# Bearing Capacity near Support Areas of Continuous Reinforced Concrete Beams and High Grillages
## 2 Materials and Methods
Before the manufacture of the experimental beams, chains of strain gauges KF5P1-5-200 (with a base of 5 mm) were glued to the longitudinal compressed and stretched reinforcements of one of the flat frames. They were pasted per the technology recommended by the manufacturer (<<Veda>> LLC, Kyiv, Ukraine). The concrete deformations of the experimental samples were measured using strain gauges with a base of 40 and 50 mm, glued, according to the generally accepted technique, to one side and top polished faces. The transition from the stress-strain measurements in the experiment was carried out using Hooke's law, and in concrete, according to the secant modulus of elasticity. The deformation of concrete of the compressed zone and the tensile reinforcement was monitored using dial gauges I-1... 8 installed with a base of 100, 150, and 200 mm (Figure 3). Vertical movements were determined using dial gauges (P-1... 5). The tilt (rotation) angles of the middle support part, the support part, and the beam span were determined using dial gauges (B-1... 8). Modeling of the stress-strain state of the research elements, in general, was carried out considering the proportionally increasing load by the transverse forces and the bending moment, utilizing a nonlinear finite element calculation in the Lira-Sapr PC using real phase diagrams of materials and the phenomenological strength criterion of [PERSON], [PERSON], and [PERSON]. Given the symmetry of the research elements, these calculations were performed for only one-half of the beam. It was conventionally divided into eight eight-node isoparametric volumetric elements (No. 236) with dimensions of 10 mm \(\times\) 10 mm \(\times\) 10 mm for convenience in modeling reinforcement, and also because granite-crushed stone of fractions 5... 10 mm was used as a large aggregate. In the calculations, we used the step and step-iterative methods, using the step-iterative dependence No. 14 of the library with the corresponding algorithm. Deformation, cracking, and fracture of research double-span-reinforced concrete beams occurred according to the rules of structural mechanics and were predictable (Figure 4). Figure 5 shows photos from the in-situ experiments, which were implemented at the Odessa State Academy of Civil Engineering and Architecture. Figure 2: General view of the test of a continuous double-span beam. Normal cracks appeared in the zone of maximum bending moments above the average support. With a further increase in the transverse load, normal cracks above the middle support developed deeper into the beam, their opening width increased, and new normal flaws appeared in the spans under concentrated forces. Subsequently, the first inclined cracks appeared, and over the middle support, it became possible to form a plastic hinge with a redistribution of internal forces and an increase in flying moments with a constant value of the reference moment. A further increase in the transverse load led to the development of normal and inclined cracks with the predominant opening of inclined cracks to failure along inclined sections. Practically all experimental specimen beams of the expressed (\(\mathbf{V}\)) series were destroyed along both inclined sections in the form of an inverted trapezoid according to the bursting pattern above the middle support, which was confirmed by the photo fixation given in [34]. Figure 3: Scheme of loading, placement of devices and stickers of strain gauges in experimental two-span beams with small, medium, and large spans of the cut, where Ri—run-meter, Di—clock-type indicator for measuring concrete deformations in a compressed zone, as at the level of the center of gravity of a tensile reinforcement, Ai—clock-type indicator for the angles of rotation of normal sections of a continuous beam. Figure 4: The mechanism of cracking, deformation, and fracture of a continuous two-span-reinforced concrete beam—grillage. Plot of M\({}_{\rm z}\) before the appearance of the plastic hinge (**a**,**b**).