Moment Distribution for Rigid Jointed Frames with Sway

The frames in Section 5.2 are prevented from any lateral movement by the support conditions. In frames where restraint against lateral movement is not provided at each level, unless the frame, the supports and the loading are symmetrical it will sway and consequently induce additional forces in the frame members.

Consider the frame indicated in Figure 5.18(a) in which the frame, supports and applied load are symmetrical.

Figure 5.18

Consider the same frame in which the load has been moved such that is now asymmetric as indicated in Figure 5.19(a)

It is evident from Figure 5.19(b) that the solution to this problem is incomplete. Inspection of the deflected shapes of each of the frames in Figure 5.18(a) and 5.19(a) indicates the reason for the inconsistency in the asymmetric frame.

Consider the deflected shapes shown in Figures 5.20 (a) and (b):

Figure 5.20

In case (a) the deflected shape indicates the equal rotations of the joints at B and C due to the balancing of the fixed-end moments induced by the load; note that there is no lateral movement at B and C.

In case (b) in addition to rotation due to the applied load there is also rotation of the joints due to the lateral movement '5' of B and C. The sway of the frame also induces forces in the members and this effect was not included in the results given in Figure 5.19(b). It is ignoring the 'sway' of the frame which has resulted in the inconsistency. In effect, the frame which has been analysed is the one shown in Figure 5.21, i.e. including a prop force preventing sway. The value of the prop force 'P' is equal to the resultant horizontal force in Figure 5.19.

Figure 5.21

The complete analysis should include the effects of the sway and consequently an additional distribution must be carried out for sway-only and the effects added to the no-

sway results, i.e. to cancel out the non-existent 'prop force' assumed in the no-sway frame.

 11 El C El El |a Final Fortes a '\n-Swiiy Forces* + ' Sway-On 1 j horfts' Sway-Ottlv Frjimc Sway Foric Final Fortes a '\n-Swiiy Forces* + ' Sway-On 1 j horfts' Sway-Ottlv Frjimc Figure 5.22 The technique for completing this calculation including the sway effects is illustrated in Example 5.4 and the solutions to Problems 5.13 to 5.18.
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