Multiple branching is a structure that branches into more than two branches. From the point of view of theoretical programming, it is redundant, since it can be implemented using binary branches. But almost all programming languages ​​have an operator that supports this structure, so let's look at it using the example of branching into three branches (block diagram in Fig. 25.2). Branching is controlled by a selector expression s, which can take the provided values a, b and c... If s = a, then the branch A, if s = b, then the branch B, and if s = s, then the branch WITH... The structure also has a branch X, which will be executed if the selector s takes a value not intended for the execution of the previous branches.

In fig. Figure 25.3 shows the implementation of this structure using binary forks.

Rice. 25.2. Block diagram of multiple branching

Rice. 25.3. Implementing Multiple Branching with Binaries

In pseudocode, multiple branching is written as follows:

choice
for s = a: Branch A
for s = b: Branch B
for s = c: Branch C
otherwise Branch X
all

The telescopic crown is a design of two parts: primary and secondary. It is mainly used for fixing. The primary part is a metal cap. The secondary crown is fixed to the prosthesis frame. When the two parts are joined together, a sturdy structure is formed. With its help, you can form a strong attachment of the prostheses, which at the same time can be easily removed.

Varieties of telescopic crowns

This mechanism was first tested in Germany at the beginning of the last century. The telescopic crown owes its name to its resemblance to a telescope. Its component parts move relative to each other in the same way. For practically centuries-old history this design managed to prove its practicality, ease of use and good aesthetics. These days, telescopic crowns can be excellent alternative option prostheses on implants.

There are two types of this design - cylindrical crowns and conical crowns. Basically, they differ in appearance. The earliest examples of telescopic crowns were made by artisans with cylindrical walls. They are characterized by a fairly snug fit. Today, such a design is advisable to use only among patients with absolutely healthy gums.

The telescopic conical crown is an improved version of the cylindrical crown. Its main advantage is considered to be the absence of the influence of errors that are possible at the manufacturing stage. This design does not allow for skewing or jamming when fixing the prosthesis. The main disadvantage of the improved system is the ability to detach the crowns upon contact with food.

Benefits of telescopic crowns

What kind positive sides can be noted in the application of this design?

1. The chewing load is evenly distributed over all teeth and gums.
2. Lack of influence on diction and bite.
3. Possibility of installation on implants.
4. Long service time.
5. Easy to use and maintain.
6. Keeping the tooth healthy for a long time.

These are not all the advantages of telescopic crowns. Everyone can note for themselves the positive aspects of using the design.

Disadvantages of telescopic crowns

Among the main disadvantages of this design are a long manufacturing period and high cost. However, the negative aspects are fully compensated for by the above advantages of crowns.

Installation indications

The use of telescopic crowns is advisable in the following cases:

• the presence of periodontal disease and loose abutment teeth;
• there is no financial ability to install implants;
• too few teeth for clasp dentures.

The need to use this design is still determined by the doctor.

Telescopic crowns: manufacturing steps

The production of the structure described in the article today is possible in two ways: stamping and casting. The first method is considered to be the simplest. However, when using casting, it is possible to obtain a more attractive appearance product through processing with modern materials.

Manufacturing of telescopic crowns begins with turning the patient's teeth under interior constructions. Then the specialist takes impressions and sends them to the laboratory. There, technicians are already making models from them and making caps. It is very important to check the parallelism of the walls of the abutment teeth so that the structure fits accurately. After trying on the caps, a plaster cast is formed from them for casting the future model. The external crown is made taking into account a gap of 0.5-1 mm. An external structure is already being made on the basis of the resulting print.

Cost and service life

Telescopic crowns are considered relatively expensive. Its cost can vary from 5 to 11 thousand rubles. If we talk about complete prosthetics, then the final price will depend on several factors simultaneously (the material used, the number of abutment teeth, etc.). It is not possible to name it exactly.

On telescopic crowns characterized by a short service life - no more than 10 years. To increase it, it is necessary to periodically visit a doctor and monitor the operation of the structure.

Aluminum stairs are a structure of two racks connected by steps. An alloy of aluminum and silicon is usually used as a material of manufacture. This ensures high strength of such products. These ladders usually have different types constructions. It depends on the purpose of their application.

Four-section ladder - a tool for a wide variety of jobs

Types of aluminum stairs

Aluminum ladders by type of construction differ into one-, two-, three- and four-section. They have from 6 to 25 steps and are used for various purposes. While doing household work a stepladder that can handle most tasks comes in handy. The most common are ladders with the main part of metal, and the legs with steps are made of plastic.

In addition to household, the following types of structures can be distinguished:

Household stairs, as well as dielectrics and most transformers have many additional parts. They increase the safety and reliability of structures.

Types of stairs

Majority modern stairs turn out to be indispensable for operation at height, both in domestic conditions and at industrial enterprises. On this basis, they are divided into used in everyday life and professional.
The first type of products is made of aluminum, has high lightness, simplicity of design and must meet important requirements- durability, ease of transportation and installation, safety, undemanding storage conditions.

Professional designs have a number of characteristic features determining the scope of their application. For example, transformers are highly functional and are often used as a platform. Telescopic ladders are very compact and allow for the same amount of work as many three-section structures.

Design features

The maximum weight of the user of aluminum ladders varies - from 100 to 150 kg. With more high rates we can say that the design is professional. The working length is measured to the last platform or step. Professional constructions are up to 15-20 meters high.

Please note: sometimes the working length can be considered the height from the floor to the penultimate step, and 120 cm is added to it. It is better to check this question with the seller.

Single-section ladders

Three-section staircase - like a stepladder, only better

This is called an attachment structure and requires vertical support. To avoid ridiculous injuries during use, the legs must be well fixed. Distinctive features of attached structures are:

1. Wide application at home. Indispensable for light repairs, work in the garden, in the country. She allows without special efforts harvest and sawed off dead tree branches.
2. A one-section ladder is not superfluous when carrying out installation and construction work. Frequent use is due to ease of use - you just have to lean against the wall and securely fasten.
3. Choice. When buying an attached one-section ladder, the main parameter that you need to pay attention to is the height. Not only the functionality of the product depends on it, but the cost. On construction market there are different options: 1.5 to 5.6 meters long.

The material of manufacture (aluminum with duralumin, magnesium, silicon) is highly durable and long term service. Although single-section aluminum side ladders are still inferior to their improved versions.

Two-piece structures

The features of these ladders include: anti-slip steps, a variety of models (from 3 to 25 steps) and the possibility of two-way climbing. The maximum step-ladder height is up to 13 meters. The advantages of the ladder include corrosion resistance, unlimited operating conditions, low weight and compactness.

Two-section aluminum ladders have 2 types of construction: folding (ladders) and sliding. The latter are distinguished by the fact that one part of them protrudes from the other. The recommended load does not exceed 150 kg. Such structures are distinguished by high functionality and convenience, they can be used as attachments.

Any staircase, the same two-section aluminum, must first of all have the necessary functionality.

Three-section stairs

With the help of such a ladder, you can easily paint ceilings and places inaccessible from the floor.

You can use such a ladder in the form of a step-ladder, an attached structure. It has transverse braces between the legs, which provides the greatest strength. The aluminum profile allows the structure to be used with a load of up to 150 kg.
It is a product for household use. As ladder usually reaches a height of 6 meters. As a stepladder it can be used at a height of 5 meters.
When folded, such a staircase most often has the following dimensions (height, width, depth): 2.5 * 0.4 * 0.15. The approximate step width is 25 mm. The plugs are made of two-component plastic.

Four-piece products

Ladders with 4 sections are called transformers. They are the most functional and are used both as ladders and in the form of attached structures. Can replace scaffolds.

main feature such stairs are a relatively rare use. They have several parts connected by hinge mechanisms. The advantage is compactness when folded, as well as high stability and reliability in use.

Distinctive features of such structures are high functionality, large working length, the ability to withstand a heavy load - up to 150 kg, the possibility of using the principle of a side ladder, the maximum simplification of complex construction work.

The small weight of the product makes it easy to carry during work. It is also convenient to be able to quickly change the height. work surface.

Advantages of the 4-section step ladder

Due to its design, the four-section ladder can cope with huge amount tasks and has a number of advantages:

• compactness;
• high resistance to different types surfaces;
• the presence of a special relief;
• high strength of the product, provided by the aluminum profile;
• convenient to store and transport;

The ladder components, due to their peculiarities, allow the ladder to withstand significant operational loads. Suitable for both hobbyists and professional builders.

The cost of aluminum stairs

Now let's turn to the most interesting question: how much do such constructions cost? Aluminum ladders, depending on the characteristics, have a large variation in cost. Below are their main types.

So, prices for structures with only 2 sections:

• two-section ladder (maximum length 314 cm, weight - 6.4 kg) aluminum - 5 thousand rubles;
• the same construction, which has a length of 427 cm, costs about 6.3 thousand rubles;
• a universal two-section ladder with a working height of 687 cm will cost the buyer 11 thousand rubles;
• sliding structures can cost from 4.5 to 12 thousand rubles;
• universal ladders can be purchased for 5.5-12.5 thousand rubles.
• three-section ladders cost from 3.5 to 11 thousand rubles, and prices for structures consisting of 4 parts vary from 5.5 to 12 thousand rubles.

As can be seen from the prices, four-section products are distinguished not only by high performance characteristics but also availability.

How to choose the right ladder

Before buying a specific product, you should decide on its necessary characteristics and the tasks of operation.

Study your ladder thoroughly for build quality before purchasing

At the right choice a ladder will certainly help you achieve lofty goals. For example, for cosmetic repair apartments will do the usual side-by-side option. First of all, consider the areas of application staircase structures:

• repair and construction works;
• household needs;
• electric installation work;
• use in large libraries;
• work in the garden.

It is necessary to select the required working height, maximum load and pay attention to the availability of special mountings.

In the case of a system of interconnected rigid bodies, the forces acting on this system can be divided into two groups:

1) external forces;

2) internal forces.

Internal forces are the forces of interaction between bodies included in this system... According to the law of equality of action and reaction, internal forces are always pairwise equal in magnitude and directly opposite in direction, but applied to two different interacting bodies of the system.

External forces are those forces with which bodies that are not part of a given system act on the bodies of this system.

Consider, for example, the system shown in Fig. 39. The weight AB beam can rotate around the axis A of the stationary cylindrical hinge and the end B rests freely on another beam CD with the weight, which is supported at the point E and is connected to the wall by the hinge.

In this case, the system consists of two bodies: a beam AB and a beam.

Internal forces for the dgnuy system are the forces of interaction between the beams, i.e. the force of pressure of the beam AB on the beam CD and the force with which the beam CD acts on the beam AB. According to the law of equality of action and reaction, the forces N, and are equal in magnitude and opposite in direction, i.e.

Weights and beams represent the forces with which these beams are attracted to the Earth, and, therefore, for a given system they are external forces, since the Earth in relation to this system is an external body. The reactions of both the hinged supports A and D, as well as the reaction of the support E, are also external forces for this system, since the articulated supports A and D and the support E do not belong to the considered system, consisting of only two beams.

When solving equilibrium problems for a system of bodies, it is necessary to take into account that all external and internal forces applied to each body separately are balanced. Consequently, in the case of a plane system of forces, one can compose three equilibrium equations for each of these bodies separately.

Thus, for a system consisting of bodies, it is possible to compose the entire equilibrium equations. Therefore, if the number of unknown forces in a given problem is not more, then such a problem is statically determined. If the number of unknowns in the problem turns out to be greater, then such a problem cannot be solved only on the basis of the equations of statics of an absolutely rigid body and therefore is statically indefinite.

Since the internal forces are pairwise equal in magnitude and directed along one straight line in opposite directions, the algebraic sum of their moments relative to any point is equal to zero and the sum of their projections onto any axis is also equal to zero. Therefore, if we compose the equilibrium equation (the equation of moments relative to any point, or the equation of projections onto any axis) for each body separately and then add all the equations, then in the resulting equation the terms containing internal forces are eliminated in pairs and, therefore , this equation will include only external forces.

Thus, if a system of bodies is in equilibrium, then the external forces applied to this system satisfy the same three equations of equilibrium as in the case of equilibrium of one absolutely rigid body. These equations represent the conditions for the equilibrium of external forces acting on the system.

All external reactions can be found from these equations if the number of these external reactions is not more than three.

If the number of external reactions turns out to be more than three, or if in the problem, in addition to external reactions, it is required to find unknown internal forces, then it is necessary to apply the method of dismemberment of the system, that is, it is necessary to consider the equilibrium of each body in the system separately and for each of these bodies to compose equations equilibrium, taking into account all the forces applied to the body in question. If the system consists, for example, of two rigid bodies, then, using the method of dismemberment, we obtain in the general case only six equations of equilibrium (three equations for each body). To compose six equations of equilibrium, another method can be used, namely: first compose three equations for the entire system as a whole (as for one absolutely rigid body) and then add three equilibrium equations to these three equations, compiled for only one of the two bodies this system. This second technique is often preferable, since only external forces enter the equilibrium equations compiled for the entire system as a whole, and therefore these equations usually turn out to be simpler.

Problems related to the equilibrium of a system of rigid bodies, depending on the type of connection of these bodies with each other, can be divided into the following four types:

1. Problems where the bodies included in the system lean freely on each other.

2. Problems where the bodies included in the system are interconnected by a flexible thread or a weightless rod, the ends of which are attached to these bodies by means of hinges.

3. Problems, where the bodies included in the system are interconnected by means of a hinge.

4. Tasks related to the determination of the forces in the bars of a flat truss.