Classification external loads, acting on structural elements.
General classification structural elements.
Technical objects and structures consist of individual parts and elements that vary widely in shape, size, and other parameters and characteristics. From the standpoint of engineering calculations, it is customary to distinguish four main groups of structural elements: rods, plates, shells, and arrays.
Rods– these are straight or curved structural elements in which one dimension (length) significantly exceeds two other dimensions (in a spatial orthogonal coordinate system), see Figure 20. Examples of structural elements such as rods: legs of a chair or table, column of a building structure, lifting rope cars, car gearbox shift lever, etc.
Z Curved rod
Straight rod
Figure 20. Diagrams of structural elements of the rod type
t (plate thickness)
Figure 21. Diagram of a plate type design element
Figure 22. Diagram of a shell type structural element (cylindrical)
Rice. 23. Diagram of an array type structural element
Plates- these are flat structural elements in which one size (thickness) is significantly smaller than the other two. Examples of plates: table top; walls and ceilings of buildings, etc., see Figure 21, from which it is clear that the thickness of the plate is significantly less than its two dimensions in plan.
Shells– these are not flat thin-walled elements structures in which one size (wall thickness) is significantly smaller than other sizes. Examples of casings: pipelines for transporting liquid and gaseous products (cylindrical casings); cylindrical, spherical or combined containers for liquids; conical bins for bulk materials; non-flat coatings of various structures, etc., see Figure 22, which shows a cylindrical shell (thin-walled cylindrical pipe), in which the wall thickness is significantly less than its diameter and length.
Arrays- these are structural elements in which all three sizes are comparable. Examples of arrays: foundation blocks machines, machines and building structures; massive bridge supports, etc., see Figure 23.
In the courses “Engineering Mechanics” and “Strength of Materials” greatest attention is devoted to the fundamental study of structural elements such as rods. Plates, shells, and arrays are studied in advanced Strength of Materials and specialty courses.
Concentrated Forces- these are forces applied to a structural element on its surface area, the dimensions of which, compared to the dimensions of the entire surface of the structural element, can be neglected. As a rule, concentrated forces are the result of the influence of another body (in particular, another structural element) on a given body (structural element). In many practically important cases, concentrated
forces can be considered applied to a structural element at a point without noticeable damage to the accuracy of engineering calculations. Units of measurement of concentrated forces N (Newton), kN (kilonewton), etc.
Volume forces- these are forces applied throughout the entire volume of a structural element, for example distributed gravity forces. Units of measurement of distributed volumetric forces N/m 3, kN/m 3, etc. The total force of gravity (N, kN) of a structural element is often conventionally taken into account in calculations as a concentrated force applied at a point called its center of gravity.
Distributed forces (loads)- these are forces applied to a part of the area (or length) of a deformable body, commensurate with the dimensions of the entire body. There are superficially distributed forces (loads), the units of measurement of which are N/m 2, kN/m 2, etc. (for example, distributed snow loads on building roofs), as well as linearly distributed loads (along the length of structural elements), the units of measurement of which are N/m, kN/m, etc. (for example, distributed pressure forces of slabs supported on beams of building structures).
Static forces (loads)– these are forces (loads) that do not change (or insignificantly change) their value, position and direction of action during the operation of the structure.
Dynamic forces (loads)– these are forces (loads) that significantly change their value, position and/or direction in short periods of time and cause vibrations of the structure.
Rated loads– these are the normal maximum loads that arise during the operation of the structure.
1) What is studied in the Strength of Materials course? What is its significance for highly skilled technical professionals?
2) What are external loads and internal forces?
3) Explain the concepts of deformation, strength, stiffness and stability.
4) Explain the concepts of homogeneity, continuity, isotropy and anisotropy.
5) Give a classification of structural elements.
6) Give a classification of external loads acting on structural elements.
1. Alexandrov A.V. and others. Strength of materials. Textbook for universities - M.: Higher. school, 2001. – 560 p. (p. 5...20).
2. Stepin P.A. Strength of materials. – M.: Higher. school, 1983. – 303 p. (p. 5...20).
3. Handbook on strength of materials/Pisarenko G.S. and others - Kyiv: Naukova Dumka, 1988. - 737 p. (p. 5...9).
Test tasks for SRS– with the help of educational literature, expand information on the following issues:
1) what are elastic forces?
2) what is the essence of the principle of the absence of initial internal efforts in the body (p. 9-10)?
3) what are the principles for schematizing external loads acting on structural elements used in engineering calculations (p. 8-11)?
4) explain the principle of independence of the action of forces (, pp. 18-20; , p. 10)?
5) explain the principle of Saint-Venant (, pp. 10-11);
6) what is the difference between deformation and displacement (, pp. 17-18; , pp. 13-14)?;
7) general concept about the method of sections (, pp. 13-16;, pp. 14-17);
8) the general concept of stresses in a deformable body, designations of normal and tangential stresses (, pp. 13-15;, pp. 17-20).
9) classification of external loads acting on structural elements (see clause 5.3).
Lecture 6. Topic 6. “Central tension-compression of straight rigid rods”
Purpose of the lecture– outline introductory provisions on the topic, the essence and application of the section method for determining internal forces in rods under central tension-compression; give basic concepts about diagrams of internal efforts.
Impacts experienced by the stand from the hand bent (see Fig. 42), the board from the load (see Fig. 44), the cylindrical rod of the bolt when screwing the nut wrench(see Fig. 45), etc., represent external forces or loads. The forces arising in the places where the rack is secured and the board is supported are called reactions.
Rice. 42
Rice. 44
Rice. 45
According to the method of application, loads are divided into concentrated and distributed (Fig. 49).
Types and classification of loads:
Concentrated loads transmit their effect through very small areas. Examples of such loads are the pressure of the wheels of a railway car on the rails, the pressure of a hoist trolley on a monorail, etc.
Distributed Loads operate over a relatively large area. For example, the weight of the machine is transmitted through the frame to the entire area of contact with the foundation.
Based on the duration of action, it is customary to distinguish between constant and variable loads. An example of a constant load is the pressure of a plain bearing - the support of shafts and axles - and its own weight on the bracket.
Variable load It is mainly the parts of periodic action mechanisms that are affected. One such mechanism is a gear transmission, in which the teeth are in the contact zone of adjacent pairs gear wheels experience variable load.
By the nature of the action loads may be static And dynamic. Static loads remain almost unchanged during the entire operation of the structure (for example, the pressure of trusses on supports).
Dynamic loads and last for a short time. Their occurrence is associated in most cases with the presence of significant accelerations and inertial forces.
Dynamic loads are experienced by parts of impact machines, such as presses, hammers, etc. Parts of crank mechanisms also experience significant dynamic loads during operation from changes in the magnitude and direction of speeds, that is, the presence of accelerations.
1.2. Classification of 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 the truss rods of an overhead crane (Fig. 1.9), the main loads are the gravity of the load being lifted 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 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 the 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 dimensions. 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, hull elements of ships, 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.
With the limit state technique, all loads are classified depending on the likelihood of their impact on regulatory and calculation.
Based on the impact of the load, they are divided into permanent and temporary. The latter can have long-term or short-term effects.
In addition, there are loads that are classified as special loads and impacts.
Constant loads– own weight of load-bearing and enclosing structures, soil pressure, prestress.
Temporary long-term loads– weight of stationary technological equipment, weight of stored materials in storage facilities, pressure of gases, liquids and bulk materials in containers, etc.
Short-term loads– standard loads from snow, wind, moving lifting and transport equipment, mass of people, animals, etc.
Special loads– seismic impacts, explosive impacts. Loads arising during the installation of structures. Loads associated with the breakdown of technological equipment, impacts associated with deformations of the base due to changes in the structure of the soil (subsidence soils, settlement of soils in karst areas and above underground workings).
There is sometimes the term “payload”. Useful are called loads, the perception of which constitutes the entire purpose of structures, for example, the weight of people for a pedestrian bridge. They can be both temporary and permanent, for example, the weight of a monumental exhibition structure is a constant load on the pedestal. For the foundation, the weight of all overlying structures also represents the payload.
When several types of loads act on a structure, the forces in it are determined as in the most unfavorable combinations using combination coefficients.
SNiP 2.01.07-85 “Loads and impacts” distinguishes:
basic combinations, consisting of permanent and temporary loads;
special combinations, consisting of permanent, temporary and one of the special loads.
For the main combination, which includes one temporary load, the combination coefficient is . With a larger number of temporary loads, the latter are multiplied by the combination factor.
In special combinations, live loads are taken into account with the combination coefficient, and the special load - with the coefficient. In all types of combinations, the constant load has a coefficient.
loaded elements
Taking into account complex stress states in calculations metal structures is carried out through the calculated resistance, which is established on the basis of testing metal samples under uniaxial loading. However, in real structures, the material, as a rule, is in a complex multicomponent stress state. In this regard, it is necessary to establish a rule for the equivalence of a complex stress state to a uniaxial one.
As an equivalence criterion, it is customary to use the potential energy accumulated in the material when it is deformed by external influences.
For convenience of analysis, the deformation energy can be represented as the sum of work on changing the volume A o and changing the shape of the body A f. The first does not exceed 13% full work during elastic deformation and depends on the average normal stress.
1 - 2υ
A o = ----------(Ơ Χ + Ơ У + Ơ Ζ) 2(2.3.)
The second work is related to shifts in the material:
A f = -------[(Ơ Χ 2 +Ơ Υ 2 + Ơ z 2 -(Ơ x Ơ y +Ơ y Ơ z +Ơ z Ơ x) + 3 (τ xy 2 +τ yz 2 + τ zx 2)] (2.4.)
It is known that the destruction of the crystalline structure of building steels and aluminum alloys is associated with shear phenomena in the material (movement of dislocations, etc.).
The work of shape change (2.4.) is an invariant, therefore, in a uniaxial stress state Ơ = Ơ we have A 1 = [(1 + ) / 3E ] Ơ 2
Equating this value to expression (2.4) and extracting Square root, we get:
Ơ pr = =Ơ(2.5)
This relationship establishes the energy equivalence of a complex stress state to a uniaxial one. The expression on the right side is sometimes called reduced voltage Ơ pr, meaning reduction to some state with uniaxial stress Ơ .
If extremely permissible voltage in metal (design resistance) is determined by the yield strength standard sample ƠT, then expression (2.5) takes the form Ơ pr = Ơ T and represents the condition of plasticity under a complex stress state, i.e. condition for the transition of a material from an elastic state to a plastic one.
In the walls I-beams near application of lateral load
Ơ x 0 . Ơ y 0 . τ xy 0. the remaining stress components can be neglected. Then the plasticity condition takes the form
Ơ pr = = Ơ T (2.6)
At points remote from the place where the load is applied, local stress can also be neglected Ơy = 0, then the plasticity condition will be further simplified: Ơ pr = = Ơ T .
With simple shear, of all stress components only
τ xy 0. Then Ơ pr = = Ơ T. From here
τ xy = Ơ T / = 0.58 Ơ T (2.7)
In accordance with this expression, SNiP adopted the relationship between the calculated shear and tensile strengths,
where is the design shear resistance; - yield strength.
The behavior under load of a centrally stretched element and a centrally compressed one, provided its stability is ensured, fully corresponds to the work of the material under simple tension-compression (Fig. 1.1, b).
It is assumed that the stresses in the cross section of these elements are distributed evenly. To ensure the load-bearing capacity of such elements, it is necessary that the stresses from the design loads in the section with smallest area did not exceed the design resistance.
Then the inequality of the first limit state (2.2) will be
Where - longitudinal force in elements; - net area cross section element; - design resistance, taken equal to , if the development of plastic deformations in the element is not allowed; if plastic deformations are permissible, then it is equal to the largest of the two values and (here and are the calculated resistances of the material in terms of yield strength and temporary resistance, respectively); - reliability coefficient for the material when calculating the structure based on temporary resistance; - coefficient of working conditions.
Checking for the second limit state comes down to limiting the elongation (shortening) of the rod from standard loads
N n l / (E A) ∆ (2.9)
where is the longitudinal force in the rod due to standard loads; - design length of the rod, equal to the distance between the points of application of the load to the rod; - elastic modulus; - gross cross-sectional area of the rod; - maximum elongation (shortening) value.
Basic concepts of technical mechanics
Modern production, defined by high mechanization and automation, offers the use large quantity various machines, mechanisms, instruments and other devices . The design, manufacture, and operation of machines is impossible without knowledge in the field of mechanics.
Technical mechanics– a discipline that includes the basic mechanical disciplines: theoretical mechanics, strength of materials, theory of machines and mechanisms, machine parts and design fundamentals.
The main tasks in technology are to ensure strength, rigidity, sustainability engineering structures, machine parts and devices.
Resistance of materials is a science that studies the principles and methods of calculating strength, stiffness and stability.
Strength is the ability of a structure to withstand external loads within certain limits without destruction.
Rigidity- this is the ability of a structure, within certain limits, to perceive the action of external loads without changing geometric dimensions(without being deformed).
Sustainability- this is the ability of a structure to maintain its shape and balance in a loaded state, as well as to independently restore its original state after it has been given some deviation from the equilibrium state.
In addition to the above requirements, the design must be economical, its weight and dimensions must be minimal. To do this, it must have a rational shape and size.
Load classification
There are external and internal forces and moments of forces.
By external forces(P) are the forces acting on points (bodies) of a given system from material points (bodies) that do not belong to this system. External forces (load) are active forces and coupling reactions.
By internal forces(Q) are called the forces of interaction between points (bodies) of a given system. They operate even in the absence of external loads. When external forces act on a body, additional internal forces accompanying deformation. These forces resist the tendency of external forces to change the shape of the body or separate one part from another. We will only study additional internal forces.
According to the method of application, loads are divided into:
1) volumetric– distributed throughout the volume of the body and applied to each of its particles (its own weight of the structure, magnetic interaction forces);
2) superficial– applied to areas of the surface and characterizing the direct contact interaction of the object with surrounding bodies:
A) concentrated(P 1) – loads acting on a platform whose dimensions are small compared to the dimensions of the structural element itself (pressure of the wheel rim on the rail);
b) distributed(P2)– loads acting along a platform (or length), the dimensions of which are not small compared to the dimensions of the structural element itself (tractor tracks press on the bridge beam).
Distributed loads are characterized by intensity q [N/m] or [ N/m 2]. If q – intensity of load distributed along an element of length a, That
If q – const, it can be taken out of the integral sign, then we get:
P2 = q ∙ a.
Loads can be permanent or temporary. Permanent operate always or for a sufficiently long time (for example, the dead weight of the structure). Temporary act episodically (for example, wind pressure).
According to the nature of the load, they are divided into:
1.static– is applied slowly, increasing from zero to the final value, and does not change;
2.dynamic– change magnitude or direction in a short period of time and are accompanied by the appearance of accelerations of structural elements. These include:
A) sudden loads – act immediately at full force (wheel of a locomotive driving onto a bridge) ,
b) drums loads – act for a short time (diesel hammer),
V) cyclical loads – act periodically (load on the teeth of a gear).