Oasys. Concrete Code Reference

Transcription

1 Conrete Code Reerene

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4 Contents Notation 6 Design Codes 7 Conrete material models 8 Units 8 Parabola-retangle 1 C2 Conined 11 Retangle 11 Bilinear 13 FIB 13 Popovis 14 Mander & Mander onined urve 16 BS811-2 tension urve 17 TR59 18 Interpolated 19 Conrete properties 2 ACI 21 AS 22 BS BS CSA A23.3 / CSA S6 26 N HK CP 29 IRS Bridge 33 Rebar material models 36 Rebar material models or dierent odes 36 lasti-plasti 37 lasti-hardening 37 Progressive yield 39 Park 4 Linear 41 Creep 42 N

5 AS Hong Kong Code o Pratie 44 ACI 29.2R IRC : IS 456 : 2 48 IRS Conrete Bridge Code :

6 Notation Symbol u t Represents Conrete strength (with ode variations) Conrete Stress Conrete strain Strain at whih onrete stress is maximum Strain at whih onrete ails Density Time Creep ator

7 Design Codes The ollowing design odes are supported to varying degrees in the Oasys sotware produts. Code Title Country Date Other versions ACI318 ACI318M AS36 BS54-4 Building Code Requirements or Strutural Conrete (ACI318-14) Building Code Requirements or Strutural Conrete (ACI318M-14) (metri version) Australian Standard Conrete Strutures 29 Steel, onrete and omposite bridges Code o pratie or design o onrete bridges USA , 28, 25, 22 USA , 28, 25, 22 Australia UK 199 IAN7/6 BS811-1 Strutural Use o Conrete Part 1. Code o pratie or design and onstrution (Inorporating Amendments Nos. 1, 2 and 3) UK , 1985 BS N uroode 2-1 UK 24 PD6687:26 BS N uroode 2-2 UK 25 CAN CSA A23.3 Design o Conrete Strutures Canada CAN CSA S6 Canadian Highway Bridge Design Code Canada 214 CYS N uroode Cyprus 24 DIN N uroode Germany 24 DIN N uroode 2-2 Germany 21 DS/N uroode Denmark 24 DS/N uroode 2-2 Denmark 25 N N Hong Kong Code o Pratie uroode 2: Design o onrete strutures Part 1-1: General rules and rules or buildings uroode 2: Design o onrete strutures. Conrete bridges - Design and detailing rules Code o Pratie or the Strutural Use o Conrete Hong Kong (AMD 27), 24, 1987

8 Hong Kong Strutures Design Manual Strutures Design Manual or Highways and Railways Hong Kong IRC:112 IRS Conrete Bridge Code Code o Pratie or Conrete Road Bridges Code o Pratie or Plain, Reinored & Prestressed Conrete or General Bridge Constrution India 211 India 1997 I.S. N uroode Ireland 24 I.S. N uroode 2-2 Ireland 25 IS 456 Plain and reinored onrete Code o Pratie India 2 NN N uroode Netherlands 24 NN N uroode 2-2 Netherlands 211 NF N uroode Frane 25 NF N uroode 2-2 Frane 26 NS-N uroode Norway 24 PN-N uroode Poland 28 SFS-N uroode Finland UN-N uroode Spain 21/ 213 UN-N uroode 2-2 Spain 21 UNI N uroode Italy 24 UNI N uroode 2-2 Italy 26 Conrete material models Units The deault units are: Stress, strength lasti modulus MPa (psi) GPa (psi) Conrete material models or dierent odes Dierent material models are available or dierent design odes. These are summarised below:

9 ACI 318 AS 36 BS 54 BS 811 CSA A23.3 CSA S6 N 1992 HK CP HK SDM IRC:112 IRS Bridge IS 456 Compression Parabolaretangle Retangle Bilinear Linear FIB Popovis C2 Conined AISC 36 illed tube xpliit Tension No-tension Linear Interpolate d BS811-2

10 TR 59 PD 6687 xpliit xpliit envelope inerred rom retangular blok PD 6687 variant o N 1992 only Parabola-retangle Parabola-retangles are ommonly uses or onrete stress-strain urves. The paraboli urve an be haraterised as d a 2 b At strains above the stress remains onstant. For most design odes the parabola is taken as having zero slope where it meets the horizontal portion o the stress-strain urve. d 1 1 2

11 The Hong Kong Code o Pratie (supported by the Hong Kong Institution o ngineers) interpret the urve so that the initial slope is the elasti modulus (meaning that the parabola is not tangent to the horizontal portion o the urve). s s d 2 1 where the seant modulus is d s In uroode the parabola is modiied n d 1 1 and 2 n 5MPa n > 5MPa C2 Conined The C2 onined model is a variant on the parabola-retangle. In this ase the onining stress inreases the ompressive strength and the plateau and ailure strains , u u.2, 2,, Retangle The retangular stress blok has zero stress up to a strain o (ontrolled by ) and then a onstant stress o d.

12 α β ACI ( - 3)/7 [.65:.85] AS ( - 28) [.65:.85] AS [.67:.85] BS54.6/.67 1 BS CSA A max(.67, ) CSA S6 1 max(.67, ) N MPa 1 - ( - 5)/2 > 5MPa.8 5MPa.8 - ( - 5)/4 > 5MPa HK CP > HK CP 27 > MPa.8 7MPa.72 1MPa

13 HK SDM.6/.67 1 IRC: MPa 1 - ( - 6)/25 > 6MPa.8 6MPa.8 - ( - 6)/5 > 6MPa IRS Bridge.6/.67 1 IS Bilinear The bilinear urve is linear to the point, d and then onstant to ailure. FIB The FIB model ode deines a shemati stress-strain urve. This is used in BS 811-2, N and IRC:112.

14 This has a peak stress FIB This is deined as FIB 1 k 2 k 2 with k Where the ator is ode dependent. Code FIB BS N MPa 1.5 IRC:112 1 MPa 1.5 Popovis There are a series o urves based on the work o Popovis.

15 These have been adjusted and are based on the Thoreneldt base urve. In the Canadian oshore ode (CAN/CSA S474-4) this is haraterised by n k 3 n 1 nk with (in MPa) k n.8 17 n n 1 k The peak strain is reerred to elsewhere as pop. pop All the onrete models require a strength value and a pair o strains: the strain at peak stress or transition strain and the ailure strain.

16 Mander & Mander onined urve The Mander 1 urve is available or both strength and servieability analysis and the Mander onined urve or strength analysis. For unonined onrete, the peak o the stress-strain urve ours at a stress equal to the unonined ylinder strength alulated rom and strain generally taken to be.2. Curve onstants are se and r se Then or strains 2 the stress an be alulated rom: r r 1 r where 1 Mander J, Priestly M, and Park R. Theoretial stress-strain model or onined onrete. Journal o Strutural ngineering, 114(8), pp , 1988.

17 The urve alls linearly rom as eo to the spalling strain u. The spalling strain an be taken To generate the onined urve the onined strength, must irst be alulated. This will depend on the level o oninement that an be ahieved by the reinorement. The maximum strain u, also needs to be estimated. This is an iterative alulation, limited by hoop rupture, with possible values ranging rom.1 to.6. An estimate o the strain ould be made rom C2 ormula (3.27) above with an upper limit o.1. The peak strain or the onined urve, is given by:,, Curve onstants are alulated rom se,, and r se as beore. is the tangent modulus o the unonined urve, given above. Then or strains u, the stress an be alulated rom:, r r 1 r where, BS811-2 tension urve BS811-2 deine a tension urve or servieability

18 TR59 Tehnial report 59 deines an envelope or use with onrete in tension or servieability. The material is assumed to behave in a linearly elasti manner, with the elasti modulus redued beyond the peak stress/strain point based on the envelope in the igures below

19 Interpolated Interpolated strain plains to ACI318 and similar odes ACI318 and several other odes give a method to ompute a value o the seond moment o area intermediate between that o the unraked, ollowing expression: I g I r, and ully raked,, values, using the I e M M r a 3 I g M 1 M r a 3 I r where M M r is the raking moment and a is the applied moment. AdSe SLS analyses determine a strain plane intermediate to the unraked and ully raked strain planes. The program determines a value or, the proportion o the ully raked strain plane to add to the proportion 1 o the unraked plane so that the resulting plane is ompatible with ACI318 s approah. Unortunately, sine ACI318 s expression is an interpolation o the inverse o the urvatures, rather than the urvatures themselves, there is no diret I onversion. It should also be noted that although g is deined as the value o seond moment o area ignoring the reinorement, it is assumed that this deinition was made or simpliity, and AdSe inludes the reinorement. Let M M 3 r a, the unraked urvature be I To ACI318, the interpolated urvature and the ully raked urvature be II. I 1 1 II, and the aim is to make this equivalent to

20 1 II I, quating these two expressions gives II I I II whih an be re-arranged to give / 1 II I N, M, M The ratio II I y z is appropriate or uniaxial bending. For applied loads, and,,,, I yi zi II yii zii unraked and ully raked strain planes and respetively, N M M N M M II y yii z zii I y yi z zi is replaed by the ratio, whih is independent o the loation hosen or the reerene point. In the absene o axial loads, this ratio ensures that the urvature about the same axis as the applied moment will omply with ACI318; in the absene o moments, the axial strain will ollow a relationship equivalent to that in ACI318 but using axial stiness as imposed to lexural stiness. The ratio M r M a by the ratio t ti is also inappropriate or general loading. For the general ase, it is replaed t, where is the tensile strength o the onrete and onrete tensile stress on the unraked setion under applied loads. ti II is the maximum I Summary: 1 1 N M M N M M II y yii z 3 1 ti zii t I y yi z zi Sine is larger or short-term loading, all urvatures and strains are alulated based on shortterm properties regardless o whether is subsequently used in a long-term servieability alulation. Conrete properties Notation onrete strength d onrete design strength t onrete tensile strength elasti modulus Poisson s ratio (.2) oeiient o thermal expansion (varies but / C assumed)

21 u strain at ailure (ULS) ax ompressive strain at ailure (ULS) plas strain at whih maximum stress is reahed (ULS) max assumed maximum strain (SLS) peak strain orresponding to (irst) peak stress (SLS) pop strain orresponding to peak stress in Popovis urve (SLS) 1 u ACI The density o normal weight onrete is assumed to be 22kg/m 3. The design strength is given in by. 85 d The tensile strength is given in quation 9-1 by. 62 t 7. 5 t (US units) The elasti modulus is given in as (US units) The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle.3 ε u (1-3β) ε u Retangle.3 ε u ε β Bilinear.3 ε u (1-2β) ε u Linear.3 ε max

22 FIB Popovis.3 ε pop C2 Conined AISC illed tube xpliit.3 ε u.3 AS The density o normal weight onrete is taken as 24kg/m 3 (3.1.3). The design strength is given in (b) by d 2 with and limits o [.67:.85] The tensile strength is given in by. 6 t The elasti modulus is given (in MPa) in as MPa mi mi MPa mi mi This tabulated in Table (MPa) (GPa)

23 The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle Retangle.3.25 ε β.3 ε β Bilinear Linear.3 ε max FIB Popovis ε max ε pop C2 Conined AISC illed tube xpliit BS 54 The density o normal weight onrete is given in Appendix B as 23kg/m 3. The design strength is given in Figure 6.1 by. 6 d

24 The tensile strength is given in as. 36 t but A.2.2 implies a value o 1MPa should be used at the position o tensile reinorement. The elasti modulus tabulated in Table 3 (MPa) (GPa) The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle.35 ε u ε RP Retangle Bilinear Linear.35 ε max FIB Popovis C2 Conined AISC illed tube

25 xpliit.35 ε u.35 RP BS 811 The density o normal weight onrete is given in setion 7.2 o BS as 24kg/m 3. The design strength is given in Figure 3.3 by. 67 d The tensile strength is given in as. 36 t but Figure 3.1 in BS implies a value o 1MPa should be used at the position o tensile reinorement. The elasti modulus is given in quation The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle ε u ε u ε RP.35* ε RP Retangle ε u ε u ε β Bilinear Linear ε u ε max FIB ε u.22 Popovis C2 Conined

26 AISC illed tube xpliit ε u ε u ε u u MPa 6 5 RP CSA A23.3 / CSA S6 The density o normal weight onrete is assumed to be 23 kg/m 3 ; see (A23.3) and (S6). The design strength is given in by d max.67, The tensile strength is given in quation 8.3 (A23.3) and in (S6). 6 t (or CSA A23.3). 4 t (or CSA S6) For normal weight onrete the modulus is given in A23.3 quation and in CSA S The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle.35 ε u (1-3β) ε u Retangle.35 ε u ε β

27 Bilinear.35 ε u (1-2β) ε u Linear.35 ε max FIB Popovis.35 ε pop C2 Conined AISC illed tube xpliit.35 ε u.35 N 1992 The density o normal weight onrete is speiied in as 22 kg/m 3. The design strength is given in by d For the retangular stress blok this is modiied to 5 MPa d d 5 MPa The tensile strength is given in Table 3.1 as MPa t 5 t 2.12 ln MPa The modulus is deined in Table The strains are deined as ε u ε ax ε plas ε max ε peak

28 Parabolaretangle ε u2 ε 2 ε 2 Retangle ε u3 ε 3 ε β Bilinear ε u3 ε 3 ε 3 ε u3 ε 3 Linear ε u2 ε 2 FIB ε u1 ε 1 Popovis C2 Conined ε u2, ε 2, ε 2, AISC illed tube xpliit ε u2 ε u2? ε u m.28 u MPa MPa. 53 k 5 u MPa MPa 3 k 5 4 u MPa 9 1 4

29 HK CP The density o normal weight onrete is assumed to be 24kg/m 3. The design strength is given in Figure 6.1 by. 67 d The tensile strength is given in as. 36 t but implies a value o 1MPa should be used at the position o tensile reinorement. The elasti modulus is deined in The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle ε u ε u ε RP Retangle ε u ε u ε β Bilinear Linear ε u ε u FIB ε u.22 Popovis C2 Conined AISC illed tube xpliit ε u ε u ε u MPa u

30 d GPa RP 1.34 d HK SDM The density o normal weight onrete is assumed to be 24kg/m 3. The design strength is given in (b) o BS 54-4 by. 6 d The tensile strength is given in as. 36 t but rom BS54 a value o 1MPa should be used at the position o tensile reinorement. The elasti modulus is tabulated in Table 21 (MPa) (GPa) The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle.35 ε u ε RP

31 Retangle Bilinear Linear.35 ε max FIB Popovis C2 Conined AISC illed tube xpliit.35 ε u.35 RP IRC 112 The density o normal eight onrete is assume to be 22kg/m 3. The design strength is given in d In A2.9(2) the strength is modiied or the retangular stress blok to. 67 d 6 MPa d MPa The tensile strength is given in by A2.2(2) by MPa t 6 t 2.27 ln MPa The elasti modulus is given in A2.3, equation A

32 The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle ε u2 ε 2 ε 2 ε u2 ε 2 Retangle ε u3 ε 3 ε β Bilinear ε u3 ε 3 ε 3 ε u3 ε 3 Linear ε u2 ε 2 FIB ε u1 ε 1 Popovis C2 Conined ε u2, ε 2, ε 2, AISC illed tube xpliit ε u2 ε u2? ε u u MPa MPa k 5 u MPa MPa.8 3 k 4 5

33 u MPa IRS Bridge The density is assumed to be 23kg/m 3. The design strength is given in (b) by. 6 d The tensile strength is given in as. 37 t The elasti modulus is tabulated in (MPa) (GPa) The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle.35 ε u ε RP Retangle Bilinear

34 Linear.35 ε max FIB Popovis C2 Conined AISC illed tube xpliit.35 ε u.35 RP IRC 456 The density is assumed to be 22 kg/m 3. The design strength is given in Figure 21by. 67 d The tensile strength is inerred rom as. 7 t The elasti modulus is deined in The strains are deined as ε u ε ax ε plas ε max ε peak Parabolaretangle Retangle.35.2 ε β Bilinear

35 Linear.35 ε max FIB Popovis C2 Conined AISC illed tube xpliit

36 Rebar material models Symbols rebar stress y rebar strength u rebar ultimate strength rebar strain p strain at whih rebar stress is maximum u strain at whih rebar ails Rebar material models or dierent odes Dierent material models are available or dierent design odes. These are summarised below: ACI 318 AS 36 BS 54 BS 811 CSA A23.3 CSA S6 N 1992 HK CP HK SDM IRC:112 IRS Bridge IS 456 lastiplasti lastihardening BS 54 Pre-stress Progressive yield Park Linear

37 Noompressio n ASTM strand xpliit lasti-plasti The initial slope is deined by the elasti modulus,. Post-yield the stress remains onstant until the ailure strain, u, is reahed. For some odes (CAN/CSA) the initial slope is redued to. lasti-hardening The initial slope is deined by the elasti modulus,, ater yield the hardening modulus, y yd governs as stress rises rom to, u u. For N 1992 the hardening modulus is deined in terms o a hardening oeiient k, k uk yd and the inal point is where the ailure strain is redued to ud.9 (typially uk ). The relationship between hardening modulus and hardening oeiient is: h

38 h k 1 uk y y k h uk y y 1 The material ails at BS 54 ud where ud uk. This is deined in uroode and related odes. In tension the initial slope is deined by the elasti modulus, e yd, until the stress reahes k. The slope then redues until the material is ully plasti, yd, at o yd. Post-yield the

39 stress remains onstant until the ailure strain, u, is reahed. For BS54 k e.8 and o.2. In ompression the initial slope is deined by the elasti modulus,, until the stress reahes k e yd or a strain o o strain reahes Pre-stress o. It then ollows the slope o the tension urve post-yield and when the the stress remain onstant until ailure The initial slope is deined by the elasti modulus,, until the stress reahes k then redues until the material is ully plasti, remains onstant until the ailure strain, and o.5. u yd, at o yd e yd. The slope. Post-yield the stress, is reahed. For BS811 and related odes k e.8 Progressive yield The initial slope is deined by the elasti modulus,, until the stress reahes k e yd. The slope then redues in a series o steps until the material is ully plasti, ater whih the stress remain onstant. The points deining the progressive yield are ode dependent.

40 Park The initial slope is deined by the elasti modulus,, until the stress reahes then zero or a short strain range, then rising to a peak stress beore ailure. yd. The slope is ud ud yd u u p p p u ud p yd

41 Linear The initial slope is deined by the elasti modulus,, until the ailure strain is reahed. No-ompression This is a linear model when in tension whih has no ompressive strength. ASTM strand The ASTM A 416 deines a stress-strain urve doe seven-wire strands. This has an initial linear relationship up to a strain o.8 with progressive yield till ailure. The stress strain urves are deined or speii strengths. For Grade 25 2 (1725 MPa) the stress-strain urve is deined as For Grade 27 (186 MPa) the stress-strain urve is deined as In the Commentary to the Canadian Bridge 3 ode a similar stress-strain relationship is deined. For Grade 1749 strand 2 Bridge ngineering Handbook, d. Wah-Fah Chen, Lian Duan, CRC Press Commentary on CSA S6-14, Canadian Highway Bridge Design Code, CSA Group, 214

42 p For Grade 186 strand p A more detailed disussion o modelling strands an be ound in the paper 4 by Devalapura and Tadros Creep N The reep oeiient is deined as t, t t t with, t RH m 1 RH / 1 1 or 35 RH m 3.1 h 1 RH / or 35 RH 2 m 3.1 h m 16.8 m 1 t. 2.1 t and t, t t t H t t.3 4 Stress-Strain Modeling o 27 ksi Low-Relaxation Prestressing Strands, Devalapura R K & Tadros M K, PCI Journal, Marh April 1992

43 And t is he age o the onrete, t the age o the onrete at the time o loading and oeiient depending on the relative humidity RH as a perentage and notional member size (in mm) h RH h or 35 H RH h or 35 H The oeiients, are m m H a 1 35 m m m.5 and h 2 A u u being the perimeter in ontat with the atmosphere. The temperature is taken into aount by adjusting the times t, t aording to t T n i 1 t i exp T t i And the ement type by modiying the times aording to t t T 9 2 t T where is -1 or slow setting ement or normal ement 1 or rapid hardening ement AS The reep oeiient is deined as k k k k , b The basi reep oeiient, b is a untion o onrete strength

44 Conrete strength, Basi reep oeiient ' (MPa) , b And k 2 t.8 t t h exp 2.8 t h k is the maturity oeiient rom Figure (B). This an be tabulated as 3 Age o onrete at time o loading Maturity oeiient k 3 7 days days days.9 > 365 days.9 k 4 is the environmental oeiient.7 arid.65 interior.6 temperate inland.5 tropial or near oast Conrete strength ator k is 5 With k 1. or 5 MPa k ' or 5 MPa 1 MPa ' ' 3 k Hong Kong Code o Pratie The reep oeiient is deined as K L K m K K e K j Oasys Ltd

45 Where the ators are derived rom ode harts. K and K an be approximated by 5 m j 5 Allowane or reep under gradually applied loading, John Blanhard, 1998 NST 4 Oasys Ltd

46 K m t 1 bl L 2 with Cement a b OPC RHPC and Kj t t t t t t with etive thikness (mm) where t, t are deined in weeks ACI 29.2R-18 The reep oeiient is deined in Appendix A as t, t d t t t t u Where t is the onrete age, t onstants or member shape and size. the age at loading and d is the average thikness and are u 2.35, t, RH, d, s,, with 1. 25, t.118 t or moist uring 1. 13, t.94 t or steam uring h or relative humidity, h. 4, RH d or t t 1 year, d d or t t 1 year, d Oasys Ltd

47 .82, s. 264 s where s is the slump in mm.88,. 24 where is the ratio o ine to total aggregate where is the air ontent in perent IRC : The reep oeiient is deined as t, t t t with, t RH m 1 RH / 1 1 or 45 RH m 3.1 h 1 RH / or 45 RH 2 m 3.1 h m m 1 t. 2.1 t and t, t t t H t t.3 And t is he age o the onrete, t the age o the onrete at the time o loading and oeiient depending on the relative humidity as a perentage and notional member size (in mm) h RH h or 45 H RH h or 45 H m 6 m H a 6 Code speiies a value o 35MPa, but 45MPa seems more orret. Oasys Ltd

48 The oeiients, are m m m.5 and h 2 A u u being the perimeter in ontat with the atmosphere. The temperature is taken into aount by adjusting the times t, t aording to t T n i 1 t i exp T t i And the ement type by modiying the times aording to t t T 9 2 t T where is IS 456 : 2-1 or slow setting ement or normal ement 1 or rapid hardening ement The reep oeiient is deined as a untion o age at loading Age at loading Creep oeiient 7 days days year 1.1 IRS Conrete Bridge Code : 1997 The reep oeiient is deined in as a untion o age at loading Age at loading Creep oeiient 7 days days year 1.1 Oasys Ltd

49 Oasys Ltd Oasys