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complete picture of various cracks adjacent to the concentrated force and to the support is designed (Fig. 3) and the width of their opening is determined. Moreover, the opening of cracks is defined as the accumulation of relative conditional concentrated mutual displacements of reinforcement and concrete in areas located on both sides of the crack:

00

4.Calculation of the distance between spatial cracks and the width of their opening in reinforced concrete structures during torsion with bending (case 2). Moreover, as shown by the practice of calculations and design of reinforced concrete structures, the distance between the first type of spatial cracks for the first level of crack formation, located along the transverse or longitudinal reinforcement can be idenitfied using the following ratio (Fig. 5, Fig. 6):

In order to determine the distance between spatial cracks of the second level of their formation, the ratio between the stresses in the reinforcement in the section I––I and in the section with the dangerous spatial crack is used which is identified according to the criterion of the maximum width of their opening.

In addition, a new level of crack formation corresponds to the load level where the following inequality is observed:

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Moving to the right along the longitudinal reinforcement, such ratios will take the following form (Fig. 6, b):

Fig.5.Designschemefordeterminingthedistancebetweenthecracksofthefirsttype(case2):

а istheschemeofeffortsandthechoiceofthecoordinatesystemto theformationofthefirstspatialcrack

At the same time, we do not go beyond the boundaries of (Fig. 6).

In the case of breaks in the longitudinal reinforcement in the area of spatial inclined cracks, the ratios (50) and (52) are somewhat modified, i.e., in addition to the stress ratio in the reinforce-

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Russian Journal of Building Construction and Architecture

ment, the ratio of the longitudinal reinforcement areas (before and after the break) is also considered. As a result, these formulas will take the following form, respectively, moving to the right:

Fig. 6. The location of an adjacent crack of the next level between two cracks of the previous level: a is along the axis of the transverse reinforcement; b is along the axis of the longitudinal reinforcement

Therefore cracking continues until failure occurs. At the same time, not one (as is customary in a number of well-known methods) but several levels of crack formation are distinguished, see system (41).

The distance between the cracks is identified using the condition according to which the elongation of concrete on the surface of the structure in the middle section (in the area between the cracks).

The analysis shows that an increase in the strains in the reinforcement with an increasing load causes a decrease in the distance between cracks. Moreover, the emergence of a new level of crack formation corresponds to the load level where the following inequality is observed

Crack formation continues until failure occurs, see system (41).

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The value is calculated before conducting special studies according to the methodology of the standards.

As a result, the general calculation algorithm is as follows:

1.In accordance with the developed methodology, the parameters of the stress-strain of the design section are determined.

2.The functional valuelcrc is determined. Then using the inequality (41) the level value lcrc is

identified.

3. The width of the crack opening is identified, but it is discussed in more detail in paragraph 5.

5. Calculation of the crack opening width in reinforced concrete structures under central tension given the effect of discontinuity. Crack opening is the accumulation of relative concentrated mutual displacements of reinforcement and concrete in areas located on both sides of the crack, i.e., development of the Thomas-Golyshev hypothesis;

Now, in accordance with the third premise, the expression (42) takes the following form:

When performing practical calculations, the crack width calculated using the formula (57) should be multiplied by the coefficient kr which takes into account the concrete dislocation in the section with a crack and also multiplied by the coefficients l , that take into consideration the duration of the load and the surface profile of the reinforcement, respectively, and determined in accordance with the standard guidelines.

Deplanation in the section with a crack (see Fig. 7) is taken into consideration using the coefficient kr. The coefficient kr is identified in accordance with the results of the studies [34]. Their analysis shows that for practical calculations a ratio can be recommended:

where ds is the diameter of the reinforcement, r is the radius of the boundary layer.

The resulting dependence takes into account the effect of a range of important factors such as reinforcement deformation in the section with a crack, distance between cracks, adhesion parameters B of the reinforcement with concrete, geometric characteristics of the section and of concrete. As a result, the general calculation algorithm is reduced to the following:

1. In accordance with the developed methodology the parameters of stress-strain of the calculating section are determined.

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2

1

2

a crc

a crc,i

a crc,b

Fig. 7. Deplanation in the section with a crack

2. The functional value lcrc is determined, then using the inequality (41) the level value lcrc is identified.

3. Using the formula (57) acrc is calculated.

Thus a method for calculating the resistance of reinforced concrete structures under the combined action of shear force, bending and torque (case 2) for the second stage of the stressstrain is suggested, which allows one to identify the actual stress-strain when there are spatial cracks while determining the distance between cracks and the width of their disclosure.

Conclusions

1.A method for calculating the resistance of reinforced concrete structures under the combined action of bending moment, torque, and shear force for the second stage of the stressstrain state (case 1 is with spatial cracks of the first type on the lower face of the structure) is considered.

The prerequisites underlying the suggested calculation method are provided. The layout of the compressed zone occurring in the spatial section of the reinforced concrete structure under the action of bending with torsion is taken into consideration. The analytical dependences are shown for identifying the internal forces occurring in two blocks: a cut-off section passing at the end of a spatial crack; formed by a spiral crack and a vertical section passing along the compressed zone of concrete through the end of the front of the spatial crack.

2.A method for calculating the resistance of reinforced concrete structures under the combined action of bending moment, torque, and shear force for the second stage of the stress-

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strain state (case 2 is with spatial cracks of the first type on the side face of the structure) is considered.

3.A method for calculating the distance between spatial cracks and the width of their opening in reinforced concrete structures during torsion with bending is taken into account (case 1 is the compressedzone ofconcretelocatedattheupperfaceofareinforcedconcrete structure).

Analytical dependences are obtained for identifying the internal forces occurring in two blocks: a cut-off section passing at the end of a spatial crack; formed by a spiral crack and a vertical section passingalongthecompressedzoneofconcretethroughtheendofthe frontofthe spatialcrack.

The projection of a dangerous spatial crack is identified as a function of a lot of variables and has a clear physical interpretation in the form of a set of spatial sections, the equilibrium of which is influenced by the parameters included in the compiled equations. Among this set of sections, there is one that corresponds to the maximum width of the opening of spatial cracks. The analysis shows that in order to determine the actual stress-strain state of reinforced concrete structures, it becomes necessary to have a full picture of crack formation during loading. Not only various levels of crack formation of spatial cracks are considered, but also formulas are designed for determining the distances between them. In order to get a full picture of the development and opening of spatial cracks, a representative volume of the reinforced concrete structure is allocated in the form of a design scheme of the second and subsequent levels. Based on the constructed calculation scheme, equations are obtained for determining the distance between spatial cracks of various types and the width of their opening.

4.A method for calculating the distance between spatial cracks and the width of their opening in reinforced concrete structures during torsion with bending is considered (case 2 is the compressed zone of concrete located at the side face of the reinforced concrete structure).

The analytical dependences are obtained for identifying the internal forces occurring in two blocks: a cut-off section passing at the end of a spatial crack; formed by a spiral crack and a vertical section passing along the compressed zone of concrete through the end of the front of the spatial crack.

The projection of a dangerous spatial crack is identified as a function of a lot of variables and has a clear physical interpretation in the form of a set of spatial sections, the equilibrium of which is influenced by the parameters included in the compiled equations. Among this set of sections, there is one that corresponds to the maximum width of the opening of spatial cracks. In order to determine the actual stress-strain of reinforced concrete structures, it becomes necessary to have a full picture of crack formation during loading. Not only various levels of

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Russian Journal of Building Construction and Architecture

crack formation of spatial cracks are considered, but also formulas are constructed for determining the distances between them. In order to get a full picture of the development and opening of spatial cracks, a representative volume of the reinforced concrete structure is allocated in the form of a design scheme of the second and subsequent levels. Based on the constructed calculation scheme, equations are obtained for determining the distance between spatial cracks of various types and the width of their opening.

References

1.Bondarenko V. M., Kolchunov V. I. Raschetnye modeli silovogo soprotivleniya zhelezobetona [Computational model of a power resistance of reinforced concrete]. Moscow, AST Publ., 2004. 472 p.

2.Golyshev A. B., Kolchunov V. I. Soprotivlenie zhelezobetona [Resistance of reinforced concrete]. Kiev, 2009.

432p.

3.Dem'yanov A. I., Kolchunov Vl. I., Yakovenko I. A. Razrabotka universal'nogo korotkogo dvukhkonsol'nogo elementa k soprotivleniyu zhelezobetonnykh konstruktsii pri kruchenii s izgibom [Development of a universal short two-pole element to the resistance of reinforced concrete structures under torsion with bending]. Izvestiya vuzov. Tekhnologiya tekstil'noi promyshlennosti, 2017, no. 4 (367), pp. 258––263.

4.Dem'yanov A. I., Kolchunov V. I., Sal'nikov A. S., Mikhailov M. M. Raschetnye modeli statiko-dinami- cheskogo deformirovaniya zhelezobetonnoi konstruktsii pri kruchenii s izgibom v moment obrazovaniya prostranstvennoi treshchiny [Calculation models of static-dynamic deformation of reinforced concrete structure under torsion with bending at the moment of formation of spatial cracks]. Stroitel'stvo i rekonstruktsiya, 2017, no. 3 (71), pp. 13––22.

5.Dem'yanov A. I., Kolchunov V. I., Pokusaev A. A. Eksperimental'nye issledovaniya deformirovaniya zhelezobetonnykh konstruktsii pri kruchenii s izgibom [Experimental studies of deformation of reinforced concrete structures under torsion with bending]. Stroitel'naya mekhanika inzhenernykh konstruktsii i sooruzhenii, 2017, no. 6, pp. 37––44.

6.Dem'yanov A. I., Sal'nikov A. S., Kolchunov Vl. I. Eksperimental'nye issledovaniya zhelezobetonnykh konstruktsii pri kruchenii s izgibom i analiz ikh rezul'tatov [Experimental studies of reinforced concrete structures under torsion with bending and analysis of their results]. Stroitel'stvo i rekonstruktsiya, 2017, no. 4 (72), pp. 17––26.

7.Dem'yanov A. I., Pokusaev A. A., Kolchunov V. I. Eksperimental'nye issledovaniya zhelezobetonnykh konstruktsii pri kruchenii s izgibom [Experimental studies of reinforced concrete structures under torsion with bending]. Stroitel'stvo i rekonstruktsiya, 2017, no. 5 (73), pp. 5––14.

8.Zalesov A. S., Khozyainov B. P. Prochnost' zhelezobetonnykh elementov pri kruchenii i izgibe [Strength of reinforced concrete elements in torsion and bending]. Izvestiya vuzov. Stroitel'stvo i arkhitektura, 1991, no. 1, pp. 1––4.

9.Kolchunov V. I., Dem'yanov A. I., Yakovenko I. A., Garba M. O. Problema privedeniya v sootvetstvie opytnykh dannykh treshchinostoikosti zhelezobetonnykh konstruktsii ikh teoreticheskim znacheniyam [The

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problem of bringing the experimental data of crack resistance of reinforced concrete structures into compliance with their theoretical values]. Nauka ta budіvnitstvo, 2018, no. 1 (15), pp. 42––49.

10.Kolchunov V. I., Sal'nikov A. S. Eksperimental'nye issledovaniya treshchinoobrazovaniya zhelezobetonnye konstruktsii pri kruchenii s izgibom [Experimental studies of crack formation of reinforced concrete structures under torsion with bending]. Stroitel'stvo i rekonstruktsiya, 2016, no. 3 (65), pp. 24––32.

11.Kolchunov V. I., Zazdravnykh E. I. Raschetnaya model' «nagel'nogo effekta» v zhelezobetonnom elemente [The estimated model of the "pin effect" in a reinforced concrete element]. Izvestiya vuzov. Ser. Stroitel'stvo, 1996, no. 10, pp. 25––29.

12.SP 63.13330.2012 Betonnye i zhelezobetonnye konstruktsii. Osnovnye polozheniya. Aktualizirovannaya redaktsiya SNiP 52-01-2003 [A set of rules 63.13330.2012 concrete and reinforced Concrete structures. Fundamentals. Updated version of SNiP 52-01-2003]. Moscow, 2012. 155 p.

13.Adheena Thomas, Afia S Hameed. An Experimental Study on Combined Flexural and Torsional Behaviour of RC Beams. International Research Journal of Engineering and Technology, 2017, vol. 04, iss. 05, pp. 1367––1370.

14.Demyanov A., Kolchunov Vl. The dynamic loading in longitudinal and transverse reinforcement at instant emergence of the spatial сrack in reinforced concrete element under the action of a torsion with bending. Journal of Applied Engineering Science, 2017, vol. 15 (2017) 3, article 456, pp. 375––380. doi:10.5937/jaes15-14663.

15.Iakovenko I., Kolchunov V., Lymar I. Rigidity of reinforced concrete structures in the presence of different cracks. MATEC Web of Conferences. 6th International Scientific Conference «Reliability and Durability of Railway Transport Engineering Structures and Buildings». Transbud-2017. Kharkiv, Ukraine, April 19–21, 2017, vol. 0216. 12 p.

16.Iakovenko I., Kolchunov Vl. The development of fracture mechanics hypotheses applicable to the calculation of reinforced concrete structures for the second group of limit states. Journal of Applied Engineering Science, 2017, vol. 15 (2017) 3, article 455, pp. 366––375. doi:10.5937/jaes15-14662.

17.Ilker Kalkan, Saruhan Kartal. Torsional Rigidities of Reinforced Concrete Beams Subjected to Elastic Lateral Torsional Buckling. International Journal of Civil and Environmental Engineering, 2017, vol. 11, no.7, pp. 969––972.

18.Khaldoun Rahal. Combined Torsion and Bending in Reinforced and Prestressed Concrete beams Using Simplified Method for Combined Stress-Resultants. ACI Structural Journal, 2007, vol. 104, no. 4, pp. 402–411.

19.Nahvi H., Jabbari M. Crack detection in beams using experimental modal data and finite element model. International Journal of Mechanical Sciences, 2005, vol. 47, pp.1477––1497.

20.Pettersen J. S. Non-Linear Finite Element Analyses of Reinforced Concrete with Large Scale Elements: Including a Case Study of a Structural Wall. Norwegian University of Science and Technology, 2014. 85 р.

21.Salnikov A., Kolchunov Vl., Yakovenko I. The computational model of spatial formation of cracks in reinforced concrete constructions in torsion with bending. Applied Mechanics and Materials, 2015, vol. 725––726, pp. 784––789.

22.Santhakumar R., Dhanaraj R., Chandrasekaran E. Behaviour of retrofitted reinforced concrete beams under combined bending and torsion: A numerical study. Electronic Journal of Structural Engineering, 2007, no. 7, pp. 1––7.

23.Vishnu H. Jariwalaa, Paresh V. Patel, Sharadkumar P. Purohit. Strengthening of RC Beams subjected to Combined Torsion and Bending with GFRP Composites. Procedia Engineering, 2013, vol. 51, pp. 282––289.

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Russian Journal of Building Construction and Architecture

BUILDING MATERIALS AND PRODUCTS

DOI10.25987/VSTU.2019.44.4.002

UDC691.53

Heydar Dehghanpour 1, Kemalettin Yılmaz 2

EVALUATION AND INVESTIGATION OF WASTE GLASS AGGREGATES AND POWDERS IN ARCHITECTURAL MORTARS

Sakarya University 1, 2

Sakarya, Turkey

1 PhD Student of the Dept. of Civil Engineering, e-mail: heydar.dehghanpour@ogr.sakarya.edu.tr 2 PhD in Engineering, Prof. of the Dept. of Civil Engineering

Statement of the problem. Glass is a material that can save raw materials if recycled. It can also lead to energy savings and reduce greenhouse gas emissions. Recycled waste glass can be used as an important component in the ceramic and tile industry. About 7 percent of the household waste composition is glass that can be recycled. Recycled glass saves hundreds of thousands of tons of raw material each year, which reduces the need for raw material extraction, creates jobs and leads to the beauty of the surrounding areas.

Results. In the present study, mechanical properties, impact properties and heat transmittances of architectural mortars produced from waste glass for use in interior and exterior facades of buildings have been examined. Three specimens from 6 different mixes formed for each test were produced: 40 × 40 × 160 mm for flexural and compressive tests and 100 × 100 × 25 mm slabs specimens for aesthetic appearance, impact and heat transmittances tests. In terms of aesthetic appearance, the specimens which are not used in sand but produced only from cement and glass products are chosen as the best mortars. The specimens containing glass crumbs and glass powder, especially M5 and M6, are also less porous than the other ones. The reason for this is that glass for cementitious mortar provides self-compacting properties, which is also observed during mixing.

Conclusions. According to the results, the mortar with mixing ratios of 1.5 : 3 : 1 (cement : glass aggregate: glass powder) seems appropriate in terms of appearance, mechanical, impact and thermal properties. It is also suggested that the self-assembly tools used to study impact and heat permeability be employed in the examination of construction building materials, because they have been found to give meaningful information in these matters.

Keywords: waste glass, architectural mortar, glass aggregate, glass powder.

Introduction. The amount of solid wastes generated due to the increase in consumption has also increased reaching environmental pollution dimensions. In all developed and developing countriessolidwastesconstitutethegreatestofsocial,economicandenvironmentalproblems [1––3].

© Dehghanpour Heydar, Yılmaz Kemalettin, 2019

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A growing awareness of environmental protection has transformed the recycled glass into a number of innovative and decorative building products. Glass recycling significantly reduces raw material usage and energy / fuel costs. The glass can be recycled indefinitely as it does not deteriorate when recycled. The evaluation of waste glass in the construction sector is a useful method in terms of designing economical, energy saving and natural welding material. In addition, aggregate and mineral materials obtained from waste glass are also compatible with the management of construction materials [4, 5]. Waste glass is used in cementitious materials for different purposes [6––8]. For this reason, in recent years, many studies have focused on the replacement of dust and aggregates from waste glass with concrete-forming materials [9––12].

Kavas et al (2004) investigated the dust of waste glass as an additive in cement. According to the results, it is appropriate to use up to 30 % of the additive amount in the cement industry and it has been shown that the general properties of the cement start to change when the contribution is added above this ratio [3]. Kılıçoğlu and Çoruh (2015) examined the alkalisilica reaction expansion in concrete prepared by using waste glass and blast furnace slag [1]. As the amount of glass powders used together with the blast furnace slag increased, a reduction in the alkali-silica reaction expansion in the concrete was observed.

Waste glass is not only used in the construction sector for the purpose of changing the properties of cementitious materials. In addition, waste glass can also be used in decorations used in building facades. In order to make architectural and decorative concrete products more attractive, the percentage of waste glass fragments should be as high as possible. In addition, the size ranges of the glasses greatly affect the aesthetics of the resulting product. Ling and Poon (2011) found that aesthetics increases significantly when the size range of the glass aggregates used in the decorative products is between 2.36 and 10 mm [13]. Ling and Poon (2011) produced architectural mortars using 100 % waste glass instead of aggregate. According to the results of the research, the general performances of architectural mortars prepared with glass aggregates at different particle sizes were found to be similar to the control mortar mixture prepared with normal sand. The 28 day pressure and flexural strengths for these products were reported to be 40 and 6 MPa, respectively. It is appropriate to use materials with these properties for architectural purposes in building applications [14].

In the present study, mechanical properties, impact properties and heat transmittances of architectural mortars produced from waste glass for use in building construction have been examined. In the mortars, the crumbs of green bottles of commonly consumed sodas were used.

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