| Title |
Variation of Moments Due to the Spring Constant K in the Thermal Loaded Winkler Beam |
| Authors |
Kwak, Soon-Seop ; Song, Kil-Ho ; Jeon, Du-Seon |
| Keywords |
Winkler Beam ; Curvature ; Generalized Function ; Moment Green Function ; Point Thermal Load ; Partial Thermal Load |
| Abstract |
The curvature of the Winkler beam due to the thermal loads is “”, where is deflection curve, is curvature by the thermal load. The differential equation of the Winkler beam, when loaded by thermal load, is , where is spring constant. When the point thermal load is applied at , the curvature becomes , where is the coefficient of thermal expansion, is thermal difference between upper and lower fiber of beam, is the depth of beam and is the Generalized Function. With the aid of characteristics of Generalized Functions, the solutions of the mentioned differential equations are obtained systematically. When the moment Green Function due to the point thermal load is obtained, we can get the moment, when the partial thermal load is applied, through integration of the moment Green Function within the given range. The results of this study show, when the beams loaded by point thermal load and partial thermal load, how the values of deflection and moments change depending on the spring constant in four cases : ①Hinge-Hinge, ②Fix-Fix, ③Hinge-Fix, ④Free-Fix. When the spring constant is zero, then the Winkler beam becomes general beam. |