INFORMATION CONCERNING MATERIALS TO BE USED IN THE DESIGN

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1 TITLE 5 DESIGN CHAPTER 8 INFORMATION CONCERNING MATERIALS TO BE USED IN THE DESIGN Artile 38. Charateristis o steel or reinorements 38.1 General The harateristis o the steel used or the design desribed in this artile, are reerred to the properties o the passive reinorements plaed in the strutural element in aord to the artile in the EN Charateristi stress-strain diagram or passive reinorement steel The harateristi stress-strain diagram is the diagram used as a basis or the alulations and assoiated in this Code with a perentage o 5% o the lowest stressstrain diagrams. The harateristi stress-strain diagram or tensioned steel is the diagram whose stress values, orresponding to strains not exeeding 10 per 1000, have a onidene level o 95% relative to the values obtained during tensile tests onduted in aordane with UNE EN The same diagram may be adopted or ompression. In the absene o aurate experimental data, the harateristi diagram may be assumed to adopt the shape in igure 38.2, and this diagram may be taken as being harateristi, i the standardised values or the yield stress given in Artile 32 are adopted. The ompression arm shall always be symmetrial to the tension arm, in relation to the origin. Figure Charateristi stress-strain diagram or passive reinorements 38.3 Design strength o steel in passive reinorements The ollowing value, yd shall be onsidered to be the design yield strength o the steel: yk = yd γ s CHAPTER 8-1

2 In whih yk is the harateristi yield stress and γ s is the partial saety oeiient deined in Artile 15. The expressions indiated are valid or tension and ompression. I steels with dierent yield stresses are used in one setion, eah shall be onsidered in the alulation, together with its orresponding diagram Design stress-strain diagram or steel in passive reinorements The design stress-strain diagram or steel in passive reinorements (in tension or ompression), shall be alulated rom the harateristi diagram using oblique ainity, parallel to Hooke s line, in a ratio o 1/γ s. When the diagram in igure 38.2 is used, the design diagram or igure 38.4 is obtained, in whih it may be noted that, starting rom yd a seond leg, with a positive slope obtained using oblique ainity rom the harateristi diagram, or a seond horizontal leg, with the latter being generally suiiently aurate, an be onsidered,. Other simpliied design diagrams may be used, provided that they produe results that are suiiently onirmed by experiene. Figure Design stress-strain diagram in passive reinorements A maximum strain o steel in tension o ε max 0.01, shall be adopted in the design 38.5 Charateristi stress-strain diagram o steel in ative reinorements The harateristi stress-strain diagram or the steel set out by its manuaturer may be used in ative reinorements (wire, bar or strand) up to a strain o at least ε p = 0.010, and so that or a given strain the tensions are exeeded in 95% o ases. I this guaranteed diagram is not available, the diagram shown in igure 38.5 may be used. This diagram omprises a irst straight setion with slope εp and a seond urve setion, starting rom 0.7 pk, deined by the ollowing expression: σ p p = +0,823 σ ε - 0,7 p para p 0,7 pk E p σ pk In whih E p is the modulus o longitudinal strain deined in CHAPTER 8-2

3 Figure Charateristi stress-strain diagram or ative reinorements 38.6 Design strength o steel in ative reinorements The ollowing shall be used or the design strength o steel in ative reinorements. pk = pd In whih pk is the harateristi yield stress and γ s is the partial saety oeiient o the steel indiated in Artile Design stress-strain diagram or steel in ative reinorements The design stress-strain diagram or the steel in ative reinorements shall be alulated rom the orresponding harateristi diagram using oblique ainity, parallel to Hooke s straight line, in a ratio o 1/γ s (see igure 38.7.a). γ s Figure 38.7.a. Design stress-strain diagram in ative reinorements For simpliiation purposes, based on pd, σ p = pd may be used (see igure 38.7b) CHAPTER 8-3

4 Figure 38.7.b. Design stress-strain diagram in ative reinorements 38.8 Modulus o longitudinal strain o steel in ative reinorements The value o E p = 200,000 N/mm 2, may be taken as the modulus o longitudinal strain in steel in reinorements omprising wires or bars, unless experimentally otherwise onirmed. The values set by the manuaturer or experimentally determined may be adopted in strands as the reiterative and noval values. In the harateristi diagram (see 38.5) the value o the reiterative modulus shall be taken. I no earlier experimental values are available prior to the projet, the value o Ep = 190,000 N/mm 2 may be adopted. When heking elongation during tensioning, the value o the noval modulus value determined experimentally shall be used Relaxation o steel in ative reinorements The relaxation ρ o steel at onstant length, or an initial tensile stress o σ pi = α max with the ration α, being between 0.5 and 0.8 or time t, may be estimated using the ollowing expression: σ p log ρ = log = K 1+ K 2 log t σ pi in whih: σp Loss o stress due to relaxation at onstant length at the end o time t, in hours. K1, K 2 Coeiients whih vary aording to the type o steel and the initial stress (igure 38.9). The steel manuaturer shall supply the relaxation values at 120 h and 1,000 h, or initial stresses o 0.6, 0.7 and 0.8 o max at a temperature o 20±1 C and shall guarantee the value at 1,000 h or α = 0.7. From these relaxation values, the oeiients K 1 and K 2 or α = 0.6, 0.7 and 0.8, may be obtained. In order to obtain relaxation with another value o α, this may be linearly interpolated by allowing or α = 0.5; ρ = 0. The value whih is obtained or the estimated lie o the struture, expressed in hours, or 1,000,000 hours in the absene o this inormation, may be taken as the inal value o p. CHAPTER 8-4

5 Figure Fatigue harateristis o ative and passive reinorements The variation in maximum stress, due to atigue loading, shall be less than the limit atigue values indiated in table Table Fatigue limit or passive and ative reinorements Type o reinorement Diret bonding Fatigue Limit σ D [N/mm 2 ] Bonding inside steel sheaths Passive reinorements: - Bars - Eletro-welded mesh Ative reinorements: - Wires - 7-wire strands - Pre-tensioned bars In the absene o speii and representative results or bent bars, the atigue limit indiated in table shall be redued depending on the ollowing ator: in whih: d Diameter o the bar. D Bending diameter. σ D, red d = 1-3 σ D D No redution in the atigue limit will be neessary in vertial stirrups with a diameter o 10 mm or less Fatigue harateristis o anhorage devies and spliing o ative reinorement Anhorage and spliing devies shall be loated, wherever possible, in setions where the minimum variations in stresses our. CHAPTER 8-5

6 Generally, the atigue limit or this type o element is lower than the limit or reinorements, and shall be supplied by the manuaturer ater speii and representative tests have been onduted. Artile 39. Charateristis o the onrete 39.1 Deinitions The design harateristi strength, k, is the value adopted in the design or ompression strength, as the basis or alulations. It is also alled the speiied harateristi strength or design strength. The atual on-site harateristi strength value, real, is the value orresponding to the 5% quantile in the ompression strength distribution o the onrete supplied to the site. The estimated harateristi strength value, est, is the value that alulates or quantiies the atual harateristi strength on site based on a inite number o standardised ompression strength test results on test piees olleted in situ. It an be abbreviated to harateristi strength. The average tensile strength value, t,m, may be alulated, in the absene o test results, using the ollowing: = 0,30 i k 50 N / mm t,m t,m k 1 2 k = 0, 58 i k > 50 N / mm I test results are not available, the harateristi strength may be allowed to be less than the tensile strength, t, k, (orresponding to the 5% quantile) indiated, as a untion o the average tensile strength, t, m, using the ollowing ormula: 2 t, k = 0.70 t, m The average lexural strength, t,m,l, is indiated by the ollowing expression, whih is a untion o the total depth o the element h in mm: = {( 1,6 h /1000) } t, m, l max t, m; t, m The units are N and mm in all these ormulae. In this Code, the expression harateristi tensile strength reers always, unless otherwise indiated, to the lower harateristi tensile strength, t, k Identiiation o onretes Conretes shall be identiied in aordane with the ollowing ormat (whih shall be shown in the drawings and the struture s Projet Tehnial Speiiations): In whih: T - R / C / TM / A T Symbol whih will be HM in the ase o a mass onrete, HA in the ase o a reinored onrete, and HP in the ase o a pre-stressed onrete. R Speiied harateristi strength, in N/mm 2. C Initial letter showing the type o onsisteny, as deined in TM Maximum aggregate size in millimeters as deined in A Designation o the environment, in aordane with CHAPTER 8-6

7 It is reommended that the ollowing series is used or the speiied harateristi strength: 20, 25, 30, 35, 40, 45, 50, 55, 60, 70, 80, 90, 100 In whih the igures indiate the speiied harateristi ompression strength o the onrete at 28 days, expressed in N/mm 2. 2 The strength o 20 N/mm is limited to mass onretes. The onrete presribed shall be suh that, in addition to mehanial strength, it ensures ompliane with the durability requirements (minimum ement ontent and maximum water/ement ratio) orresponding to the environment o the strutural element and indiated in Charateristi stress-strain diagram o the onrete The harateristi stress-strain diagram o the onrete depends on a large number o variables: age o the onrete, duration o loading, shape and type o ross-setion, nature o the set o load ators in a ross-setion, type o aggregate, moisture level et. Given the diiulty o providing a harateristi stress-strain diagram or onrete appliable to eah speii design, the simpliied harateristi diagrams suh as those provided in Artile 21 may be used or pratial purposes, Design strength o the onrete The ollowing value shall be used as the design ompression strength o the onrete: in whih: d = α α Fator whih takes aount o the atigue in the onrete when it is subjeted to high levels o ompression stress due to long duration loads. The value o α = 1, is used in this Code. k The harateristi design strength. γ Partial saety oeiient used in the values indiated in Artile 15. The ollowing value shall be onsidered as the onrete s design tensile strength. in whih : td = α t α Fator whih takes aount o the atigue in the onrete when it is subjeted to high levels o ompression stress due to long duration loads. The value o α t = 1, is used in this Code. t, k Charateristi tensile strength. γ Partial saety oeiient used in the values indiated in Artile 15. k γ γ t, k 39.5 Design stress-strain diagram or the onrete When designing setions subjeted to a normal set o load ators in ross-setion, one o the ollowing diagrams shall be used or Ultimate Limit States: CHAPTER 8-7

8 a) Retangular parabola diagram This omprises a parabola o degree n and a retilinear segment (Figure 39.5.a). The vertex o the parabola is on the absissa ε 0 (strain o the onrete under ultimate load in simple ompression), and the end vertex o the retangle is on the absissa ε u ( (ultimate bending strain o the onrete ). The maximum ordinate in this diagram orresponds to a ompression o d. Figure 39.5.a. Parabola-retangle alulation diagram Figure 39.5.a. Paraboli-retangular design diagram The equation in this parabola is: n ε = σ d 1 1 i 0 ε ε 0 ε0 σ = d i ε 0 ε ε u The values o the maximum ompressive strain in the onrete under simple ompression, ε 0, are as ollows: ε = 0,002 0 i k 50 N/mm 2 ( ) 0, 50 ε 0 0, , i k > 50 N/mm 2 = k The ultimate strain values, ε u, are provided by: ε = 0,0035 i k 50 N/mm 2 u ( 100 ) 4 k ε u = 0, , i k > 50 N/mm 2 CHAPTER 8-8

9 And the value n, whih deines the exponent o the parabola is obtained as ollows: n = 2 i k 50 N/mm 2 [( 100 )/100] 4 n = 1,4 + 9,6 k i k > 50 N/mm 2 b) Retangular diagram This is ormed rom a retangle whose depth λ(x) h, and size, η(x) d, depend on the depth o the neutral axis, x (igure 39.5.b) and the onrete s strength. The values are: η η ( x) = η ( x) = 1 ( 1 η) h x i 0 < x h i h x < where: λ λ ( x) x = λ h x h i 0 < x h ( x) = 1 ( 1 λ) i h x < η = 1,0 i k 50 N/mm η = 1,0 - (k-50)/200 i k > 50 N/mm 2 2 λ = 0,8 i i k 50 N/mm λ = 0,8 - (k-50)/400 i k > 50 N/mm 2 2 Figure 39.5.b. Retangular alulation diagram ) Other alulation diagrams, suh as paraboli, bi-retilinear, trapezoidal, et. diagrams shall be aepted, provided that the results obtained rom these are satisatorily equivalent to those rom the retangle-parabola, and err on the side o saety Modulus o longitudinal deormation o the onrete The ollowing shall be adopted as the longitudinal seant modulus o deormation, E m at 28 days (slope o the seant o the atual urve σ-ε)): E = m m CHAPTER 8-9

10 This expression shall be valid provided that the tensions in servie onditions do not exeed the value o 0.40 m, with m being the average ompression strength o the onrete at 28 days. The initial modulus o longitudinal deormation o the onrete at 28 days, with regard to transient or rapidly varying loads (with the slope o the tangent at the origin), shall be taken to be approximately equal to E = β E Em k β E = 1,30 1, Figure Diagrammati representation o the stress-strain relationship in onrete 39.7 Shrinkage o onrete When alulating the shrinkage value, the various inluential variables have to be taken into onsideration, in partiular: ambient humidity, the thikness or smallest dimension o the element, the onrete s omposition, and the time whih has elapsed sine it was produed, whih deines how long shrinkage ontinues Creep in onrete The stress-dependent strain at time t, or a onstant stress, σ(t 0 ), o less than 0.45 m, applied at t 0, may be alulated in aordane with the ollowing riterion: 1 ϕ ( ) ( ) ( t, t ) 0 ε σ t, t = t 0 σ 0 + E,t 0 E28 in whih t 0 and t are expressed in days. The irst sum in brakets represents the instantaneous strain or a unit o stress, and the seond a unit o reep, in whih: E 28 Modulus o instantaneous longitudinal strain in the onrete, with the tangent at the origin, at 28 days as deined in E, t0 Seant value o the longitudinal strain in the onrete at time, t 0 applied to the load, as deined in ϕ(t,t0) Creep oeiient. CHAPTER 8-10

11 39.9 Poisson s rate A mean value o 0.20 shall be used or Poisson s rate, relating to elasti deormations at normal tensions in use Thermal expansion oeiient A igure o 10-5 shall be used CHAPTER 8-11