Differential Equation Method For Effects Of Creep And Shrinkage In Steel-Concrete Composite Beam

The distribution of sectional forces will be occured in the composite girder subject to long-term load because of creep and shrinkage. It will have a negative effect on the safety of structures to add these changes of section forces even though the external load remain unchanged. Consequently, calculation methods for the distribution of sectional force and flexural deflection will be deduced and mechanical behavior of the composite girder will be expounded in the thesis. Then the calculation methods will be checked by contrasting with the results of finite element analysis and test. Besides, the analysis results from DISCHINGER’s method and RUSCH’s method can check them each other. The finished works and conclutions of this thesis are listed as follows:(a) The differential equation of the stress-strain relationship for concrete will be deduced respectively by the theories of DISCHINGER and RUSCH. Then the differential equations for redistribution forces, in the situations of shrinkage and creep whith no restraints or with restraints, will be deduced and be solved.(b) The differential equations for redistribution forces on composite cross section subject to static moments and normal forces will be obtained and solved respectively according to the theories of DISCHINGER and RUSCH. Then approximate calculation methods for redistribution forces could be gained by simplifying the solution procedure. And the fomula of flexural deflection for simply supported composite beam could be deduced from the internal force analysis.(c) The formula of the secondary internal force for the continuous composite beam will be built according to force method and virtual work principle. The analysis results show that the secondary internal force has nothing to do with creep in the situations that each spans of the continuous composite beam have same length and same creep character. And the secondary internal force will relate to creep if and only if in the situation that each spans of the continuous composite beam have different length and creep character. Haoever, shrinkage is one of the reasons in any case.(d) The differential equations for redistribution forces on composite cross section subject to bending moments and normal forces developing in time will be obtained and solved respectively according to the theories of DISCHINGER and RUSCH. And then the fomula of flexural deflection for continuous composite beam could be deduced from the internal force analysis.