Application Of Strut-and-tie Model In Reinforced Concrete Beams With Shear Span Ratio Less Than 2.5

Shorter beams usually refer to beams with a shear-span ratio of less than 2.5,the strain distribution in the member is complex,and the normal section strain no longer conforms to the plane section assumption.There are three methods of flexure and shear design in Chinese code for shorter beams at the same time.Among them,three shear design methods are all empirical formulas,flexure design methods mainly originate from the plane section assumption or modify the inner force arm based on the plane section assumption.According to these three methods,there will be different safety degrees and guarantee rates,and the flexure and shear problems of shorter beams cannot be unified.It is worth discussing which method can better meet the accuracy of capacity prediction and design safety.At present,the strut-and-tie model method(short for “STM method”)has been included in many national codes for the design of beams with small shear span ratio.Compared with the empirical method,the STM provides a design method with clear mechanical concept and relatively simple calculation,and can unify the flexure and shear failure in one model.However,the STM is subjective when it is established,different calculation methods of the effective strength of the member will also affect the prediction results of the bearing capacity.How to establish the STM can better reflect the performance of the shorter beam is worthy of further study.Based on these problems,the main work of this paper is as follows:(1)Collect the test data of short beams to form a database.The capacity of test beams in the database is predicted and compared by using three methods in Chinese codes and STM methods in other national codes.(2)An iterative method is proposed to establish the strut and tie model in a short beam.(3)Based on the design concept of "strong shear-weak bending",a STM method is proposed to meet the design parameters of Chinese code.The results shows:(1)In the prediction of flexure capacity,the prediction results of the GB 50010-2010 formula are closest to the test value,but the safety factor and guarantee rate are lower when the shear span ratio is less than 1;the guarantee rate of the CECS 39:92 formula is higher in its scope of application,however the predicted value of the capacity is too high outside its scope;the safety factor and guarantee rate of the GB 50010-2010-G formula basically don’t change with the shear span ratio,which is more suitable for flexure design.(2)In the prediction of shear capacity,the prediction result of GB 50010-2010 formula is too conservative when the shear span ratio is less than 1.5,and the safety factor for beams with web reinforcement is lower than that of beams without web reinforcement;The prediction result of the CECS 39:92 formula is more accurate within its applicable scope,but the guarantee rate is small.The guarantee rate of GB 50010-G formula is high,and the safety factor and guarantee rate basically do not change with the shear span ratio and distributed reinforcement ratio,which is more suitable for shear design.(3)The STM method in the codes of different countries adopts different calculation methods for the effective strength of the strut,then different calculation results will be obtained when it is used for the shear capacity calculation.The STM method in ACI 318-02 code can more accurately predict the shear strength of beams with and without web reinforcement.(4)Using iterative method to establish STM for shorter beams can uniquely determine the size of CCC node in the model,and the calculation results for flexure capacity are more accurate than the GB 50010-2010 formula.(5)The STM method proposed in this paper is more accurate in capacity prediction and safer in shear design,it also conform to the design concept of "strong shear-weak bending".