# strength

Physical size
Surname strength
Formula symbol mostly ${\ displaystyle f}$
Size and
unit system
unit dimension
SI Pa  = N / m 2 = kg · m -1 · s -2 M · L −1 · T −2
cgs Ba = dyn / cm 2 = cm −1 g s −2

The strength of a material describes the ability to withstand mechanical loads before failure occurs and is specified as mechanical stress (force per cross-sectional area). The failure can be an impermissible deformation , in particular a plastic (permanent) deformation or a break .

The strength depends on:

• the material ,
• the temporal course of the load (constant, changing, swelling) and
• the type of stress (tension, compression, bending, shear).

Depends the failure of several Zugspannungskomponenten from, it may prove useful to have a reference voltage to form.

Materials with high strength can be subjected to higher stresses than materials with low strength. The former are therefore generally suitable for lightweight construction , especially materials with a high specific strength (strength per density). However, high-strength materials are generally more difficult to machine. For favorable formability (machinability by forging and similar processes) and machinability (machinability by milling, drilling, and others), a low strength is generally considered to be desirable. Pure metals usually have a lower strength than alloys .

A number of similar characteristics must be distinguished from strength: stiffness describes the relationship between elongation and mechanical stress , while the hardness of a material describes its resistance to penetrating bodies. The toughness is a measure of the ability of a material deformation energy record (plastic) without breaking. The material properties partly depend on one another (see for example hardness and strength ).

## Types of strengths

One differentiates:

wherein a certain amount of elastic expansion or plastic deformation of the test specimen can be specified or be associated with it.

## Yield point

If the strains on a component are measured as a function of the different forces applied, measurement curves are obtained from which the technically relevant strength parameters can be determined and stress-strain diagrams can be created. The tensile strength curves from the uniaxial tensile test are considered to be particularly important in this context . Different strengths can be achieved depending on the type of material, material condition, temperature, loading and loading speed.

A distinction is made between the terms when a force is applied

• strength
• Formula symbols (for metals):${\ displaystyle R_ {m} \,}$
• Unit symbol : MPa ( )${\ displaystyle = \ mathrm {\ tfrac {N} {mm ^ {2}}}}$
• and the yield strength or yield strength i. d. Usually smaller than the strength
• Formula symbol (for metals): or${\ displaystyle R_ {p} \,}$${\ displaystyle R_ {e} \,}$
• Unit symbol: (= MPa)${\ displaystyle \ mathrm {\ tfrac {N} {mm ^ {2}}}}$

The stress value in relation to the elongation is assigned to a certain plastic deformation , for example 0.2% permanent elongation. This so-called “ yield point” is then noted in relation to the technical 0.2% yield point, i.e. in relation to the technical elongation value of 0.2%. The (pronounced) yield point only plays a role with unalloyed and low-alloy steels in certain heat treatment conditions, especially with structural steel . ${\ displaystyle R_ {p0 {,} 2}}$

The minimum or guaranteed value of the strengths is incorporated into the mechanical design of components.

## Component design using the example of "steel wire"

The minimum tensile strength for a steel (S235JR - formerly St37-2), which is used in structural steelwork, is 370 N / mm², depending on the quality. Its minimum yield strength, however, is 235 N / mm². If a sample of this steel, which has a cross-section of 1 mm², were to be loaded with a force in a tensile test, this would have to be at least 370 N around the sample (to a certain percentage; usually the 95% fractile value ) to tear up. 370 N correspond to the weight of a mass of 37.7 kg on earth. From this it can be concluded that when attempting to lift a mass of 37.7 kg or greater with this steel wire, failure of the material can no longer be ruled out. With this load, the wire is already permanently (plastically) deformed. Since this should usually not be permitted, the minimum yield strength is often used in the mechanical design of components . This value indicates the stress in the material up to which essentially only elastic deformation takes place. This means that with a tensile force of 235 N on a sample with a cross-section of 1 mm², this sample stretches, but essentially returns to its original state without permanently (plastically) deforming. A mass of 23.9 kg can be determined here, with the weight of which this material can be loaded in the tensile test, but behaves elastically. ${\ displaystyle R_ {e} \,}$ ${\ displaystyle F _ {\ mathrm {z}}}$

## Safety factor

For safety reasons , the specified parameters in technical applications are generally divided by a safety factor that takes into account the uncertainties in assessing the stress and the spread of the resistance values , but also depends on the possible damage if the component fails.

### Concrete construction

In the basic document of Eurocode 3, the recommended partial safety factor for permanent and temporary design situations is γ c = 1.5 for concrete and γ s = 1.15 for reinforcing steel as well as for prestressing steel . In unusual design situations, γ c = 1.2 for concrete and γ s = 1.0 for reinforcing steel and prestressing steel.

### steel construction

In steel construction in Austria and Germany, the safety factor against failure for steel according to Eurocode 3 is γ M2 = 1.25 , analogous to the basic document . According to the basic document Eurocode 3, a safety factor of 1.0 against flowing (γ M0 and γ M1 ) is proposed. B. was adopted in Austria and Great Britain, however, Germany deviates (exclusively) with the recommended value γ M1 in the national annex (but not with γ M0 ) and chooses γ M1 for buildings (excluding exceptional design situations) 1.1, the value for γ M0 is also chosen to be 1.0 (except for stability checks in the form of cross-section checks with internal forces according to the second order theory). It should be noted that the loads are safeguarded by their own factors (see semi-probabilistic partial safety concept of Eurocode 0 ).

### Composite structures made of steel and concrete

The basic document of Eurocode 4 refers to Eurocode 2 with regard to partial safety factors for concrete and reinforcing steel and to Eurocode 3 for structural steel, profiled sheets and fasteners.

### Timber construction

According to Eurocode 5, the design value of strengths is calculated as follows: ${\ displaystyle X_ {d} = k _ {\ mathrm {mod}} \ cdot {\ frac {X_ {k}} {\ gamma _ {M}}}}$

k mod is the modification coefficient of the strengths to take into account the service classes and classes of the load duration. This is between 0.2 ≤ k mod  ≤ 1.1; for medium (long-term) impacts, k mod for solid wood as well as glued laminated wood in usage classes 1 (indoor areas) and 2 (roofed) is 0.8; in service class 3 (weathered) 0.65 and for brief impacts, k mod for solid wood as well as glued laminated timber in service classes 1 (inside) and 2 (roofed) is 0.9; in service class 3 (weathered) 0.7.

For extraordinary situations, γ M is equal to 1 and for the basic  combination 1.2 ≤ γ M ≤ 1.3, where for solid wood and for connections γ M is 1.3 and for glued laminated timber γ M  = 1.25.

As the parameters are always determined only in the uniaxial tensile test, components are but often claimed multiaxially (z. B. waves to bending and torsion, wherein the bend, strictly speaking, in itself means a multi-axial stress) applies it, with the aid of a resistance hypothesis uniaxial comparison voltage to be determined, which can then be compared with the known strength.

Vibrating and also many generally moving components are loaded periodically. These loads cannot be adequately described with the aid of the above-mentioned characteristic values, since there the material fails even at significantly lower loads. Such loads are recorded with the help of the fatigue strength.

## High strength materials

Metals that achieve particularly high strength values ​​compared to their "normal strength" through certain tempering processes are called high strength . Likewise, some metal alloys are referred to as high-strength, which have been specially developed for such high loads that common metals and materials cannot be used.

## literature

• Eckard Macherauch, Hans-Werner Zoch: Internship in materials science. 11., completely revised. u. exp. Ed., Vieweg-Teubner, Wiesbaden 2011, ISBN 978-3-8348-0343-6 .

## Individual evidence

1. Arndt, Brüggemann, Ihme: Strength theory for industrial engineers , Springer, 2nd edition, 2014, p. 7.
2. ^ Eckard Macherauch, Hans-Werner Zoch: Internship in materials science. 11., completely revised. u. exp. Ed., Vieweg-Teubner, Wiesbaden 2011, p. 157 ff.
3. CEN / Stress Value TC 250: EN 1993-1-1: 2010-12: Dimensioning and construction of steel structures - Part 1-1: "General rules and rules for building construction" . German-language edition Edition. 2010, p. 48 .
4. a b c Austrian Standards Institute : ÖNORM B EN 1993-1-1: 2007-02-01: Design and construction of steel structures - Part 1-1: "General design rules" . 2007, p. 5 (National specifications for ÖNORM EN 1993-1-1, national explanations and national supplements).
5. a b c German Institute for Standardization : DIN EN 1993-1-1 / NA: 2010-12: National Annex - Nationally defined parameters - Eurocode 3: Design and construction of steel structures - Part 1-1: General design rules and rules for the Building construction . 2010, p. 8 .
6. British Standards Institution : NA + A1: 2014 to BS EN 1993-1-1: 2005 + A1: 2014 UK National Annex to Eurocode 3: Design of steel structures . 2014, p. 4 (Part 1-1: General rules and rules for buildings).
7. for unusual design situations, γ M1 = 0 is also in Germany