Classification of force loads: external and internal. Classification of loads and structural elements

Classification of External Forces (Loads) Strength of Materials

External forces in strength of materials are divided into active And reactive(connection reactions). Loads are active external forces.

Loads by application method

By application method loads there are voluminous(own weight, inertial forces) acting on each infinitesimal element of volume, and surface ones. Surface Loads are divided into concentrated loads And distributed loads.

Distributed Loads are characterized by pressure - the ratio of the force acting on a surface element normal to it to the area of ​​this element and are expressed in the International System of Units (SI) in pascals, megapascals (1 PA = 1 N/m2; 1 MPa = 106 Pa), etc. etc., and in the technical system - in kilograms of force per square millimeter, etc. (kgf/mm2, kgf/cm2).

In compromising materials, they are often considered surface loads, distributed along the length of the structural element. Such loads are characterized by intensity, usually denoted q and expressed in newtons per meter (N/m, kN/m) or in kilograms of force per meter (kgf/m, kgf/cm), etc.

Loads according to the nature of changes over time

Based on the nature of changes over time, they are distinguished static loads- increasing slowly from zero to its final value and then not changing; And dynamic loads causing large inertial forces.

Assumptions of strength of material

Assumptions of Sopromat Sopromat

When constructing a theory of calculation for strength, stiffness and stability, assumptions related to the properties of materials and the deformation of the body are made.

Assumptions related to material properties

Let's first consider assumptions related to material properties:

assumption 1: the material is considered homogeneous (its physical and mechanical properties are considered the same at all points;

assumption 2: the material completely fills the entire volume of the body, without any voids (the body is considered as a continuous medium). This assumption makes it possible to use methods of differential and integral calculus when studying the stress-strain state of a body, which require continuity of the function at each point of the volume of the body;

assumption 3: the material is isotropic, that is, its physical and mechanical properties at each point are the same in all directions. Anisotropic materials – the physical and mechanical properties of which change depending on the direction (for example, wood);

assumption 4: the material is perfectly elastic (after removing the load, all deformations completely disappear).

Deformation Assumptions

Now let's look at the main assumptions related to body deformation.

assumption 1: deformations are considered small. From this assumption it follows that when drawing up equilibrium equations, as well as when determining internal forces body deformation can be ignored. This assumption is sometimes called the initial size principle. For example, consider a rod embedded at one end into a wall and loaded at the free end with a concentrated force (Fig. 1.1).

The moment in the embedment, determined from the corresponding equilibrium equation using the method of theoretical mechanics, is equal to: . However, the straight position of the rod is not its equilibrium position. Under the action of force (P), the rod will bend, and the point of application of the load will shift both vertically and horizontally. If we write down the equilibrium equation of the rod for the deformed (bent) state, then the true moment arising in the embedment will be equal to: . Taking the assumption that the deformations are small, we believe that the displacement (w) can be neglected compared to the length of the rod (l), that is, then . The assumption is not possible for all materials.

assumption 2: movements of body points are proportional to the loads causing these movements (the body is linearly deformable). For linearly deformable structures, the principle of independence of the action of forces is valid ( superposition principle): the result of the action of a group of forces does not depend on the sequence of loading the structure with them and is equal to the sum of the results of the action of each of these forces separately. This principle is also based on the assumption of the reversibility of loading and unloading processes.

When solving problems of structural strength, external forces, or loads, are called the forces of interaction of the structural element under consideration with the bodies associated with it. If external forces are the result of direct, contact interaction of a given body with other bodies, then they are applied only to points on the surface of the body at the point of contact and are called surface forces. Surface forces can be continuously distributed over the entire surface of the body or part of it. The amount of load per unit area is called load intensity, is usually denoted by the letter p and has the dimensions N/m2, kN/m2, MN/m2 (GOST 8 417-81). It is allowed to use the designation Pa (pascal), kPa, MPa; 1 Pa = 1 N/m2.

The surface load reduced to the main plane, i.e. the load distributed along the line, is called the linear load, is usually denoted by the letter q and has the dimensions N/m, kN/m, MN/m. The change in q along the length is usually shown in the form of a diagram (graph).

In the case of a uniformly distributed load, the diagram q is rectangular. When in action hydrostatic pressure Diagram q is triangular.

The resultant of the distributed load is numerically equal to the area of ​​the diagram and is applied at its center of gravity. If the load is distributed over a small part of the surface of the body, then it is always replaced by a resultant force, called concentrated force P (N, kN).

There are loads that can be represented in the form of a concentrated moment (pair). Moments M (Nm or kNm) are usually designated in one of two ways, or in the form of a vector perpendicular to the plane of action of the pair. Unlike the force vector, the moment vector is depicted as two arrows or a wavy line. The torque vector is usually considered to be right-handed.

Forces that are not the result of contact of two bodies, but are applied to each point of the volume of the occupied body (own weight, inertial forces) are called volumetric or mass forces.

Depending on the nature of the application of forces over time, static and dynamic loads are distinguished. A load is considered static if it increases relatively slowly and smoothly (at least over a few seconds) from zero to its final value, and then remains unchanged. In this case, we can neglect the accelerations of the deformed masses, and therefore the forces of inertia.

Dynamic loads are accompanied by significant accelerations of both the deformable body and the bodies interacting with it. The inertial forces arising in this case cannot be neglected. Dynamic loads are divided from instantly applied, impact loads into recurrent ones.

The instantly applied load increases from zero to maximum within a fraction of a second. Such loads occur when the combustible mixture in the engine cylinder is ignited. internal combustion, when starting off a train.

An impact load is characterized by the fact that at the moment of its application the body causing the load has a certain kinetic energy. Such a load occurs, for example, when driving piles using a pile driver, in the elements of a forging hammer.

1.2. Classification external forces and structural elements

External forces acting on structural elements,” as is known from the course of theoretical mechanics, are divided into active and reactive (reactions of connections). Active external forces are usually called. The origin and nature of the action of the load are determined by the purpose, operating conditions and design features of the considered element. For example, for the drive shaft shown in Fig. 1.8, the loads are the forces acting on the gear teeth and the tension of the belt branches, as well as the gravity force of the shaft itself and the parts mounted on it (gear and pulley).

For truss bars overhead crane(Fig. 1.9) the main loads are the gravity forces of the lifted load and the trolley; The gravity forces of the truss are of less importance.

The main load on the steam boiler drum is the pressure of the steam in it.

If the structural element in question moves with acceleration, then the loads acting on it also include inertial forces.

The forces of gravity of a given part of the structure and the forces of inertia arising during its accelerated movement are volumetric messages, that is, they act on every infinitesimal element of volume. Loads transmitted from one structural element to another are classified as surface forces.

Surface layers are divided into concentrated and distributed. It should be remembered that concentrated forces, of course, do not exist - this is an abstraction introduced for the convenience of technical calculations. A force is considered concentrated if it is transmitted to a part over an area whose dimensions are negligible in comparison with the dimensions of the structural element itself. For example, the pressure force of a car wheel on a rail can be considered as concentrated, since although the wheel and rail at the point of contact are deformed, the dimensions of the area resulting from this deformation are negligible compared to the dimensions of both the rail and the wheel.

Loads distributed over a certain surface are characterized by pressure, i.e., the ratio of the force acting on a surface element normal to it to the area of ​​this element, and, therefore, expressed in pascals (1 Pa = 1 N/m~), MPa, etc.

In many cases, one has to deal with loads distributed along the length of a structural element. for example, we can talk about the force of gravity per unit length of a beam, and if the cross-section of the beam is not constant, then the force of gravity per unit length will be variable.

The load distributed along the length is characterized by intensity, usually denoted by q and expressed in units of force per unit of length: N/m, kN/m, etc.

According to the nature of changes over time, they are distinguished: static loads, increasing slowly and smoothly from zero to its final value; Having reached it, they do not change in the future. An example is centrifugal forces during the acceleration period and during the subsequent uniform rotation of a rotor;

repeated loads, changing many times over time according to one or another law. An example of such a load is the forces acting on the teeth of gear wheels;

short duration loads, applied to the structure immediately or even with an initial speed at the moment of contact (these loads are often called dynamic or drums). An example of impact is, for example, the load taken by the parts of a steam hammer during forging.

The issue of bonds and their reactions is discussed in sufficient detail in the course of theoretical mechanics. Here we will limit ourselves to just a reminder of the most common types of connections.

Articulating support(simply connected support) is schematically depicted as shown in Fig. 1.10, a. The reaction of such a support is always perpendicular to the supporting surface.

Articulated-fixed support(double-connected support) is shown schematically in Fig. 1.10, b. The reaction of the articulated-fixed support passes through. the center of the hinge, and its direction depends on the active forces acting. Instead of finding the numerical value and direction of this reaction, it is more convenient to search separately for its two components.

In a hard seal(three-connected support) a reactive pair of forces (moment) and a reactive force arise; it is more convenient to represent the latter in the form of its two components (Fig. 1.11).

If the connection is a rod with hinges at the ends (Fig. 1.12), then the reaction is directed along its axis, that is, the rod itself works in tension or compression.

The shapes of structural elements are extremely diverse, but with a greater or lesser degree of accuracy, each of them can be considered in calculations either as a beam, or as a shell or plate, or as an array.

In the field of strength of materials, they mainly study methods of calculations for the strength, rigidity and stability of a beam, that is, a body whose two dimensions are small compared to the third (length). Let's imagine a flat figure moving along a certain line in such a way that the center of gravity of the figure is on this line, and the plane of the figure is perpendicular to it. The body obtained as a result of such movement is the beam (Fig. 1.13).

The flat figure, by the movement of which the beam is formed, is its cross section, and the line along which its center of gravity moved is the axis of the beam.

The axis of a beam is the geometric location of the centers of gravity of its cross sections. Depending on the shape of the axis of the beam and how its cross-section changes (or remains constant), they are distinguished straight and curved beams with a constant, continuously or stepwise changing cross-section (Fig. 1.14). Some examples of parts calculated as straight beams include the drive shaft (see Fig. 1.8), any of the overhead crane truss rods (see Fig. 1.9); the hook of this crane is calculated as a curved beam.

Plate and shell(Fig. 1.15) are characterized by the fact that their thickness is small compared to other sizes. The plate can be considered as special case shell, so to speak, a “straightened” shell. Examples of parts considered as shells and plates are various tanks for liquids and gases, plating elements of ship hulls, submarines, and aircraft fuselages.

Array call a body, all three dimensions of which are quantities of the same order, for example, a foundation for a car, a ball or a roller of a rolling bearing.

As practice shows, the topic of load collection raises greatest number questions for young engineers starting their professional activity. In this article I want to consider what permanent and temporary loads are, how long-term loads differ from short-term ones and why such a separation is necessary, etc.

Classification of loads by duration of action.

Depending on the duration of action, loads and impacts are divided into permanent And temporary . Temporary loads are in turn divided into long-term, short-term And special.

As the name itself suggests, permanent loads valid throughout the entire period of operation. Live loads appear during certain periods of construction or operation.

include: own weight of load-bearing and enclosing structures, weight and soil pressure. If prefabricated structures (crossbars, slabs, blocks, etc.) are used in the project, the standard value of their weight is determined on the basis of standards, working drawings or passport data of the manufacturing plants. In other cases, the weight of structures and soils is determined from design data based on their geometric dimensions as the product of their density ρ and volume V taking into account their humidity under the conditions of construction and operation of structures.

The approximate densities of some basic materials are given in table. 1. Approximate weights of some rolled and finishing materials are given in table. 2.

Table 1

Density of basic building materials

Material	Density, ρ, kg/m3
Concrete: - heavy - cellular	2400 400-600
Gravel	1800
Tree	500
Reinforced concrete	2500
Expanded clay concrete	1000-1400
Brickwork with heavy mortar: - made of solid ceramic bricks - made of hollow ceramic bricks	1800 1300-1400
Marble	2600
Construction waste	1200
River sand	1500-1800
Cement-sand mortar	1800-2000
Mineral wool thermal insulation boards: - not subject to load — for thermal insulation of reinforced concrete coverings — in ventilated facade systems — for thermal insulation of external walls followed by plastering	35-45 160-190 90 145-180
Plaster	1200

table 2

Weight of rolled and finishing materials

Material	Weight, kg/m2
Bituminous shingles	8-10
Plasterboard sheet 12.5 mm thick	10
Ceramic tiles	40-51
Laminate 10 mm thick	8
Metal tiles	5
Oak parquet: — 15 mm thick — thickness 18 mm — thickness 22 mm	11 13 15,5
Roll roofing (1 layer)	4-5
Sandwich roofing panel: — thickness 50 mm — thickness 100 mm — thickness 150 mm — thickness 200 mm — thickness 250 mm	16 23 29 33 38
Plywood: — thickness 10 mm — 15 mm thick — 20 mm thick	7 10,5 14

Live loads are divided into long-term, short-term and special.

relate:

— load from people, furniture, animals, equipment on the floors of residential, public and agricultural buildings with reduced standard values;

— loads from vehicles with reduced standard values;

— weight of temporary partitions, grouts and footings for equipment;

— snow loads with reduced standard values;

— weight of stationary equipment (machines, motors, containers, pipelines, liquids and solids, filling equipment);

— pressure of gases, liquids and granular bodies in containers and pipelines, overpressure and air rarefaction that occurs during ventilation of mines;

— loads on floors from stored materials and racking equipment in warehouses, refrigerators, granaries, book depositories, archives of similar premises;

— temperature technological influences from stationary equipment;

— weight of the water layer on water-filled flat surfaces;

— vertical loads from overhead and overhead cranes with a reduced standard value, determined by multiplying the full standard value of the vertical load from one crane in each span of the building by the coefficient:

0.5 - for groups of operating modes of cranes 4K-6K;

0.6 - for the 7K crane operating mode group;

0.7 - for the 8K crane operating mode group.

Groups of crane modes are accepted according to GOST 25546.

relate:

— the weight of people, repair materials in areas for maintenance and repair of equipment with full standard values;

— loads from vehicles with full standard values;

— snow loads with full standard values;

— wind and ice loads;

— loads from equipment arising in start-up, transition and test modes, as well as during its rearrangement or replacement;

— temperature climatic influences with full standard value;

- loads from movable lifting and transport equipment (forklifts, electric vehicles, stacker cranes, hoists, as well as overhead and overhead cranes with full standard values).

relate:

— seismic impacts;

— explosive effects;

- loads caused by sudden disturbances technological process, temporary malfunction or breakdown of equipment;

- impacts caused by deformations of the base, accompanied by a radical change in the structure of the soil (when soaking subsidence soils) or its subsidence in areas of mining and karst.

Statistical loads do not change over time or change very slowly. When subject to statistical loads, strength calculations are carried out.

Re-variables loads repeatedly change value or value and sign. The action of such loads causes metal fatigue.

Dynamic loads change their value in a short period of time, they cause large accelerations and inertial forces and can lead to sudden destruction of the structure.

It is known from theoretical mechanics that, depending on the method of applying loads, there can be focused or distributed on the surface.

In reality, the transfer of load between parts occurs not at a point, but at a certain area, i.e. the load is distributed.

However, if the contact area is negligibly small compared to the dimensions of the part, the force is considered concentrated.

When calculating real deformable bodies in the resistance of materials, replace distributed load should not be concentrated.

The axioms of theoretical mechanics in the strength of materials are used to a limited extent.

You cannot transfer a pair of forces to another point on a part, move a concentrated force along the line of action, and you cannot replace a system of forces with a resultant when determining displacements. All of the above changes the distribution of internal forces in the structure.

During construction and operation, the building experiences various loads. External influences can be divided into two types: power And non-force or environmental influences.

TO forceful impacts include different kinds loads:

permanent– from the own weight (mass) of the building elements, soil pressure on its underground elements;

temporary (long-term)– from the weight of stationary equipment, long-term stored cargo, dead weight permanent elements buildings (for example, partitions);

short-term– from the weight (mass) of mobile equipment (for example, cranes in industrial buildings), people, furniture, snow, wind;

special– from seismic impacts, impacts resulting from equipment failures, etc.

TO non-forceful relate:

temperature effects causing changes linear dimensions materials and structures, which in turn leads to the occurrence of force effects, as well as affecting the thermal conditions of the room;

exposure to atmospheric and ground moisture, and vaporous moisture contained in the atmosphere and indoor air, causing a change in the properties of the materials from which the building’s structures are made;

air movement causing not only loads (with wind), but also its penetration into the structure and premises, changing their humidity and thermal conditions;

exposure to radiant energy sun (solar radiation) causing, as a result of local heating, a change in the physical and technical properties of the surface layers of materials, structures, changes in the light and thermal conditions of the premises;

exposure to aggressive chemical impurities contained in the air, which in the presence of moisture can lead to the destruction of the material of building structures (the phenomenon of corrosion);

biological effects caused by microorganisms or insects, leading to the destruction of structures made of organic building materials;

exposure to sound energy(noise) and vibration from sources inside or outside the building.

Where the effort is applied loads are divided into concentrated(e.g. weight of equipment) and evenly distributed(own weight, snow).

Depending on the nature of the load, they can be static, i.e. constant in magnitude over time and dynamic(drums).

In direction - horizontal (wind pressure) and vertical (own weight).

That. a building is subject to a variety of loads in terms of magnitude, direction, nature of action and location of application.

Rice. 2.3. Loads and impacts on the building.

There may be a combination of loads in which they will all act in the same direction, reinforcing each other. It is these unfavorable combinations of loads that building structures are designed to withstand. The standard values ​​of all forces acting on the building are given in DBN or SNiP.

5. Centrally tensioned steel elements: operation scheme, application, strength calculation

Centrally stretched elements- these are elements in the normal section of which the point of application of the longitudinal tensile force N coincides with the point of application of the resultant forces in the longitudinal reinforcement.

Centrally stretched elements include arch stringers, lower chords and downward braces of trusses and other elements (Fig. 51).

Centrally tensioned elements are designed, as a rule, to be prestressed.

Basic principles for the design of centrally tensioned elements:

The rod working reinforcement without prestressing is connected along its length by welding;

Lap joints without welding are allowed only in slab and wall structures;

Tensile prestressed reinforcement in linear elements should not have joints;

IN cross section prestressed reinforcement is placed symmetrically (to avoid eccentric compression of the element);

Eccentrically stretched elements- these are elements that simultaneously stretch longitudinal force N and bend with a moment M, which is equivalent to eccentric stretching by force N with eccentricity e o relative to the longitudinal axis of the element. In this case, two cases are distinguished: when the longitudinal tensile force N applied between the resultant forces in tension and compression reinforcement, and the position when the force is applied beyond a given distance.

Eccentrically stretched elements include the lower chords of braced trusses and other structures.

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