Stress-Strain Curves of High Strength Concrete at Heightened Temperatures
Abstract—the stress-strain curve of High Strength Concrete (HSC) depends on temperature conditions. Elevated temperatures affect the strength, ductility, elastic modulus and brittleness of concrete. A study will be conducted to investigate the effect of elevated temperatures on the stress-strain curves of HSC. The stress-strain curve tests will be conducted at temperatures of 25°C, 100°C, 200°C, 400°C, 600°C, 800°C, and 1000°C with six variables of HSC. The variables will depend on the type of aggregate (lightweight, siliceous and carbonate aggregates) with and without steel fibers. Different types of aggregates will be used because they affect stress-strain curves and fire resistance. The research will consider the use of steel fibers since they improve the ductility and mechanical behavior of HSC. A constant exposure duration of 72 hours will be used, and stress-strain relationship monitored over this time. Two cylindrical HSC of 80MPa and 100MPa will be used, and a control specimen of 40MPa will also be investigated. A constant dimension of 100mm x200mm for cylindrical specimen will be used for this experiment. The results will be tabulated and analyzed using software called Statistical Analysis System (SAS).
Keywords— HSC, Stress-strain curve, Fire resistance, High Temperatures
igh Strength Concrete (HSC) has continued to gain popularity especially in the construction of high-rise buildings and long spanned bridges. Generally, concrete with strength less than 55MPa is classified as Normal strength concrete (NSC) while that with compressive strength above 55MPa is HSC, a subset of High-Performance concrete (HPC) . The substitution of HSC for NSC is a common practice due to improved strength and durability of HSC. Despite the rise in the application of HSC in buildings, there’s need to study the stress-strain curve and behavior of HSC when subjected to extreme temperatures to since fire safety is one of the design considerations for any structure.
The process of making HSC involves reduction of water to cement ratio and the addition of admixtures to improve the workability of concrete. Silica fume is also incorporated in the concrete mix to increase its strength. Consequently, the reduced water-cement ratio lowers its porosity making HSC less resistant to fire and more brittle compared to NSC . A clear understanding of fire resistance of HSC, when exposed to high temperatures for a specific duration is required. The basis for this is that in case the other ways of containing fire fail, the last resort in line of defence is the structural integrity.
Concrete fails in different ways when exposed to extreme temperatures. From the early 1950s, various studies have been conducted to predict the behavior of concrete when exposed to fire    . According to the research findings conducted by , extremely high temperatures make HSC more susceptible to failure through spalling than NSC. The reason for this is due to the high volume of silica in HSC . Additionally, rapid temperature increment is likely to cause spalling in concrete as compared to gradual temperature rise. The mechanical properties of concrete which change due to high temperatures are elastic modulus, strength and volumetric stability.
The design of structural elements requires that engineers consider serviceability and safety limit states. A collaborative research program, between the National Research Council of Canada (NRCC) and National Chiao Tung University (NCTU), Taiwan attempted to investigate the behavior of high-performance concrete columns . However, design guidelines for fire resistance of HSC were not developed at this stage. Currently, numerical calculations of fire resistance of concrete are acceptable but consume much time. These calculations also require material properties of concrete, and the stress-strain relationship of HSC is necessary for calculation and prediction of fire resistance of HSC. This research will help in coming up with design guidelines since the final curves will allow engineers to extrapolate and check if the structural designs of HSC conform with the fire safety requirements.
It is hypothesized that the addition of steel fibers on lightweight HSC improves its ductility more than the addition of similar steel fibers on plain HSC and this affect the stress-strain curve. The main objective of this research will be to develop stress-strain curves of high strength concrete when subjected to high temperatures and evaluate the endurance of HSC to fire. These will be achieved through variation of aggregates but maintaining concrete mix design and duration of exposure. Some of the research questions that this research should answer at the end of the exercise include:
i. How does compressive strength of concrete behave with an increase in temperature?
ii. How is the stress and strain of HSC affected at extreme temperatures?
iii. What effect does high temperature have on the ductility and brittleness of HSC?
II. LITERATURE REVIEW
Research on HSC has been done by different scholars to investigate various aspects of this material. According to the research conducted by , the experiment methodology involved the use of four different HSC cylinders exposed to temperatures of 20°C, 100°C, 200°C, 400°C, 600°C, and 800°C. They concluded that the strain of HSC at peak loading increases from 0.003 at room temperature and pressure to 0.02 at 800°C. The results from stress-strain tests also showed that below 600°C, HSC exhibited brittle properties, but when the temperatures were above 600°C it exhibited ductile properties. The study also showed that the type of aggregate affects the ultimate strain of HSC since carbonate aggregates attained more considerable strain than siliceous. Additionally, it was evident that HSC lost its strength by approximately 75% for temperatures above 800°C.
Another study by  involved comparison of HSC and NSC under pre-loaded and loaded conditions when exposed to transient high temperatures. It showed that initially, when exposed to high temperatures between 100°C and 300°C, HSC lost its strength by up to 15-20%. However, it regained the strength by about 8-15% due to continuous exposure of temperatures between 300°C and 400°C.
While studying the effect of high temperatures on the residual strength of HSC,  used twelve HSC mixtures including lightweight concrete and two types of aggregates. Each concrete made with a specific type of aggregate was made with and without adding polypropylene fibers. At the end of the experiment, they noted a significant loss of residual strength at a constant temperature of 300°C. It was also concluded that the residual strengths of HSC at exposed temperatures of over 300°C are different from residual strength for NSC.
In an attempt to compare the strength between HSC made using Portland pozzolana cement (PPC) and Ordinary Portland cement (OPC),  made standard square cubes of 150mm and crushed at different days. They concluded that HSC made with PPC has better strength than those made using OPC because they retained more residual compressive strength.
Other scholars such as    and  attempted to explain the reason for the decreased strength of concrete due to high temperatures. They give reasons such as the development of micro-cracks attributed by thermal incompatibility between aggregate phase and cement paste. Others reason that the destruction of gel structure during extreme heating and decomposition of calcium hydroxide into lime then lime re-hydration are some of the reasons why the strength of concrete deteriorate when the temperatures are extremely high.
A. Stress-Strain Curve HSC
The shape of stress-strain curves for uniaxial loading depends on various conditions. The stress-strain behavior of concrete depends on various factors such as temperature, the rate of loading, type of aggregates, specimen size, cement properties and other factors  . Strain rate, shape and size of specimen, type of testing machine used, type of strain gage, and specimen vs. machine stiffness are some of the factors which affect uniaxial stress-strain diagram. Concrete properties which also strongly affect the stress-strain diagram include age of concrete at the time of testing, properties of cement, water-cement ratio, curing, aggregate type and properties .
The literature on the stress-strain behavior of HSC has not been widely covered due to the difficulty encountered in measuring the descending portion of the curve. Experiments were done by  and used specimen of 3”x6” to obtained stress-strain curves of HSC. However,  noted that it was difficult to attain the descending part of the curve experimentally. Reports compiled by  and  also attempted to explain the behavior of HSC. While exposing concrete specimen of 4’’X8” and 3”x9” at a constant circumferential strain rate and varied axial strain,  drew stress-strain curves. Researchers explain that the existing differences between HSC and NSC include;
i. At maximum stress, HSC has higher strain and at the descending part of the curve, HSC has steeper slope.
ii. HSC has more linear stress-strain relationship to a high percentage of the maximum stress.
Experimental study by  revealed that the length of straining gauges affects the shape of strain-stress curve at descending part of the curve.
To successfully attain the objectives of this research and compile stress-strain curves for HSC at elevated temperatures, qualitative observational method will be used. Experiment will be conducted and resulted tabulated. Further analysis using Statistical Analysis System (SAS). To achieve all these, the steps outlined in figure 1 (Appendix) will be followed.
Test cylinders of 100mmx200mm will be used. The mix design to use will be presented as shown in table 1. For temperatures below 200°C, a ventilated oven will be used but for over 200°C, electrically heated furnace will be used. The specimen will be subjected to temperatures of 25°C, 100°C, 200°C, 400°C, 600°C, 800°C, and 1000°C. Before heating specimen t temperatures above 100°C, all the samples will be placed in an oven maintained at 60°C for 72 hours to avoid explosion. A constant rate of heating of 200°C/hr in electric furnace will be used. The stress-strain test will be done on a closed-loop servo-control 220 Kip hydraulic pump actuator with a loading frame. Before performing the test, the machine in figure 2 will be calibrated against the samples temperatures using thermocouples.
Figure 1: Stress-strain test equipment loading frame with furnace
B. Material properties and specimen
The characteristics of materials affect strength of resultant concrete. In this case, fine aggregates, coarse aggregates, cement, water and admixtures will be used.
This experiment will use PPC considering the research findings by  which proved that PPC results in better strength than OPC. Cement acts as a binding material in concrete. The PPC will be checked to conform to ASTM 150.
Pure distilled water without impurities will be used for this experiment. The cement water ratio will be closely monitored since it affects the strength of resultant concrete.
The experiment will use river sand obtained from the local market. Generally, fine aggregates fill the voids between coarse aggregates.
The aggregates will vary from siliceous, carbonate and lightweight. Course aggregates significantly contribute to the strength of resultant concrete. To obtain lightweight high strength concrete, this study will use flashag since it was experimentally approved to be sufficient for making HSC in a study done by . The reason for checking on lightweight concrete is that engineers seek for alternatives of reducing dead loads and it is proper to find fire resistance of this type of concrete too. The maximum size of course aggregate will be 3/8 inches. Granite will be used for siliceous aggregate and limestone for carbonate aggregate.
Admixtures modify the properties of concrete mix. Silica fume powder will be used to improve the strength of concrete since it has high Si02 content and very reactive with PPC . Superplasticizers will be used to enhance workability while reducing water-cement ratio. Superplasticizers are the main chemical admixtures which increase the strength of concrete.
This research will use six different specimen of 100mmx200mm. Three cylindrical cubes made of lightweight, carbonate and siliceous aggregates with and without steel fibres will be used. The experiment will adopt concrete of strength 40, 80 and 100MPa.
Table 1 is proposed to be used for calculating the mix design
Table 1: Proposed tabular form for obtaining mix design
A strain control technique will be used to get data in the descending part of the stress-strain curve of concrete. Instantaneous stress related strain denoted as
is a function of temperature and applied stress. The shape of stress-strain curve of HSC at elevated temperatures are defined by the peak stress
and the initial value for the Modulus of Elasticity,
The following model can be used to find
and T denotes Temperature
IV. DATA ANALYSIS, EXPECTED OUTCOMES AND FOLLOW UP ACTIVITIES
A. Data Analysis
The data collected will be analyzed using SAS and stress-strain curves developed. A typical graph of stress-strain relationship of HSC when subjected to high temperatures is shown in figure