Stress-strain curves of prestressing steel after exposure to elevated temperatures

Transcription

1 Southern Cross University 23rd Australasian Conference on the Mechanics of Structures and Materials 24 Stress-strain curves of prestressing steel after exposure to elevated temperatures Zhong Tao University of Western Sydney Publication details Tao, Z 24, 'Stress-strain curves of prestressing steel after exposure to elevated temperatures', in ST Smith (ed.), 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23), vol. II, Byron Bay, NSW, 9-2 December, Southern Cross University, Lismore, NSW, pp ISBN: epublications@scu is an electronic repository administered by Southern Cross University Library. Its goal is to capture and preserve the intellectual output of Southern Cross University authors and researchers, and to increase visibility and impact through open access to researchers around the world. For further information please contact epubs@scu.edu.au.

2 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23) Byron Bay, Australia, 9-2 December 24, S.T. Smith (Ed.) STRESS-STRAIN CURVES OF PRESTRESSING STEEL AFTER EXPOSURE TO ELEVATED TEMPERATURES Zhong Tao* Institute for Infrastructure Engineering, University of Western Sydney Penrith, NSW 275, Australia. (Corresponding Author) ABSTRACT To evaluate the damage to a structure after fire exposure, the residual mechanical properties of structural materials need to be evaluated first. A literature review is conducted to analyse the major factors influencing the post-fire properties of prestressing steel. Existing test data are collected from an extensive survey of the available literature. A simplified stress-strain model is developed for prestressing steel in residual conditions (i.e. after heating and cooling to room temperature). Measured stress-strain curves are used to verify the accuracy of the proposed model. KEYWORDS Prestressing steel, stress-strain curves, post-fire, temperature effects, damage evaluation. INTRODUCTION The prestressing technology has been widely used in prestressed concrete. In general, prestressing steel is more sensitive to temperature than ordinary hot rolled steel (Gales et al. 2). In the past, many tests were carried out to evaluate the residual mechanical properties of prestressing steel after fire exposure. However, due to the many influencing factors, such as heating temperature, exposure time, steel type, heating rate, cooling method, and initial loading, it is not possible to accurately investigate all influencing factors in a particular condition. In particular, there were errors due to uncertainties in the measurements themselves. Preferably, all published test data should be collected and used to make a comprehensive and reliable evaluation. Furthermore, post-fire stress-strain models of materials are required to conduct an accurate structural analysis for fire-damaged prestressed concrete members and structures. No such model for prestressing steel, however, is available in any current design codes. A literature review is presented in this paper to describe the influence of several different factors on the residual mechanical properties of prestressing steel. Utilising the collected test data, a simplified stress-strain model is developed; finally, the accuracy of the proposed model is verified against the available experimental stress-strain diagrams. LITERATURE REVIEW Three basic types of high-strength prestressing tendons, namely cold-drawn wires, strands and highstrength bars are used in concrete structures. Nowadays, strands are the most commonly used type of prestressing steel. In North America, low-relaxation strands have become the standard product. Prestressing steel is manufactured from high-carbon steel with pearlitic (eutectoid composition) or near-pearlitic microstructure, which is a two-phased, lamellar structure consisting of alternating layers of alpha-ferrite (pure iron) and cementite (Fe 3 C). The carbon content by weight normally varies from.7 to.85%. The heavy drawing process severely elongates individual grains in the direction of the longitudinal axis of the steel. The high values of strength of the steel are obtained thanks to the decrease of interlamellar spacing during the drawing process, which causes the dislocations at the This work is licensed under the Creative Commons Attribution 4. International License. To view a copy of this license, visit 7

3 ferrite/cementite interphase to block (Toribio 24). Influence of Heating and Cooling Exposure to a certain temperature level may lead to a decay of the mechanical properties of steel. For prestressing steel, the influence becomes apparent after heating to temperatures higher than 3C. The test results reported by Felicetti et al. (29) indicate that the decrease in yield stress is only 5% for reinforcing steel heated up to 7C and cooled to room temperature, whereas the decrease is 64.% for prestressing steel heated to the same temperature. This comparison exemplifies the significant sensitivity of prestressing steel to heating when compared to reinforcing steel. Influence of Cooling Method The cooling rate affects the microstructure of steel. To investigate the influence of the cooling rate on the post-fire behaviour of prestressing steel, three cooling methods, namely cooling in air (CIA), cooling in furnace (CIF), and cooling with water jet (CWJ), were adopted by some researchers. The cooling rate of CIF is the lowest, followed by that of CIA, whereas the cooling rate of CWJ is the highest. When heated below 7C, no evident influence on the mechanical properties of prestressing steel was found for the different cooling methods. On the contrary, considerable variation in test results are found for specimens heated above 7C. After heating at temperatures above 7C, the steel generally has a slightly higher strength when the CIA method is used. The lowest values are obtained when the steel is kept in the furnace to cool down. Influence of Heating Rate and Hold Time Period of Heating In civil structures, prestressing steel is expected to be insulated by a concrete cover. Its rate of heating in fire depends on the fire intensity, location of the prestressing steel, concrete embedment, and many other factors. In previous tests, the heating rate selected varied from 3 to 2 C/min. Statistical analysis indicates that the mechanical properties of prestressing steel are not obviously affected by the heating rate. The hold time period (t s ) of heating may affect the performance of prestressing steel after fire exposure. To guarantee a uniform distribution of the temperature, the specimen needs to be kept in the furnace at the reference temperature level for a minimum time, which depends mainly on the diameter of the specimen. The test results reported by different researchers consistently demonstrate that increasing t s has a detrimental influence on the residual yield stress and tensile strength of prestressing steel. This can be attributed to the continuous influence of t s on the dislocations and microstructure of the prestressing steel. The strength decrease, however, is normally within %. Influence of Steel Type No obvious difference was found between steel wires and steel strands in terms of influence of fire exposure. This is also true for different types of prestressing steel, including as-drawn, stress-relieved and low-relaxation steel. For as-drawn wires or strands, however, an increase in.2% proof stress (f p.2 ) up to 29% was observed after heating to temperatures of 2C or 3C. Unheated as-drawn prestressing steel exhibits significant nonlinearity. It actually goes through a stress-relieving process when heated to temperatures around 2-3C, and the elastic range of the wires or strands can be increased in comparison to the original as-drawn condition. This explains the increase in f p.2 for the as-drawn prestressing steel after the particular heat treatment. Therefore, a generalised post-fire stressstrain relationship is suitable for different types of prestressing steel without special consideration for as-drawn wires and strands. Influence of Preloading Most post-fire tests conducted on prestressing steel were carried out starting from zero stress level. To simulate the actual fire conditions, preloading was applied in some tests. In general, no obvious ACMSM

4 detrimental effect of preloading on prestressing steel was observed. POST-FIRE STRESS-STRAIN MODEL Test Data The aim of this research is to develop a simplified stress ()-strain () model for prestressing steel after heating and cooling to room temperature. For this purpose, an extensive survey of the available literature was carried out. A total of 246 test data and 37 - curves were collected from 6 studies. The tensile strength at room temperature (f p ) ranges from,248 to 2,89 MPa, whereas the maximum temperature T ranges from to 9C. For the collected test data, most researchers reported the residual tensile strength (f pt ) and yield stress, but less information is available for the residual modulus of elasticity (E pt ) and in particular the ultimate strain ( ut ) corresponding to f pt. Most collected curves were reported to a strain level of 3-5%, which is significant for most structural applications. Stress-Strain Curve Expression Figure shows a typical - curve reported by Felicetti et al. (29) for prestressing steel at room temperature. The high-strength steel does not show a well-defined yield point. The initial response to the strain increment is linear elastic (from Point O to Point A), followed by non-linear work-hardening of the material (from Point A to Point C). After reaching the tensile strength at Point C, the curve enters into necking and failure stage. A simple idealised bi-linear - relation is suggested in Eurocode 2 (24), as shown in Figure. This model can be expressed as: Ep for fp. / Ep ( u )( fp fp.) () fp for fp. / Ep u u fp. / Ep For simplicity, the above bi-linear model will be referred to as EC2 model hereafter. In this model, the relation can be determined by four parameters, i.e., f p., f p, E p and u, where f p. and E p are the.% proof stress and modulus of elasticity at room temperature, respectively; and u is the ultimate strain corresponding to f p. Using experimental values for these parameters, the prediction from EC2 model is compared with the test curve shown in Figure, which indicates a very good agreement. f p f. B A EC2 model C Test curve (Felicetti et al. 29) O f. /E p Figure. Simplified - model for prestressing steel at room temperature Fire-damaged prestressing steel exhibits less strain hardening during tensile deformation compared with unheated prestressing steel. Therefore, it is decided that the bi-linear EC2 - relation can be used for post-fire prestressing steel, and possible revisions to the material parameters are required to consider the influence of fire damage. The revised - model is expressed as follows for post-fire prestressing steel: u ACMSM

5 EpT for fp.t / EpT ( ut )( fpt fp.t ) (2) fpt for fp.t / EpT ut ut fp.t / EpT where f pt and f p.t are the residual tensile strength and.% proof stress, respectively, for the steel heated to a temperature T; E pt is the residual modulus of elasticity; and ut is the ultimate strain corresponding to f pt. Determining f pt The ratios of f pt /f p for the collected data are shown as a function of T in Figure 2. According to the previous literature review and discussion, the test data for specimens heated above 7C are discarded if the specimens were cooled in air or by water jet. This is done for two reasons: first, if heated over 7C, specimens cooled in furnace have statistically lower strength compared with specimens cooled in other methods; and second, since prestressing steel is embedded in concrete, it is expected that prestressing steel is more likely to cool down slowly as in a furnace due to the heat sink effect of the concrete. A nonlinear regression analysis is performed, and Eq. 3 is proposed to predict f pt. The coefficient of determination R 2 is.966, which indicates very high correlation between the ratio of (f pt /f p ) and T. According to Eq. 3, no strength loss occurs when T is below 2C, and a sharp decrease in tensile strength takes place when T is between 4C and 7C. After that, a relatively stable residual tensile strength is achieved. At a heating temperature of 7C, the predicted loss of tensile strength is 63.5%. f / f.27 pt p.37 T / 5 (3) 7 Formulae to predict the residual tensile strength were proposed by Tao et al. (23) for post-fire hotrolled and cold-worked/heat-treated reinforcing steel. Using those formulae, the predictions for reinforcing steel are shown in Figure 2 as well. Compared with reinforcing steel, much significant loss of tensile strength is expected for prestressing steel after heating to 4C and above. Determining f p.t Various arbitrary methods have been proposed for defining the yield point of high-tensile steel, such as the. % proof stress (f p. ),.2% proof stress (f p.2 ) or.% strain (f p ). For the test data collected, only.2% proof stresses were reported in the majority of the references. Although there are some discrepancies between the yield stresses determined by using different definitions, it can be assumed that the percentages of strength loss are the same regardless of different yield stress definitions. In the following, f p.t /f p. is replaced by f p.2t /f p.2 or f pt /f p if the ratios of f p.t /f p. were not reported. f p.2t and f pt are the residual.2% proof stress and stress at % elongation, respectively, for prestressing steel heated to a temperature T. Figure 3 shows the experimental values of (f p.t /f p. ). Once again, the test data for specimens heated over 7C are discarded if the specimens were cooled in air or by water jet. The trend of the loss in yield stress against temperature is similar to that of tensile strength, which can be seen from Figures 2 and 3. Therefore, a formula similar to Eq. 3 is proposed to predict f p.t : f / f.5 p.t p..76 T / 56 (4) 5 Similarly, formulae have been presented by Tao et al. (23) to predict the residual yield stress of post-fire hot-rolled and cold-worked/heat-treated reinforcing steel. Compared with reinforcing steel, much more significant loss of yield stress is also expected for prestressing steel after heating to 4C and above, as shown in Figure 3. ACMSM

6 .2 Hot-rolled reinforcing steel (Tao et al. 23).2 Hot-rolled reinforcing steel (Tao et al. 23) f pt /f p R 2 = f / f.27 pt p.37 T / Temperature T (C) Cold-worked reinforcing steel (Tao et al. 23) Figure 2. Ratio of f pt /f p as a function of T f p.t /f p R 2 =.97 f / f.5 T / 5 p.t p Figure 3. Ratio of f p.t /f p. as a function of T Temperature T (C) Cold-worked reinforcing steel (Tao et al. 23) Determining E pt The variation in the ratio of E pt /E p increases once the exposed temperature T is over 5C. When T is below 7C, the heat exposure has little effect on the residual modulus of elasticity E pt. However, a reduction in E pt was found when T is over 7C. Eq. 5 is proposed to predict E pt. Ep T 7C E pt (5) ( T 2.5 T ) Ep 7C T 9C Determining ut Test data of ut is extremely scarce, which was either directly reported or retrieved from the full-range - curves. No obvious trend can be observed on ut as the temperature increases. Before a solid conclusion can be reached, the ratio of ( ut / u ) may be taken as unity for the temperature range 2-6C. Beyond this temperature range, it is on the safe side for ductility if ut / u is taken as unity. Comparison between and Test Curves The collected test curves are further used to verify the proposed - model for fire-damaged prestressing steel. In the calculations, four parameters including f p., f p, E p and u need to be used. In general, reasonably good agreement is achieved between the predictions and measured - curves, as shown in Figure 4. CONCLUSIONS Prestressing steel is very sensitive to temperature, and heat exposure can bring in a significant decrease of the mechanical properties. A bi-linear stress-strain model has been developed for prestressing steel after exposure to elevated temperatures and cooling to room temperature. In general, the predicted stress-strain curves show good agreement with the available test results. The models are valid for wires and strands with a tensile strength ranging from,2 MPa to 2, MPa, and a heating temperature not higher than 9C. Further tests are still required to investigate the influence of heat exposure on the ultimate strain and modulus of elasticity for prestressing steel. In particular, more full-range stress-strain curves should be reported. These test data can be used to further verify the proposed model and improve the prediction accuracy if required. ACMSM

7 Stress (MPa) Stress (MPa) Stress (MPa) Stress (MPa) Test (Felicetti et al. 29) T=4C, E p=95, MPa, f p=,935 MPa, f p.2=,73 MPa, u=.93, 2.7 mm strand Test (Moore 28) T=26C, E p=78,6 MPa, f p=,96 MPa, f p=,76 MPa, u=.8, 9.5 mm strand Strain (a) Strain (b) Test (MacLean 27) 6 4 Test (MacLean 27) 4 T=5C, E p=24, MPa, f p=2,2 MPa, f p.2=,843 MPa, u=.3, 4.4 mm wire 2 T=7C, E p=24, MPa, f p=2,2 MPa, f p.2=,843 MPa, u=.3, 4.4 mm wire Strain Strain (c) (d) Figure 4. Comparison between stress-strain relation model and test curves REFERENCES British Standards Institution (24) Design of concrete structures Part -: General rules and rules for buildings, Eurocode 2, BS EN 992--:24, London, U.K. Felicetti, R., Gambarova, P.G. and Meda, A. (29) Residual behavior of steel rebars and R/C sections after a Fire, Construction and Building Materials, Vol. 23, No. 2, pp Gales, J., Bisby, L.A. and Gillie, M. (2) Unbonded post tensioned concrete in fire: A review of data from furnace tests and real fires, Fire Safety Journal, Vol. 46, No. 4, pp MacLean, K.J.N. (27) Post-fire sssessment of unbonded post-tensioned concrete slabs: Strand deterioration and prestress loss, Master s Thesis, Department of Civil Engineering, Queen s University, Ontario, Canada. Moore, W.L. (28) Performance of fire-damaged prestressed concrete bridges, Master s Thesis, Faculty of the Graduate School, Missouri University of Science and Technology, Rolla, Missouri, U.S.A. Tao, Z., Wang, X.Q. and Uy, B. (23) Stress-strain curves of structural and reinforcing steels after exposure to elevated temperatures, Journal of Materials in Civil Engineering, ASCE, Vol. 25, No. 9, pp Toribio, J. (24) Relationship between microstructure and strength in eutectoid steels, Materials Science and Engineering: A, Vol , pp ACMSM