Experimental study of the structural behavior of non-prismatic reinforced concrete frame using different types of concrete under static and repeated load

This paper experimentally investigates the behavior of a non-prismatic concrete frame using different types of concrete under static and repeated loads. The parametric study includes changing the type of concrete (conventional concrete, steel fiber reactive powder concrete (SF-RPC) and glass fiber reactive powder concrete (GF-RPC)) and loading type (static and repeated). The results were presented and discussed the effect of SF-RPC and GF-RPC on frame behavior, and compared with the conventional concrete frame through the first crack load, ultimate load and failure mode, load–deflection curve, and the frame-deflected shape. There were evidences of improvement in the frame properties, such as a change in the failure mode, an increase in the ultimate load, as well as an increase in the stiffness of the frame in all the types of loading. The ultimate static load increased by 45.9 and 40.5% for SF-RPC and GF-RPC frames, respectively. Using RPC improves fatigue resistance, as the ultimate load decreases by only 2% under the influence of repeated load. In comparison, the conventional concrete frame decreases by 27%. The use of RPC in the specimens improves the shear strength and stiffness of the frame. The RPC is environmentally friendly through the use of recycled materials in mixtures (silica fume, steel fiber, and glass fiber), and also the structural sections are small; thus, the gasses emitted (CO2) are few. As well as, it eliminates the need to consume new materials and impede construction for the public, because of the extension of the structural life.


Introduction
Reactive powder concrete (RPC) is a type of cement-based composite, a special type of high-performance concrete (HPC) that was discovered in 1995 by Richard and Cheyrezy (1995).It consists of several main materials to improve the microstructure of concrete, such as cement, silica fume, fine aggregate, super plasticizer, and a small amount of water and elimination of the coarse aggregate.It has superior mechanical properties and high durability.RPC was exposed to brittle failure more than conventional concrete due to its very dense microstructure, so fibers are added to improve its ductility.The commonly used type of fiber was steel fiber (SF), which was a volumetric proportion of concrete (Algburi et al., 2018;chang et al., 2009;Lee et al., 2007;Malik & Foster, 2010).The researchers found that increasing the fiber size ratio 0, 1, 2, 3, and 4 increases the compressive strength of concrete (Yunsheng et al., 2008).Ju et al. (2007) found that adding 1.5% SF gives better compressive strength than a lower percentage of SF.
The use of RPC with SF in many structural members, for example, Alwash and Baker (2018) presented a practical study of a simply supported beam to investigate the effect of using RPC on flexural behavior.Study the effect of changing the volume ratios of SF on the ultimate load of the beam and compare it with conventional concrete.The results showed that changing the percentage of SF from (0-2) % leads to an increase in the ultimate load from (8-85) % compared to conventional concrete.Kareem and Deyab (2020) studied a continuous beam with two spans using RPC with different SF ratios (0, 0.6, 1.3, 1.8, and 2.5%) and compared it with a conventional concrete beam.The results showed an increase in the ultimate load when using RPC, as well as an increase in the ultimate load when increasing the SF ratio, as the increase ranged from 23 to 90%.
After the success of using SF in RPC mixtures, many researchers resorted to the discovery of new fibers that could add improvements to the properties of RPC, including glass fibers (GF).There is very little research on using GF in RPC mixtures, and GF is very useful in improving the properties of flexural strength and splitting tensile of concrete (; Raza et al., 2020a,;Ali & Qureshi, 2018, 2019;Ali et al., 2019, b;Liu et al., 2018).GF has been used in some structural applications with strength (40-60) Mpa (Ferreira & Branco, 2007).GF is not as effective as SF in mechanical properties, but it has other benefits such as corrosion resistance, which gives long life to RPC, and is lightweight (equivalent to 1/3 the weight of SF) (Raza et al., 2020a;b).
Resif (2020) used the GF-RPC as a repair material for a simply supported beam with conventional concrete.Prisms of GF-RPC were used in specific zones (lower mid-beam, upper mid-beam, lower edge-beam).The results showed that the repaired beam gives better behavior than the original beam in the ultimate load, first cracking, and deflections.
Reinforced concrete buildings contribute to environmental impacts, as the gasses emitted as a result of the greenhouse at the present time represent a global challenge, where 77% of the emissions emitted are carbon dioxide (Kaveh et al., 2020).Therefore, the researchers resorted to the optimal use of concrete and steel reinforcement by redistributing the concrete variable sections according to the presence of high stresses (Kaveh & Bakhshpoori, 2019).Changing the sections of the members in the width of members causes complications in the construction, so it is preferable to be in the depth.The use of variable depth of the sections provides additional benefits as it facilitates the passage of many utilities and equipment such as electricity, refrigeration, sewage, etc. (Archundia-Aranda et al., 2013;Tena-Colunga et al., 2008).Dawood and Abdulkhaleq (2017) studied continuous beams with prismatic and non-prismatic sections for the purpose of knowing the effect of changing the sections in depth using conventional concrete and RPC.The results confirmed an increase in the ultimate load of the beams when using non-prismatic sections, where the increase was 51% for the RPC and 4-19% for the conventional concrete.Kaveh (2020) theoretically studied the effect of using non-prismatic sections on the final cost of the project as well as greenhouse gas emissions (CO 2 ).It was concluded that the use of nonprismatic sections will reduce the final cost by 7%, while the emitted gasses will decrease by 3-14%.
The main objects of this work were the casting, curing, and testing of six specimens of non-prismatic reinforced concrete frames under static and repeated load.All specimens have identical geometry and reinforcement.Conventional concrete was used in two specimens, one was tested under static load and the other repeated load.SF-RPC was used also in two specimens as it was the most common material in RPC.As for GF-RPC, the most recent topic and the least studied, two specimens were also cast for the purpose of demonstrating the behavior of the frame with GF-RPC and making comparisons with SF-RPC and conventional concrete.Comparisons focused on the ultimate frame load, type of failure, first crack, load-deflection curves in the middle of the beam, and frame-deflected shape.All specimens used are non-prismatic sections (variable in depth).The ratio of the small depth to the large depth used on the specimens was (1/3) (Kadhim, 2007).While, the other dimensions of the frame were determined according to the instructions of the acceptance criteria for moment frames based on structural testing (ACI T1.1-01 2001).

Specimens design and details
To study the effect of using GF-RPC on the concrete frame and compare it with SF-RPC and conventional concrete, six specimens were prepared, cast, cured, and tested and divided into two groups.Each group includes three specimens with different concrete materials.Group A specimens were tested under static load while group B was tested under repeated load.The symbols of the specimens used and their details are shown in Table 1.
The length of the columns in the frames used was 1000 mm, and the cross-section was prismatic with dimensions (150 * 150) mm.While the length of the beam was 1000 mm, and the cross-section was non-prismatic in depth (tapering), as it begins at the edges (170 * 150) mm and continues to decrease until reaching the middle of the beam

Group
Symbol Type of material Type of load Notes and has dimensions (130 * 150) mm.The reinforcement design was the same for all specimens and was in accordance with the requirements of the American Concrete Institute (ACI-318, 2019).For columns, 4Ø10 was used for longitudinal steel bars, and Ø6@120 mm for ties.While, the beam reinforcement was 2Ø10 to resist positive moments and also 2Ø10 to resist negative moments, and Ø6 @60 mm to resist shear stresses.Figure 1 shows the dimensions and steel reinforcement details of the specimens used.
The reinforcing steel was fixed in the wooden mold well using plastic spacers with a dimension of 20 mm to maintain an adequate distance between the reinforcing steel and the mold.When casting concrete into the mold, vibrators were used to reduce air gaps in the concrete.After 24 h of casting the specimens, the molds were opened and the curing stage begins.The specimens are covered with canvas to keep the specimens moist when sprayed water for the required period.Before the testing, the specimens were cleaned well and painted to show the cracks well upon testing.For the purposes of differentiating between the specimens, two colors were used, white for conventional concrete specimens and yellow for RPC specimens.Figure 2 shows the stages of casting and curing specimens.

Mix proportion and material properties
In this study, three types of concrete were used, where conventional concrete represented the first type and consists of Portland cement, fine aggregate, and coarse aggregate, as this mixture was designed according to ACI-211.1-2004.The second type of concrete used was SF-RPC, which consisted of Portland cement, silica fume, fine sand with a maximum size of 0.6 mm, superplasticizer, and addition to steel fibers with 1.5% of the total volume of mixture to give ductility to the concrete.The third type was GF-RPC, and it has materials similar to the second type, except that glass fiber is added instead of steel fiber.All materials used in this study are in accordance with the standard of ASTM.Many trial mixtures of the three types were mixed  to reach the optimal proportions of the materials.Table 2 presents the proportion of materials used in this study.
The mixing sequence of the RPC contents and the time needed to mix each material is necessary to obtain high compressive strength and other physical and mechanical properties.Figure 3 shows the sequence mixing for RPC where first, cement, sand, and silica fume were mixed for about 10 min.Then the superplasticizer and water were added in two steps and mixed for 10 min.When the mixture was able to flow, the fiberglass or steel fiber was added and mixed for an additional 5 min (Yang et al., 2010).
Deformed bars were used for all diameters used in this study.Reinforcing steel with a diameter of Ø10 was used for the main longitudinal reinforcement of columns and beams, while Ø6 was used for tied and stirrups, all of which are according to ASTM.In SF-RPC mixtures, micro-steel fibers with a length of 12-14 mm and a diameter of 0.2-0.25 mm were used, while in GF-RPC mixture alkali-resistant glass fibers with a length of 12 mm and a diameter of 0.14 mm were used.Table 3 shows the mechanical properties of steel reinforcement, SF, and GF.

Mechanical properties of solid concrete
Table 4 presents the mechanical properties of the tests of the used concrete mixtures (both types of RPC and conventional concrete).The compressive strength of RPC was determined after testing six cubes with dimensions of 50*50*50 mm.The researchers (Aziz & ahmed, 2012;Graybeal & Davis, 2008;Mossa & Ali, 2023) concluded that the cube test result was equal to or very close to the cylinder test result mentioned in ASTM C1856 (2017).For the conventional concrete, six cubes with dimensions 150 * 150 * 150 mm was tested.Flexural test of the concrete used tested according to the ASTM C78-C78M-15a (2015).The modulus of elasticity of RPC was calculated according to the (Eq. 1 ) (Grayeabl, 2007), while the conventional concrete was calculated according to the (Eq. 2 ) (ACI 318-19, 2019).

Testing and instrumentation
The specimens were tested by applying two point load on the beam.To prevent the occurrence of local crushing below the loading point, rubber plates were placed to avoid stress concentration, while support cups were placed at the bottom of the columns."The supporting cups were approximately fixed.The proof for that is the rotation in the deflected shape of the columns near the cups is approximately zero or minimal values at the large loads" (Al-hussainy, 2015).
(1)  To measure the deflection of the beam, two dial gages were used below the beam, where the first was below the left point load, while the other was below the mid-span of the beam.While measuring the deformation of the columns, two dial gages were placed next to the left column, where the first was at a height of 620 mm from the base of the column, while the other was approximately at the top of the column.All dial gages have an accuracy of 0.01 mm. Figure 4 shows the position of the dial gages and support cups.
The specimens in this study were tested using a universal testing machine with a capacity of 2000 kN.In static testing, the load was applied gradually until failure.While in repeated load, the load was applied like in the static load specimens but in the form of many cycles.Where each cycle was applying loading gradually up to approximately 65% of the ultimate load of static load specimens, after which the unloading frame and rests for some time (about three  minutes), after which the second cycle is performed, and so on up to ten cycles.Then after that, the frame was loading up for failure as shown in Fig. 5.

Experimental results and discussion
The results of the investigations and discussion of this study focused on the first visible crack load and crack pattern, the ultimate load for each specimen and the type of failure, the behavior of the load-deflection curve at the mid-span of the beam, as well as the study of the overall deformation behavior of the frame by the deflected shape of the frame.

First crack and crack pattern
The general behavior of cracks for all specimens was almost similar because the geometric shape of all specimens was the same.The frame begins to crack in the middle of the beam of the zone where the positive moment was greatest.
Then cracks appear in the upper corners of the joints, which were diagonally toward the inner corner of the joint, and the outer face of the columns also suffers from cracks.As the loads continue to be applied, the cracks increase in number, length, and width.The first visible cracking load of the control frame (F-C-1) was 30 kN.In the F-S-1 specimen, the effect of SF-RPC appears very clear, as the first crack load was increased by 127%, while in F-G-1, the increase was 30%, as shown in Table 5.The number of cracks in F-G-1 was more than the control frame due to the presence of GF, which acts as a bonding bridge inside the concrete, which does not prevent the appearance of cracks but rather prevents their growth and propagation.The number of cracks in F-S-1 was less than F-G-1, despite the presence of fibers in the concrete, due to the concrete strength of SF-RPC being higher than GF-RPC, and thus increases the rigidity of the specimen, which also causes the delay in the appearance of the first visible crack.And also the surface texture of GF is rougher than SF.Thus, the frictional forces with the concrete particles are greater so the prevention of propagation of cracks was better.
In the tested specimens under repeated load, the first cracking load was close to the specimens under static load, because the first cracking occurred in the first cycle of loading.While the propagation of cracks was less than that of the static load specimens, where it was noticed that no new cracks appear in the late loading cycles, where the first cracks increase and decrease in width when loading and unloading.Figure 6 shows the pattern of cracks in the tested specimens.

Ultimate load and type of failure
The use of frame with the SF-RPC and GF-RPC increases the ultimate load of the frame, as Fig. 7 shows the percentages of increase or decrease in the ultimate load of the specimens used according to the control frame (F-C-1).Shear and flexural failure were the determinants of frame failure.Changing the type of concrete from conventional concrete to RPC with both types of fibers changes the behavior of failure, where when using conventional concrete, direct shear failure was the cause of the collapse of the frame, while when using RPC, plastic hinges at the joints and then flexural or shear failure occurs.
The failure behavior of the F-C-1 and F-C-2 specimens was less fragile, as many cracks appear and a large deformation occurs before failure, because the presence of non-prismatic sections develops arch-action theory and makes the distribution of damage along the taper before the formation of diagonal shear cracks, and this confirms the results of previous research on the non-prismatic beams (Macleod, 1994).
The use of frame with the SF-RPC increases the ultimate load by 45.9% compared to the frame with the conventional concrete and changes the failure behavior of the specimen.In the control frame, the failure of the specimen was due to shear stresses, while in F-S-1, the shear resistance was improved as a result of the use of SF-RPC, which provides very high shear strength compared to conventional concrete, and thus the failure changes into the flexural failure at the middle of the beam after the occurrence of plastic hinges at the joints of the frame.The load of the first plastic hinge and the load of the collapse of the specimen were close because the negative moments were slightly larger than the positive moment.The ultimate load of the F-G-1 was 45.5% higher than the control frame and the failure type was similar to that of the F-S-1.
In the repeated load, the ultimate load was reduced for all the tested specimens compared to their counterparts in the static test, due to loading and unloading.The percentage of reduction was 27, 2, and 2% for specimens F-C-2, F-S-2, and F-G-2, respectively.The effect of RPC was very clear about the behavior of the frame, as it improves the resistance of concrete to repeated loads by 25%, and therefore it can be used by members exposed to fatigue stresses.The type of failure was similar in the case of the tested under static load except for the F-G-2 specimen, which suffers shear failure after the occurrence of plastic hinges at the joints.

Load-deflection curve at beam mid-span
For the static test, the frame behavior of the load-deflection curve at the mid-span of the beam changes according to the change of the type of concrete as shown in Fig. 8.The use of frame with the conventional concrete has a linear load-deflection curve behavior up to 35kN, after which the relationship becomes non-linear where a higher increase in deflection commensurate to the applied load up to 140kN load, which deflection starts with a very high increase until the specimen fails.For the frame with the RPC specimens, the load-deflection relationship for SF and GF concrete was applicable until the load 170kN, after which the F-G-1 begins to deform more than the F-S-1.
Figure 9 shows the load-deflection curves of the specimens tested under repeated load.It is noticed that in the unloading stage after the first cycle, the deformation does not return to zero due to the occurrence of cracks in the The use of the frame with RPC improves the stiffness of the frame, as a clear improvement was noted in the behavior of the frame to resist deformations for all the frame with the RPC specimens and for all types of loading compared to the frames with the conventional concrete.

Deflected shape of frames
The deformation of the whole frame with the change of load for all the specimens tested was shown in Fig. 10.The deformation of the columns of specimens F-S-1 and F-G-1, especially in the middle of the column, was less than the control frame, due to the effect of RPC, which makes the columns stiffer than conventional concrete.

Conclusion
This research presents an experimental study of the results and discussions of six non-prismatic concrete frames tested under static and repeated load.The study aims to explore the effect of RPC using different fibers (SF and GF) on the concrete frame, and compare the results with the conventional concrete frame, and explain the reasons for the differences.The most important points of conclusion from this study can be summarized as follows: 1.The use of the same proportions materials of RPC with SF and GF fibers gives higher compressive strength for SF-RPC than for GF-RPC.While for the flexural strength, the GF-RPC was higher than the SF-RPC.2. The use of frame with GF-RPC increases the first crack load 27-30% more than the frame with conventional While in F-S-1 and F-S-2, the crack propagation was the least due to the SF. 4. The ultimate load of F-S-1 and F-G-1 increases by 45.9% and 40.5%, respectively, compared to the control frame (F-C-1). 5.The effect of repeated loading on frame with RPC was less than that of frame with conventional concrete, as the ultimate load decrease for both specimens F-S-2 and F-G-2 was only 2%, while in F-C-2, the decrease was 27% compared to the same specimens under static load.Therefore, it is very useful when used in members subject to fatigue stress.6.The results confirmed that the use of a non-prismatic concrete frame in the beam makes the shear failure less brittle.7. The use of frame with RPC improves the shear strength properties of concrete and changes the failure type of frame from shear failure as in F-C-1 to flexural failure as in F-S-1 and F-G-1.
8. The stiffness of the frame with the RPC was higher than that of the frame with the conventional concrete for all types of loading (static and repeated).9. RPC mixes are environmentally friendly through the use of recycle material within the materials used in its composition, such as silica fume, steel fiber, and glass fiber.Also, the use of RPC in structural members reduces the necessary cross-sections of members, thus reducing the amount of CO 2 emitted from concrete and creating a more environmentally friendly structure.

Fig. 1
Fig. 1 Dimensions and steel reinforcement details of the frames

Fig. 2
Fig. 2 The casting process a arrangement of the steel reinforcement, b adding fibers, c casting the concrete, d concrete in molds, e finish casting, f curing

Fig. 4 a
Fig. 4 a Presence of the dial gages in the frame.b Dimensions of the cup supports

Fig. 6
Fig.6The crack patterns and failure modes of the tested frames

Table 1
Symbols of specimens

Table 3
Mechanical properties of steel reinforcement bar, SF, and GF *According to the manufacturer's database Type Diameter (mm) Yield strength (MPa)

Table 5
Results of tested specimens