Permissible stresses

Table 2.4

Fig.2.22

Fig.2.18

Fig.2.17

Rice. 2.15

For tensile tests, tensile machines are used, which make it possible to record a diagram in the coordinates “load - absolute elongation” during the test. The nature of the tensile diagram depends on the properties of the material being tested and on the strain rate. A typical view of such a diagram for mild steel under static load application is shown in fig. 2.16.

Consider the characteristic sections and points of this diagram, as well as the corresponding stages of sample deformation:

OA - Hooke's law is valid;

AB - residual (plastic) deformations appeared;

BC - plastic deformations increase;

SD is the yield point (strain growth occurs at a constant load);

DK - hardening area (the material again acquires the ability to increase resistance to further deformation and perceives the force increasing to a certain limit);

Point K - the test was stopped and the sample was unloaded;

KN - unloading line;

NKL – sample reloading line (KL – hardening section);

LM is the section of the load drop, at the moment the so-called neck appears on the sample - local narrowing;

Point M - sample break;

After rupture, the sample has the form approximately shown in Fig. 2.17. The fragments can be folded and the length after the test ℓ 1 and the diameter of the neck d 1 can be measured.

As a result of processing the tensile diagram and measurements of the sample, we obtain a number of mechanical characteristics that can be divided into two groups - strength characteristics and plasticity characteristics.

Strength characteristics

Limit of proportionality:

The greatest stress up to which Hooke's law is valid.

Yield strength:

The smallest stress at which deformation of the sample occurs with a constant tensile force.

Tensile strength (tensile strength):

The highest voltage noted during the test.

Tension at break:

The stress at break determined in this way is very arbitrary and should not be used as a characteristic of the mechanical properties of steel. The convention is that it was obtained by dividing the force at the moment of rupture by the initial cross-sectional area of ​​the sample, and not by its actual area at rupture, which is much less than the initial one due to the formation of a neck.

Plasticity characteristics

Recall that plasticity is the ability of a material to deform without breaking. The characteristics of plasticity are deformation, therefore, they are determined according to the measurement data of the sample after destruction:

∆ℓ os \u003d ℓ 1 - ℓ 0 - residual elongation,

is the area of ​​the neck.

Relative elongation after break:

. (2.25)

This characteristic depends not only on the material, but also on the ratio of the dimensions of the sample. It is in connection with this that standard samples have a fixed ratio ℓ 0 = 5d 0 or ℓ 0 = 10d 0 and the value of δ is always given with an index - δ 5 or δ 10, and δ 5 > δ 10.

Relative contraction after break:

. (2.26)

Specific work of deformation:

where A is the work spent on the destruction of the sample; is found as the area bounded by the stretch diagram and the abscissa axis (figure area OABCDKLMR). The specific work of deformation characterizes the ability of a material to resist the impact of a load.

Of all the mechanical characteristics obtained during testing, the main strength characteristics are the yield strength σ t and the ultimate strength σ pc, and the main plasticity characteristics are the relative elongation δ and the relative narrowing ψ after rupture.

Unloading and reloading

When describing the tension diagram, it was indicated that at point K the test was stopped and the sample was unloaded. The unloading process was described by the straight line KN (Fig. 2.16), parallel to the straight section OA of the diagram. This means that the elongation of the sample ∆ℓ′ P, obtained before the start of unloading, does not completely disappear. The missing part of the elongation on the diagram is represented by the segment NQ, the remaining part is represented by the segment ON. Therefore, the total elongation of the sample beyond the elastic limit consists of two parts - elastic and residual (plastic):

∆ℓ′ P = ∆ℓ′ up + ∆ℓ′ os.

This will continue until the sample breaks. After rupture, the elastic component of the total elongation (segment ∆ℓ yn) disappears. The residual elongation is represented by the segment ∆ℓ os. If, however, the loading is stopped and the sample is unloaded within the OB section, then the unloading process will be depicted by a line coinciding with the load line - the deformation is purely elastic.

Upon repeated loading of the sample with length ℓ 0 + ∆ℓ′ os, the loading line practically coincides with the unloading line NK. The limit of proportionality increased and became equal to the voltage from which the unloading was performed. Further, straight line NK turned into curve KL without a yield plateau. The part of the diagram located to the left of the NK line turned out to be cut off, ᴛ.ᴇ. the origin of coordinates has moved to point N. Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, as a result of drawing beyond the yield strength, the sample changed its mechanical properties:

one). the limit of proportionality has increased;

2). the platform of fluidity has disappeared;

3). the relative elongation after the break has decreased.

This change in properties is called hard work.

Hardening increases the elastic properties and reduces the ductility. In some cases (for example, during mechanical processing), the hardening phenomenon is undesirable and it is eliminated by heat treatment. In other cases, it is created artificially to improve the elasticity of parts or structures (treatment with shot of springs or drawing cables of lifting machines).

Stress diagrams

To obtain a diagram characterizing the mechanical properties of the material, the primary tensile diagram in the P - ∆ℓ coordinates is rebuilt in the σ - ε coordinates. Since the ordinates σ \u003d P / F and the abscissas σ \u003d ∆ℓ / ℓ are obtained by dividing by constants, the diagram has the same form as the original one (Fig. 2.18, a).

From the diagram σ – ε it is seen that

ᴛ.ᴇ. the modulus of normal elasticity is equal to the tangent of the angle of inclination of the rectilinear section of the diagram to the abscissa axis.

It is convenient to determine the so-called conditional yield strength from the stress diagram. The fact is that most structural materials do not have a yield point - a straight line smoothly turns into a curve. In this case, the stress at which the relative residual elongation is equal to 0.2% is taken as the value of the yield strength (conditional). On fig. 2.18, b shows how the value of the conditional yield strength σ 0.2 is determined. The yield strength σ t, determined in the presence of a yield platform, is often called physical.

The descending section of the diagram is conditional, since the actual cross-sectional area of ​​the sample after the formation of the neck is much less than the initial area, according to which the coordinates of the diagram are determined. You can get the true stress if the magnitude of the force at each time P t is divided by the actual cross-sectional area at the same time F t:

On fig. 2.18, a, these voltages correspond to the dashed line. Up to the ultimate strength, S and σ practically coincide. At the moment of rupture, the true stress significantly exceeds both the tensile strength σ pch and even more so the stress at the moment of rupture σ r. We express the neck area F 1 through ψ and find S p.

Þ Þ .

For ductile steel ψ = 50 - 65%. If we take ψ = 50% = 0.5, then we get S р = 2σ р, ᴛ.ᴇ. the true stress is greatest at the moment of rupture, which is quite logical.

2.6.2. Compression test of various materials

The compression test provides less information about the properties of the material than the tensile test. Nevertheless, it is absolutely extremely important for characterizing the mechanical properties of the material. It is carried out on samples in the form of cylinders, the height of which is not more than 1.5 diameters, or on samples in the form of cubes.

Consider the compression diagrams of steel and cast iron. It is worth saying that for clarity, we will depict them in one figure with the tension diagrams of these materials (Fig. 2.19). In the first quarter - tension diagrams, and in the third - compression.

At the beginning of loading, the steel compression diagram is an inclined straight line with the same slope as in tension. Then the diagram passes into the yield region (the yield plateau is not as pronounced as in tension). Further, the curve slightly bends and does not break, because the steel sample is not destroyed, but only flattened. The modulus of elasticity of steel E in compression and tension is the same. The yield strength σ t + = σ t - is also the same. The compressive strength cannot be obtained, just as it is impossible to obtain plasticity characteristics.

The tensile and compression diagrams of cast iron are similar in shape: they curve from the very beginning and break off when the maximum load is reached. At the same time, cast iron works better in compression than in tension (σ pc - = 5 σ pc +). Tensile strength σ pch - ϶ᴛᴏ is the only mechanical characteristic of cast iron obtained during a compression test.

The friction that occurs during the test between the plates of the machine and the ends of the sample has a significant effect on the results of the test and on the nature of the destruction. A cylindrical steel sample takes on a barrel shape (Fig. 2.20, a), cracks appear in the cast-iron cube at an angle of 45 0 to the direction of the load. If the influence of friction is excluded by lubricating the ends of the sample with paraffin, cracks will appear in the direction of the load and the greatest force will be less (Fig. 2.20, b and c). Most brittle materials (concrete, stone) collapse under compression similarly to cast iron and have a similar compression pattern.

Of interest is the test of wood - anisotropic, ᴛ.ᴇ. having different strength based on the direction of force in relation to the direction of the fibers, the material. The more widely used glass-reinforced plastics are also anisotropic. When compressed along the fibers, the wood is much stronger than when compressed across the fibers (curves 1 and 2 in Fig. 2.21). Curve 1 is similar to the compression curves of brittle materials. The destruction occurs due to the shift of one part of the cube relative to the other (Fig. 2.20, d). When compressed across the fibers, the wood does not collapse, but is pressed (Fig. 2.20, e).

When testing a steel sample in tension, we found a change in mechanical properties as a result of drawing to the appearance of noticeable residual deformations - hardening. Let's see how the sample behaves after hardening during a compression test. Figure 2.19 shows the diagram as a dotted line. Compression proceeds along the curve NC 2 L 2 , which is located above the compression diagram of the sample not subjected to hardening OC 1 L 1 , and almost parallel to the latter. After hardening by tension, the limits of proportionality and fluidity under compression decrease. This phenomenon is called the Bauschinger effect after the scientist who first described it.

2.6.3. Determination of hardness

A very common mechanical and technological test is the determination of hardness. This is due to the speed and simplicity of such tests and the value of the information obtained: hardness characterizes the state of the surface of the part before and after technological processing (hardening, nitriding, etc.), it can be used to indirectly judge the magnitude of the tensile strength.

material hardness It is customary to call the ability to resist the mechanical penetration of another, more solid body into it. The values ​​characterizing hardness are called hardness numbers. Determined by different methods, they are different in size and dimension and are always accompanied by an indication of the method of their determination.

The most common method is according to Brinell. The test essentially consists in the fact that a hardened steel ball of diameter D is pressed into the sample (Fig. 2.22, a). The ball is kept for some time under load P, due to which an imprint (hole) with a diameter d remains on the surface. The ratio of the load in kN to the surface area of ​​the imprint in cm 2 is commonly called the Brinell hardness number

. (2.30)

To determine the Brinell hardness number, special test devices are used, the indentation diameter is measured with a portable microscope. Usually HB is not calculated according to the formula (2.30), but is found from the tables.

Using the hardness number HB, it is possible to obtain an approximate value of the tensile strength of some metals without destroying the sample, since there is a linear relationship between σ st and HB: σ st = k ∙ HB (for mild steel k = 0.36, for high-strength steel k = 0.33, for cast iron k = 0.15, for aluminum alloys k = 0 .38, for titanium alloys k = 0.3).

A very convenient and widespread method for determining hardness according to Rockwell. This method uses a 120 degree apex angle diamond cone with a 0.2 mm radius or a 1/16 inch (1.5875 mm) diameter steel ball as the indenter to be pressed into the sample. The test takes place according to the scheme shown in Fig. 2.22b. First, the cone is pressed in with a preload P 0 = 100 H, which is not removed until the end of the test. With this load, the cone plunges to a depth h 0 . Further, the full load P = P 0 + P 1 is applied to the cone (two options: A - P 1 = 500 H and C - P 1 = 1400 H), while the indentation depth increases. After removing the main load P 1 remains the depth h 1 . The imprint depth obtained due to the main load P 1, equal to h \u003d h 1 - h 0, characterizes the Rockwell hardness. The hardness number is determined by the formula

, (2.31)

where 0.002 is the scale division value of the hardness tester indicator.

There are other methods for determining hardness (according to Vickers, according to Shore, microhardness), which are not considered here.

2.6.4. Comparison of properties of different materials

All steels shown in the figure -40, St6, 25KhNVA, manganese - have much higher strength characteristics than low-carbon steel St3. High-strength steels have no yield point, elongation at break δ is much smaller. For the increase in strength, one has to pay with a decrease in ductility. Aluminum and titanium alloys have good ductility. At the same time, the strength of the aluminum alloy is higher than that of St3, and the volumetric weight is almost three times less. A titanium alloy has strength at the level of high-strength alloy steel with almost half the volumetric weight. Table 2.4 shows the mechanical characteristics of some modern materials.

The last two lines of the table show the characteristics of polymer composite materials, which are characterized by low weight and high strength. Composites based on superstrong carbon fibers are distinguished by particularly outstanding properties - their strength is approximately two times higher than the strength of the best alloy steel and an order of magnitude higher than low-carbon steel. Οʜᴎ steel is one and a half times stiffer and almost five times lighter. They are used, of course, in military technology - aircraft and rocket manufacturing. In recent years, they have also begun to be used in civilian areas - automotive industry (bodies, brake discs, exhaust pipes of racing and expensive sports cars), shipbuilding (hulls of boats and small boats), medicine (wheelchairs, parts of prostheses), mechanical engineering for sports ( frames and wheels of racing bicycles and other sports equipment). The widespread use of this material is still hindered by its high cost and low manufacturability.

Summarizing all the above about the mechanical properties of various materials, we can formulate the main features of the properties of ductile and brittle materials.

1. Brittle materials, in contrast to ductile ones, are destroyed with minor residual deformations.

2. Plastic materials equally resist stretching and compression, brittle materials - good compression and bad stretching.

3. Plastic materials resist shock loads well, brittle materials - poorly.

4. Fragile materials are very sensitive to the so-called stress concentration(local bursts of stresses near places of a sharp change in the shape of parts). The stress concentration affects the strength of parts made of plastic material to a much lesser extent. More on this below.

5. Brittle materials are not amenable to technological processing associated with plastic deformation - stamping, forging, drawing, etc.

The division of materials into ductile and brittle is conditional, since under certain conditions, brittle materials acquire plastic properties (for example, with high all-round compression) and, on the contrary, ductile materials acquire brittle properties (for example, mild steel at low temperature). For this reason, it is more correct to speak not about plastic and brittle materials, but about their plastic and brittle fracture.

As already mentioned, parts of machines and other structures must satisfy the conditions of strength (2.3) and rigidity (2.13). The value of allowable stresses is set based on the material (its mechanical characteristics), the type of deformation, the nature of the action of loads, the operating conditions of structures and the severity of the consequences that may occur in case of destruction:

n – safety factor, n > 1.

For parts made of plastic material, the dangerous state is characterized by the appearance of large residual deformations, in connection with this, the dangerous stress is equal to the yield strength σ op = σ t.

For parts made of brittle material, the dangerous state is characterized by the appearance of cracks, in connection with this, the dangerous stress is equal to the ultimate strength σ op = σ pc.

All the above operating conditions of the parts are taken into account by the safety factor. Under all conditions, there are some general factors that are taken into account by the safety factor:

1. Heterogeneity of the material, therefore, the spread of mechanical characteristics;

2. Inaccuracy in setting the values ​​and nature of external loads;

3. Approximation of calculation schemes and calculation methods.

Based on the data of a long practice in the design, calculation and operation of machines and structures, the value of the safety factor for steel is assumed to be 1.4 - 1.6. For brittle materials under static load, a safety margin of 2.5 - 3.0 is taken. So, for plastic materials:

. (2.33)

For brittle materials

. (2.34)

When comparing the properties of ductile and brittle materials, it was noted that the stress concentration affects the strength. Theoretical and experimental studies have shown that the uniform distribution of stresses over the cross-sectional area of ​​a stretched (compressed) rod in accordance with formula (2.2) is violated near places of a sharp change in the shape and size of the cross-section - holes, fillets, fillets, etc.
Hosted on ref.rf
Near these places, local bursts of stress occur - stress concentration.

As an example, consider the stress concentration in a stretchable strip with a small hole. The hole is considered small if the condition d ≤ 1/5b is met (Fig. 2.27, a). In the presence of concentration, the voltage is determined by the formula:

σ max = α σ ∙ σ nom . (2.35)

where α σ is the stress concentration factor determined by the methods of the theory of elasticity or experimentally on models;

σ nom – rated voltage, ᴛ.ᴇ. stress calculated for this part in the absence of stress concentration.

For the case under consideration (α σ = 3 and σ nom = N/F), this problem is, in a certain sense, the classical problem of stress concentration and is usually called the Kirsch problem by the name of the scientist who solved it at the end of the 19th century.

Consider how the strip with the hole will behave as the load increases. In a plastic material, the maximum stress at the hole will become equal to the yield strength (Fig. 2.27, b). The stress concentration always decays very quickly; therefore, even at a small distance from the hole, the stress is much less. Let's increase the load (Fig. 2.27, c): the voltage at the hole does not increase, because A plastic material has a fairly extended yield point; already at some distance from the hole, the stress becomes equal to the yield point.

Permissible stresses - concept and types. Classification and features of the category "Permissible stresses" 2017, 2018.

To assess the strength of structural elements, the concepts of working (design) stresses, limiting stresses, allowable stresses and safety margins are introduced. They are calculated according to the dependencies presented in paragraphs 4.2, 4.3.

Operating (calculated) voltages  and  characterize the stress state of structural elements under the action of operational load.

Limit stresses  lim and  lim characterize the mechanical properties of the material and are dangerous for the structural element in terms of its strength.

Permissible stresses [  ] and [  ] are safe and ensure the strength of the structural element in these operating conditions.

Margin of safety n establishes the ratio of limit and allowable stresses, taking into account the negative impact on the strength of various unaccounted factors.

For the safe operation of mechanism parts, it is necessary that the maximum stresses arising in loaded sections do not exceed the value allowed for a given material:

;
,

where
and
- the highest stresses (normal  and tangential ) in the dangerous section;
and are the allowable values ​​of these stresses.

With complex resistance, equivalent voltages are determined
in a dangerous section. The strength condition has the form

.

Permissible stresses are determined depending on the limiting stresses  lim and  lim obtained during testing of materials: under static loads - tensile strength
and τ AT for brittle materials, yield strength
and τ T for plastic materials; under cyclic loads - endurance limit and τ r :

;
.

safety factor are appointed based on the experience of designing and operating similar structures.

For parts of machines and mechanisms operating under cyclic loads and having a limited service life, the allowable stresses are calculated according to the following dependencies:

;
,

where
- the coefficient of durability, taking into account the specified service life.

Calculate the coefficient of durability according to the dependence

,

where
– basic number of test cycles for a given material and type of deformation;
- the number of loading cycles of the part corresponding to the specified service life; m - an indicator of the degree of the endurance curve.

When designing structural elements, two methods of strength calculations are used:

design calculation for allowable stresses to determine the main dimensions of the structure;

verification calculation to assess the performance of the existing structure.

5.5. Calculation examples

5.5.1. Calculation of stepped bars for static strength

R

For each of the presented schemes, we determine:

1. Type of deformation:

cx. 1 - stretching; cx. 2 - torsion; cx. 3 - pure bend.

2. Internal force factor:

cx. 1 - normal force

N = 2F = 2800 = 1600 H;

cx. 2 – torque M X = T = 2Fh = 280010 = 16000 N mm;

cx. 3 – bending moment M = 2Fh = 280010 = 16000 N mm.

3. Type of stresses and their magnitude in sections A and B:

cx. 1 - normal
:

MPa;

MPa;

cx. 2 - tangents
:

MPa;

MPa;

cx. 3 - normal
:

MPa;

MPa.

4. Which of the stress diagrams corresponds to each loading scheme:

cx. 1 - ep. 3; cx. 2 - ep. 2; cx. 3 - ep. one.

5. Fulfillment of the strength condition:

cx. 1 – the condition is met:
MPa
MPa;

cx. 2 - the condition is not met:
MPa
MPa;

cx. 3 - the condition is not met:
MPa
MPa.

6. The minimum allowable diameter that ensures the fulfillment of the strength condition:

cx. 2:
mm;

cx. 3:
mm.

7. Maximum allowable forceFfrom the strength condition:

cx. 2:
H;

cx. 3:
N.

The calculation for strength and stiffness is carried out by two methods: allowable stresses, deformations and the method of permissible loads.

Voltage, at which a sample of a given material is destroyed or at which significant plastic deformations develop, are called marginal. These stresses depend on the properties of the material and the type of deformation.

Voltage, the value of which is regulated by technical specifications, is called permitted.

Allowable voltage- this is the highest stress at which the required strength, rigidity and durability of a structural element is ensured under the specified conditions of its operation.

The allowable stress is a fraction of the limit stress:

where is the standard safety factor, a number showing how many times the allowable stress is less than the limit.

For plastic materials the allowable stress is chosen so that under any inaccuracies in the calculation or unforeseen operating conditions, no residual deformations occur in the material, i.e. (yield strength):

where - safety factor in relation to .

For brittle materials, allowable stresses are assigned from the condition that the material does not collapse, i.e. (ultimate strength):

where - safety factor in relation to .

In mechanical engineering (under static loading), safety factors are taken: for plastic materials =1,4 – 1,8 ; for the fragile =2,5 – 3,0 .

Strength calculation for allowable stresses is based on the fact that the highest design stress in the dangerous section of the bar structure does not exceed the allowable value (less than - no more than 10%, more - no more than 5%):

Rigidity rating bar structure is carried out on the basis of checking the condition of tensile stiffness:

The value of the permissible absolute deformation [∆l] assigned separately for each design.

Permissible load method is that the internal forces arising in the most dangerous section of the structure during operation should not exceed the permissible load values:

, (2.23)

where is the breaking load obtained as a result of calculations or experiments, taking into account the experience of manufacturing and operation;

- safety factor.

In what follows, we will use the method of allowable stresses and strains.

2.6. Verification and design calculations

for strength and rigidity

The strength condition (2.21) makes it possible to carry out three types of calculations:

– verification- according to the known dimensions and material of the rod element (the cross-sectional area is given BUT and [σ] ) to check if it is able to withstand the given load ( N):

; (2.24)

– design– by known loads ( N- given) and the material of the element, i.e., according to the known [σ], select the required cross-sectional dimensions to ensure its safe operation:

– determination of permissible external load- according to known dimensions ( BUT- given) and the material of the structural element, i.e., according to the known [σ], find the allowable external load:

Rigidity rating bar structure is carried out on the basis of checking the stiffness condition (2.22) and formula (2.10) in tension:

. (2.27)

The value of the allowed absolute deformation [∆ l] is assigned separately for each construct.

Similar to the strength condition calculations, the stiffness condition also involves three types of calculations:

– hardness test a given structural element, i.e. checking the fulfillment of condition (2.22);

– calculation of the designed bar, i.e. selection of its cross section:

– health setting of a given bar, i.e. the determination of the allowable load:

. (2.29)

Strength analysis any design contains the following main steps:

1. Determination of all external forces and reaction forces of supports.

2. Construction of graphs (diagrams) of force factors acting in cross sections along the length of the rod.

3. Construction of graphs (epures) of stresses along the axis of the structure, finding the maximum stress. Checking the strength conditions in places of maximum stress values.

4. Construction of a graph (epure) of the deformation of the bar structure, finding the deformation maxima. Checking stiffness conditions in sections.

Solution. For determining N, using the ROSE method, mentally cut the rod in sections I−I and II−II. From the condition of equilibrium of the part of the rod below the section I−I (Fig. 9.b) we get (stretch). From the equilibrium condition of the rod below the section II−II (Fig. 9c) we get

from where (compression). Having chosen the scale, we build a diagram of longitudinal forces ( rice. 9g). In this case, the tensile force is considered positive, and the compressive force is negative.

The stresses are equal: in the sections of the lower part of the rod ( rice. 9b)

(stretching);

in sections of the upper part of the rod

(compression).

On the selected scale, we plot the stress diagram ( rice. 9d).

To build a diagram δ determine the displacement of characteristic sections B−B and S−S(moving section A−A equals zero).

cross section B−B will move up as the top shrinks:

The displacement of the section caused by tension is considered positive, caused by compression - negative.

Moving a section S−S is the algebraic sum of the displacements B−B (δ V) and elongation of a part of the rod with a length l1:

On a certain scale, we set aside the values ​​and , connect the obtained points with straight lines, since under the action of concentrated external forces, the displacements linearly depend on the abscissa of the rod sections, and we obtain a graph (epure) of displacements ( rice. 9e). It can be seen from the diagram that some section D–D does not move. Sections located above the section D–D, move up (the rod is compressed); sections located below are moved down (the bar is stretched).

Questions for self-control

1. How are the values ​​of the longitudinal force in the cross sections of the bar calculated?

2. What is a diagram of longitudinal forces and how is it built?

3. How are the normal stresses distributed in the cross sections of a centrally stretched (compressed) rod and what are they equal to?

4. How is a diagram of normal tensile (compressive) stresses plotted?

5. What is called absolute and relative longitudinal deformation? Their dimensions?

6. What is called cross-sectional stiffness in tension (compression)?

8. How is Hooke's law formulated?

9. Absolute and relative transverse deformations of the rod. Poisson's ratio.

10. What is called the allowable voltage? How is it chosen for ductile and brittle materials?

11. What is called the safety factor and on what main factors does its value depend?

12. What are the mechanical characteristics of the strength and plasticity of structural materials.