Several studies have aimed at finding the optimum number of vertical members to use for each stub. However, the strength and stiffness of the stub girder are insignificantly affected by this choice and a number between 3 and 7 is usually chosen. As a rule of thumb, it is advisable to have one vertical per foot length of stub, but this is only a guideline.

The verticals are placed at uniform intervals along the length of the stub, usually with the outside members close to the stub ends. Figure 33.5 illustrates the approach. As for end conditions, these vertical members are assumed to be rigidly connected to the top and bottom chords of the Vierendeel girder.

One vertical member is placed at each of the locations of the floor beams. This member is assumed to be pinned to the top and bottom chords, as shown in Figure 33.5, and its stiffness is conservatively set equal to the moment of inertia of a plate with a thickness equal to that of the web of the floor beam and a length equal to the beam depth. In the example, tw = 0.25 in.; the beam depth is 15.69 in. This gives a moment of inertia of

and the cross-sectional area is

The Vierendeel model shown in Figure 33.5b indicates that the portion of the slab that spans across the opening between the exterior end of the exterior stub and the support for the slab (a column, or a corbel of the core of the structural frame) has been neglected. This is a realistic simplification, considering the low rigidity of the slab in negative bending.

Figure 33.5b also shows the support conditions that are used as input data for the computer analysis. In the example, the symmetrical layout of the girder and its loads make it necessary only to analyze one half of the span. This cannot be done if there is any kind of asymmetry and the entire girder must then be analyzed. For the girder that is shown, it is known that only vertical displacements can take place at midspan; horizontal displacements and end rotations are prevented at this location. At the far ends of the bottom chord only horizontal displacements are permitted and end rotations are free to occur. The reactions that are found are used to size the support elements, including the bottom chord connections and the column.

The structural analysis results are shown in Figure 33.7, in terms of the overall bending moment, shear force and axial force distributions of the Vierendeel model given in Figure 33.5b. Figure 33.7d repeats the layout details of the stub girder, to help identify the locations of the key stress resultant magnitudes with the corresponding regions of the girder.

The design of the stub girder and its various components can now be done. This must also include deflection checks, even though research has demonstrated that the overall design will not be governed by deflection criteria [6]. However, since the girder has to be built in the shored condition, the girder is often fabricated with a camber, approximately equal to the dead load deflection [6,11].

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