Page 226 - Bridge and Highway Structure Rehabilitation and Repair
P. 226

CHAPTER 5                         LOAD AND RESISTANCE FACTOR RATING AND REDESIGN            201




            The smaller the deflection limit, the higher the required moment of inertia:
                                               2
                                        lim 3 L % /12 Ec                            (5.4)
            The higher the material strength, the lower the deflection limit, i.e., a more stringent require-


        ment. This limitation in existing design specifications penalizes the use of high strength material.
        Rational design methods ensure that higher performance materials are used, while structural
        serviceability and durability are achieved.

            Equation 5.4 also shows that the ratios of span to depth and span to deflection are not inde-
        pendent, as this equation can be rewritten in the following form (noting c 3 d/2):
                                        /L 3 L % /24d E c                           (5.5)
            If k 3 1/24E,   /L 3 k % /24 E c 3 k % L/d                              (5.6)
            Stress, %, increases for stronger steel and a shorter span. Therefore, the span-to-defl ection
        ratio (L/ ) tends to control for shorter spans while the span-to-depth (L/d) limit controls for
        longer spans.

            Figure 5.6 shows deflection as a function of span-to-depth ratio. L/ , limit has signifi cant
        impact on the use of high strength steel. For shallow HPS 70W steel, girders, L/800 defl ection

        limit is exceeded while strength is acceptable. Design specifications need to revise the limit for
        HPS 70W and above.
        5.3.7 Factors Affecting Defl ections

            These factors may be summarized as:
        1. Effective span length (between center lines of bearings).
        2. Varying beam depth (with and without cover plates).
        3. Beam width (assumed constant).
        4. Depth of haunch (minimum 1 in to maximum 4 in).
        5. Depth of slab (assumed constant).
        6. Effective width of flange (Ell beam width for fascia girder and T-beam width for interior

            girder as defined by AASHTO code).

        7. Beam stiffness or EI value (including top and bottom longitudinal reinforcement in deck
            slab) for longitudinal bending.







                                 (HPS70W steel)
                                                             (Hybrid girder)
                  ( L /800 deflection limit)




                                             (Grade 50 steel)









        Figure 5.6  Comparison of defl ection curves versus L/d for different material strength.
   221   222   223   224   225   226   227   228   229   230   231