| Title |
Mechanical Interpretation of Influence Functions in Winkler Beam |
| Authors |
Kwak Soon-Seop ; Song Kil-Ho |
| Keywords |
Influence Function ; Green Function ; Mechanical Interpretation ; Influence line ; Double Moment ; Double Shear ; Moment Hinge ; Shear Hinge ; Infinite and Semi-infinite Winkler Beam |
| Abstract |
The purpose of this study is to interpretate mechanically the influence functions for the infinite and semi-infinite Winkler beams. The results of study are the followings: (1) The influence function for deflection on ξ with a unit load at x is the deflection function at x by the unit load atξ. (2) The influence function for angle on ξ is the deflection function at x by the unit moment at ξ. (3) The influence function for moment on ξ is the deflection function at x by the double moment(M0=EIβ/2) at ξ when the point ξ is assumed as moment hinge. In this case the angle difference between θξ+ and θξ- is 1 even though the values of θξ+ and θξ- at ξ are dependent on the circumstances. (4) The influence function for shear at ξ is the deflection function at x by the double shear(V0=EIβ3) at ξ when the point ξ is assumed as kinds of shear hinge. Here the deflection difference between yξ+ and yξ- is 1 and each value of deflection yξ+ and yξ- is also dependent on the circumstances and β4=k/4EI, k is spring constant in Winkler base. Here, Muller-Breslau's principle has been proved as correct. In other words, when we need the influence functions for deflection, slope, moment, shear at ξ, it is sometimes more convenient to apply unit force, unit moment, unit slope difference between ξ+ and ξ-, unit deflection difference between ξ+ and ξ- at ξ and get the deflection functions for each case. Those deflection functions are the same as the influence functions for the deflection, slope, moment and shear respectively. |