The SNiP code is widely used in the so-called post-Soviet Union or Commonwealth of Independent States (CIS) countries for the design plans of reinforced and prestressed concrete structures, and the aim of this study is to present the modification factors of the existing shear design equation for the concrete contribution specified in the SNiP code. The ratio of the horizontal distance from the support to the end of the inclined crack to the projection of the inclined crack;
Introduction
General
In addition, various studies have still been conducted to develop the rational shear design equation to estimate the so-called shear contribution of concrete (i.e., Vc. term) in North America, Europe, and East Asia [11, 12]. This study aims to propose a rational modification factor for improving the displacement design equation specified in SNiP code by using a currently available updated large displacement database [11].
Aims & Objectives
Literature Review
Shear Transfer Mechanisms
Thus, the ability of the member to resist shear is directly proportional to the depth of the concrete compression zone. It means that increasing the compression zone leads to an increase in the load-bearing capacity of the part.
Major factors for shear capacity
However, tests conducted by Kani [24] showed that concrete strength in the range of 17.2-34.5 MPa does not affect the shear capacity of rectangular reinforced concrete beams. The test results showed that the increase in depth does not affect the shear capacity of the element.
Brief overview of shear strength models
Empirical data show that a reasonably correct estimate of shear capacity is provided by "the sum of the diagonal crack strength and the shear reinforcement contribution calculated using a 45-degree beam", although no mechanical reason suggests that the diagonal crack load is the same concrete contribution to the ultimate shear resistance. Fenwick and Paulay [32] assumed that the contribution of the compressive zone to the shear capacity is only 25%.
SNiP code model
3.1: “the shear contribution of concrete (Vc) can be estimated as the sum of the components normal to the principal compressive stress direction, and its direction can be considered in the shear strength model using cotd c/. It can be seen that the tensile strength of concrete varies from about 15 % and up to 5 % of the compressive strength for normal strength concrete and high strength concrete respectively. Therefore, it was decided to express the shear resistance of concrete as follows for small values of a d/.
To determine the contribution of shear reinforcement (Vs) to the total shear resistance, it was assumed that all shear reinforcements located in the projection line of the inclined shear crack will contribute the resisting force uniformly, as shown. There is a possibility of sudden brittle failure of the part with a small amount of shear reinforcement. To ensure that shear reinforcement can withstand shear, a minimum value for shear reinforcement must be established.
This condition cannot be satisfied if the value of Mb is changed to 6 2. As mentioned earlier, Eq. 3.14) must be derived to find the minimum resistance surface. With evenly distributed load: balancing force. equation can be expressed as follows: where qi is a uniformly distributed load subjected to the beam. 3.16) must be derived to find the minimum resistance surface.
Shear Database
Filtration process
Filtering samples with small value of compressive strength and web width was done to reflect the real practice. Furthermore, to ensure that the test specimens fail due to shear but not to bending, only the test specimens were selected for which the capacity ratios between the shear strength and the shear force at the flexural strength (Vtest/Vflex) were less than or equal to 1.1. are. where a margin of 10% was introduced to avoid the conservatism of the nominal flexural strengths determined on the basis of the ACI318 code.
Database for reinforcement concrete beams
The only criterion, which has been applied to the longitudinal reinforcement for reinforced concrete beams, is the presence of reinforcement in the sample. Many specimens have concrete compressive strength ranging from 12 MPa to 35 MPa, and high-strength concrete more than 60 MPa is used in 180 specimens, which are about 61% and 19% of the total number of specimens, respectively. accumulated testing. It is well known that the effective section depth (d) can significantly affect the shear forces and section behaviors of RC beams with and without shear reinforcement, and thus this so-called size effect was mainly addressed in the proposed modifying factor for the design of cutting. SNiP code model.
Database for prestressed concrete beams
Distribution of samples by the compressive strength of concrete is almost the same as in database with reinforced concrete beams. For both with and without shear reinforcement, approximately half of tests (147 tests: 70 tests without stirrups and 77 tests with stirrups) do not have longitudinal reinforcement in database.
Proposed modification factors
However, according to recent studies, it has been clearly observed that the shear strength of RC beam elements is greatly influenced by the longitudinal reinforcement ratio (w). The derivation of the modification factor () was derived based on the tensile strength of concrete specified in the SNiP code. Part (a) of this figure shows that the current SNiP model generally overestimates the shear capacity of lightly reinforced elements whose longitudinal reinforcement ratio is less than 2.0%, and they also show tendencies to underestimate as the reinforcement ratio increases. .
This factor shows that the maximum effect of the pressure can only be achieved on 25% of the total shear capacity. Part (a) of this figure shows that the current SNiP model generally underestimated the shear capacity. It is clear that even the minimum value of the SNiP equation produces much stronger results than other two codes.
It can be easily understood and there are no unclear conditions for calculating the length of oblique crack projections. In calculations, all the shear strengths were taken as the nominal strengths without considering the strength reduction factors. From this table, it can be concluded that the modification process makes the current equation more accurate in both element types, reinforcement and prestressed, because the COV was reduced in all cases.
Shear design models specified in international building codes
ACI318-14 –Shear strength model
According to ACI318-14, the maximum allowable compressive strength of concrete is limited to 69 MPa. This means that the shear stress of AB beams ( .. v V b d) with concrete compressive strength above 69 MPa should be considered as 1.41 MPa. The shear strength of a prestressed concrete beam provided by concrete can also be calculated using simple and detailed equations.
According to ACI318-14, it considers two types of cracks, web shear cracking and flexural-shear cracking. The shear capacity of the concrete to prevent both types of cracking should be calculated and their minimum should be chosen as the controlling strength. The equation is the same for both reinforced and prestressed concrete sections, and can be expressed as follows:
Eurocode2 (EC2)
CSA-A23.3
Additionally, when x is estimated to be negative value, it must be taken as zero and this cannot be greater than 0.003. x) using Eq. 6.9), the factored moment and shear force cannot be used for the shear strength evaluations using the shear database, and therefore the iterative calculation procedures were used in this study until the assumed bending moment.
Comparative study
- Compressive strength of concrete
- Longitudinal reinforcement ratio
- Shear span-to-depth ratio
- Effective member depth
37], the shear contribution of concrete (Vc) is significantly influenced by the compressive strength of concrete (f 'c. Figures from the appendices show the ratios of shear strength (Vtest /Vcal) of the test subjects, estimated from each model according to the compressive strength of concrete (f 'c. All models for shear strength evaluation for reinforced concrete elements, they estimated the shear strengths of the test specimens reasonably well without a significant bias trend.
Furthermore, they overestimated the shear strength of some low compressive strength concrete test specimens. Figures from the appendices show comparisons of the shear strength evaluated by each shear design model according to the longitudinal reinforcement ratio. The CSA-A23.3 code model takes good account of the combined effect between shear force and bending moment, as shown in Eq.
This result indicates that the effect of the shear span-to-depth ratio (a d/) could be negligible compared to the longitudinal reinforcement ratio. The shear strengths of members without transverse reinforcement decrease as the effective depth of the member (d) increases, which is known as the size effect. The figures from the appendices show the shear strength ratios ( .. V V ) estimated from the shear design models against the effective depth of the member.
Conclusions
The EC2 and CSA-A23.3 code models showed relatively small scatters regardless of member size, while other models showed underestimating trends as the effective member depth increases. The CSA-A23.3 and EC2 code models provided good analytical accuracy compared to other code models, and EC2 in particular provided the most conservative analysis results for reinforced concrete beams. The SNiP code model provided mostly conservative but poor prediction performances in estimates of the shear strengths of the RC test specimens.
Since the SNiP and ACI code equations cannot take into account the effect of the longitudinal reinforcement ratio, the shear strengths of the lightly reinforced members were therefore underestimated. On the other hand, most code models already consider the effect of member depth, except for the SNiP and ACI318 code models. By introducing the simple modification factors, the modified SNiP model presented the accurate analysis results on the shear strengths of the RC beam specimens, and its analytical accuracy was greatly improved compared with the existing SNiP code model.
In addition, the form of the proposed model is simple enough to be adopted in practices. 2] Die fib (International Federation for Structural Concrete), “The fib in Russia: New Standards,” Structural Concrete, Vol. 4] SNIP Concrete and Reinforced Concrete Structures, Ministry of Regional Development of the Russian Federation, Moscow, Russia pp.
Ultimate shear strength of structural concrete elements without transverse reinforcement derived from a mechanical model (SP-885). P., “The modified compression field theory for reinforced concrete elements subjected to shear”, ACI Journal, Proceedings Vol. C., and Hognestad, E., “Shear strength of reinforced concrete beams, part 1: tests of simple beams.”.
