Perform the classification of loads by application method. Strength of materials. The main tasks of the section. Classification of loads. Brickwork on a heavy solution

Classification of external loads acting on structural elements.

General classification of structural elements.

Technical objects and structures consist of separate parts and elements that are distinguished by a large variety in shape, sizes, other parameters and characteristics. From the standpoint of engineering calculations, it is customary to distinguish between four main groups of structural elements: rods, plates, shells, arrays.

Rod - These are direct or curvilinear elements of structures, in which one size (length) significantly exceeds two other sizes (in the spatial orthogonal coordinate system), see Figure 20. Examples of structural structures of rods: legs of the chair or table, construction structure, rope lifting Machines, lever switching box change car and dr.

Z curve rod

Straight rod

Figure 20. Schemes of elements of structures of rods

t. (plate thickness)

Figure 21. Plate type design element diagram

Figure 22. Shell type design element diagram (cylindrical)

Fig. 23. Massage type design element scheme

Plates - These are flat elements of structures that have one size (thickness) significantly less than two others. Examples of plates: table lid; Walls and ceiling floors of buildings, etc., see Figure 21, from which it can be seen that the plate thickness is significantly less than two sizes in the plan.

Shell- These are non-plain thin-walled elements of structures, in which one size (wall thickness) is significantly less than other sizes. Examples of shells: pipelines for transporting liquid and gaseous products (cylindrical shells); cylindrical, spherical or combined containers for liquids; conical bins for bulk materials; Non-plating various structures, etc., see Figure 22, where the cylindrical shell (thin-walled cylindrical tube) is shown, in which the wall thickness is significantly less than its diameter and length.

Arrays - These are elements of structures that have all three sizes commensurate. Examples of arrays: Foundation blocks of machines, machinery and building structures; Massive supports of bridges and others, see Figure 23.

In the courses "Engineering Mechanics" and "Material Resistance", the most attention is paid to the fundamental study of the elements of the structures of the rods. Plates, shells and arrays are studied in expanded courses "Material resistance" and in special courses.

Concentrated forces - These are the forces attached to the design element on the site of its surface, the sizes of which compared with the size of the entire surface of the design element can be neglected. As a rule, focused forces are the result of the influence on this body (element of the structure) of another body (in particular, another element of the design). In many practically important cases concentrated

forces can be without noticeable damage to the accuracy of engineering calculations are considered applied to the element of the structure at the point. Units of measurement of concentrated forces H (Newton), KN (Kilonuteton), etc.

Volumetric forces - These are the forces applied throughout the volume of the design element, such as distributed gravity. Units of measurement of distributed volumetric forces N / m 3, KN / m 3, etc. The total force of gravity (H, KN) of any element of the structure is often calculated as a concentrated force attached at a point called its center of gravity.

Distributed Forces (Loads) - These are the forces attached to the part of the area (or length) of the deformable body, commensurate with the sizes of the entire body. There are superficially distributed forces (loads), the units of measurement of which N / m 2, KN / m 2, etc. (for example, distributed snow loads on building coverage), as well as linearly distributed loads (along the length of structural elements), the units of measurement of which N / m, KN / M, etc. (for example, distributed pressure forces based on building structures on the beams).

Static forces (load) - These are the forces (loads) that do not change (or insignificant changing) their meaning, position and direction of action during the operation of the structure.

Dynamic Forces (Loads) - These are the forces (loads), significantly change their value, position and / or direction in short periods of time and causing oscillations of the structure.

Nominal loads - This is normal maximum loads arising from the operation of the design.

Control questions:

1) What is studied in the course "Material resistance"? What is its value for highly qualified technical specialists?

2) What is external loads and internal efforts?

3) Explain the concepts of deformation, strength, rigidity and stability.

4) Explain the concepts of homogeneity, continuity, isotropy and anisotropy.

5) Give the classification of structural elements.

6) Give the classification of external loads acting on the elements of the structures.

1. Alexandrov A.V. and others. Resistance of materials. Tutorial for universities - M.: Higher. Shk., 2001. - 560 p. (p. 5 ... 20).

2. Stepin P.A. Strength of materials. - M.: Higher. School, 1983. - 303 p. (p. 5 ... 20).

3. Handbook of the resistance of materials / Pisarenko G.S. And others. - Kiev: Nookova Dumka, 1988. - 737С. (p. 5 ... 9).

Control tasks for SRS- With the help of educational literature, information on the following issues:

1) What is the strength of elasticity?

2) What is the essence of the principle of lack of initial internal efforts in the body (, p. 9-10)?

3) What are the principles of the schematization of external loads acting on structural elements used in engineering calculations (p. 8-11)?

4) Explain the principle of independence of the forces (p. 18-20;, p. 10)?

5) explain the principle of Saint-Vienna (p. 10-11);

6) What is the difference between deformation from moving (, p. 17-18;, p. 13-14)?;

7) the general concept of the cross sections method (, p. 13-16;, p. 14-17);

8) the general concept of stresses in the deformable body, notation of normal and tangent stresses (, p. 13-15;, p. 17-20).

9) Classification of external loads acting on structural elements (see clause 5.3).

Lecture 6. Topic 6. "Central stretching-compression of straight rigid rods"

The purpose of the lecture - state introductory provisions on the topic, essence and application of the cross sections method to determine the internal efforts in rods under central tension compression; Give the initial concepts about domestic efforts.

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Overview

The main tasks in the technique are to ensure the strength, stiffness, stability of engineering structures, parts of machinery and instruments.

Science, in which the principles and methods of settlement of strength, rigidity and sustainability are called material resistance .

Strength b is the ability of the structure within certain limits to perceive the effect of external loads without destruction.

Rigidity - This is the ability of the structure within certain limits to perceive the effect of external loads without changing geometric sizes (not deformed).

Sustainability - The property of the system independently restore the initial state after it was given some deviation from the state of equilibrium.

Each engineering calculation consists of three stages:

Idealization of the object (the most essential features of the real design are allocated - the calculated scheme is created).
Analysis of the calculation scheme.
Reverse transition from the calculated scheme to the real design and formulation of conclusions.

Material resistance is based on the laws of theoretical mechanics (static), methods of mathematical analysis, material science.

Load classification

There are external and internal forces and moments. External forces (loads) are active forces and communication reactions.

By the nature of the load, the load is divided into:

static - it is applied slowly, which is zero to the final value, and do not change;
dynamic - change the amount or direction in a short period of time:
- sudden e - they act right at full strength (the wheel of a locomotive driven by the bridge),
- drums - operate for a short time (diesel-hammer),

Classification of structural elements

Kernel (Bar) - body whose length L exceeds its transverse dimensions B and H. The axis of the rod is a line connecting the centers of severity of sequentially arranged sections. The cross section is the plane perpendicular to the axis of straggle.

Plate - The body of a flat shape, in which length A and width b is greater than the thickness h.

Shell - The body bounded by two closely located curvilinear surfaces. The shell thickness is made compared to other overall dimensions, the radius of the curvature of its surface.

The massive body (array) is a body that all sizes of one order.

Strain stem

When loading bodies by external forces, they can change their shape and sizes. Changing the shape and size of the body under the action of external forces is called deformation .

Deformations are:

elastic - disappear after the cessation of their forces caused;
plastic - Do not disappear after the cessation of the action that caused them.

Depending on the nature of external loads, such types of deformations are distinguished:

stretching compression - the state of resistance, which is characterized by lengthening or shortening,
shift r - the displacement of two adjacent surfaces relative to each other at a constant distance between them,
torsion - Mutual turn of transverse sections relative to each other,
bend - Consistent with axis curvature.

There are more complex deformations that are formed by a combination of several main.

Linear deformation and are associated with the movement of points or sections along a straight line (stretching, compression).

Corner deformations associated with a relative turn of one section relative to the other (tapping).

Basic hypotheses and principles

Hypothesis about the solidity of the material : The body, solid and continuous to deformity, remains the same in the deformation process.

Hypothesis about homogeneity and isotropy : At any point of the body and in any direction, the physico-mechanical properties of the material are considered the same.

Hypothesis of deformation : Compared with the size of the deformation body, so small that they do not change the positions of the external forces acting on the body.

Hypothesis about perfect elasticity : At the given low limits of deformation, all the bodies are perfectly elastic, i.e. The deformations are completely disappearing after the cessation of loads.

Hypothesis of flat sections : The cross section is flat before deformation remains flat and after deformation.

The law of a bitter and hypothesis about the smallness of deformations make it possible to apply superposition principle (the principle of independence or addition of forces): body deformations caused by actions of several forces are equal to the amount of deformations caused by each force.

Saint-Vennic but : Statically equivalent to the systems forces acting on a small, compared to the total body sizes, its part, with a sufficient distance from this part cause the same body deformations.

The principle of hardening : The body, experiencing, has solidified and can be used to apply the static equations.

Domestic powers. Section method

Domestic powers - These are the forces of mechanical interaction between the particles of the material arising in the process of deformation as a material reaction to the external load.

To find and define internal forces apply section method (Rose), which comes down to the following operations:

conventionally cut the body into two parts by the secular plane (P-Rifle);
we discard one of the parts (o - discard);
replace the effect of the discarded part on the innermost (efforts) (s - replace);
from the equilibrium conditions of the system of forces acting on the remaining part, the internal forces are determined (y - equilibrium equations);

As a result of the cross-section cross section, the broken links between the parts are replaced by the internal forces, which can be reduced to the main vector R and the main point of the inner forces. When designing them on coordinate axis we obtain:
N - longitudinal (axial) force,
QY - transverse (re-release) power
Qz - transverse (re-release) power
MX - torque
My - bending moment
MZ - bending moment

If external forces are known, all six internal components can be found from equilibrium equations

Voltage

Normal voltages, tangent stresses. Full tension.

Determining the dependence between external forces, on the one hand, and voltage and deformation, on the other, - the main task of the resistance of materials .

Stretching and compression

Stretching or compression is often found in the elements of machines or structures (stretching the cable of the crane when lifting the cargo; engine connecting rod, stem cylinders in lifting vehicles).

Stretching or compression - This is the case of loading straightened, which is characterized by its elongation or shortening. Stretching or compression is caused by the forces acting along the axis of the straggle.

When stretching, the rod extends, and its transverse dimensions decrease. Changing the initial length of the straggle called Absolute lengthening When tensile or absolute shortening in compression. The ratio of absolute elongation (shortening) to the initial length of the straggle is called relative lengthening .

In this case:

the rod axis remains a straight line,
the cross sections of the rod decrease along its axis parallel to themselves (because the cross section is the plane perpendicular to the axis of the straggle, and the axis is a straight line);
cross sections remain flat.

All stroke fibers are lengthened on the same magnitude and their relative elongations are the same.

The difference between the corresponding transverse sizes after the deformation and before it is called absolute transverse deformation .

The ratio of absolute transverse deformation to the appropriate initial size is called relative transverse deformation .

There is a ratio between the transverse and longitudinal deformations. Poisson's ratio - a dimensionless value in the range of 0 ... 0.5 (for steel 0.3).

In transverse sections arise normal tensions i. The dependence of stresses from deformations establishes the law of the throat.

In cross section, the rod occurs one internal power factor - longitudinal power N . The longitudinal force N is the resultant normal stress, which is numerically equal to the algebraic sum of all external forces acting on one of the parts of the dissected straightened and directed along its axis.

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An example of calculating the strait of cylindrical transmission
An example of calculating the strait of cylindrical transmission. The choice of material, the calculation of the allowable stresses, the calculation on the contact and flexural strength.

Example Solving Beam Beam Tasks
In the example, the line of transverse forces and bending moments are built, a dangerous cross-section has been found and a mellover is selected. The task is analyzed by the construction of an EPUR using differential dependencies, a comparative analysis of various transverse sections of the beam was conducted.

Example Solving Task Task
The task is to check the strength of the steel shaft at a given diameter, material and allowable voltages. During the solution, the plots of torque, tangent stresses and spinning angles are being built. Own weight of the shaft is not taken into account

Example Solving Tensile Testing-Compression Rod
The task is to check the strength of the steel rod at given to the allowed voltages. During the solution, the supports of the longitudinal forces, normal stresses and movements are being built. Own weight rod is not taken into account

Application of the theorem on the preservation of kinetic energy
An example of solving the task of applying the theorem on the preservation of the kinetic energy of the mechanical system

Statistical Loads do not change over time or change very slowly. Under the action of statistical loads, it is calculated for strength.

Repeated variables Loads repeatedly change the value or value and sign. The effect of such loads causes metal fatigue.

Dynamicloads change their value in a short period of time, they cause greater acceleration and inertia forces and can lead to sudden destruction of the design.

From theoretical mechanics it is known that by the method of application loads can be focused or distributed on the surface.

Really, the transfer of the load between the parts is not at the point, but at some site, i.e. the load is distributed.

However, if the contact site is negligible compared with the size of the part, the force is considered concentrated.

When calculating the real deformable bodies in the resistance of materials, it should not be replaced by a distributed load.

Axioms of theoretical mechanics in the resistance of materials are used limited.

You can not tolerate a pair of forces to another point of the part, move the focused force along the line of the action, you can not replace the system to replace the resultant when determining movements. All of the above changes the distribution of domestic forces in the design.

In the process of construction and operation, the building is experiencing the action of various loads. External influences can be divided into two types: force and nonalovy or environmental impact.

TO silov The impacts include various types of loads:

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

temporary (long) - on the weight of stationary equipment, long-stored cargo, the own weight of the constant elements of the building (for example, partitions);

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

special - from seismic impacts, effects as a result of equipment accidents, etc.

TO nesilov relate:

temperature effectscausing changes in linear dimensions of materials and structures, which in turn to the occurrence of power influences, as well as affecting the thermal regime of the room;

impact of atmospheric and soil moisture, as well as vaporous moisturethe premises contained in the atmosphere and in the air, causing a change in the properties of materials from which the building structures are made;

air movement causing not only load (under wind), but also its penetration into the construction and premises, the change in their humidity and thermal regime;

impact of radiant energy Sun (solar radiation) caused by local heating a change in the physico-technical properties of surface layers of material, structures, a change in the light and thermal regime of the premises;

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

biological impactscaused by microorganisms or insects leading to the destruction of structures from organic building materials;

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

At the place of application effort load divided by focused (for example, the weight of the equipment) and uniform distributed (Own weight, snow).

By the nature of the workload can be static. permanent in time and dynamic (shock).

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

So The building has a variety of loads in terms of the size, direction, nature of the action and the place of the application.

Fig. 2.3. Load and exposure to the building.

There may be such a combination of loads, in which they all act in one direction, reinforcing each other. It is on such unfavorable combinations of loads that the building designs are calculated. The regulatory values \u200b\u200bof all efforts acting on the building are shown in DBN or SNiV.

5. Central-stretched steel elements: work scheme, application, strength calculation

Central stretched elements - These are elements, in the normal section of which point of application of longitudinal stretching N. Coincides with the point of the application of the equal effort in the longitudinal reinforcement.

The centrally stretched elements include arches, bottom belts and downlink farms and other elements (Fig. 51).

Centrally stretched elements are designed, as a rule, pre-tense.

Basic principles for the design of centrally stretched elements:

The rod working reinforcement without pre-stress is connected along the welding length;

The junctions of the messenger without welding are allowed only in slab and wall structures;

Stretched pre-stress fittings in linear elements should not have joints;

In cross section, the pre-stressed reinforcement is placed symmetrically (in order to avoid the extracentrate compression of the element);

Essentrenno-stretched elements - these are elements that are simultaneously stretched by the longitudinal force N. And bend moment M.that is equivalent to outcidentren stretching by force N. with eccentricity E O.relative to the longitudinal axis of the element. At the same time distinguish 2 cases: when the longitudinal stretching force N. It is applied between the resultant efforts in the stretched and compressed fittings, and the position is applied outside the distance.

Especially stretched elements include the lower belts of rigorous farms and other designs.

Permanent loads.(q.) Depending on the duration of the load, the load is divided into permanent and temporary. By permanent loads are the weight of carrier and enclosing structures of buildings and structures, weight and pressure of soils, the effects of pre-stress of reinforced concrete structures.

Temporary loads. Long load (P) . These include: the weight of stationary equipment at the floors - machines, devices, engines, tanks, etc.; Pressure of gases, liquids, bulk bodies in tanks; weight of specific content in warehouses, refrigerators, archives, libraries and similar buildings and structures; mounted part of the temporary load in residential buildings, in service and household premises; long temperature technological impacts from stationary equipment; Loads from one suspended or one bridge crane multiplied by coefficients: 0.5, 0.6... depending on the type of crane

Short-term load. (S) These include: the weight of people, parts, materials in the areas of service and repair of equipment - the passages and other areas free of equipment; part of the load on the overlap of residential and public buildings; loads arising from the manufacture, transportation and installation of structural elements; loads from suspended and bridge cranes used in the construction or operation of buildings and structures; Snow and wind loads; Temperature climatic effects.

Special loads. These include: seismic and explosive effects; loads caused by a malfunction or equipment breakdown and a sharp disruption of the process (for example, with a sharp increase or decrease in temperature, etc.); The impact of uneven deformations of the base, accompanied by a radical change in the structure of the soil (for example, the deformation of the sedentary soils during soaking or choresomerous soils during thawing), etc.

Regulatory loads. They are installed by norms or nominal values. Regulatory permanent loads are taken by the design values \u200b\u200bof geometric and structural parameters and on average density values. Regulatory temporary technological and installation loads are installed at the highest values \u200b\u200bprovided for normal operation; Snow and wind - on average of annual adverse values \u200b\u200bor by adverse values \u200b\u200bcorresponding to a specific average period of their repetitions.

Estimated load. Their values \u200b\u200bwhen calculating structures for strength and stability determine the multiplication of the regulatory load on the reliability coefficient by load γfusually more than a unit. Accurateness of reliability in the action of the weight of concrete and reinforced concrete structures γ f -1\u003e 1. The reliability factor in the action of the weight of the structures used in the calculation of the status of the position against ascent, overturning and slipping, as well as in other cases where the mass decreases deteriorates the working conditions of the design, adopted γ f \u003d 0.9. When calculating structures at the embodiment stage, the calculated short-term loads are multiplied by the coefficient of 0.8. When calculating structures on deformations and movements (according to the second group of limit states), the calculated loads take equal regulatory values \u200b\u200bwith the coefficient ΓT \u003d.1.

Combination of loads. The designs should be calculated on various combinations of loads or their corresponding efforts if the calculation is carried out according to the scheme of an inelastic state. Depending on the composition of the taken into account, the loads distinguish: main combinations,include constant, long and short-term loads or efforts from them; special combinations,including constant, long, possible short-term and one of the special loads or efforts from them.

In the main combinations, when taking into account at least two time loads, their calculated values \u200b\u200b(or their corresponding efforts) are multiplied by the coefficients of the combination of equal: for long-term loads F1 \u003d 0.95; For short-term F2 \u003d 0.9. When accounting for one time load F1 \u003d F2 \u003d L. Norms allowed when taking into account three and more short-term loads, their calculation values \u200b\u200bare multiplied by the coefficients of combinations: F 2 \u003d L- for the first to the degree of importance of short-term load; F 2 \u003d 0.8 - for the second; F2 \u003d 0.6 - for the rest.

In special combinations for long-term loads F1 \u003d 0.95, for short-term f 2 \u003d 0.8, except for cases specified in the designations of building and structures in seismic areas.

1.4. Depending on the duration of the validity of the load, constant and temporary (long, short-term, special) loads should be distinguished.

1.5. Loads arising from the manufacture, storage and transportation of structures, as well as in the construction of structures, should be taken into account in the calculations as short-term loads.

Loads arising at the stage of operation of structures should be considered in accordance with PP.1.6-1.9.

a) the weight of parts of structures, including the weight of carrier and enclosing building structures;

b) the weight and pressure of soils (embankments, backfills), mining pressure.

The pre-stress-strokes that persist in the design or base should be taken into account in the calculations as force from constant loads.

a) weight of temporary partitions, gravy and sweeping for equipment;

b) the weight of stationary equipment: machines, devices, motors, tanks, pipelines with reinforcement, supporting parts and insulation, belt conveyors, permanent lifting machines with their ropes and guides, as well as the weight of liquids and solids that fill equipment;

c) the pressure of gases, liquids and bulk bodies in containers and pipelines, excessive pressure and air loss that occurs when ventilation of mines;

d) load on overlapping from stored materials and shelving equipment in warehouses, refrigerators, granaries, books, archives and similar premises;

e) temperature technological impacts from stationary equipment;

e) the weight of the water layer on the water-filled plane coatings;

g) the weight of the sediments of production dust, if its accumulation is not excluded by the relevant activities;

h) loads from people, animals, equipment on overlapping residential, public and agricultural buildings with reduced regulatory values \u200b\u200bshown in Table. 3;

i) vertical loads from bridge and suspended cranes with a reduced regulatory value, determined by multiplying the full regulatory value of the vertical load from one crane (see clause 4.2) in each span of the building on the coefficient: 0.5 - for groups of modes of Cranes 4K-6K ; 0.6 - for a group of operation of cranes 7K; 0.7 - for a group of operation of the cranes 8k. Crane modes groups are accepted according to GOST 25546 - 82;

k) Snow loads with a reduced regulatory value defined by multiplying the complete regulatory value in accordance with the indications of clause 5.1 on the coefficient: 0.3 - for the III of the Snow Area: 0.5 - for the IV region; 0.6 - for V and VI areas;

l) Temperature climatic effects with reduced regulatory values \u200b\u200bdefined in accordance with the indications of PP. 8.2 - 8.6, provided \u003d
=
=
=
=0,
=
= 0;

m) the impact due to deformations of the base that are not accompanied by a fundamental change in the structure of the soil, as well as the thawing of the easers;

h) Impact due to changes in humidity, shrinkage and creep materials.

a) loads from equipment arising in pump-stop, transitional and test modes, as well as during its permutation or replacement;

b) the weight of people, repair materials in the maintenance and repair areas of the equipment;

c) loads from people, animals, equipment on overlapping residential, public and agricultural buildings with full regulatory values, except for the loads specified in paragraph 1.7, a, b, g, d;

d) load from mobile lifting and transport equipment (loaders, electrocarbers, stackers, telphers, as well as from bridge and suspended cranes with a full regulatory value);

e) snow loads with full regulatory value;

(e) Temperature climatic effects with full regulatory value;

g) wind loads;

h) ice-free loads.

a) seismic effects;

b) explosive effects;

c) loads caused by sharp impaired technological process, temporary malfunction or equipment breakdown;

d) the impact due to deformations of the base, accompanied by a fundamental change in the structure of the soil (when soaking by the sediments) or sedimentation in the areas of mine workings and in karst.