A portal frame
In this step, we'll consider our first frame structure - the classic portal frame with pinned bases. Along the way, we'll explore how the bending moment behaves at the rafter-to-column joint; we'll see how lateral thrust develops at the supports and see what effect lateral wind loading has on the structure - often the most troublesome load case for a portal frame structure. We'll also explore the effect of different support types and what introducing a hinge does to the structure's response.
1.0 The idea
Fundamentally, the behaviour of a frame structure follows all of the same rules that the beams we've looked at already do. Rigid joints between the rafters and columns restrain the rafter ends from rotating freely and vice versa. This reduces the sagging moment in the rafters and introduces hogging moments in the rafters at the rafter-to-column connection.
Because we must have joint equilibrium, the hogging on the rafter side of the joint is matched by an equivalent magnitude moment on the column side of the joint - so loading on the rafters causes bending in the rafters which is transmitted around the joint and into the columns. If the column base is pinned, we know the moment must reduce to zero at the base, which means a lateral thrust develops to keep the column in equilibrium.
In two dimensions, statics gives us three equilibrium equations. A pinned-base portal has four support reactions, so there is one too many reactions for statics alone to solve for. To find the thrust, we also need to consider how the frame deforms: compatibility plays the same role here as it did for the propped cantilever in step 3.
Fixing both bases gives six reactions and three degrees of indeterminacy. Keeping the bases pinned and adding a hinge at the apex would give us back an additional equation, rendering the structure statically determinate and effectively turning it into a three-pinned arch. We'll use the three-pinned frame for the hand check below.
2.0 The model
The model consists of five nodes and four members, two rafters and two columns. Each column is 6 m high, and the ridge of the frame is a further 1.5 m above this. The columns are UB 533 x 210 x 92 and the rafters are UB 457 x 191 x 67, each 6.185 m long. The bases of both columns are pinned.