Bending resistance of high performance concrete elements

Transcription

1 High Performane Strutures and Materials IV 89 Bending resistane of high performane onrete elements D. Mestrovi 1 & L. Miulini 1 Faulty of Civil Engineering, University of Zagreb, Croatia Faulty of Civil Engineering, University of Rijeka, Croatia Abstrat Our previous researh was foused on reative powder onrete (RPC). In this artile high performane onrete (HPC) will be analyzed. With high performane onrete both load bearing apaity and esthetis are ombined to ahieve superior struture. Due to lesser dimensions of walls and olumns, spae in high rise buildings is better utilized. With the ombination of steel with high yield strength and dutility, diffiulties with dense longitudinal and shear reinforement are avoided. In this artile urrent knowledge about the properties, tehnology and omposition of high strength onrete is presented. Important parameters needed for the analysis of load-bearing (ultimate limit state), dutile and servieable (servieability limit state) reinfored onrete elements subjeted to bending, with or without longitudinal fore, are onsidered. These parameters are: design of ompressive stress diagram, dutility, defletion, and rak width restraint. The impat of tensile, ompression and shear reinforement are analyzed. The results are ompared with values for normal strength onrete. The use of high strength onrete is reommended. Keywords: high performane onrete, bending resistane, dutility. 1 Introdution Conrete with ompression strength of more than 60 N/mm is alled high performane onrete (HPC). The first high performane onrete was made in Today, onrete lasses C55/57 to C110/115 (aording to EC regulations) are alled high performane onretes. Conretes with higher ompression strength are alled ultra high performane onretes. It must be noted that high performane and ultra high performane onretes have doi:10.495/hpsm080101

2 90 High Performane Strutures and Materials IV durability enhanements that derease maintenane osts and lengthen the servie life of a struture. This is vital for strutures in aggressive environments (sea bridges et). The hoie of ingredients, prodution, transportation and finally uring for this onrete is very demanding and at the same time this is more important than for normal onretes. Buildings with high performane onretes are beoming more and more popular, espeially in seismially ative regions. Using high performane onrete results in less material being used, effetively meaning that the struture has smaller mass and as a result of this, seismi fores are lower. These strutures an be made dutile; they have the apaity to dissipate energy (plasti deformation of hinges), whih also ontributes to eonomial aspets. Dutile strutures an be alulated by the linear elasti theory and by the linear plasti theory, whih means that distribution of fores is more uniform, material is better utilised and less steel is used. A very important advantage of dutile strutures is the avoidane of brittle failure of elements and the whole struture. Very often, strutures made of high performane onretes have big spans and are designed for huge loads. A high ratio of live load/selfweight ombined with esthetial properties is also the main harateristi of high performane onrete. In ombination with high yield strength steel, the dutility problems due to dense longitudinal and shear reinforement are avoided. High performane onretes are also used for bridges where bearing apaity and durability are very important. Bridge olumns made of this material have a smaller ross setion, whih an be very important for free profile under bridges. Disadvantages of high performane onrete are: loss of dutility, whih is manly a problem for higher lasses and separation of the protetive layer due to reinforement (the area lose to the plasti hinges). Due to the dereased dutility, odes in some ountries have adopted their alulations for shear reinforement (USA), on the other hand in some ountries (Canada), where seismi ativity is high, use of high performane onrete is restrited. New experimental results suggest that the dutility limit has shifted from 55 N/mm (as suggested earlier) to 75 N/mm. Separation of the protetive layer an also be avoided using steel fibres (miro reinfored onrete). Steel fibres bond onrete ross setions very effetively and help in the forming of plasti hinges. In this artile urrent knowledge about the properties, tehnology and omposition of high performane (strength) onrete is presented. Important parameters needed for the analysis of load-bearing (ultimate limit state), dutile and servieable (servieability limit state) reinfored onrete elements subjeted to bending, with or without longitudinal fore, are onsidered. General properties and tehnology When making high performane onrete and hoosing ingredients, speial are must be taken. Conrete ingredients are ement, aggregate, water, hemial and mineral additives. The ratio of ingredients depends upon the desired properties and type of struture. The main problem is often ompatibility between ement and additives, whih is typial for high performane onretes. The methodology for testing ompatibility between ingredients is not standardized, so assessment

3 High Performane Strutures and Materials IV 91 depends fully upon probation mixtures. High performane onretes have a large amount of ement (>400 kg/m 3 ) and a lower water/ement ratio. The grain size distribution is haraterized by a dominant smaller grain size and a higher proportion of smaller frations. Superplastiizer is primarily used to derease the partiipation ratio of water in the onrete mixture. Additional additives are seleted on the basis of the requirements of the partiular appliation (strength, stiffness, freeze-thaw durability, or resistane to hemial attak). One of most effiient mineral additives is silia fume (silia fume is pozzolani additive). The brittleness of onrete rises with ompression strength. This an be partially avoided using fibres (as shown in figure 1). The improvement effet strongly depends upon the amount and type of fibres, frition between partiles and the quality of the ement matrix. For improvement of dutility and other properties (tensile strength, rak limitation and dynami response) steel fibres are usually used. Figure represents dependene upon the water/ement ratio and ompression strength that is often used when designing the onrete mixture. It is evident that for the same water/ement ratio a different ompression strength an be ahieved. This is primarily beause of mineral and hemial additives. Prodution proesses, transport, build in, and finally uring are muh more omplex than with normal onretes, so speial are must be taken. One of the most devastating effets when dealing with high performane onrete is autogeni shrinking. Autogeni shrinking is the result of a lesser volume of hydration produts than materials that enter proess. Autogeni shrinking begins immediately after the hydration finishes. Compared to normal onrete, high performane onrete is a homogeneous material. Most rules and equations regulating normal onretes an t be used for high performane onrete (this is espeially important for equations onerning bending strength). For the relation between ompressive (f ) and bending strength (f r ), the following equations an be used (see eqns. (1) and ()). High strength fibre Tensile stress Brittle onrete matrix Strain Figure 1: Stress-strain urves for onrete matrix and fibres.

4 9 High Performane Strutures and Materials IV Compression strength (MPa) Figure : Water/ement ratio Water/ement ratio and ompression strength after 8 days. f f r r 1 [ N / ] = 0.94 f mm (1) 4 [ N / ] = f f mm The relation between the modulus of elastiity (E ) and the ompressive strength of high performane onretes is given in eqns. (3) and (4). 3 Parameters for design E E 8 [ kn ] [ kn / ] 3 10 f + / mm () = (3) = 5 f mm (4) The mathematial relationship for strain-stress is given by Thorebfeld, Tomaszewitz and Jensen [10] in eqn. (5). σ is onrete stress, f k is the harateristi ompressive strength of onrete, ε is strain aused by stress σ and ε u is the limit strain of onrete (orresponds to f k ) σ ε n = (5) f ε nk n 1 + ( ε / ε ) k u u Values of other marks are given in eqns. (6) (8). k=1 for ε /ε u <1 (6) k=0.67+f k /6 for ε /ε u >1 (7) n=0.8+f k /17 (8)

5 High Performane Strutures and Materials IV 93 Limit strain is given in eqn. (9). E is the modulus of elastiity and is given in eqn. (10). fk n ε u = (9) E n 1 E 330 f (10) = k For design aording to ENV 199, designed ompressive strength f d must be alulated. Mansur et al [] suggest a modified stress-strain diagram, whih inorporates the influene of shear reinforement and steel fibres. Eqn (11) is given for the growing branh and eqn. (1) for the delining branh. Coeffiient β is given in eqn. (13). k 1 and k are orretion fators, E it is the initial modulus of elastiity, f 0 is peek stress and ε o is the deformation that orresponds to peek stress. β ( ε ε σ = / 0 ) f0 (11) β 1+ ( ε / ε β 0 ) k1 β ( ε ε σ = / 0 ) f0 (1) k β + ε ε β 1 1 ( / 0 ) k 1 β = (13) 1 fo /( ε0 / Eit ) Figure 3: Stress-strain aording to EC and CEB/FIB. Aording to Euroode regulations, for the stress-strain diagram the seond order parabola is used. This is shown in figure 3. For ompressive strength, a linear or paraboli diagram is assumed (this is experimentally proven for onrete of maximal ompressive strength of 60 N/mm ). Coeffiient α is assumed to be 0.85 for all ross setion shapes, exept for the ase where the width of the ompressive area shrinks from the neutral axis towards the ompressive edge (α=0.8 in that ase). For higher strength onrete eqn. (14) an be used.

6 94 High Performane Strutures and Materials IV 4 Dutility 10 α = (14) 0.85 f k A very important property of reinfored-onrete strutures is dutility or the ability to resist deformations very lose to the limit load without affeting bearing apaity. High performane onrete is a brittle material, so dutility demand is ruial. Most building odes have analytial equations for lassifiation of dutility. Experimental results show that a higher lass of onrete subjeted to bending and axial fore (or without axial fore) has higher dutility. This result must be taken very arefully as this is valid only for onrete with ompression strength up to 80 N/mm. Higher lasses are very sensitive and dutility dereases very quikly. The dutility of elements subjeted to bending is usually lassified by the oeffiient of dutility (loal dutility) defined by the ratio of limit urvature (Φ u ) and urvature when tensile steel reahes yield strength (Φ y ). Other ways to measure (assess) dutility are given in eqn. (15). δ u is maximal defletion in the mid span of the beam under 85% failure load and δ y is maximal defletion when the steel reahes yield strength. µ = δ / δ (15) d u y Many building odes, suh as the Amerian ACI, limit the oeffiient of tensile reinforement. This is done to ahieve better dutility. The oeffiient of tensile reinforement is limited as given in eqn. (16) for standard design situations and eqn. (17) for situations where redistribution of the bending moment is expeted. ρbs is the balaned oeffiient of reinforement and is defined in eqn. (18). ρ < ρ bs (16) ρ < 0. 5 ρ bs (17) ρbs 0,85 αv f = k f yk ε u E s ε u Es + f yk (18) European regulations [7] limit the height of the ompressive area. For higher ratios the use of double reinforement is proposed. For elements subjeted to bending, ompressive reinforement resists in ompressive stresses and thereby ontributes to dutility. Shear reinforement mainly ontributes to shear stresses, but it also entangles the ompressive area and ontributes towards higher ompressive strength and dutility. Some authors [8] have onluded that shear reinforement is ruial for dutility. For this reason, European regulations [9] limit maximal spaing between shear reinforement.

7 High Performane Strutures and Materials IV 95 5 Servieability The first rak aused by the bending of onrete element happens when the bending moment is equal to the raking moment as defined in eqn. (19). f r is tensile strength, I g is the moment of inertia, y t is the distane from the tensile border to the neutral axis. f r I g M r = (19) yt In eqn. (19) the tensile strength is most problemati, for whih only approximation is available. Many authors were investigating this problem, but until now no solution is given. If we ompare alulated vs. experimental values for the rak moment, variations of almost 40% our. Theoretial models prove that if shrinkage of onrete is inorporated, the variation is muh smaller, but this immensely ompliates the alulations. For that purpose, effetive modulus of elastiity is (E eff(t,τ) ) proposed as in eqn. (0). Φ(t,τ o ) is reep oeffiient in time t for onrete loaded at time τ o, λ(t,t o ) is the aging oeffiient (a value of 0.8 an be assumed). E ( τ o ) Eeff ( t, τ o ) = (0) 1+ χ( t, t ) Φ( t, t ) 6 Conlusion In this artile an overview of the properties, tehnology and omposition of high strength onrete is given. Important parameters (equations) for design of this onrete are given. It is shown that for this kind of material different equations are appliable. A proposal for a ompressive design diagram is given. The dutility of elements is investigated and it is shown that dutility inreases for ompressive strengths between 40 N/mm to 70 (80) N/mm and than rapidly dereases. The main fators that inrease dutility (ompressive strength, tensile and shear reinforement) are given and analyzed. It must be onluded that the future of high performane (strength) onrete is very bright, but additional experiments are needed to suessfully inorporate speifi properties of these onretes. Referenes [1] Skazli, M., Tomii, I., Reinfored onrete elements made of high performane onrete subjeted to bending, Gradevinar, pp , Zagreb, 006. [] Mansur, M.A, Chin, M. S., Wee, T. H., Flexural behavior of high strength onrete beams, ACI Strutural Journal, Vol. 94, No.6, [3] Radi, J., Conrete strutures manual, Croatian University Press, 006. [4] Tomii, I., Conrete strutures, Skolska Knjiga, Zagreb, o o

8 96 High Performane Strutures and Materials IV [5] Neevska Svatanovska, G., High strength onrete Maedonian researh, Gradevinar, pp , Zagreb, 004. [6] Edward Nawy, G., Fundamentals of high-performane onrete, John Wiley & Sons: New York, 001 [7] Euroode : Design of onrete strutures. Part 1-1: Basi rules and regulations for buildings (HRN ENV ), Zagreb, 004. [8] Rashid, M.A., Mansur, M.A., Reinfored High-Strength Conrete Beams in Flexure, ACI Strutural Journal, Vol. 10, No. 3, pp , 005 [9] Euroode 8: Design of Strutures for Earthquake Resistane, Part 1: General Rules, Seismi Ations Rules for Buildings, CEN, Brussels, 003. [10] Collins, M. P., Mithell, D., MGregor, J. G., Strutural Design Considerations for High-Strength Conrete, Conrete International, Vol. 15, No. 5, pp. 7 34, 1993.