RELIABILITY OF STRUCTURES AND STRUCTURAL MATERIALS

Transcription

1 RELIABILITY OF STRUCTURES AND STRUCTURAL MATERIALS Ing. Jan Koláček, Ph.D. Ing. Jiří Strnad, Ph.D.

2 Reliability of structures A structure shall be design in such a way that it will, during its intended life, with appropriate degrees of reliability: sustain all actions (according to codes) and remain fit for the use for which it is required rate of failure of structure rising strain limited deflection collapse unserviceable limitation of crack (causing environment) development of cracks local failure ULS SLS Ultimate Limit State Serviceability Limit State 1. cracks loads characteristic (service load) design (extreme load) 2

3 Reliability of structures shall be designed to have adequate: structural resistance serviceability durability rate of failure of structure rising strain limited deflection collapse unserviceable limitation of crack (causing environment) development of cracks local failure ULS SLS Ultimate Limit State Serviceability Limit State 1. cracks loads characteristic (service load) design (extreme load) 3

4 Reliability of structures Design working life probable service life given according to category in codes Adequately durable structure guarantee of the function of the structure during the design working life 4

5 Reliability of structures Basic criteria of design - reliability, economy reliability condition: E R effect of actions effect of loads F and others influences resistance of structure material property X, character of structure geometrical data a (dimensions, effect of imperfections) 5

6 Reliability of structures Uncertainty of design reliability probability parameters of random quantity mean value μ, mean-root-square error σ, safety index β = μ / σ Individual partial factors γ for actions (loads), materials, calculation models, etc. 6

7 Reliability of structures Methods of design deterministic (permissible stress design, degrees of safety), probabilistic (currently semi probabilistic only) limit states Method of design permissible stress design Reliability condition structure resistance serviceability Notice σ k σ dov α k α dov σ dov = f m / k degrees of safety s. E k R m α k α dov s is specified degree of safety limit states E d R d E d C d using γ 7

8 Reliability of structures n R dov = R m / k s = R m / E m effect of actions φ(e) E d R d resistance of structure φ(r) E m R dov E d R d R m E R permissible stress design degree of safety limit states E m R dov s = R m / E m s norm E d R d 8

9 Reliability of structures Individual partial factors relation between individual partial factors: 9

10 Reliability of structures Consequences classes Consequences Class Description Examples of buildings and civil engineering works Minimum values for β Referen. period 1 year/50 years Factor K FI for actions CC3 (RC3) High consequence for loss of human life, or economic, social or environmental consequences very great Grandstands, public buildings where consequences of failure are high (e.g. a concert hall) 5,2 / 4,3 1,10 CC2 (RC2) Medium consequence for loss of human life, economic, social or environmental consequences considerable Residential and office buildings, public buildings where consequences of failure are medium (e.g. an office building) 4,7 / 3,8 1,00 CC1 (RC1) Low consequence for loss of human life, and economic, social or environmental consequences small or negligible Agricultural buildings where people do not normally enter (e.g. storage buildings), greenhouses 4,2 / 3,3 0,90 10

11 Reliability of structures Limit states states beyond which the structure no longer fulfils the relevant design criteria. We distinguish: Ultimate limit states (ULS) - concern the safety of people or of the structure (states before collapse) Serviceability limit states (SLS) concern the functioning of the structure under normal use (the comfort of people, the appearance of structure) others limit states (e.g. durability) are not checked (as detailing provisions only) Limit states shall be related to design situations (requirements of the structures) 11

12 Reliability of structures rate of failure of structure rising strain limited deflection collapse unserviceable limitation of crack (causing environment) development of cracks local failure ULS SLS Ultimate Limit State Serviceability Limit State 1. cracks loads characteristic (service load) design (extreme load) 12

13 Reliability of structures Design situations sets of physical conditions representing the real conditions occurring during a certain time interval for which the design will demonstrate that relevant limit states are not exceeded persistent normal use transient temporary conditions (during execution) accidental exceptional conditions (fire, explosion, impact of vehicles) seismic seismic events 13

14 Reliability of structures Ultimate limit states (ULS) EQU static equilibrium E d,dst E d,st STR failure or excessive deformation E d R d GEO like STR, but concern the ground (strength of soil) E d R d FAT fatigue failure D d 1 14

15 Reliability of structures Serviceability limit states (SLS) that concern effect: deformation affects appearance, comfort of people or the functioning of the structure (including the functioning of machines or services) vibration causes discomfort to people or limit structure functional effectiveness damage affects appearance, durability or serviceability of the structure E d C d SLS check on concrete structures these: stress control (effect of damage) crack control (effect of damage) deflection control (effect of deformation) 15

16 Reliability of structures Durability ensured by the help of: suitable choice of construction material, structural conception, design of members, etc. protection against the environmental actions and chemical attack keep detailing provisions (e.g. concrete cover) regular maintenance quality of works 16

17 Reliability of structures Durability depends on environmental conditions: physical chemical physical attack, arising from e.g.: temperature change development of cracks abrasion vehicle travel (from wheels) water penetration (erosion of surface) Environmental conditions according to chemical attack are classified according to exposure classes. 17

18 Reliability of structures Exposure classes 18

19 Reliability of structures Exposure classes 19

20 Reliability of structures Exposure classes 20

21 We distinguish them among: progressive CONCRETE (reinforced concrete, prestressed concrete, etc.) STEEL traditional MASONRY TIMBER other GLASS ALUMINIUM PLASTICS 21

22 CONCRETE consists of 4 components: aggregate cement+lime+fly ash (hydraulic binder) water additives, admixture construction types of concrete plain concrete reinforced concrete (RC) prestressed concrete 22

23 CONCRETE advantages: durability compressive strength fire resistance monolithy disadvantages: low tensile strength formwork and shoring low strength-to-weight ratio volume changes and time-dependent behaviour 23

24 CONCRETE material behaviour: strength limit stress due to material is failed stress-strain diagram for concrete a) cube strength f c,cube b) cylinder strength f c 24

25 CONCRETE cylinder strength f c (denotes f c,cyl ) standard cylinder specimen 300 x 150 failure of vertical cracks in the middle of the length of specimen general strength to computing is usually about 80% of the cube strength 25

26 CONCRETE (Compressive) Strength is random quantity (variable) and has this statistical distribution: 5% fractile e.g. f ck or f ctk,0,05 for ULS mean value e.g. f cm or f ctm for SLS 5% fractile mean value 95% fractile 95% fractile e.g. f ctk,0,95 26

27 CONCRETE Schematic stress-strain diagram (short-term loading) Tangent modulus E c =1,05 E cm Secant modulus E cm I linear behaviour region II development of cracks kvazielastic region III hardening region IV creep of material 27

28 CONCRETE design stress-strain diagram 28

29 CONCRETE notation concrete class C 25/30 C Concrete 25 characteristic cylinder compressive strength f ck 30 characteristic cube compressive strength f ck,cube design strength of concrete: in compr.: f cd = a cc f ck / g c [MPa] in tens.: f ctd = a ct f ctk,0,05 / g c [MPa] a cc - long term effects on the compressive strength a ct - long term effects on the tensile strength g c partial safety factor for concrete (for persistent design situation 1,5) 29

30 CONCRETE 30

31 CONCRETE others characteristic : density r c = kg / m 3 coefficient for thermal expansion a c = K -1 Poisson's ratio n = 0,2 31

32 REINFORCING STEEL all bars which are suitably located in concrete designed to resist tensile stresses quantity and location are governed by static analysis is a low carbon (less than 0,24 % of carbon), alloyed, hot-rolled steel (either without additional treatment, or heat treated, or coldformed) 32

33 REINFORCING STEEL material behaviour: hot rolled steel cold worked steel 33

34 REINFORCING STEEL material behaviour: characteristic yield stress f yk (5% fractile) ratio of tensile strength to yield stress k = (f t / f yk ) k characteristic maximum strain e uk elongation at maximum load bend-ability no cracking after first bend weld-ability according to EN weldable / unweldable 34

35 REINFORCING STEEL Sortiment according to surface: smooth, with rib B500A B500B (according to ČSN) is classified according to nominal diameter (size) and nominal cross-section area are relative to the diameter of equivalent specific weight (kg / m) slick bar 35

36 REINFORCING STEEL Sortiment BARS direct rod (not as a roll) smooth or ribbed surface, maximum length of m nominal diameter of: 6, 8, 10, 12, 14, 16, 18, 20, 22, 25, 28, 32 mm 36

37 REINFORCING STEEL Sortiment COILS supplied at rolls, than they are processed smooth or ribbed surface sortiment: ribbed 6, 8, 10, 12, 14; smooth 5.5, 6, 8, 10 37

38 REINFORCING STEEL Sortiment WELDED FABRIC is welded to cross longitudinal and transversal wires ribbed surface wire spacing 100 x 100, 150 x 150, 200 x 200 mm sortiment: ribbed surface 4, 5, 6, 8, 10 (rolls or sheets) maximal length of 6,0 m; width of 2,4 m 38

39 REINFORCING STEEL notation according to EC B 500 B B is reinforcing steel (bars) 500 characteristic yield stress f yk B class of ductility notation according ČSN type of technical process 10 is reinforcing steel (bars) 50 1/10 characteristic yield stress f yk 5 type of heat treatment 39

40 REINFORCING STEEL 40

41 REINFORCING STEEL 41

42 REINFORCING STEEL Stress-strain diagrams A idealised B1 diagram with inclined top branch e ud = 0,9 e uk B2 with horizontal top branch no restriction of e ud a e uk 42

43 REINFORCING STEEL Design characteristics design yield stress: f yd = f yk / g s [MPa] modulus of elasticity E s = 200 GPa g s partial safety factor for reinforcing steel (for persistent design situation 1,15) density r = 7850 kg / m 3 coefficient for thermal expansion a c = K -1 Poisson s ratio n = 0,3 43

44 Durability of concrete structures is ensured by: concrete cover c suitable class of concrete according to exposure classes e.g. for X0 is min. class of concrete C16/20, for XD1 min. class of concrete C30/37 spacing and nominal diameter of bars affect the crack width e.g. smaller diameter and spacing = smaller crack width 44

45 PRESTRESSING REINFORCEMENT main load bearing reinforcement required properties are reached through chemical composition and special production processes (high strength) is non-alloyed or lowalloyed (carbon content up to 0,90 %), hot-rolled steel material behaviour is similar to with reinforcing steel 45

46 PRESTRESSING REINFORCEMENT Sortiment WIRES low-alloyed hot-rolled steel with high content of carbon heated to C and then slowly cooled (homogenisation) = PATENTED further treated by cold-drowning (patented, cold drawn wires), that increases its strength smooth shape of stress-strain diagram without apparent yield strength diameters of 3-10 mm, plain or indented surface 46

47 PRESTRESSING REINFORCEMENT Sortiment DEFORMED BARS alloyed hot-rolled steel yield strength up to 800 MPa and tensile stress up to 1000 MPa smooth or deformed surface diameters of mm, length of 6-30 m 47

48 PRESTRESSING REINFORCEMENT Sortiment STRAND commonly composed of 7 wires central wire around which 6 others wires are spun into spiral easier stress of a large number of wires at the same time improves the bond between the strand and the grout or concrete internal stress is removed through stress-relieving strain tempering 48

49 PRESTRESSING REINFORCEMENT notation according to EC Y-1860-S7-15,2 Y prestressing reinforcement 1860 characteristic tensile stress f pk 15,2 diameter of strand [mm] S7 strand composed of 7 wires characteristic 0,1% proofstress of prestressing reinforcement f p0,1k for calculation only 49

50 PRESTRESSING REINFORCEMENT Stress-strain diagrams (similar to reinforcing steel) A idealised B1 diagram with inclined top branch e ud = 0,9 e uk B2 with horizontal top branch no restriction of e ud a e uk 50

51 PRESTRESSING REINFORCEMENT Design characteristic design yield stress: f pd = f p0,1k / g s [MPa] modulus of elasticity E p = 205 GPa wires, deformed bars E p = 195 GPa strands density r = 7850 kg / m 3 coefficient for thermal expansion a c = K -1 g s partial safety factor for prestressing reinforcement (for persistent design situation 1,15) Poisson s ratio n = 0,3 51

52 MASONRY for vertical load bearing structure, eventually for vaults masonry elements: full brick, hollow brick, silicate units, burned brick a bond of masonry element is important here properties depends on mortar quality, strength of masonry elements and masonry arrangement 52

53 MASONRY Design characteristics characteristic compression strength: f k = k f b 0,7 f 0,3 m [MPa] design compression strength : f d = f k / g M [MPa] modulus of elasticity: E = a sec f k [MPa] k coefficient depended on the arrangement of masonry (gaps) f b strength of masonry element f m strength of mortar g M partial safety factor of masonry (according to morter quality and class of masonry element 2-2,5) a sec constant for masonry from burned bricks

54 References Procházka, J., Štemberk, P.: Concrete structures 1, Nakladatelství ČVUT, Praha, 2007 Procházka, J., Štemberk, P.: Design procedures for reinforced concrete structures, Nakladatelství ČVUT, Praha, 2009 Navrátil, J.: Prestressed concrete structures, akademické nakladatelství CERM, s.r.o., Brno, 2006 Bajer, M., Pilgr, M., Veselka, M.: Konstrukce a dopravní stavby, Moduly BO01-MO1, Studijní opory VUT v Brně. Karmazínová, M., Sýkora, K., Šmak, M.: Konstrukce a dopravní stavby, Moduly BO01-MO2, Studíjní opory VUT v Brně. Procházka, J., Štěpánek, P., Krátký, J., Kohoutková, A., Vašková, J.: Navrhování betonových konstrukcí 1 prvky z prostého a železového betonu, ČBS Servis, s.r.o., Praha,

55 THANK YOU FOR YOUR ATTENTION 55