Study On Fictitious Beam Method Considering Torsional Stiffness On Box-shaped Hollow Slab

Reinforced concrete hollow floor is becoming more and more widely used in recentyears. This structure has obvious advantages in saving the concrete and reducing thefloor height and weight, but the current calculation method still needs to be explored.As a cavity structure system, the accurate calculation of reinforced concrete hollowfloors is very difficult. So simplified calculation method of hollow floor is used tocalculate this structure.The current method of calculating can be summarized ascontinuous method and the discrete method. Fictitious method divide the floor intostrips vertically and horizontally, and then in accordance with the principle of equivalentbending stiffness of cross beam system, it belongs to a discrete method. The advantageof this method is that, it can greatly reduce the computational elements so as to simplifythe calculation. But in the process of segmentation, cutting the original connection canlead to weakening of the whole structure, and to underestimate the bearing capacity, thestructure can’t fully exert the advantages.Based on the FEM, this paper has made a thorough study on fictitious beammethod. The main work of this paper are as follows:(1) By calculating a single span plate with column under vertical load, this thesisfound that,I-shaped cross section and rectangular cross section beam model can notmatch the solid well.Pointing out that the fictitious beam method will underestimate thetorsional stiffness due to cutting the hollow slab apart.(2) From the shear flow in hollow slab,this thesis try to recover the integrity of thewhole slab in the fictitious beam method.A formular to calculating torsional stiffness iscarried out. To test the feasibility of the method in this thesis, and prove the necessity ofconsidering torsional stiffness in fictitious beam method,a variety of model withdifferent boundary conditions have been calculated.Calculation results shows thatmethod in this thesis matches well with the solid model.I-shaped cross section has adistinct difference with solid model,rectangular cross section is better than I-shaped,butstill insufficient in torsional stiffness.Underestimating of the torsional stiffness will leadto inaccurate moment results in vertical load,the column strip moment will be toolarge,thus will lead to uneconomic reinforcement on the region,and also let the local bartoo dense.(3) In order to save memory when calculating large structures,this thesis further simplified the fictitious beam method,and applied the reduced beam method to calculatea model,results shows that reduced beam method in this thesis can match the beammethod which do not reduce beams.