Portal Frames with Sway Due to Horizontal Load:
It has been shown above that a portal frame having a lack of symmetry or subjected to unsymmetrical or horizontal loads will exhibit 'sway'. This means that the joints free to move in the horizontal direction will move in that direction causing the concerned members to rotate in their plane. If this 'member rotation' or 'cord rotation' is clockwise, it has been shown in Section 3.3 (Eq. (3.10)) that it will induce fixed end moments equal to - 6EI Δ/l 2 (anticlockwise moments) where Δ is the amount of 'sway' or relative lateral movement of the member. In the moment distribution method, first it is assumed that there is no sway and the moment distribution is carried out for the fixed end moments caused by external loading only. Next a second distribution known as 'sway distribution' is carried out for the frame for sway moments only. These 'sway moments' have to be adjusted by multiplying them by a 'factor' so as to satisfy the conditions of horizontal equilibrium. As Δ is generally not known the sway moments which are in the ratio of (Ei. Ii/Li) of the concerned members are assumed as convenient integral numbers in that ratio. Finally, the correction factor and correct moments are determined by writing down the conditions of horizontal equilibrium. These 'sway moments' are then algebraically added to the fixed end moments due to external loads (already determined), giving the final joint moments. In the example here a case of pure sway (without any external load moments) is given and the method of solving it is shown.