Research On The Calculation Formula Of Reinforced Concrete Members Under Shear And Torsion

It is pointed out that the Tri-linear Model in Concrete Structure Design Code(GB 50010-2010) for calculating the bearing capacity of reinforced concrete members under the combined action of shear and torsion enlarges the 1/4 Circular Arc Mod el and lead to an unsafe design. The formula proposed by Ding Dajun using the 1/4 Circular Arc Model understates the bearing capacity of concrete in choosing the reduction factor of concrete shearing capacity. Adopting the Linear Model, the formula proposed by Huang Liang makes the design too conservative. The main research contents of this paper are as follows:On the basis of the 1/4 Circular Arc Model and the Modified Tri-linear Model two modified formulas are provided. Practical examples show that Formula 1 and Formula 2 are more secure than the GB 50010-2010 formula. The numerical examples show that modified formula 1 and 2 are not only totally conform to the 1/4 Circular Arc Model, but also approximatively conform to the Linear Model proposed by Huang Liang, and their calculation results are quite similar. The two modified formulas are more economical than the formulas proposed by Ding Dajun and Huang Liang.The equations of torsion-shear bearing capacity correlation hidden in GB 50010-2010 formula, formula proposed by Ding Dajun, formula proposed by Huang Liang and two modified formulas are deduced from theoretical perspective and compared with the 1/4 Circular Arc. Through analyzing an example, it shows that dangerous region exists in curves of GB 50010-2010 formula and dangerous region expands with low stirrup ratio; curves of the formula proposed by Ding Dajun and formula proposed by Huang Liang are almost straight lines and the calculations are partially too conservative; curves of modified formula 1 and 2 are close to 1/4 Circular Arc with good security and economy.Reliabilities of the formulas above are analyzed to considering the load effect ratio, load combination, strength grade of rebar and concrete, member section size and loads of upper limit. The results show that for the second-level security structure when a ductile torsion-type failure occurs, reliability indices of GBJ 10-89 and GB 50010-2002 formulas cannot meet the demand of 3.7 in Unified standard for reliability design of building structures GB 50069-2001; reliability index of GB 50010-2010 formula cannot meet the demand in GB 50069-2001 with low concrete grade and high stirrup grade and it is lower when the design loads are close to the loads of upper limit; reliability indices of the other four formulas fit the demand in GB 50069-2001.The balance and the reason of shear and torsional reliability indeces of the formulas are studied. Example analysis indicates the shear and torsional reliability indices of GB 50010-2010 and the formula proposed by Ding Dajun are unbalanced with the variation of torsion-shear ratio; whereas, the formula proposed by Huang Liang and modified formula 1 overcome the shortcoming; the balance of the shear and torsional reliability indices of the modified formula 2 is well when the torsion-shear ratio is less than 0.75 and the modified formula 2 delays the emergence of imbalance to a large extent compared with the GB 50010-2010 formula.To sum up, using modified formula 1 and 2 when calculating shear-torsion bearing capacity is recommended; under special conditions, either improving the reinforcement ratio or calculating in accordance with the formula proposed by Huang Liang. If so, the safety and economy of design can be guaranteed.