Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 11 The elastic-perfectly-plastic model, Figure 3.4, assumes that the members deform as linear elastic elements until the applied moment reaches the full plastic moment M p . The subsequent behaviour is assumed to be perfectly plastic without strain hardening. With elastic-perfectly-plastic analysis, the load is applied in small increments, with hinges inserted in the analysis model at any section that reaches its full plastic moment, M p as illustrated in Figure 3.6. If the appropriate computer software is used, it should be possible to predict hinges that form, rotate, then unload or even reverse. The final mechanism will be the true collapse mechanism and will be identical to the lowest load factor mechanism that can be found by the rigid-plastic method. The elastic/perfectly-plastic method has the following advantages:  The true collapse mechanism is identified.  All plastic hinges are identified, including any that might form and subsequently unload. Such (transient) hinges would not appear in the final collapse mechanism but would nevertheless need restraint.  Hinges forming at loads greater than ULS can be identified. Such hinges do not need restraint, as the structure can already carry the ULS loads. This may produce economies in structures where the member resistance is greater than necessary, as occurs when deflections govern the design or when oversize sections are used.  The true bending moment diagram at collapse, or at any stage up to collapse, can be identified. 3.2.4 Elastic vs. plastic analysis As discussed in Section 3.1, plastic analysis generally results in more economical structures because plastic redistribution allows smaller members to carry the same loads. For frames analysed plastically, haunch lengths are generally around 10% of the span. Where deflections (SLS) govern design, there is no advantage in using plastic analysis for the ULS. If stiffer sections are selected in order to control deflections, it is quite possible that no plastic hinges form and the frame remains elastic at ULS. The economy of plastic analysis also depends on the bracing system, because plastic redistribution imposes additional requirements on the restraint to members, as discussed in Section 6.3. The overall economy of the frame might, therefore, depend on the ease with which the frame can be restrained. Plastic analysis should only be contemplated if commercial software is available. The more sophisticated software packages carry out second order ( P- ∆ ) elastic-plastic analysis directly, significantly simplifying the overall design process. The ready availability of elastic/plastic design software makes it as easy to adapt full plastic analysis. The resulting limitation to Class 1 sections, which are required at potential hinge positions, is not significant.