Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 6 3 ULTIMATE LIMIT STATE 3.1 General Methods of frame analysis at the Ultimate Limit State fall broadly into two types – elastic analysis (see Section 3.2.2) and plastic analysis (see Section 3.2.3). The latter term covers both rigid-plastic and elastic-plastic analyses. The formation of hinges and points of maximum moment and the associated redistribution of moment around the frame that are inherent to plastic analysis are key to the economy of most portal frames. They ‘relieve’ the highly stressed regions and allow the capacity of under-utilised parts of the frame to be mobilised more fully. These plastic hinge rotations occur at sections where the bending moment reaches the plastic moment or resistance at load levels below the full ULS loading. An idealised ‘plastic’ bending moment diagram for a symmetrical portal under symmetrical vertical loads is shown in Figure 3.1. This shows the position of the plastic hinges for the plastic collapse mechanism. The first hinge to form is normally adjacent to the haunch (shown in the column in this case). Later, depending on the proportions of the portal frame, hinges form just below the apex, at the point of maximum sagging moment. A portal frame with pinned bases has a single degree of indeterminacy. Therefore, two hinges are required to create a mechanism. The four hinges shown in Figure 3.1 only arise because of symmetry. In practice, due to variations in material strength and section size, only one apex hinge and one eaves hinge will form to create the mechanism. As there is uncertainty as to which hinges will form in the real structure, a symmetrical arrangement is assumed, and hinge positions on each side of the frame restrained. 1 1 1 1 Position of plastic hinges Figure 3.1 Bending moment diagram resulting from the plastic analysis of a symmetrical portal frame under symmetrical vertical loading