Calculation Of Bending Moment Of Annular Plate Foundations And Of Circular And Annular Pile Caps

Plate foundations and pile foundations are commonly used as foundations of chimneys.In the current chimney design code,expressions for calculating the bending moment of annular plate foundations are developed based on the theory of plastic limit analysis.However,regarding to the current code expressions,inadequacies exist.Firstly,as a structure with high safety margin,the plastic limit analysis method which is used to calculate the bending moment of the chimney foundations,guarantees the economic effect but reduces the safety;Secondly,the flexural stiffness of the annular plate cannot be estimated directly,and thus the restraint of the ring wall on the plate cannot be determined clearly.In addition,pile caps of high-rise constructions such as chimneys are mostly circular and annular,but for the calculation of bending moments for the reinforcement for circular pile caps and annular pile caps,the Chinese code does not give corresponding expressions.In view of the above shortages,deflections and internal forces of annular plate foundations and of circular and annular pile caps under the action of loads were derived on the basis of the elastic small-deflection theory of thin plates,and expressions of bending moments for the reinforcement were proposed.Main research works in this paper are as follows:(1)Based on the elastic small-deflection theory of thin plates,bending moments for outer cantilever parts of annular plates subjected to uniformly distributed loads and linearly distributed loads,as well as for inner cantilever parts of annular plates which are clamped and simply supported at the ring walls were derived,and elastic expressions for calculating bending moments for reinforcement of the annular plate foundation were proposed.(2)Based on the elastic small-deflection theory of thin plates,deflections and internal forces of circular and annular plates under circumferential line loads were derived,and elastic expressions for calculating bending moments of pile caps were proposed.(3)The proposed expressions were applied to the design examples of annular plate foundations and of circular and annular pile caps to calculate bending moments for the reinforcement,and were compared with those obtained by SAP2000 FE analysis and code expressions.Studies show that for the bending moment for bottom reinforcement of annular plate foundations,results obtained from the proposed expressions are 1.10~1.36 times of those by code expressions,leading to a safer design.Analysis of design examples of annular plate foundations shows that,compared with code expressions,results obtained from the proposed expressions are closer to those of the three-dimensional finite element analysis and safer for design.Analysis of design examples of circular and annular pile caps shows that the numerical difference between the results obtained from the proposed expressions and those of the finite element software is small,and the proposed expressions are more conservative for design.The above analysis results demonstrate that the elastic expressions applied to annular plate foundations and to circular and annular pile caps to calculate bending moments can guarantee the safety of the reinforcement and provide a reference for the design of chimney foundations.