The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordin...The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.展开更多
Although commonly used, no design method is available for steel web tapered tee section cantilevers. This paper investigates the bending stresses of such beams. Relationships between the maximum compressive stress and...Although commonly used, no design method is available for steel web tapered tee section cantilevers. This paper investigates the bending stresses of such beams. Relationships between the maximum compressive stress and the degree of taper were investigated. An analytical model is presented to determine the location of the maximum stress when subjected to a uniformly distributed load or a point load at the free end and was validated using finite element analysis and physical tests. It was found that the maximum stress always occurs at the support when subjected to a uniformly distributed load. When subjected to a point load at the free end and the degree of taper is up to seven, it was found that Miller＇s equation could be used to determine the location of the maximum stress. However, it is shown that when the degree of taper is greater than seven, Miller＇s equation does not accurately predict the location and the analytical model should be used. It was also found that the location of the maximum stress was solely dependent on the degree of taper, while a geometric ratio, fl was required to determine the magnitude of the maximum stress. A simple method that predicts the magnitude of the maximum stress is proposed. The average error in the prediction of the magnitude of the maximum stress is found to be less than 1.0%.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 1043203)the Foundation of Ningbo University (No. 2005014), China
文摘The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.
文摘Although commonly used, no design method is available for steel web tapered tee section cantilevers. This paper investigates the bending stresses of such beams. Relationships between the maximum compressive stress and the degree of taper were investigated. An analytical model is presented to determine the location of the maximum stress when subjected to a uniformly distributed load or a point load at the free end and was validated using finite element analysis and physical tests. It was found that the maximum stress always occurs at the support when subjected to a uniformly distributed load. When subjected to a point load at the free end and the degree of taper is up to seven, it was found that Miller＇s equation could be used to determine the location of the maximum stress. However, it is shown that when the degree of taper is greater than seven, Miller＇s equation does not accurately predict the location and the analytical model should be used. It was also found that the location of the maximum stress was solely dependent on the degree of taper, while a geometric ratio, fl was required to determine the magnitude of the maximum stress. A simple method that predicts the magnitude of the maximum stress is proposed. The average error in the prediction of the magnitude of the maximum stress is found to be less than 1.0%.
