Proof of strength

Computational proof of strength on cranked snap hook based on the maximum principal strain, calculated using the finite element method (FEM)

Experimental proof of strength in the test laboratory

Two different connections that lead to a different proof of strength

The load-bearing capacity of a normal force bar can be determined with a proof of strength

The strength verification is a central task in the design of components or structures and was clearly formulated following Navier and Redtenbacher von Rebhann in 1856 for the beam theory on the basis of the elasticity theory . It consists in showing that the load-bearing capacity of a construction or the strength of the material exclude failure under the intended loads and the relevant conditions with sufficient certainty . Failure can occur depending on the requirements, the occurrence of impermissibly large or irreversible, z. B. mean plastic deformation , micro-damage or a break.

The proof of strength, also called proof of load-bearing capacity , is carried out mathematically and / or experimentally according to the state of the art and the recognized rules of engineering (" best practice "), depending on the requirements and the phase of component development.

A similar task also arises in the stability and stability verification .

Concepts

Computational proof of strength

Computational proofs of strength are mostly carried out on the basis of stresses , especially in mechanical engineering and apparatus engineering and in construction; in principle, however, they can also take place on the basis of deformations, which can be useful in many cases. In both cases, the stresses and / or strains determined on the component or structure are compared with the relevant material properties expressed by characteristic values ​​or limit values in the corresponding conditions.

• Strength condition:

${\displaystyle \sigma _{\mathrm {V,max} }\leq \sigma _{\mathrm {zul} }=\sigma _{\mathrm {G} }\cdot {\frac {C}{S}}}$

• Deformation condition:

${\displaystyle \varepsilon _{\mathrm {V,max} }\leq \varepsilon _{\mathrm {zul} }=\varepsilon _{\mathrm {G} }\cdot {\frac {C}{S}}}$

Therein mean:

• ${\displaystyle \sigma _{\mathrm {V,max} }}$or : the maximum value occurring in the component equivalent stress or equivalent strain determined from the decisive strength hypothesis ${\displaystyle \varepsilon _{\mathrm {V,max} }}$

• ${\displaystyle \sigma _{\mathrm {zul} }}$or : Permissible value of tension or strain ${\displaystyle \varepsilon _{\mathrm {zul} }}$

• ${\displaystyle \sigma _{\mathrm {G} }}$or : Stress or strain limit value for the underlying failure type, e.g. B. or for breaking strength or elongation at break , z. B. or for yield stress or elongation, etc. ${\displaystyle \varepsilon _{\mathrm {G} }}$ ${\displaystyle \sigma _{\mathrm {B} }}$ ${\displaystyle \varepsilon _{\mathrm {B} }}$ ${\displaystyle \sigma _{\mathrm {Y} }}$ ${\displaystyle \varepsilon _{\mathrm {Y} }}$

• ${\displaystyle C}$: Influence factor for the consideration of influences that are or are not recorded in the limit value , such as B. structural changes due to hardening , welding , size influences, temperature influences, environmental influences and the like. a. m. Depending on the influence, it can be ≤ 1.0 or ≥ 1.0. ${\displaystyle \sigma _{\mathrm {G} }}$ ${\displaystyle \varepsilon _{\mathrm {G} }}$ ${\displaystyle C}$ ${\displaystyle C}$

• ${\displaystyle S}$: Safety factor to define a safety distance from the failure limit , depending on various factors such as failure type, failure consequences, uncertainty of the load assumptions, overload probability , load type, reliability of the material parameters , deviations between the calculation model and reality, etc. a. m. Usually > 1.0. Known exceptions are predetermined breaking points with = 1.0. ${\displaystyle S}$ ${\displaystyle S}$

Corresponding conditions must also be met for the fracture mechanical strength verification.

Experimental proof of strength

Experimental proof of strength is usually carried out on prototypes or on structures on the object itself, e.g. B. Test series for components in vehicle and aircraft construction, load tests for bridges, etc.

Certain components

For proof of the strength of certain construction elements such as drive shafts , pressure vessels and devices, pipelines , springs , bearings , riveted connections , screw connections , welded connections , gear wheels etc. or structures, the relevant regulations, standards and guidelines must be observed.

literature

• N / A : Computational proof of strength for machine components . FKM guideline [2] . Ed .: Forschungskuratorium Maschinenbau (FKM). 6th edition, VDMA Verlag Frankfurt am Main 2012.
• Dieter Radaj: proof of strength. Part I Basic Procedure; Part II Special Procedure. Welding technology series of specialist books No. 64. Deutscher Verlag für Schweißtechnik Düsseldorf 1974.
• Kurt Wellinger, Herbert Dietmann: Strength calculation . 3rd edition, Alfred Kröner Verlag Stuttgart 1976.
• Georg Menges: Easier understanding of the material behavior when considering deformation. Progress report VDI series 5, No. 12. VDI-Verlag Düsseldorf 1971.

Individual evidence

1. ^ Karl-Eugen Kurrer : History of structural engineering. In search of balance , Ernst & Sohn Berlin 2016, pp. 88f., ISBN 978-3-433-03134-6
2. ↑ Computational proof of strength for machine components . FKM guideline. Ed .: Forschungskuratorium Maschinenbau (FKM). 6th edition, VDMA Verlag Frankfurt am Main 2012.
3. ↑ Johannes Kunz: A plea for the expansion-related design . In: Kunststoffe 101 (2011) No. 4, pp. 50–54. ( PDF )
4. ↑ Fracture mechanical strength verification for machine components . FKM guideline. Ed .: Forschungskuratorium Maschinenbau (FKM). VDMA Verlag Frankfurt am Main 2009 Archived copy ( memento of the original dated February 11, 2017 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. . 
5. ^ AD 2000 regulations [1] . Paperback (in particular series B calculation and series S special cases ). Ed .: Association of TÜV eV (VdTÜV), 8th edition, Beuth Verlag Berlin 2013.
6. ↑ VDI 2204 sheet 2: Design of plain bearings; Calculation . VDI-Verlag Düsseldorf 1992.
7. ↑ VDI 2230: Systematic calculation of highly stressed screw connections . VDI-Verlag Düsseldorf 2014/2015.
8. ↑ DVS rules for construction and calculation [ Archived copy ( memento of the original dated February 11, 2017 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. ]. Ed .: German Association for Welding and Allied Processes eV (DVS), Düsseldorf.