A braced building frame

In the Beams and frames pathway, the braced frame lay in a single plane. It had two bays, two storeys and X bracing in one bay, and the wind could only come from one side. A real building has frame lines running in two directions, and the wind can blow from either direction. In this step, we'll build that building in the 3D canvas. It has two bays of 6 m each way and two storeys of 4 m, with nine columns, 24 beams and 24 braces, a dead load on every beam and a wind case from each direction. We'll see that each frame line carries the wind applied to it through its own bracing, we'll check one line by hand exactly as we checked the 2D frame, and we'll read an envelope over two ULS combinations. We'll also meet the Layers panel, which is how you find your way around a model this size.

1.0 The idea

Wind loading on a building frame is simulated, as before, by a horizontal force at each floor level. The job of the structure is to provide a lateral load path that takes that force back down to the foundations. In the 2D pathway, there was one path to think about. In three dimensions, there are two. A wind from X needs a load path in the X direction, and a wind from Y needs one in the Y direction.

So, how does a 3D frame model share the wind between its frame lines? Well, the key thing to understand before reading any numbers in this step is that a frame model has no floor diaphragm. In a real building, the floor slab ties every column at a level together and moves as one stiff plate, so the wind on the whole face can be collected and sent to one braced bay somewhere on the plan. Our model does not have this. The floor beams tie the frame lines together at their joints, but a grid of beams is far less stiff in plan than a slab, so the bracing in one line can't resist the wind applied to another. In other words, each frame line acts independently. A line with no bracing carries its wind by portal action, through the bending of its columns, no matter how well the line next to it is braced.

This is why this model has X bracing in the first bay of frame line, in both directions. There are three lines along X and three along Y, each with its own pair of braces in each storey. And it means that every frame line along X, read on its own, is the same braced frame we analysed in the Beams and frames pathway, with two bays, two storeys, 20 kN at each floor and bracing in one bay. The hand check is the same too. A section through the storey gives the storey shear, the two braces share it, and the overturning moment of the wind about the base is resisted by the vertical reactions along the line. We'll do it once for one line, because the other two are the same.