Well      06/07/2019

Staircases cantilever design features. Design features of a cantilever staircase Construction of a cantilever staircase

Convince ordinary person The reliability of a cantilever staircase structure can sometimes be difficult. In this case, the elegance of cantilever stairs works against them. However, for people who understand, this is a great opportunity to demonstrate the capabilities of engineering and interior ergonomics.

Indeed, the cantilever staircase can be called the most spectacular among other interfloor staircases. Its steps “float” in the air, and the structure itself does not take up much space and does not obscure the light.

Modern minimalist styles do not tolerate waste of space, which is unceremoniously taken away by a concrete or traditional wooden staircase on stringers. Today, designers are faced with the task of creating light and transparent stairs. These include suspended, bolt, spinal and cantilever staircases. The last type of stairs is more suitable than others for fans of minimalism and hi-tech. There are no unnecessary parts in such stairs. In fact, these are only the steps themselves, which are attached to a wall, pillar or other supports on only one side. But stairs without railings are quite rare in practice. Rather, such stairs serve more for demonstration purposes. The railing can be made minimally noticeable, but it will significantly increase the safety of the stairs.

For further conversation we will need precise knowledge of “staircase” terminology.

Baluster- a stand used to support the railing.

Console- shelf structure, rigidly fixed at one end using a bracket or clamp.

Kosour- the supporting beam of the staircase on which the steps are attached.

Railing- stair railing.

Riser- step height; a vertically installed bar that covers the space under the step.

Handrail- part of the railing that is grasped by hand when descending/ascending the stairs.

Prokid- detail of the railing parallel to the flight.

Tread- the horizontal part of the step on which the foot is placed.

Pillar(staircase) - the outermost post of the railing, which rests on the ceiling.

Bowstring(staircase) - a load-bearing beam that holds the steps attached to it at the ends.

Traction- a rod or cable with which the steps of a suspended staircase are attached to the upper ceiling.

Cantilever staircases are generally not sold in finished form. They are ordered for a specific object and according to the specific requests of the home owner. However, models from the catalog are taken as a basis, which are then adapted to the conditions of the object. European companies try to make as few changes as possible, using factory components. This allows you to reduce the cost of the stairs. In Russia there are also companies involved in the production of cantilever staircases, but the latter are manufactured individually.

Support for cantilever stairs

The controversial appearance of the cantilever staircase, which many people are even afraid to climb for the first time, has its own engineering explanation. I should immediately note that the construction of a cantilever staircase is a rather labor-intensive and complex task. The load-bearing base for the cantilever steps is laid in the wall at the stage of its construction. Each step of a cantilever staircase must unwaveringly withstand a load of at least 150 kg, not counting the weight of the railing. This refers to the load on the extreme point of the suspended step.

Installation of steps. The wall into which the steps of the cantilever staircase will be mounted must be made of heavy wall materials, for example, in the form of brickwork. The ends of the steps are walled up in it, deepening them by at least 20 cm with a maximum flight width of 80 cm. Each step must be sandwiched by at least 10 rows of masonry. If the wall is made of porous ceramic blocks, expanded clay concrete blocks or slotted bricks, then the depth of the steps is increased to 30-40 cm. However, the thickness of the wall does not always allow this. When installing steps in aerated concrete, each of them must be reinforced with a heavy concrete element.

Certain requirements are also imposed on the material from which the steps are made. It must be a very hard and elastic material. Reinforced concrete is widely used for these purposes. There is no need to be afraid of the brutality of this material, since it is always possible to finish concrete with anything. Well, for fashionable style loft concrete steps- that's it.

To embed brackets into the wall, meter-long sections are embedded to a depth of 25-30 cm profile pipe. The outlets make up 2/3 of the length of the steps. Such large overhangs make it possible to use almost any material for the manufacture of the steps themselves, up to chipboard or MDF. The steps in this design rest on steel brackets and are therefore freed from the load-bearing load. Metal fasteners are hidden in selected grooves and holes in the steps. I note that, despite all the clarity of pinching or embedding steps, such work must be carried out under architectural supervision. It's even better to instruct this work reputable construction company.

Another method of constructing a cantilever staircase involves anchoring. The method is good, first of all, because it allows the installation of steps after the construction of the supporting wall is completed. For each step there is a separate welded bracket, which is secured with 4-6 anchor bolts with a length of 150 mm and a diameter of at least 10 mm. But this method is only suitable in cases where the wall is made of solid brick. Neither aerated concrete nor slotted brick will withstand such a load - the anchors will become loose, and the steps will be in danger of collapse.

Mounting on a metal frame supporting structure. If the wall near which the cantilever staircase should be attached does not have sufficient load-bearing capacity, then this complicates the matter, but does not deprive the chance of realizing the plan. The only one the right decision this will involve the creation of a powerful steel profile frame, which will serve as the basis for the cantilever steps. The frame-frame is made up to the ceiling. One end of it is attached to the upper, the other - to the lower ceiling. Cantilever supports for steps can either be welded to the frame or bolted. The supporting structure (frame-frame) is covered with plasterboard, after which it looks like an ordinary wall.

The frame-frame can be replaced by a steel bowstring attached to the upper and lower ceilings on powerful support platforms. A string secured in this way will be subject to significant torsional loads when walking up stairs. To withstand them, it must be in the form of a truss with longitudinal, transverse and diagonal stiffeners. This design can be compared to the boom of a crane. But even with this, it is rarely possible to achieve a feeling of “solidity” of the steps. Therefore, the most reliable method is walling or fastening using a frame frame.

Methods for strengthening a cantilever structure. Attaching a step to only one side requires extreme strength, which is not easy to achieve. To stabilize the steps, you can resort to an additional, but little noticeable supporting structure. To avoid “keying”, the cantilever steps can be connected to each other with bolts, transferring the load to the floor. Each cantilever stage is connected with one bolt, not two. These bolts can be disguised as fencing parts or hidden in treads. The use of bolts allows you to reduce the load on the wall brackets, which makes them less powerful. By connecting two adjacent steps, we halve the load on the cantilever mounting of each of them. Thus, for one step, the power of a pair of rods 400-600 mm long and 30-40 mm in diameter, which are embedded in the wall to a depth of only 80-160 mm, is enough.

Another way to secure cantilever steps is to fasten their edges to the ceiling using ties in the form of steel cables with a diameter of 8-10 mm, the slack of which is removed by installed lanyards (screw hooks). A suspended belay looks less massive than a side belay. If desired, the cables can be passed through chrome pipes.

The standards of this section establish the maximum deflections and movements of load-bearing and enclosing structures of buildings and structures when calculating according to the second group of limit states, regardless of the building materials used.

The standards do not apply to hydraulic structures, transport, nuclear power plants, as well as supports air lines power transmission, open distribution devices and antenna communication structures.

GENERAL INSTRUCTIONS

10.1. When calculating building structures for deflections (bends) and movements the condition must be met

where f is the deflection (bending) and displacement of a structural element (or the structure as a whole), determined taking into account the factors influencing their values, in accordance with paragraphs. 1-3 recommended applications 6;

f u - maximum deflection (bending) and displacement established by these standards.

The calculation must be made based on the following requirements:

a) technological (ensuring conditions for normal operation of technological and handling equipment, instrumentation, etc.);

b) structural (ensuring the integrity of adjacent structural elements and their joints, ensuring specified slopes);

c) physiological (prevention of harmful effects and sensations of discomfort during vibrations);

d) aesthetic and psychological (providing favorable impressions from the appearance of structures, preventing the feeling of danger).

Each of these requirements must be met in the calculation independently of the others.

Limitations on structural vibrations should be established in accordance with the regulatory documents of paragraph 4 of recommended Appendix 6.

10.2. Design situations for which deflections and displacements, their corresponding loads, as well as requirements regarding construction lifting should be determined, are given in paragraph 5 of the recommendation.

10.3. The maximum deflections of structural elements of coatings and ceilings, limited based on technological, structural and physiological requirements, should be counted from the curved axis corresponding to the state of the element at the time of application of the load from which the deflection is calculated, and those limited based on aesthetic and psychological requirements - from the straight line connecting supports of these elements (see also paragraph 7 of recommended Appendix 6).

10.4. Deflections of structural elements are not limited based on aesthetic and psychological requirements, if they do not worsen the appearance of the structures (for example, membrane coverings, inclined canopies, structures with a sagging or raised lower chord) or if the structural elements are hidden from view. Deflections are not limited based on the specified requirements for structures of floors and coverings above rooms with short-term occupancy of people (for example, transformer substations, attics).

Note. For all types of coatings, the integrity of the roofing carpet should, as a rule, be ensured by constructive measures (for example, the use of expansion joints, the creation of continuous coverage elements), and not by increasing the rigidity of the load-bearing elements.

10.5. The load reliability coefficient for all loads taken into account and the dynamic coefficient for loads from forklifts, electric vehicles, overhead and overhead cranes should be taken equal to one.

Reliability coefficients for liability must be taken in accordance with mandatory Appendix 7.

10.6. For structural elements of buildings and structures, the maximum deflections and movements of which are not specified by this and other regulatory documents, vertical and horizontal deflections and movements from constant, long-term and short-term loads should not exceed 1/150 of the span or 1/75 of the cantilever overhang.

VERTICAL LIMIT DEFLECTIONS OF STRUCTURE ELEMENTS

10.7. The vertical maximum deflections of structural elements and the loads from which the deflections should be determined are given in Table. 19. Requirements for gaps between adjacent elements are given in paragraph 6 of recommended Appendix 6.

Table 19

Structural elements

Requirements

Vertical limit deflections f u

Loads for determining vertical deflections

1. Beams crane tracks for overhead and overhead cranes controlled by:

from the floor, including hoists (hoists)

Technological

From one tap

from the cabin with groups of operating modes (according to GOST 25546-82):

Physiological

and technological

2. Beams, trusses, crossbars, purlins, slabs, decking (including transverse ribs of slabs and decking):

a) coverings and ceilings open to view, with a span of l, m:

Aesthetic-psychological

Permanent and temporary long-term

b) coverings and ceilings with partitions underneath them

Constructive

Leading to a decrease in the gap between load-bearing elements structures and partitions located under the elements

c) coatings and ceilings if they contain elements susceptible to cracking (screeds, floors, partitions)

Effective after the completion of partitions, floors, screeds

d) coverings and ceilings in the presence of hoists (hoists), suspended cranes controlled by:

Technological

l/300 or a/150 (the lesser of the two)

Temporary, taking into account the load from one crane or hoist (hoist) on one track

from the cockpit

Physiological

l/400 or a/200 (the lesser of the two)

From one crane or hoist (hoist) on one path

e) floors exposed to:

Physiological

and technological

transported cargo, materials, units and elements of equipment and other moving loads (including trackless floor transport)

0.7 full standard values ​​of live loads or loads from one loader (the more unfavorable of the two)

loads from rail transport:

narrow gauge

From one train of cars (or one floor machine) on one track

broad gauge

3. Elements of stairs (flights, platforms, stringers), balconies, loggias

Aesthetic-psychological

The same as in pos. 2, a

Physiological

Determined in accordance with clause 10.10

4. Floor slabs, flights of stairs and landings, the deflection of which is not hampered by adjacent elements

Concentrated load 1 kN (100 kgf) in the middle of the span

5. Lintels and curtain wall panels over window and doorways(crossbars and glazing purlins)

Constructive

Leading to a decrease in the gap between the load-bearing elements and the window or door filling located under the elements

Aesthetic-psychological

The same as in pos. 2, a


Designations adopted in table. 19:

l is the design span of the structural element;

a is the pitch of beams or trusses to which suspended crane tracks are attached.

Notes: 1. For the console, instead of l, you should take twice its reach.

2. For intermediate values ​​of l in pos. 2, and the maximum deflections should be determined by linear interpolation, taking into account the requirements of paragraph 7 of the recommended Appendix 6.

3. In pos. 2, and the figures indicated in brackets should be taken for room heights up to 6 m inclusive.

4. Features of calculating deflections by position. 2, d are indicated in paragraph 8 of the recommended Appendix 6.

5. When limiting deflections by aesthetic and psychological requirements, the span l is allowed to be taken equal to the distance between internal surfaces load-bearing walls(or columns).

10.8. The distance (gap) from the top point of the overhead crane trolley to the bottom point of the bent load-bearing structures of the coverings (or objects attached to them) must be at least 100 mm.

10.9. The deflections of the covering elements must be such that, despite their presence, a roof slope of at least 1/200 in one of the directions is ensured (except for cases specified in other regulatory documents).

10.10. The maximum deflections of floor elements (beams, crossbars, slabs), stairs, balconies, loggias, premises of residential and public buildings, as well as household premises of industrial buildings, based on physiological requirements, should be determined by the formula

(26)

where g is the acceleration of free fall;

p - standard value of the load from people exciting vibrations, taken according to table. 20;

p 1 - reduced standard value of load on floors, taken according to table. 3 and 20;

q is the standard value of the load from the weight of the calculated element and the structures resting on it;

n is the frequency of application of load when a person walks, taken according to the table. 20;

b - coefficient accepted according to the table. 20.

Table 20


Designations adopted in table. 20:

Q is the weight of one person, taken equal to 0.8 kN (80 kgf);

a - coefficient taken equal to 1.0 for elements calculated according to the beam scheme, 0.5 - in other cases (for example, when supporting slabs on three or four sides);

a - pitch of beams, crossbars, width of slabs (flooring), m;

l is the design span of the structural element, m.

Deflections should be determined from the sum of loads y A1 p + p 1 + q, where y A1 is the coefficient determined by formula (1).

HORIZONTAL LIMIT DEFLECTIONS OF COLUMNS AND BRAKE STRUCTURES FROM CRANE LOADS

10.11. Horizontal maximum deflections of columns of buildings equipped with overhead cranes, crane trestles, as well as beams of crane tracks and brake structures (beams or trusses) should be taken according to Table. 21, but not less than 6 mm.

Deflections should be checked at the mark of the head of the crane rails from the braking forces of the trolley of one crane, directed across the crane runway, without taking into account the roll of the foundations.

Table 21


Designations adopted in table. 21:

h - height from the top of the foundation to the head of the crane rail (for one-story buildings and indoor and outdoor crane trestles) or the distance from the axis of the floor beam to the head of the crane rail (for upper floors multi-storey buildings);

l is the design span of the structural element (beam).

10.12. The horizontal maximum proximity of crane tracks of open trestles from horizontal and eccentrically applied vertical loads from one crane (without taking into account the roll of foundations), limited based on technological requirements, should be taken equal to 20 mm.

HORIZONTAL MAXIMUM DISPLACEMENTS AND DEFLECTIONS OF FRAME BUILDINGS, INDIVIDUAL ELEMENTS OF STRUCTURES AND SUPPORTS OF CONVEYOR GALLERIES FROM WIND LOAD, ROLLING FOUNDATIONS AND TEMPERATURE CLIMATIC INFLUENCES

10.13. Horizontal limit movements frame buildings, limited based on design requirements (ensuring the integrity of the filling of the frame with walls, partitions, window and door elements), are given in Table. 22. Instructions for determining movements are given in paragraph 9 of recommended Appendix 6.

10.14. Horizontal movements frame buildings should be determined, as a rule, taking into account the roll (rotation) of the foundations. At the same time, loads from the weight of equipment, furniture, people, stored materials and products should be taken into account only with a continuous uniform loading of all floors of multi-story buildings with these loads (taking into account their reduction depending on the number of floors), with the exception of cases in which, under normal operating conditions other loading is provided.

The tilt of the foundations should be determined taking into account the wind load, assumed to be 30% of the standard value.

For buildings up to 40 m high (and supports of conveyor galleries of any height) located in windy regions I-IV, the tilt of the foundations caused by the wind load may not be taken into account.

Table 22


Designations adopted in table. 22:

h is the height of multi-story buildings, equal to the distance from the top of the foundation to the axis of the roof beam;

h s - floor height in one-story buildings, equal to the distance from the top of the foundation to the bottom truss structures; in multi-storey buildings: for the lower floor - equal to the distance from the top of the foundation to the axis of the floor beam; for other floors - equal to the distance between the axes of adjacent crossbars.

Notes: 1. For intermediate values ​​of h s (according to item 3), horizontal limit movements should be determined by linear interpolation.

2. For the upper floors of multi-story buildings designed using roofing elements of single-story buildings, the horizontal maximum displacements should be taken the same as for single-story buildings. In this case, the height of the upper floor h s is taken from the axis of the interfloor crossbar to the bottom of the rafter structures.

3. Pliable fastenings include fastenings of walls or partitions to the frame that do not prevent the frame from moving (without transferring forces to the walls or partitions that could cause damage structural elements); for rigid ones - fastenings that prevent mutual displacement of the frame, walls or partitions.

4. For one-story buildings with curtain walls(and also in the absence of a hard disk covering) and multi-storey shelves, the maximum displacements can be increased by 30% (but accepted no more than h s /150).

10.15. Horizontal movements of frameless buildings due to wind loads are not limited if their walls, partitions and connecting elements are designed for strength and crack resistance.

10.16. Horizontal maximum deflections of half-timbered posts and crossbars, as well as hinged ones wall panels from wind loads, limited based on design requirements, should be taken equal to l/200, where l is the design span of racks or panels.

10.17. The horizontal maximum deflections of the supports of conveyor galleries from wind loads, limited based on technological requirements, should be taken equal to h/250, where h is the height of the supports from the top of the foundation to the bottom of the trusses or beams.

10.18. The horizontal maximum deflections of columns (racks) of frame buildings from temperature, climatic and shrinkage influences should be taken equal to:

h s /150 - for walls and partitions made of brick, gypsum concrete, reinforced concrete and curtain panels,

h s /200 - for walls lined with natural stone, ceramic blocks, glass (stained glass), where h s is the height of the floor, and for one-story buildings with overhead cranes - the height from the top of the foundation to the bottom of the crane track beams.

In this case, temperature effects should be taken without taking into account daily fluctuations in outside air temperatures and temperature differences from solar radiation.

When determining horizontal deflections from temperature, climatic and shrinkage influences, their values ​​should not be summed up with deflections from wind loads and tilting of foundations.

MAXIMUM DEFLECTIONS OF ELEMENTS OF INTER-STORY FLOOMS FROM PRELIMINARY COMPRESSION FORCES

10.19. The maximum deflections f u of interfloor ceiling elements, limited based on design requirements, should be taken equal to 15 mm at l £ 3 m and 40 mm at l ³ 12 m (for intermediate values ​​l the maximum deflections should be determined by linear interpolation).

The deflections f should be determined from the pre-compression forces, the self-weight of the floor elements and the weight of the floor.

Quite often, when designing houses, a contractor has to deal with problems of saving space when placing flights of stairs and creating certain interiors. This is due to the fact that these structures are quite bulky and require a lot of space for their normal functioning.

That is why many craftsmen are interested in the question of how to make a cantilever staircase with their own hands, since a similar type of this device can help solve this problem.

At first glance, this device gives the impression that it consists of separate sections that are suspended in the air. However, it should be noted that creating a cantilever staircase requires a lot of effort.


Properties

  • This product has an original appearance, which, with the right approach, can fit into any interior. (see also the article Interior of a hallway with a staircase in a private house - “recipes” for a cozy environment)
  • To create such a design it is necessary minimal amount material.
  • Space savings when using console devices increase significantly.
  • Creating stairs of this type is quite problematic and is associated with a lot of different difficulties.
  • When designing such a staircase structure, it is necessary to carry out very accurate calculations and measurements, since a load of at least 150 kg must be placed on a step fixed on one side.

Advice!
Before choosing a cantilever staircase for your home, you need to weigh all the advantages and disadvantages of this device and make a decision that is ideally suited to specific conditions.


Manufacturing

  • First of all, you need to understand that this ladder is mounted on one support. In this case, the installation instructions assume the installation of additional fasteners in the form of hanging systems, but the main load does not fall on them.
  • To solve the problems of installing consoles, two installation methods are used. The first of them involves fastening the steps during the manufacturing process of the walls. The second method is to install a supporting structure, which may look like a column.
  • After the steps are installed, cables or slings are attached to them from the other edge, which are secured to the ceiling. Thus, the result is a structure in the form of individual staircase elements, fixed on one side to a wall or column, and on the other side, suspended on cables.
  • It is worth noting that the suspension system itself begins to act as a barrier, but to increase safety, you can stretch additional elements, the purpose of which is to reduce gaps.
  • Railings for cantilever stairs should be installed on the wall. They can be purchased in specialized stores, and the price of such products is sometimes so low that self-production It just doesn't make sense.
  • It is very important to use a water level when carrying out all work., for the correct placement of parts in space.
  • It is worth noting that not all types of these systems are equipped with suspensions. There are completely independent products that can withstand significant weight without additional support.

Advice!
When organizing a suspension system, it is necessary to create a certain level of tension that will support the steps in one position.
If the tension is too strong, you can loosen the area of ​​the main fixation.

Buy or make it yourself

First of all, you need to understand that the main criterion in the manufacture of flights of stairs is safety. At the same time, console devices require only high-quality elements and accurate measurements during their manufacture and installation. Therefore, such designs must be created very carefully, paying attention to even minor details.


Considering the complexity of such work, some craftsmen prefer to purchase finished products. They will definitely have correct forms, appropriate fasteners and will withstand the required load. However, installation must be carried out strictly according to the instructions, which must be included in the delivery package.

Advice!
By purchasing ready product, you should make sure that fasteners are available, since not all manufacturers include them with the parts.
You should also check all elements for visible defects.

Conclusion

In the video presented in this article you will find additional information on this topic. Also, based on the text stated above, you can get an idea of ​​the design and structure of cantilever stairs and methods of their installation.

At the same time, we can conclude that it is better to purchase this product ready-made, since factory parts have a large margin of strength and reliability.

A stringer in a staircase is called an inclined one metal beam, on which the steps rest.

This calculation applies to metal stringers made from rolled channels.

Attention! In the article, the font periodically flies off, after which, instead of the sign for the angle of inclination of the stairs "alpha", the sign "?" is displayed. I apologize for the inconvenience.

Initial data.

Width flight of stairs 1.05 m ( stair steps prefabricated LS11, weight of 1 stage 105 kg). Number of stringers – 2. H = 1.65 m – half the height of the floor; l 1 = 3.7 m – stringer length. The angle of inclination of the stringer is α = 27°, cosα = 0.892.

Collection of loads.

As a result, the current standard load on the inclined stringer is equal to q 1 n = 449 kg/m 2, and the calculated load q 1 r = 584 kg/m 2.

Calculation (selection of the stringer section).

The first thing to do in this calculation is to bring the load per 1 sq. m of the march area to the horizontal and find the horizontal projection of the stringer. Those. essentially at the actual length of the stringer l 1 and load per 1 sq.m march q 1, we translate these values ​​into the horizontal plane through cosα so that the relationship between q and l remained in force.

For this we have two formulas:

1) the load per 1 m 2 of the horizontal projection of the march is equal to:

q = q 1 /cos 2 α;

2) the horizontal projection of the march is equal to:

l = l 1 cosα.

Please note that the steeper the angle of inclination of the stringer, the shorter the length of the flight projection, but the greater the load per 1 m 2 of this horizontal projection. This is precisely what preserves the relationship between q and l which we strive for.

As proof, consider two stringers of the same length 3 m with the same load 600 kg/m2, but the first is located at an angle of 60 degrees, and the second - 30. The figure shows that for these stringers the projections of the load and the length of the stringer are very different from each other, but the bending moment is the same for both cases.

Let us determine the standard and calculated value of q, as well as l for our example:

q n = q n 1 /cos 2 α = 449/0.892 2 = 564 kg/m 2 = 0.0564 kg/cm 2 ;

q р = q р 1 /cos 2 α = 584/0.892 2 = 734 kg/m 2 = 0.0734 kg/cm 2 ;

l = l 1 cosα = 3.7*0.892 = 3.3 m.

In order to select the cross section of the stringer, it is necessary to determine its moment of resistance W and moment of inertia I.

We find the moment of resistance using the formula W = q р a l 2 /(2*8mR), where

q р = 0.0734 kg/cm 2 ;

l= 3.3 m = 330 cm – length of the horizontal projection of the stringer;

m = 0.9 – coefficient of operating conditions of the stringer;

R = 2100 kg/cm 2 – design resistance steel grade St3;

8 – part of the well-known formula for determining the bending moment (M = ql 2 /8).

So, W = 0.0734*105*330 2 /(2*8*0.9*2100) = 27.8 cm 3.

We find the moment of inertia using the formula I = 150*5*aq n l 3 /(384*2Ecos?) , where

E = 2,100,000 kg/cm 2 – elastic modulus of steel;

150 – from the condition of maximum deflection f = l/150;

a = 1.05 m = 105 cm – march width;

2 – number of stringers in a march;

5/348 is a dimensionless coefficient.

For those who want to understand in more detail the determination of the moment of inertia, let us turn to Linovich and derive the above formula (it differs slightly from the original source, but the result of the calculations will be the same).

The moment of inertia can be determined from the formula for the permissible relative deflection of the element. The deflection of the stringer is calculated by the formula: f = 5q l 4 /348EI, from where I = 5q l 4/348Ef.

In our case:

q = aq n 1 /2 = aq n cos 2 ?/2 – distributed load on the stringer from half the march (in the comments they often ask why the kosour is considered to cover the entire load of the march, and not half - so, the two in this formula exactly gives half the load);

l 4 = l 1 4 = (l/cos?) 4 = l 4/cos? 4 ;

f = l 1 /150 = l/150cos? – relative deflection (according to DSTU “Deflections and displacements” for a span of 3 m).

If we plug everything into the formula, we get:

I = 150*cos?*5aq n cos 2 ? l 4 /(348*2E l cos 4?) = 150*5*aq n l 3 /(348*2Ecos?).

Linovich has essentially the same thing, only all the numbers in the formula are reduced to the “coefficient With depending on the deflection." But since in modern standards the requirements for deflections are stricter (we need to limit ourselves to 1/150 instead of 1/200), then for ease of understanding all numbers are left in the formula, without any abbreviations.

So, I = 150*5*105*0.0564*330 3 /(384*2*2100000*0.892) = 110.9 cm 4.

We select a rolling element from the table below. Channel No. 10 suits us.

This calculation was carried out according to the recommendations of the book by L.E. Linovich. “Calculation and design of parts of civil buildings” and provides only the selection of the cross-section of a metal element. For those who want to understand the calculation in more detail metal stringer, as well as with the design of staircase elements, it is necessary to refer to the following regulatory documents:

SNiP III-18-75 “Metal structures”;

DBN V.2.6-163:2010 “Steel structures”.

In addition to calculating the stringer using the above formulas, you also need to do a calculation for instability. What it is? The stringer may be strong and reliable, but when walking up the stairs it feels like it is shaking with every step. The feeling is not pleasant, so the standards provide for the following condition: if the stringer is loaded with a concentrated load of 100 kg in the middle of the span, it should bend no more than 0.7 mm (see DSTU B.V.1.2-3:2006, table 1, paragraph 4).

The table below shows the results of calculations for instability for a staircase with steps 300x150(h), this is the most convenient size of steps for a person, at different floor heights, and therefore different stringer lengths. As a result, even if the above calculation gives a smaller cross-section of the element, you need to finally select the stringer by checking the data in the table.

March projection length Lx, m

March height N, m

Stringer length L, m

Rolled channel number GOST 8240-97, DSTU 3436-96

Number of bent channel GOST 8278-83

I-beam number GOST 8239-89

Dimensions of bent square pipe GOST 30245-94, DSTU B.V.2-6-8-95

In order to correctly design a staircase, you can use standard series:

1.450-1 “Stairs made of prefabricated reinforced concrete steps on steel stringers”;

1.450-3 "Steel stairs, platforms, stepladders and fences."

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Are cantilever staircase structures as convenient as they sometimes want us to believe? In order to understand this issue, you must first understand what cantilever stairs are: the features of their structure. This staircase is considered the most effective among many other one-story staircases. The structure itself is not large, and the steps seem to “float” in the air.

Application

Today, during the construction or improvement of a home, there is a struggle for every square meter free space. Having chosen concrete or wooden stairs on stringers, you can immediately say goodbye to a fairly decent part of the free space, as can be seen in the photo. But there are a number of light and transparent stairs that not only will not take up much space, but will also be an excellent design solution, fitting perfectly into the interior of the room.


The cantilever staircase option is most suitable for connoisseurs of minimalism and lovers of high-tech style. Nothing superfluous - this is how this species can be briefly described. These are ordinary steps, attached on one side to a wall or any other support. Of course, you can’t do without a fence, but it can be almost invisible, but at the same time responsible for safety.

Terminology

For those who are not strong in construction, here are some frequently used terms that will help you better understand this article:

  • Baluster – posts intended to support railings;
  • The console is a tightly fitted shelf system;
  • Stringer - a supporting structure used to fasten steps;
  • Railing - staircase fence;

  • A riser is a plank fixed vertically that covers the space under the step. Equal to the height of the step;
  • Handrail - part of the railing necessary for the convenience of ascending or descending steps;
  • Prokid - a fencing zone located parallel to the march;
  • Tread – a horizontal element of a step;
  • Post - the outermost post of the railing resting on the ceiling;
  • Bowstring - an inclined structure that supports steps attached to it at the ends;
  • Tie rod is a cable necessary for fastening steps to the upper floor.


Cantilever staircases are not provided when assembled. They are made to individual orders. But catalog models often serve as the basis. In this case, it is advisable to make a minimum of changes so that replacement of factory components is not required. Although decent companies, both in Europe and in Russia, replace components exclusively with factory ones.

Making a support

Those who encounter a cantilever staircase for the first time will be a little surprised by it. appearance and perhaps they will even be afraid to climb it. But its structure has a completely engineering explanation, and its construction is a painstaking and complex process, as shown in the video. The first thing that is laid in the process of constructing a staircase is a supporting structure for the steps, which can withstand a load of 150 kg, without taking into account the weight of the railings. Moreover, this weight is calculated for the extreme point of the suspended step.


Installation

It is very important to know what the wall is made of, to which the steps of the cantilever staircase will later be attached. It's best if it's brickwork, or other heavy materials. This is necessary because it is in the wall that the ends of the steps are installed with your own hands, buried at least 20 cm with a flight width of 80 cm. The size of the recess must be increased to 30-40 cm if the wall consists of expanded clay concrete blocks or slotted bricks, as seen in the photo.