1 Introduction

In China, reinforced concrete structures were first built in the Republic of China era from 1912 to 1949. In the numerous buildings built in this era, reinforced concrete buildings account for a large proportion. Nowadays, in the Chinese national cultural heritage conservation units, especially in the provincial and municipal cultural heritage conservation units, reinforced concrete buildings of the Republic of China era represent a considerable number of heritages. For example, according to Ref. ^[1], the existing reinforced concrete buildings of the Republic of China era account for 64.2% of the total existing buildings of this era in Nanjing. Reinforced concrete buildings in the Republic of China era are developed in a special historical period transferring from the ancient architectural structures to the contemporary architectural structures. Chinese modern concrete buildings are very different from present concrete buildings in many ways, such as material properties, structural calculation methods and structural configurations. For example, the longitudinal rebars of Chinese modern concrete buildings are commonly rectangular ribbed rebars which are very different from the present round deformed rebars (as shown in Fig. 1).

The structural calculation method of reinforced concrete structure evolves through several stages. The first stage is the allowable stress calculation method, and then it is the plastic state calculation method, and then it is the limit state calculation method, and last it is the probabilistic limit state calculation method^[2].

In China, there are very few research reports about the structural calculation method of Chinese modern reinforced concrete buildings. Zhao^[3] referenced the American code for concrete structure, and presented the structural calculation methods of members of Chinese modern concrete structures. Zhang^[4]studied the structural calculation methods of Chinese modern concrete structures and presented the calculation methods and the configurations of concrete beams, concrete columns, concrete slabs, and concrete foundations. Chen^[5]studied the calculation methods of internal forces of Chinese modern concrete structures, and introduced the structural calculation methods of concrete beams, concrete columns, concrete slabs, and concrete foundations based on a case study. Wang^[6] introduced the structural calculation methods of Chinese modern concrete structure based on the case studies. Chen^[7] introduced the regulations of British concrete structural design. Wang^[8] made a brief introduction of the structural regulations of Shanghai International Settlement of the Republic of China era. The reports above were all published in the Republic of China era, and only introduced the original structural calculation methods of Chinese modern concrete buildings. Lin et al.^[9] carried out an experiment of the rebars taken from a modern concrete building in Shanghai, and presented the relevant yield strength and limited tensile strength. Wang^[10] studied the repair methods of a modern concrete building in Xiamen, and presented the adaptive test methods of concrete strength, durability problem, and rebar quality. Shi^[11] studied the conservation methods of the modern concrete buildings in Wuhan, and preliminary put forward the adaptive strengthening and repair methods for these buildings. Chen et al.^[12] carried out the test and assessment of a modern concrete building built in 1930s, and then presented the relevant strengthening and repair methods.

In Europe, North America and New Zealand, a lot of research on conservation methods of historic concrete buildings has been carried out. Peter et al.^[13] researched the history, the material properties, the defect causes, and the conservation strategies of historic concrete structures in New Zealand. Denis^[14]studied the concrete characteristics and the repair principles of the historic concrete in Scotland. Gebregziabhier^[15] researched the durability problems, the repair principles, and the repair methods of the 20^th century reinforced concrete heritage structures. Gonalves^[16] studied the corrosion of concrete reinforcement and the survey techniques used to detect corrosion in historic concrete structure. Luca et al.^[17]carried out the research on the electrochemical realkalisation technique used to stop rebar corrosion in carbonated concrete. Dimitri^[18] studied the reliability of a multi-storey historic concrete building based on the FEM analysis, considering the uncertainty of the material performance, the geometry shape, the load and the structural model. Coney^[19] studied the method and process of repair and conservation of historic concrete structure. Ince et al.^[20] introduced the repair methods of a historic concrete building in Moscow. Searls et al.^[21]studied the repair methods of the city hall of Atlanta built in 1930. Qazi^[22] researched the structural performance of a historic concrete building under earthquake loads.

So far, the present research mainly focuses on conservation techniques of historic concrete buildings, and the comparative study on structural calculation methods of reinforced concrete members of Chinese modern reinforced concrete buildings is still in an early stage. In this paper, the comparative studies on the original calculation method and the present calculation methods of shear behavior of reinforced concrete beams of Chinese modern reinforced concrete buildings are carried out with the consideration of the actual material properties and structural configurations.

2 Material Properties and Structural Configurations

According to Refs.^[3-8], the structural calculation method of Chinese modern reinforced concrete buildings is the allowable stress calculation method based on elastic theory.

2.1 Allowable Stress and Safety Factor

According to Refs.^[3-5], the limited strength, the allowable stress, and the safety factors of concrete and rebar of the Republic of China era are shown in Table 1.

The results in Table 1 show that the structural safety factors of the Chinese original structural calculation method are in a range of 3.55 to 4.00, namely, the structural safety reservation of the Chinese original structural calculation method is relatively large.

2.2 Actual Material Properties

According to Refs.^[3-5], the concrete mixture of the Republic of China era is often made in a ratio of 1(cement): 2(sand): 4(gravel) by volume. The compressive strength can reach 8.28 MPa after the maintenance of a week, 13.78 MPa after the maintenance of four weeks, 20.69 MPa after the maintenance of four months, and 24.13 MPa after the maintenance of twelve months, respectively. The appropriate diameter of the gravel in the concrete is required to be from 12.7 mm to 25.4 mm, and the appropriate diameter of the sand in the concrete is required to be about 1.27 mm. According to the conversion analysis, the strength grade of concrete of the Republic of China era is comparable to the present strength grade of C15 concrete. For the original structural calculation method of the Republic of China era, the limited compressive strength of concrete is 16.56 MPa, and the allowable stress of concrete is 4.14 MPa. Through the on-site tests of 12 Chinese typical modern concrete buildings, 154 data of concrete compressive strength have been collected and analyzed, as shown in Table 2. The results show that the compressive strength of concrete of the Republic era is between 10 MPa and 20 MPa, and the results coincide with the requirement of the Chinese original structural calculation method. Through the statistical analysis of these data, the test results of compressive strength of concrete cubes overall follow the rule of normal distribution, and the average of the compressive strength of concrete cubes is 16.36 MPa, as shown in Fig. 2.

According to Refs.^[3-5], the limited tensile strength of rebar of the Republic of China era is required to be more than 441.54 MPa, and the allowable stress of rebar of the Republic of China era is required to be more than 110.38 MPa. The physical and mechanical performance of 66 rebars including 36 rectangular rebars and 30 round rebars taken from different cities and different buildings are tested and analyzed. The results show that the yield strength of the rectangular rebars overall follow the rule of normal distribution, and the average of them is 278.60 MPa. The yield strength of the round rebars also overall follow the rule of normal distribution, and the average of them is 350.65 MPa.

According to the requirements of the Chinese present design code for concrete structure^[23-24], standard values of material strength need to ensure 95% guarantee rate, and test results of material strength shall follow the rule of normal distribution. f_k=f_m-1.645×σ, where f_k is standard value of material strength; f_m is average value of material strength; σ is standard deviation of material strength. f=f_k/γ, where f is design value of material strength, and γ is partial factor.

According to the actual test results, for the Chinese present structuralcalculation method, the standard value of compressive strength of concrete cubes of the Republic of China era is obtained as follows: f_cuk=f_cum-1.645σ_cu=16.36-1.645×4.79=8.48 MPa. The relevant standard value of axial compressive strength of concrete is obtained as follows: f_ck=0.67f_cuk=0.67×8.48=5.68 MPa. The relevant standard value of tensile strength of concrete is obtained as follows: f_tk=0.88×0.395f_cuk^0.55(1-1.645δ_fcu)^0.45=1.20 MPa. The standard value of yield strength of rectangular rebar of the Republic of China era is achieved as follows: f_yk=f_ym-1.645σ_y=278.60-1.645×29.81=229.56 MPa. The standard value of yield strength of round rebar of the Republic of China era is achieved as follows: f_yk=f_ym-1.645σ_y=350.65-1.645×44.88=276.82 MPa. The relevant design value of axial compressive strength of concrete is obtained as follows: f_c=f_ck/γ_c=5.68/1.35=4.21 MPa. The relevant design value of tensile strength of concrete is obtained as follows: f_t=f_tk/γ_c=1.20/1.35=0.89 MPa. The design value of yield strength of rectangular rebar of the Republic of China era is obtained as follows: f_y=f_yk/γ_y=229.56/1.1=208.69 MPa. The design value of yield strength of round rebar of the Republic of China era is obtained as follows: f_yv=f_yk/γ_y=276.82/1.1=251.65 MPa.

According to Refs.^[23-26], for the American present structural calculation method, according to the conversion analysis, the compressive strength of concrete cylinders of the Republic of China era is obtained as follows: f_c′= f_cuk×0.846/1.003=7.15 MPa. The relevant tensile strength of concrete is obtained as follows: f_t′=0.333f_c′=0.89 MPa. In the American code of ACI 318, there is no difference between standard value and design value, so the yield strength of rectangular rebar of the Republic of China era is obtained as follows: f_yk=229.56 MPa. The yield strength of round rebar of the Republic of China era is obtained as follows: f_yk=276.82 MPa. For the European present structural calculation method, the characteristic value of compressive strength of concrete of the Republic of China era is obtained as follows: f_ck=f_cuk/1.226=6.92 MPa. The relevant characteristic value of tensile strength of concrete is obtained as follows: f_tk=0.7×0.3×f_ck^2/3=0.76 MPa. The design value of compressive strength of concrete of the Republic of China era is obtained as follows: f_c= f_ck/γ_c =6.92/1.5=4.61 MPa. The relevant design value of tensile strength of concrete is obtained as follows: f_t=f_tk/γ_c=0.76/1.5=0.51 MPa. The design value of yield strength of rectangular rebar of the Republic of China era is obtained as follows: f_y=f_yk/γ_y=229.56/1.15=199.62 MPa. The design value of yield strength of round rebar of the Republic of China era is obtained as follows: f_yv=f_yk/γ_y=276.82/1.15=240.71 MPa.

The concrete cover thickness of Chinese original structural calculation method is required to be more than 38.1 mm for beams or columns. 139 test data of concrete cover thickness of beams and columns have been collected from 9 typical Chinese modern concrete buildings. According to the analysis of these data, the average of the concrete cover thickness of beams or columns is 35.96 mm. The results are shown in Table 3. The test results of concrete cover thickness of beams and columns approximately follow the rule of normal distribution, as shown in Fig. 3, but the discreteness of these test data is relatively large because of restriction of construction techniques and damages in the wars at that time.

3 Comparative Analysis on the Original Calculation Method and the Present Calculation Methods of Shear Behavior of Reinforced Concrete Beams

According to Refs.^[3-5], the calculation diagram of shear capacity of concrete reinforced beam of the Chinese original structural design method is shown in Fig. 4.

According to the Chinese original structural calculation method, shear force of concrete reinforced beam is born by concrete and hoop rebar.Concrete part only contributes shear bearing capacity calculated by the allowable stress of concrete, and hoop rebars contribute the other shear bearing capacity. The calculation formulas of diameter, shape, and distance of hoop rebars of concrete reinforced beam are as follows:

${v}'=\frac{V}{bjd}$

(1)

${{x}_{c}}=6\left( \frac{\left[ {v}'-{{v}_{1}} \right]l}{{{v}'}} \right)$

(2)

${{V}_{2}}=\frac{\left( {v}'-{{v}_{1}} \right)b{{x}_{c}}}{2}$

(3)

${{N}_{V}}=\frac{{{V}_{2}}}{{{f}_{V}}{{A}_{V}}{{^{\prime }}^{\prime }}}$

(4)

$S=\frac{{{f}_{V}}{{A}_{V}}{{^{\prime }}^{\prime }}}{\left( {v}'-{{v}_{1}} \right)b}$

(5)

where V is the maximum shear force of beam; v′ is the maximum shear stress of beam; j is the ratio of the arm of force to the distance between center of tensile rebar and compressive side of beam; b is the width of beam; d is the distance between center of tensile rebar and compressive side of beam; v₁ is the allowable shear stress of concrete, and it is 0.41 MPa; x_c is the distance between the support and the location of zero shear force; l is the span of beam; V₂ is the total shear bearing capacity of all hoop rebars; N_v is the quantity of hoop rebars; f_v is the allowable shear stress of hoop rebars; A_v″ is equal to the area of single leg of hoop rebar multiply the number of legs of hoop rebar; S is the minimum distance of hoop rebars close to support.

Comparing with the present calculation methods including the Chinese present calculation method, the American present calculation method and the European present calculation method, the Chinese original calculation method is founded based on the theory of elastic material mechanics, shear force is undertaken by concrete part and hoop rebar part together. The design strength of hoop rebar is its allowable stress. The Chinese present calculation method is founded based on the theory of semi empirical and semi theoretical model, shear force is undertaken by concrete part and hoop rebar part together. The design strength of hoop rebar is its yield strength. The American present calculation method is founded based on the theory of modified truss model, shear force is undertaken by concrete part and hoop rebar part together. The design strength of hoop reinforcement is its yield strength. The European present calculation method is founded on the theory of truss model, shear force is undertaken by hoop rebar part when hoop rebar is yielding or concrete part when concrete is crushed. The design strength of hoop rebar is its yield strength. The calculation models of these four methods are very different.

In this paper, taking examples of the simply supported beams, the comparative studies on calculation methods of shear behavior of reinforced concrete beams of Chinese modern reinforced concrete buildings are carried out. The calculation methods include the Chinese original calculation method, the Chinese present calculation method, the American present calculation method and the European present calculation method.

Some typical rectangular beams bearing distributed loads are taken as the examples for calculation, considering different cross section dimension from 250 mm×500 mm (width×height) to 450 mm×900 mm (width×height), different span, and different live loads. For the Chinese original structural calculation method (M₁), the design strength of concrete and rebar are the relevant allowable stress. The allowable stresses of concrete and rebar are obtained according to Table 1. For the Chinese present structural calculation method (M₂), the design compressive strength of concrete is: f_c=4.21 MPa, the design tensile strength of concrete is: f_t=0.89 MPa, the design shear strength of rebar is: f_yv=251.65 MPa. For the American present structural calculation method (M₃), the design compressive strength of concrete is: f_c=7.15 MPa, the design tensile strength of concrete is: f_t=0.89 MPa, the design shear strength of rebar is: f_yy=276.82 MPa. For the European present calculation design method (M₄), the design strength of concrete is: f_c=4.61 MPa, the design tensile strength of concrete is: f_t=0.51 MPa, the design shear strength of rebar is: f_yy=240.71 MPa. The comparison of calculation results with different methods are shown in Tables 4 and 5.

The results in Tables 4 and 5 show that the maximum design shear forces of the Chinese original structural calculation method are 36%-38%, 53%-56% and 47%-49% less than those of the Chinese, the American and the European present structural calculation methods respectively. The calculation area of the hoop rebars of the Chinese original structural calculation method are 85%-99% lager than those of the Chinese present structural design method, and are 0%-64% and 0%-35% less than those of the American and the European present structural calculation methods respectively. So, in term of maximum shear capacity of reinforced concrete beam, without considering earthquake loads, the shear capacity of the Chinese original structural calculation method is smaller than that of the Chinese present structural calculation method, but is larger than that of the American present structural calculation method and that of the European present structural calculation method. In other words, according to the requirements of the Chinese present structural calculation method, the shear bearing capacity of concrete beams of the Republic of China era are basically safe. But according to the requirements of the American present structural calculation method and the European present structural calculation method, the shear bearing capacity of concrete beams of The Republic of China era are not safe.

4 Conclusions

1) he original structural calculation method of reinforced concrete structure of the Republic of China era is based on the allowable stress design method. The design safety factors are 3.55-4.00.

2) ccording to the statistic analysis of the test results of compressive strength of concrete cubes, the test data follow the rule of normal distribution, and the average compressive strength of concrete cubes of the Republic of China era is 16.36 MPa, and the standard value of compressive strength of concrete cubes of the Republic of China era is 8.48 MPa. The test results coincide with the requirements of the Chinese original structural calculation method.

3) ccording to the statistical analysis of the test results of strength of rebars, the test data of rectangular rebars and round rebars overall follow the rule of normal distribution, and the standard value of the yield strength of rectangular rebars is 229.56 MPa, and the standard value of the yield strength of round rebars is 276.82 MPa.

4) ccording to the statistical analysis of the test results of concrete cover thickness, the test results of concrete cover thickness of beams and columns approximately follow the rule of normal distribution. The average of the concrete cover thickness of beams and columns is 35.96 mm. The actual concrete cover thickness of columns and beams are appreciably less than the requirement of the Chinese original structural calculation method. The discreteness of these test data is relatively large because of the restriction of construction techniques at that time.

5) Based on the comparative analysis of the different structural calculation methods, in term of calculation area of hoop rebars of reinforced concrete beam, without considering earthquake loads, the Chinese original structural calculation method is safer than the Chinese present structural calculation method, but is more unsafe than the American present structural calculation method and the European present structural calculation method.

6) he original structural calculation method of reinforced concrete structures of the Republic of China era doesn’t consider earthquake loads, while many of these buildings are located in earthquake prone area. These buildings lack aseismic structural configurations, and will be dangerous when an earthquake happens. The structural assessment method and the structural safety level of reinforced concrete structures of the Republic of China era with considering earthquake loads will be further studied in future.