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534 Mathematical Approach
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The following parameters need to be considered in analysis: 1 2 3 4 5 Plan aspect ratio Skew angles and curved slabs Number of girders Spacing of girders Boundary conditions: Simply supported Continuous Fixed Girders framing into integral abutments Girders framing into semi-integral abutments Fascia girder de ections are also affected by the thickness of the sidewalk on the cantilever side Hence, variations in the deck slab thickness need to be considered for fascia girders for bridge decks with sidewalks For serviceability and durability, the maximum live load de ection calculated from any of the above methods must be less than the AASHTO criteria
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6 Method of computing de ections: De ections affect bending moment and shear force distribution Live load de ections are usually computed by one of the following methods: Stiffness matrices Strain energy Double integration method Harmonic analysis Finite difference method Finite element method The current method prescribed by AASHTO is using a line girder and applying multiple lane reductions There are approximations in the method of applying live load distribution from each lane for load sharing on the single girder under consideration Code de ection calculations are based on the use of distribution coef cients (DF), which may not give a true de ection value in all cases due to the complexity of bridge geometry It may be desirable to calibrate the line girder code method against a three-dimensional model using the stiffness method Software such as SAP2000 or ADINA may be used
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535 Large De ections in Single Spans
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Large de ections in a single span truss (Figure 55) require nonlinear analysis since the load de ection curve becomes nonlinear when compared to continuous span de ections 1 Large de ection causes fracture and debonding of the wearing surface due to excessive work done In timber construction, fasteners loosen 2 Stiffness of entire deck width considered: De ection DF Number of lanes/number of lanes 3 Additional shear de ection occurs under heavy truck load, especially for cantilever overhangs 4 Arching action at the supports in composite deck slabs may reduce de ection
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536 Primary Effects of De ections
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1 The two design criteria for strength and de ection are linked together When there is no de ection, there is no stress The higher the de ection, the higher the slope and resulting curvature (Figure 55) An increase in curvature gives rise to an increase in bending moment
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Figure 54 Use of three column hammerhead piers in place of wall piers
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