333 Methods of Analysis and Modeling 3331 General Observations

In general, any number of methods of analysis may be used to determine the bending moments, shear forces, and axial forces in the components of the stub girder. However, it is essential to bear in mind that the modeling of the girder, or, in other words, how the actual girder is transformed into an idealized structural system, should reflect the relative stiffness of the elements. This means that it is important to establish realistic trial sizes of the components, through an appropriate preliminary design procedure. The subsequent modeling will then lead to stress resultants that are close to the magnitudes that can be expected in actual stub girders. Based on this approach, the design that follows is likely to require few changes, and those that are needed are often so small that they have no practical impact on the overall stiffness distribution and the final member forces. The preliminary design procedure is therefore a very important step in the overall design.

33.3.2 Preliminary Design Procedure

It is not necessary to make any assumptions about the stress distribution over the depth of the girder, other than to adhere to the strength model that was developed for normal composite beams [3,10]. The stress distribution will vary anyway along the span because of the openings. The strength model of Hansell et al. [ 10] assumes that when the ultimate moment is reached, all or a portion of the slab is failing in compression, with a uniformly distributed stress of 0.85f-. The steel shape is simultaneously yielding in tension. Equilibrium is therefore maintained and the internal stress resultants are determined using first principles. Tests have demonstrated excellent agreement with theoretical analyses that utilize this approach [4-6,10].

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