Experimental research of the impact of upper reinforcement on the tension membrane action of narrow three-span reinforced concrete slabs

The aim of the paper was to demonstrate the influence of reinforced steel parameters and quantity on the failure mechanism of four three-span models of reinforced concrete strips with the dimensions 7140×500×190 mm. Two models had only bottom reinforcement, while two were reinforced at the bottom and upper sides. The paper contains the description of the experimental stand and models along with the results of experimental tests which were compared with the results of the calculations based on traditional methods.


Introduction
The experimental research discussed in the article is the follow-up of the investigations of the behavior of narrow reinforced concrete slabs in an emergency situation induced by overloading [9,10]. The most common reason of overloading in slab structures is the improper operation of a building which results e.g. from the excessive load exerted on parts or entire surfaces of floors. The second reason of overloading are the faults made at the design stage (e.g. improperly defined amount of reinforcement) or during the construction of buildings (e.g. supplying the concrete of incorrect strength parameters), resulting in damaging of the structure even with the correct value of load. The purpose of the research was to determine the maximum value of the load that the reinforced concrete slab will be able to carry due to the membrane work, which appears in continuous elements in the event of even a slight vertical displacement. The first works in the field of the membrane work were carried out by Park (1964) [8], followed by Black (1975) [4], Desaya and Kulkarnia (1977) [5] as well as Hawkins and Mitchell (1979) [6]. Based on the analysis literature, the summary was made by Mitchell and Cook (1984) [7]. However, the above-mentioned works were performed on spatial models, which hinders conducted the analysis. An analysis of narrow slabs working in one direction was proposed to partially simplify the first approach to recognizing the problem. The paper presents the results of the research of two models with the dimensions of 7140×500×190 mm, where upper support reinforcement was applied. Such a method of reinforcing is commonly applied in engineering practice.

Description of the experimental models
Similarly to papers [9,10], the test models have been designed as narrow slabs of a typical slab-column structure with unidirectional reinforcement. In order to conduct the tests, two identical models with the shape of a flat reinforced concrete slab with the dimensions of 7140×500×190 mm (Fig. 1) have been constructed. Similarly to papers [9,10], it has been assumed that the length of the tested part of the slab would exceed the height of the cross-section ca. 30 times. In order to reinforce the models, bars with a diameter of 12 mm were used (no. 1 in Fig. 1), made from class C steel according to [3]. The reinforcement ratio was (Model 1ρ = 1.0%, Model 2 ρ = 2.0%). As a transverse reinforcement, bars with a diameter of 8 mm (no. 2 in Fig. 1) made from class C steel according to [3] were used. The models, apart from the bottom reinforcement, also feature upper reinforcement with the same number of bars (Fig. 1). View of the bottom and upper reinforcement can be found in Fig. 2. Prior to concreting, the bottom reinforcement was welded to steel plates (no. 3 in Fig. 3). In the last stage of the preparatory works, steel plates were immobilized in the test stand (Fig. 4). The model was built using concrete compound based on the formula identical to research [9,10].

Description of the test stand
The test stand on which the research models were arranged consisted of two supports allowing to slide and turn the slab (no. 2 in Fig. 3) placed on concrete blocks (no. 3 in Fig. 3) with a spacing of 5250 mm. In order to stabilize the model during the research and afterwards, additional supports were placed on its ends (no. 8 in Fig. 3) -supports R1 and R4. The model was loaded with the set of 18 hydraulic actuators (no. 6 in Fig. 3) arranged in six measurement points. Compared to the research [9,10], actuators with better parameters were used, allowing to carry out the tests until the reinforcing bars were ruptured. The displacements were measured using eleven sensors placed every 750 mm (no. 6 in Fig. 3). The horizontal interlocking of the model was made of two horizontally arranged sheets (no. 4 in Fig. 3, Fig. 4a) locked with steel angle struts.

Fig. 3.
The test stand according to [9,10] (1-test model; 2-articulated sliding support allowing to slide and turn the model simultaneously; 3-concrete base of the articulated support; 4-horizontal model stabilization system; 5-inductive sensors to measure the vertical displacements of the upper surface in the tested models; 6-model load system consisting of six sets of hydraulic cylinders; 7-vertical reaction R1 and R4 measuring system; 8-auxiliary items supporting the ends of the test model).

Description of the research methodology
Similarly to [9,10], the same procedure was applied in the tests of each analyzed model. The test program consisted of the following four stages: • Stage 0: This stage of tests included: placing the model on the supports, reading the support reactions, determining the weight of the element, static calculations of the proper distribution of the support reactions, rectification of the model on supports, and blocking the horizontal displacements of the tested element ends.
• Stage 1: The initial loading of the model with a horizontal force of H1 = H2 = 6 kN was aimed at adjusting the measurement system to the model and the test stand. After the first loading cycle the measuring apparatus was reset and the actual course of the test began. • Stage 2: A single loading cycle included applying a load on the tested model to the value equal to 10% of the design load that determines flexural destruction of a given element. • Stage 3: The consecutive loading cycles were applied on the tested model until the moment of its flexural destruction. • Stage 4: The final stage of the tests included a single loading cycle of the test model until the moment of its total failure resulting from the rupture of the reinforcement bars.

Materials
The reinforcement of the models consisted of bars made of medium ductility steel of class C according to [3] (1.15 < ftk/fyk < 1.35). The results of testing the steel have been collected in Table 1. The models were constructed of concrete based on Portland cement and aggregate with the diameter of the grains up to 8 mm. On the day of testing, i.e. after 32 days of concrete curing, the mechanical parameters were determined in compliance with PN-EN 12390-3:2011 [1,2] standard. Table 2 contains the mean values of the mechanical parameters which were always determined on six samples. Although the compound used was identical to the one applied in tests [9,10], the parameters of the obtained concrete differed slightly.

Results of the laboratory tests
In the course of the research, the loading force was measured along with the corresponding vertical displacement in the centre of the span of the investigated slab ( Fig. 5 and Fig. 6), and the image of the emerging cracks was prepared. Detailed values of displacements and loads are presented in Table 3. In order to determine the impact of the upper reinforcement on the load-bearing capacity of the tested models, Table 3, Fig. 5 and Fig. 6 contain results obtained for models with the same amount of bottom reinforcement: Model 3 according to [9] and Model 4 according to [10].
In the course of the research and in papers [9,10], the hydraulic loading system was applied, where in the case of a violent deformation of the test element the pressure in the hydraulic system decreases, causing a partial discharge of the test model. Fig. 5 and Fig. 6 include markings of points where a temporary discharge of elements occurred as a result of concrete crushing.

Determination of theoretical values of failure loads
Theoretical values of failure loads causing the flexural destruction of the models have been determined according to [3], taking into account geometrical and material details of the models. Table 4 includes both the values of experimental and calculation load: 1 -theoretical design value of variable load (exceeding the dead weight of the element), taking into account the safety and material coefficients, at which flexural destruction of the element should occur Calculations were carried out according to [3]. In the calculations, it was assumed that the load-bearing capacity of models with bottom and both bottom and upper reinforcement would be determined solely taking into account the bottom reinforcement. 2 -theoretical characteristic variable load (exceeding the dead weight of the element) at which flexural destruction of the element should occur Calculations were carried out according to [3]. The value of load was determined with the assumption that all safety coefficients equal 1.0. 3 -theoretical characteristic variable load (exceeding the dead weight of the element) at which tensioning destruction should occur The value of load has been determined in a way applied for a perfect tension member with the following calculation assumptions [9,10]: -the shape of tension member axis deflection is determined with the formula of the catenary curve; -the length l' of the tension member after deformation in the failure state is equal to the initial length increased by the percentage elongation Agt determined on the basis of material tests of steel; -the value of horizontal reaction H equals the force transferred by the reinforcing bars. 4 -experimental value of load (exceeding the dead weight of the element) at which flexural destruction of the element occurred 5 -experimental value of load (exceeding the dead weight of the element) at which research was interrupted due to technical reasons 6 -experimental value of load (exceeding the dead weight of the element) at which reinforcing bars were ruptured

Analysis of the results
The research led to the following conclusions: • In each tested model, a uniform image of cracking with significant apertures of cracks was obtained on lateral surfaces, which points at substantial yielding of the reinforcement and high influence of steel ductility on the possibility of a local redistribution of internal forces. What is more, at the moment of failure of Model 1 and Model 2 very high slab deflections were obtained (608 mm -Model 1 and 770 mm -Model 2 respectively). The proportion of deflection in relation to the slab span equalled a/l = 1/8.61 in Model 1 and a/l =1/6.82 in Model 2.
• The values of load at which flexural failure of the element occurred in the course of the research (4 according to Table 4) with Model 3 and Model 4 were close to theoretical characteristic values of the load (2 according to Table 4). The comparison of the same load values with Model 1 and Model 2 exhibited a significant impact of upper reinforcement on the load-bearing capacity of the compressed slab zone. Values obtained in the course of the research of Model 1 and Model 2 were over 2 times higher than the theoretical values. • As predicted, failure of the support zone in Model 1 occurred at R2 support. As a result of rupturing the reinforcing bars, a plastic hinge emerged, and the model started to operate in a way identical to a model with bottom reinforcement bars only. In Model 2, a plastic hinge also emerged over R2 support, induced by the loss of adhesion of all upper reinforcement bars.