Calculation of channel ceilings. Calculation of metal beams online (calculator)

When constructing residential buildings and other structures, everyone is faced with the need correct calculation and installation of the ceiling. The overlap is horizontal design located inside the building, which divides it vertically into adjacent rooms (floors, attic, etc.). Besides, this design is a load-bearing structure, since it takes all the loads coming from furniture, people, equipment and the ceiling itself and transfers them either to the walls or to the columns (depending on the type of structure).

Types of floors

According to their purpose, floors can be divided into:

• basement - separate the first floor of the building from ground floor or basement
• interfloor - aimed at separating floors of a building from each other
• attics. The first ones. From the name of the second type it follows that they. The latter separate attic space from a residential building.

Depending on the design features ceilings can be divided into tile and beam:

• Tiled floors are most often installed in large stone houses using reinforced concrete slabs.
• Beam floors used in the construction of low-rise buildings residential buildings. Metal or wooden beams can be used for their installation.

Channel for floors

Let's take a closer look at structures made from channel beams for flooring as a load-bearing base. They are the ones who bear the entire load falling on the floors of the second floor. If U-shaped rolled products are used to install the ceiling, then the following points must be taken into account:

• the channel must be laid vertically, since the moment of resistance of the section in this direction is several times higher than the value of the moment in the opposite direction
• The laying scheme is as follows: from the middle of the ceiling, the profile should be turned in the opposite direction, since the center of gravity of the channel does not belong to its wall

This laying scheme is necessary to compensate for tangential stresses. It should be remembered that ceiling channels are subject to bending stresses.

Calculation of channel bending for floors

We will calculate the channel for the ceiling based on following conditions. There is a room measuring 6x8 m. The pitch of the floor channel beams is p = 2 m. It is logical to assume that the channel should be laid along a short wall, which will reduce the maximum bending moment acting on it. Standard load per one square meter will be 540 kg/m2, and the calculated one – 624 kg/m2 (according to SNiP, taking into account the reliability factors for each load component). Let the ceiling channel on each side rest on a wall 150 mm long. Then the working length of the channel will be:

• L = l+2/3∙lоп∙2 = 6+2/3∙0.15∙2 = 6.2 m

Load per one linear meter channel will be (normative and calculated, respectively):

• qн = 540∙р = 540∙2 = 1080 kg/m = 10.8 kN
• qр = 540∙р = 624∙2 = 1248 kg/m = 12.48 kN

The maximum moment in the channel section will be equal (for standard and design load):

• Mn = qn∙L2/8 = 10.8∙6.22/8 = 51.9 kN∙m
• Мр = qр∙L2/8 = 12.48∙6.22/8 = 60 kN∙m

Let us determine the required moment of resistance of the section using the expression:

• Wtr = Мр/(γ∙Ry)∙1000, where

Ry = 240 MPa – resistance of steel C245, calculated
γ = 1 – operating conditions coefficient

Then Wtr = 60/(1∙240)∙1000 = 250 cm3

Selection of cross-section and checking for channel rigidity

Using the reference book (see GOST 8240-97 or GOST 8278-83), we select a channel profile that has a moment of resistance greater than the design one. IN in this case suitable channel 27P, Wx = 310 cm3, Ix = 4180 cm4. Next, it is necessary to check the strength and bending rigidity of the channel (deflection of the whip).

Test of strength:

• σ = Мр/(γ∙Wx)∙1000 = 60∙1000/(1∙310) = 193 MPa< Ry = 240 МПа, что подтверждает условие прочности

Test for rigidity, channel bending where the relative deflection f/L must be less than 1/150 and is determined by the expression:

• f/L = Mn∙L/(10∙E∙Ix) = 60∙103∙620/(10∙2.1∙105∙4180) = 1/236<1/150

The rigidity condition is ensured. Consequently, this channel can be used for ceilings according to the described scheme. The channel number can be reduced if the rods are laid in smaller increments.

It is not economically profitable to use for interfloor or attic floors. For example, when the span is too large and therefore large cross-section wooden beams are required to cover it. Or when you have a good friend who sells not lumber, but rolled metal.

In any case, it will not hurt to know how much the ceiling can cost if you use metal beams rather than wooden ones. And this calculator will help you with this. With its help, you can calculate the required moment of resistance and moment of inertia, which for selection of metal beams for flooring according to assortments based on strength and deflection conditions.

The floor beam is calculated for bending as a single-span simply supported beam.

Calculator

Related calculators:

Instructions for the calculator

Initial data

Terms of Use:

Span length (L)- the distance between the two inner edges of the walls. In other words, the span that the calculated beams cover.

Beam pitch (P)- step in the center of the beams through which they are laid.

Type of overlap- if you will not live on the top floor, and it will not be heavily cluttered with things dear to your heart, then choose "Attic", in other cases - "Interfloor".

Wall length (X)- the length of the wall on which the beams rest.

Beam characteristics:

Beam length (A)- the largest beam size.

Weight 1 lm. - this parameter is used as if in the second stage (after you have already selected the desired beam).

Design resistance Ry - this parameter depends on the steel grade. For example, if the steel grade is:

• C235 - Ry = 230 MPa;
• C255 - Ry = 250 MPa;
• C345 - Ry = 335 MPa;

But usually Ry = 210 MPa is used in the calculation in order to protect oneself from various kinds of “force majeure” situations. After all, we live in Russia - they will bring rolled metal from the wrong grade of steel and that’s it...

Elastic modulus E- this parameter depends on the type of metal. For the most common ones, its value is:

• steel - E = 200,000 MPa;
• aluminum - E = 70,000 MPa.

Values standard and design loads are indicated after their collection for covering.

Price for 1 t- cost of 1 ton of rolled metal.

Result

Strength calculation:

W required - required moment of resistance of the profile. It is located according to the assortment (there are GOSTs for profiles). The direction (x-x, y-y) is selected depending on how the beam will lie. For example, for a channel and an I-beam, if you want to place them (i.e. the larger size is directed upward - [ And Ι ), you need to select "x-x".

Deflection calculation:

J required - minimum permissible moment of inertia. Selected according to the same assortments and according to the same principles as W required

Other options:

Number of beams- the total number of beams that is obtained when laying them along the wall X in increments P.

total weight- weight of all beams length A.

Price- costs for the purchase of metal floor beams.

1. Load collection

Before starting the calculation of a steel beam, it is necessary to collect the load acting on the metal beam. Depending on the duration of action, loads are divided into permanent and temporary.

• own weight of the metal beam;
• own weight of the floor, etc.;

• long-term load (payload, taken depending on the purpose of the building);
• short-term load (snow load, taken depending on the geographical location of the building);
• special load (seismic, explosive, etc. Not taken into account within this calculator);

Loads on a beam are divided into two types: design and standard. Design loads are used to calculate the beam for strength and stability (1st limit state). Standard loads are established by standards and are used to calculate beams for deflection (2nd limit state). Design loads are determined by multiplying the standard load by the reliability load factor. Within the framework of this calculator, the design load is used to determine the deflection of the beam to reserve.

After you have collected the surface load on the floor, measured in kg/m2, you need to calculate how much of this surface load the beam takes on. To do this, you need to multiply the surface load by the pitch of the beams (the so-called load strip).

For example: We calculated that the total load was Qsurface = 500 kg/m2, and the beam spacing was 2.5 m. Then the distributed load on the metal beam will be: Qdistributed = 500 kg/m2 * 2.5 m = 1250 kg/m. This load is entered into the calculator

2. Constructing diagrams

Next, a diagram of moments and transverse forces is constructed. The diagram depends on the loading pattern of the beam and the type of beam support. The diagram is constructed according to the rules of structural mechanics. For the most frequently used loading and support schemes, there are ready-made tables with derived formulas for diagrams and deflections.

3. Calculation of strength and deflection

After constructing the diagrams, a calculation is made for strength (1st limit state) and deflection (2nd limit state). In order to select a beam based on strength, it is necessary to find the required moment of inertia Wtr and select a suitable metal profile from the assortment table. The vertical maximum deflection fult is taken according to table 19 from SNiP 2.01.07-85* (Loads and impacts). Point 2.a depending on the span. For example, the maximum deflection is fult=L/200 with a span of L=6m. means that the calculator will select a section of a rolled profile (I-beam, channel or two channels in a box), the maximum deflection of which will not exceed fult=6m/200=0.03m=30mm. To select a metal profile based on deflection, find the required moment of inertia Itr, which is obtained from the formula for finding the maximum deflection. And also a suitable metal profile is selected from the assortment table.

4. Selection of a metal beam from the assortment table

From two selection results (limit state 1 and 2), a metal profile with a large section number is selected.

One of the main structural elements used to construct the floors of attics or second-floor rooms, mainly in low-rise individual construction, is a wooden or metal beam, which simultaneously serves as a floor joist and a base for attaching ceiling coverings. The widespread use of beam floors was facilitated by the low cost of initial building materials and the possibility of constructing floors without the use of lifting mechanisms.

Lag deflection

Entering some, especially old, houses, even with the naked eye you can notice the deflection of the ceilings of the second floor, or, more rarely, the floor of the first floor, which is a consequence of incorrect calculation of the load-bearing capacity of the logs or exceeding the permissible load on the floors. As the practice of operating multi-storey buildings built in the first half of the 50s of the twentieth century, where wooden interfloor ceilings were used, suggests, by the year 2000 the amount of deflection of the ceilings ranged from 70 to 100 mm, which led to the need for major repairs of the building with strengthening of the load-bearing elements of the floors . And this is provided that an accurate engineering calculation of loads and lag sections is carried out at the design stage. And what can we say about individual development, when the calculation of the load-bearing capacity of the logs was carried out “by eye” on the advice of “competent” specialists.

Very often, the amount of deflection of the joists is influenced by the quality of the material used, excessive moisture in the wood, insufficient thickness of the rolled metal from which the beam is made, and many other different reasons that lead to sagging, for example, the ceiling of the second floor under load. An incorrect calculation of the load-bearing capacity can lead not only to the deflection of the log, but also to the complete destruction of the structure and the collapse of the floor downwards, and when no one expects this.

When is it necessary to strengthen the logs?

If the owner of the house notices sagging of the upper floor, then the first thing that needs to be done is to take simple measurements and assess the condition of the structures, the magnitude of the static load in order to determine the amount of sagging of the ceiling or changes in the curvature of the floor to decide on the need to strengthen the logs.

Any ceilings, under the influence of their own weight, the static load of structures and objects installed on them, sag over time. The permissible sagging value is taken to be 1:300, that is, if a three-meter beam sagged by 10 mm, there is no cause for concern, but if this value is greater, then measures must be taken to eliminate the deformation and strengthen the structure.

Strengthening metal structures

Metal structures used as interfloor beams can be strengthened with additional rolled metal products using welding or bolting. To do this, the surface of the floor or ceiling is dismantled, if necessary, adjustable supports are placed under the floor beams to eliminate deformation, and the structure is reinforced with standard rolled metal products of the required cross-section, the calculation of which is carried out using special tables and methods.

Strengthening wooden elements

Depending on their condition, existing structural elements of a wooden floor can be strengthened in several ways:

1. Using timber overlays, performing a simple mathematical calculation, when the width of the existing beam is subtracted from the table value of the cross-section of the required floor beam. The timber and the beam are fastened using bolts with metal plates that prevent the destruction of the wood at the fastening point and weakening of the structure. The existing beam is raised with jacks until a level floor surface is obtained, after which the overlay and the beam are fastened together;
2. Using metal strips with a thickness of 10 mm and a width 10-20% less than the height of the beam as overlays. To prevent the strip from deforming and reducing strength, the number of fastening bolts should be increased by 25% compared to wooden elements. Overlays are installed on one or both sides of the beam, depending on the load on the load-bearing elements of the floor of the upper floor;
3. Wooden floor beams damaged by insects or putrefactive bacteria can be strengthened using prosthetics welded from a rod in the form of a spatial truss, or using a channel of the required size. The channel installed as a prosthesis is selected from a standard range of rolled metal, and to manufacture a spatial rod truss it is necessary to perform a rather complex strength calculation, which only a qualified specialist can do.
4. Strengthening the load-bearing capacity of interfloor structures can be done by installing an additional number of beams, but this work requires making holes in the load-bearing walls, which in some cases is difficult to do.

When using metal elements to strengthen load-bearing interfloor structures, especially for destroyed parts that need to be removed, it is necessary to provide for the installation of elements on which the floorboards of the upper floor will be fixed. The fastening must be reliable and durable, eliminating the possibility of loosening and squeaks.

Logs reinforced in various ways make it possible to increase the load-bearing capacity of load-bearing interfloor structures and the overall safety of operation of existing buildings without significant investment and a large amount of construction work.

Provides stability not only with a reliable foundation, but also with a system of durable floors. They are also necessary in any case in order to equip a basement or garage under it, and build a roof above it. Overlapping structures take up to 20 percent or more of all construction costs. Therefore, their installation is a very serious and responsible matter.

Installation of interfloor ceilings in a timber house

• Interfloor;
• Basement;
• Basement.

The greatest load in the house falls on the basement and basement. Their horizontal partitions must withstand the weight of kitchen equipment, as well as the weight of the internal walls dividing the first floor into the hallway and dining room.

Scheme for arranging concrete interfloor slabs

In addition, they, together with the foundation, must ensure stable rigidity of the body made of any material: wood, brick, aerated concrete. For some, it rises above ground level. If it is heated, then the structure covering it is practically no different from interfloor devices.

The horizontal partition, designed to separate floors, has a relatively small load: its own weight, furniture, residents. It is important that for a comfortable stay it has good sound insulation. or this problem is not so acute. Moisture insulation and insulation are important for them.

Types of floors by material

• Wooden;
• Reinforced concrete;
• Metal.

However, in some cases, when building a house, you can do without them, because according to the structural design, the following types of floors are used:

Some ceiling systems are supported by horizontal beams. They are not required for the installation of other beams; slabs of the required sizes ordered at the factory are sufficient. They are laid in the house using lifting equipment. And monolithic floors are poured directly on the construction site. Prefabricated monolithic devices between floors are a combination of beam supports and a concrete monolith.

Coffered horizontal structures are usually used for arranging the ceiling. On their lower side there are ribs that make up rectangles, which together resemble the surface of a wafer. They are used very rarely in private housing construction. A tent roof is a flat slab bordered by ribs. Usually one is enough for the ceiling of the entire room, to the size of which it is made.

Arched devices are necessary when it is necessary to cover the shaped spans of houses. In private one- and two-story houses, aerated concrete slabs are used. The overlapping structure made of it has very good sound insulation and retains heat for a long time, so additional insulation in interfloor partitions may be unnecessary. The material is light, odorless, and does not emit any fumes or harmful substances.

Its fire resistance is also very high. But it needs effective waterproofing, as it absorbs environmental moisture well.

In construction practice, partitions with a mixture of various materials are used. Wooden beams are reinforced with metal to increase strength. Monolithic structures use a variety of permanent formwork. Sometimes their main part is hollow concrete panels, and the ceiling of a semicircular bay window is made of aerated concrete slabs, which can be easily given any shape and thickness using a hand saw.

Option for aerated concrete block floor construction

This variety of materials expands the architectural capabilities of ceiling devices, their sound insulation and insulation.

Requirements for floors

General requirements apply to all interfloor devices:

1. Strength is the ability to withstand the weight of all building elements.
2. Rigidity that allows you not to bend under the weight of your own weight or heavy things on the floor.
3. Effective thermal insulation and sound insulation of floors.
4. Fire resistance, which is characterized by resistance to fire for some time.
5. Service life corresponding approximately to the time of use of the entire building.

Wooden beams

In the construction of country houses, larch or pine solid beams are widespread. They are used for the installation of floors 5 m wide. And for large spans, glued ones are used, the strength of which is much higher.

Installation of floors made of wooden beams

Rounded timber is a wonderful building material for floors. It is laid with the north side down, identifying it at the end by the density of the growth rings in the wooden log. In Rus', huts have long been built with the stronger side of the round timber facing out.

A wooden I-beam has high strength. Its profile is the letter “H”, glued together in the factory from three parts. Some craftsmen assemble it in a home workshop or in the country. Interfloor partitions using them provide effective insulation and excellent sound insulation.

Scheme of the construction of wooden floors made of logs

They are very convenient not only for lining the ceiling, laying insulating materials and laying the subfloor, but also for installing all communications. The niches in the I-beam seem to be specially designed for hidden installation of water supply pipes, gas pipelines and electrical wires.

Wooden beams are used in almost any low-rise dwelling: wooden, block. But most of all they are suitable for buildings made of aerated concrete blocks. This material is porous, inferior in strength to all others and cannot withstand the point load of load-bearing beams. Since wood is not heavy, aerated block walls can easily withstand its weight. Installation of the overlapping structure is possible without the use of complex technical means. And it will cost the developer relatively inexpensively.

Laying wooden beams

Builders are aware of the shortcomings of wood and try to reduce them to a minimum. Before installing the ceiling, all wooden parts are treated with antiseptics to prevent rotting and damage by insects. The places where timber beams come into contact with brick, concrete slabs and aerated concrete blocks are insulated with various materials.

And in order to increase fire safety, the wood is treated with solutions that do not allow it to flare up immediately when an open fire appears.

The installation of interfloor structures begins with pre-prepared load-bearing beams. They are laid parallel to the short wall of the home. The laying step depends on the width of the span, but on average it is 1 m. Next, you will need simple materials that provide insulation, and you cannot do without the following tools:

The process of laying a wooden floor from beams and boards

• saws;
• hammer;
• assembly knife;
• roulette;
• construction stapler.

The beams are reinforced with anchors in the niches of the brick wall. But before laying, they make an oblique cut at the ends of the timber and impregnate it with an antiseptic. The area of ​​contact between the wood and the brick is tarred and wrapped in roofing felt. The ends of the supports in the niches must be tightly closed. The gaps can be eliminated with polyurethane foam.

Then floor joists are laid on the supporting beams, and rubber pads are placed under them to reduce the vibration of the structure. The ceiling is lined underneath. Attic and basement ceiling systems require insulation. Interfloor partitions can do without it, but good sound insulation is required.

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