beams in the floor. The closer the beams, the higher their consumption of beams, the strength of the overlap, but the deflection and maximum load decrease. and concentrated load, which are defined by standards and depend on the type of premises, the number of residents or employees, the type and amount of furniture or equipment in them, and other features of their use.
- Cover type. This refers to interfloor floors with increased requirements for relative deflection, which is 1/250; attic floors, the requirements for which are lower - 1/200; coatings and floorings, the relative deflection of which is 1/150.
The last 3 items are also defined as operating conditions hardwood floor, which depend directly on the features of the construction.
Result and calculation example
How the wooden beam calculator works and how the load is calculated are the main questions to be answered here.
The 2 main indicators that determine the quality of the floor are the distributed load on the floor itself, as well as the concentrated load on the crossbars, if they are used. The quality of the crossbar also depends on the method of fixing it.
The online calculator automatically shows how big the stock will be distributed load and deflection at the overlap. Or vice versa, it will indicate an overload.
Calculation example
For example, the following input parameters are used: pine timber, single-span for interfloor overlapping, 6 meters long, has a square section of 120 by 120 millimeters. They will be located in increments of 40 centimeters with a load on the beam, which is 60 kilograms per square meter.
The moment of inertia of the section will be 1728 cm⁴, and such beams weigh 43 kilograms each.
As a result, the calculated deflection of such an overlap will be 23 millimeters (or 1/261 of the relative deflection). It will have a deflection margin of 1.04 times and collapse under a load of 845 kilograms.
For the corresponding crossbar with a concentrated load of 90 kg, the calculated deflection will be 23 millimeters, and the deflection margin will be 1.04 times. The design will not withstand loads over 422 kilograms.
Consequently, building experts will recommend not to use a floor between floors with such indicators, since the deflection margin is too small.
The optimal deflection index is from 1.5 to 3, respectively. The higher this indicator, the higher the wood consumption, but the lower the deflection margin, the less stable the building as a whole and its elements in particular will turn out.
Benefits of a calculator
Using the calculator, the builder can independently select the necessary parameters, selecting each of the available or desirable options and calculating more profitable materials and type of beams.
With the advent of summer, the construction season begins for companies, owners of cottages, summer cottages. Someone builds a gazebo, a greenhouse or a fence, other people block the roof or build a bathhouse. And when the customer is faced with the question of load-bearing structures, more often the choice is made on a profile pipe due to low cost and bending strength with low weight.
What load acts on the profile pipe
Another question is how to calculate the dimensions of the profile pipe in such a way as to get by with "little blood" and buy a pipe suitable for the load. For the manufacture of railings, fences, greenhouses, you can do without calculations. But if you are building a canopy, a roof, a visor, you cannot do without serious load calculations.
Every material resists external loads, and steel is no exception. When the load on profile pipe does not exceed the allowable values, then the structure will bend, but will withstand the load. If the weight of the load is removed, the profile will return to its original position. If the permissible load values are exceeded, the pipe deforms and remains so forever, or breaks at the bend.
To eliminate negative consequences, when calculating a profile pipe, consider:
- dimensions and section (square or rectangular);
- structural stress;
- steel strength;
- types of possible loads.
Classification of loads on a profile pipe
According to SP 20.13330.2011, the following types of loads are distinguished by the duration of action:
- constants, the weight and pressure of which does not change with time (the weight of building parts, soil, etc.);
- temporary long-term (weight of stairs, boilers in the cottage, plasterboard partitions);
- short-term (snow and wind, the weight of people, furniture, transport, etc.);
- special (earthquakes, explosions, car impact, etc.).
For example, you are building a canopy in the courtyard of the site and using a profile pipe as a supporting structure. Then, when calculating the pipe, consider the possible loads:
- canopy material;
- snow weight;
- strong wind;
- possible collision of a car with a support during an unsuccessful parking in the yard.
To do this, use SP 20.13330.2011 "Loads and impacts". It has maps and rules necessary for the correct calculation of the profile load.
Calculation diagrams of the load on the profile pipe
In addition to the types and types of load on the profiles, the types of supports and the nature of the load distribution are taken into account when calculating the pipe. The calculator calculates using only 6 types of calculation schemes.
Maximum load on the profile pipe
Some readers are wondering, "Why do such complicated calculations when I need to weld a porch railing." In such cases, there is no need for complex calculations, taking into account the nuances, since you can resort to ready-made solutions (Tab. 1, 2).
| Profile dimensions, mm | ||||||
|---|---|---|---|---|---|---|
| 1 meter | 2 meters | 3 meters | 4 meters | 5 meters | 6 meters | |
| Pipe 40x40x2 | 709 | 173 | 72 | 35 | 16 | 5 |
| Pipe 40x40x3 | 949 | 231 | 96 | 46 | 21 | 6 |
| Pipe 50x50x2 | 1165 | 286 | 120 | 61 | 31 | 14 |
| Pipe 50x50x3 | 1615 | 396 | 167 | 84 | 43 | 19 |
| Pipe 60x60x2 | 1714 | 422 | 180 | 93 | 50 | 26 |
| Pipe 60x60x3 | 2393 | 589 | 250 | 129 | 69 | 35 |
| Pipe 80x80x3 | 4492 | 1110 | 478 | 252 | 144 | 82 |
| Pipe 100x100x3 | 7473 | 1851 | 803 | 430 | 253 | 152 |
| Pipe 100x100x4 | 9217 | 2283 | 990 | 529 | 310 | 185 |
| Pipe 120x120x4 | 13726 | 3339 | 1484 | 801 | 478 | 296 |
| Pipe 140x140x4 | 19062 | 4736 | 2069 | 1125 | 679 | 429 |
| Profile dimensions, mm | ||||||
|---|---|---|---|---|---|---|
| 1 meter | 2 meters | 3 meters | 4 meters | 5 meters | 6 meters | |
| Pipe 50x25x2 | 684 | 167 | 69 | 34 | 16 | 6 |
| Pipe 60x40x3 | 1255 | 308 | 130 | 66 | 35 | 17 |
| Pipe 80x40x2 | 1911 | 471 | 202 | 105 | 58 | 31 |
| Pipe 80x40x3 | 2672 | 658 | 281 | 146 | 81 | 43 |
| Pipe 80x60x3 | 3583 | 884 | 380 | 199 | 112 | 62 |
| Pipe 100x50x4 | 5489 | 1357 | 585 | 309 | 176 | 101 |
| Pipe 120x80x3 | 7854 | 1947 | 846 | 455 | 269 | 164 |
Using ready-made calculations, remember that tables 2 and 3 indicate the maximum load, from which the pipe will bend, but not break. When the load is eliminated (cessation of strong wind), the profile will regain its original state. Exceeding the maximum load even by 1 kg leads to deformation or destruction of the structure, so buy a pipe with a margin of safety 2 to 3 times the limit value.
Methods for calculating loads on a profile pipe
To calculate the loads on profiles, the following methods are used:
- load calculation using reference tables;
- use of the pipe bending stress formula;
- determination of the load using a special calculator.
How to calculate load using lookup tables
This method is accurate and takes into account the types of supports, the fixing of the profile on the supports and the nature of the load. To calculate the deflection of a profile pipe using reference tables, the following data is required:
- the value of the moment of inertia of the pipe (I) from the tables of GOST 8639-82 (for square pipes) and GOST 8645-68 (for rectangular pipes);
- span length value (L);
- pipe load value (Q);
- the value of the modulus of elasticity from the current SNiP.
These values are substituted into desired formula, which depends on the fixation on the supports and the distribution of the load. For each design scheme deflection formula loads change.
Calculation by the formula of maximum stress when bending a profile pipe
The bending stress calculation is calculated using the formula:
where M is the bending moment of the force and W is the resistance.
According to Hooke's law, the elastic force is directly proportional to the magnitude of the deformation. Now substitute the values for the desired profile. Further, the formula is refined and supplemented based on the characteristics of the steel for the profile pipe, load, etc.
Yulia Petrichenko, expert
Calculator for calculating the load on a profile pipe
The calculation of a profile pipe for deflection is a complex and time-consuming process. To do this, you need to carefully study GOSTs and other regulations, study the types of supports and loads on the future structure, build a diagram, add a margin of safety. The slightest mistake in the calculations will lead to a sad ending. Therefore, without knowing physics and Sopromat, it is better to entrust the calculations of critical structures (roofing, frame) to professionals. They will help to accurate calculations at lower cost.
If you have solved the issue of calculating the load on a profile pipe, share your experience and tell us why you used it in the comments!
Wooden beams for floors in private construction are often used. Lightness, affordability and the possibility of self-assembly compensate for the ability to ignite, be damaged by fungus and rot. In any case, when erecting a second or more floors, it is simply necessary to calculate the wooden floor beams. The online calculator that we present in this review will help you cope with this task simply and quickly.
