Bending Moment For Concrete Circular Plate Foundation Of Chimney Based On Elastic Theory

The design code of chimney foundation GB50051 in China calculates the bending moment of reinforced concrete circular plates with the theory of limit equilibrium.Although this method is widely used in engineering design and has achieved good results,but there are some problems at the same time.First,the calculation result of this formula for large cantilevered structures is small,indicate that the design method is not safe.Second,the code formulas which based on the theory of limit equilibrium theory overemphasize the economics of basic reinforcement design,make safety indicator reduced and is contrary to the elastic theory calculation method of the normative system.Therefore,it is necessary to study the calculation method of chimney plate foundation bending moment based on the elasticity theory.According to the revision of the current chimney design code,the study of chimney plate foundation bending moments is carried out based on elastic thin plate theory and finite element analysis method in this paper,.The work and main conclusions are as follows:?1?Based on the force diagrams of foundation slabs that do not consider foundation deformation,the elastic bending moment formulas of the circular plate are derived with the conditions of uniform load and linear load respectively.The elastic theory solution of the circular plate under uniform load with the fixed-clamped and simply supported constrains are proposed.The elastic theoretical solution under the linear load are also obtained.The analysis of the elastic solution shows that the maximum circumferential bending moment of the circular foundation?outer cantilever?under uniform load and the linear load is located at r=b,and the maximum circumferential bending moment of the inner cantilever is located at the center of the bottom plate.?2?We establish the finite element models for a circular slab foundation with different r₁/r_z ratios under uniform loads,and discuss the constraints of the tube wall on the plate foundations based on the analysis results.The results show that the simulation results of the radial moments?outer cantilever?of the circular foundation are closer to those of the fixed constraint,while the simulation results of inner cantilever are quite different from those of the simple support and the fixed constraint.That is,the actual support between the chimney tube and the circular foundation outer overhang is close to the fixed constraint.The actual support and constraint of the inner cantilever are between the simply supported and the fixed constraint.?3?Based on this,this paper proposes the bending moment's formulas of the circular foundation based on elastic thin plate theory.And finite element software was carried out to analyze the circular foundation under real load which comes from calculation examples in the literature.There is a small difference between the results of the finite element analysis and the proposed formula.The calculation result of the radial bending moment?outer cantilever?is larger than those of the finite element analysis.The bending moment of the inner cantilever is slightly smaller than the finite element analysis result.Therefore,the proposed formula proposed in this paper is both economical and reasonable.