A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with stiffness $${k_x},\,\,{k_y}$$ and $${k_\theta }$$ respectively. The limiting values of $${k_x},\,\,{k_y}$$ and $${k_\theta }$$ are :

For the beam shown below, the stiffness coefficient $${K_{22}}$$ can be written as

The stiffness coefficient $${k_{ij}}$$ indicates

For linear elastic frame, if stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will be