Size influencing factor

The size influencing factor , often known under the English term size effect , represents a strength dependency in technical mechanics depending on the dimensions. There are two important effects:

• the larger / longer the sample (e.g. a rope, concrete cube), the more likely it is to have a defect, which means that the strength decreases with the size;
• In the case of wood, branches can weaken the cross-section locally by a few cm, and the tensions as well as the neutral grain must be shifted / redirected here. With large cross-sections, a local weak point is less of a problem than with small ones, so the strength increases with large cross-sections.

Rope example

If you have two weightless ropes that have identical properties and that are loaded under identical constant loads and one is twice as long as the other, the probability (under an ideal load application) that the longer rope will fail earlier is twice as high. As a result, the expected strength of the longer rope is statistically lower.

Concrete cubes

If you take the same concrete for two different sized cubes with the same largest grain and once make / cut out a cube in the size of the largest grain and once make / cut out a cube that is significantly larger, the smaller one will statistically not only scatter more, but also endure more. The reason for this lies in the fact that the stresses are for the most part dissipated through the areas where there is a lot of rock grain, and so the stresses do not have to be guided through the weaker cement stone matrix .

Wood

Eurocode 5 allows the following increases for flexural and tensile strength for solid wood less than 15 cm: ${\displaystyle \rho _{k}\leq 700\,\mathrm {kg/m^{3}} }$

${\displaystyle k_{h}=\min \left\{{\begin{aligned}\left({\frac {150\,{\textrm {mm}}}{h}}\right)^{0{,}2}\\1{,}3\\\end{aligned}}\right.}$.

For glued laminated timber (less than 600 mm) the tensile strength can be increased by the following value:

${\displaystyle k_{h}=\min \left\{{\begin{aligned}\left({\frac {600\,{\textrm {mm}}}{h}}\right)^{0{,}1}\\1{,}1\\\end{aligned}}\right.}$ .

literature

• Zdeněk P. Bažant : Identification of strain-softening constitutive relation from uniaxial tests by series coupling model for localization . In: Cement and Concrete Research . tape 19 , no. 6 , November 1989, ISSN  0008-8846 , pp. 973-977 , doi : 10.1016 / 0008-8846 (89) 90111-7 .
• ZP Bažant , MT Kazemi: Determination of fracture energy, process zone longth and brittleness number from size effect, with application to rock and conerete . In: International Journal of Fracture . tape 44 , no. 2 , July 1990, ISSN  0376-9429 , p. 111-131 , doi : 10.1007 / bf00047063 .
• Energetic-Statistical Size Effect in Quasibrittle Failure at Crack Initiation . In: ACI Materials Journal . tape 97 , no. 3 , 2000, ISSN  0889-325X , doi : 10.14359 / 9879 .
• Zdenĕk P. Bažant , Jaime Planas: Fracture and Size Effect in Concrete and Other Quasibrittle Materials . Routledge, 2019, ISBN 978-0-203-75679-9 , doi : 10.1201 / 9780203756799 .
• Zdeněk P. Bažant , Arash Yavari: Is the cause of size effect on structural strength fractal or energetic – statistical? In: Engineering Fracture Mechanics . tape 72 , no. 1 , January 2005, ISSN  0013-7944 , p. 1-31 , doi : 10.1016 / j.engfracmech.2004.03.004 .
• Zdenĕk P. Bažant , Isaac M. Daniel, Zhengzhi Li: Size Effect and Fracture Characteristics of Composite Laminates . In: Journal of Engineering Materials and Technology . tape 118 , no. 3 , July 1, 1996, ISSN  0094-4289 , p. 317-324 , doi : 10.1115 / 1.2806812 .
• Zdeněk P. Bažant , S.-D. Pang: Mechanics-based statistics of failure risk of quasi-small structures and size effect on safety factors . In: Proceedings of the National Academy of Sciences . tape 103 , no. 25 , June 12, 2006, ISSN  0027-8424 , p. 9434-9439 , doi : 10.1073 / pnas.0602684103 .
• Zdeněk P. Bažant , Sze-Dai Pang: Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture . In: Journal of the Mechanics and Physics of Solids . tape 55 , no. 1 , January 2007, ISSN  0022-5096 , p. 91-131 , doi : 10.1016 / j.jmps.2006.05.007 .
• Zdeněk P. Bažant , Miroslav Vořechovský, Drahomír Novák: Asymptotic Prediction of Energetic-Statistical Size Effect from Deterministic Finite-Element Solutions . In: Journal of Engineering Mechanics . tape 133 , no. 2 , February 2007, ISSN  0733-9399 , p. 153-162 , doi : 10.1061 / (asce) 0733-9399 (2007) 133: 2 (153) .
• Zdeněk P. Bažant , Yunping Xi: Statistical Size Effect in Quasi ‐ Brittle Structures: II. Nonlocal Theory . In: Journal of Engineering Mechanics . tape 117 , no. November 11 , 1991, ISSN  0733-9399 , pp. 2623-2640 , doi : 10.1061 / (asce) 0733-9399 (1991) 117: 11 (2623) .
• Zdeněk P. Bažant , Yong Zhou, Isaac M. Daniel, Ferhun C. Caner, Qiang Yu: Size Effect on Strength of Laminate-Foam Sandwich Plates . In: Journal of Engineering Materials and Technology . tape 128 , no. 3 , 2006, ISSN  0094-4289 , p. 366 , doi : 10.1115 / 1.2194557 .
• Peter Grassl, Zdeněk P. Bažant : Random Lattice-Particle Simulation of Statistical Size Effect in Quasi-Brittle Structures Failing at Crack Initiation . In: Journal of Engineering Mechanics . tape 135 , no. 2 , February 2009, ISSN  0733-9399 , p. 85-92 , doi : 10.1061 / (asce) 0733-9399 (2009) 135: 2 (85) .
• FP Glasser: Book reviews Size effect in concrete structures Mihoski H., Okamura H. and Bazant ZP (Editors) Spon, London, 1994 0 419 19040 6, £ 69.00 . In: Advances in Cement Research . tape 7 , no. January 25 , 1995, ISSN  0951-7197 , pp. 45-46 , doi : 10.1680 / adcr.1995.7.25.45-2 .
• Phoenix SL, Ibnabdeljalil M., C.-Y. Hui: Size effects in the distribution for strength of brittle matrix fibrous composites . In: International Journal of Solids and Structures . tape 34 , no. 5 , February 1997, ISSN  0020-7683 , p. 545-568 , doi : 10.1016 / s0020-7683 (96) 00034-0 .
• RILEM Committee TC-QFS: Quasibrittle fracture scaling and size effect . In: Materials and Structures . tape 37 , no. 272 , August 17, 2004, ISSN  1359-5997 , p. 547-568 , doi : 10.1617 / 14109 ( rilem.net [accessed December 4, 2019]).

Individual evidence

1. ^ Zdeněk P. Bažant: Size Effect in Blunt Fracture: Concrete, Rock, Metal . In: Journal of Engineering Mechanics . tape 110 , no. 4 , April 1984, ISSN  0733-9399 , pp. 518-535 , doi : 10.1061 / (asce) 0733-9399 (1984) 110: 4 (518) .
2. ↑ EUROPEAN COMMITTEE FOR STANDARDIZATION: Eurocode 5: Dimensioning and construction of wooden structures Part 1-1: General - General rules and regulations for building construction (consolidated version) . In: ON-Komitee ON-K 012 timber construction; Austrian Standards Institute / Österreichisches Normungsinstitut (Ed.): ÖNORM EN . tape 1995-1-1 , no. 1995-1-1 . Austrian Standards Institute / Österreichisches Normungsinstitut (ON), Vienna July 1, 2009, 3.2 Vollholz (3), p. 30 (140 p., Online [accessed on December 4, 2019] Original title: Eurocode 5: Design of timber structures - Part 1-1: General - Common rules and rules for buildings (consolidated version) Eurocode 5: Conception et calcul des structures en bois - Partie 1-1: Généralités - Règles communes et règles pour les bâtiments (version consolidée) .).
3. ↑ EUROPEAN COMMITTEE FOR STANDARDIZATION: Eurocode 5: Dimensioning and construction of wooden structures Part 1-1: General - General rules and regulations for building construction (consolidated version) . In: ON-Komitee ON-K 012 timber construction; Austrian Standards Institute / Österreichisches Normungsinstitut (Ed.): ÖNORM EN . No. 1995-1-1 . Austrian Standards Institute / Österreichisches Normungsinstitut (ON), Vienna July 1, 2009, 3.3 Glulam (3), p. 32 (140 p., Online [accessed on December 4, 2019] Original title: Eurocode 5: Design of timber structures - Part 1-1: General - Common rules and rules for buildings (consolidated version) Eurocode 5: Conception et calcul des structures en bois - Partie 1-1: Généralités - Règles communes et règles pour les bâtiments (version consolidée) .).