Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 3 2 SECOND ORDER EFFECTS IN PORTAL FRAMES 2.1 Frame behaviour The strength checks for any structure are valid only if the global analysis gives a good representation of the behaviour of the actual structure. When any frame is loaded, it deflects and its shape under load is different from the un-deformed shape. The deflection causes the axial loads in the members to act along different lines from those assumed in the analysis, as shown diagrammatically in Figure 2.1 and Figure 2.2. If the deflections are small, the consequences are very small and a first-order analysis (neglecting the effect of the deflected shape) is sufficiently accurate. However, if the deflections are such that the effects of the axial load on the deflected shape are large enough to cause significant additional moments and further deflection, the frame is said to be sensitive to second order effects. These second order effects, or P-delta effects, can be sufficient to reduce the resistance of the frame. These second order effects are geometrical effects and should not be confused with non-linear behaviour of materials. As shown in Figure 2.1, there are two categories of second order effects: Effects of deflections within the length of members, usually called P-  (P-little delta) effects. Effects of displacements of the intersections of members, usually called P-  (P-big delta) effects. 1 4 3 2 1 2 3        Figure 2.1 Asymmetric or sway mode deflection