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Dr Ana M. Ruiz-Teran Transverse schemes for bridge decks. Part 1: Beams

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Types of transverse schemes for bridge decks

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Types of transverse schemes for bridge decks: Beam deck: Slab deck: Box girder:

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Type of beams

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Deck with precast PC I beams Deck with precast PC U beams Deck with in-situ RC/PC beams Composite deck with steel girders

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Transverse distribution of internal forces in beam decks

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Deflection of a beam-and-slab deck under axle load Transverse-distribution coefficients for the longitudinal bending moments: Ratio between the bending moment taken by one beam and the bending moment that this beam would take in the case of a uniform distribution

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Transverse flexural stiffness of the slab: The larger the transverse flexural stiffness of the beam-and-slab deck, the larger the required transverse shear load (V) for guaranteeing compatibility, the larger the transverse distribution of the applied load, the smaller the transverse-distribution coefficients The larger the depth of the slab, the larger the transverse flexural stiffness of the beam-and-slab deck The smaller the transverse spacing between beams, the larger the transverse flexural stiffness of the beam-and-slab deck Factors affecting the transverse distribution of longitudinal bending moments (I):

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Torsional stiffness of the beams: The larger the torsional stiffness of the beams, the larger the required transverse shear load (V) for guaranteeing compatibility, the larger the transverse distribution of the applied load, the smaller the transverse-distribution coefficients The larger the torsional constant of the beams, the larger the torsional stiffness of the beams The larger the restriction to the transverse rotation of the beams at the support sections, the larger the torsional stiffness of the beams Factors affecting the transverse distribution of longitudinal bending moments (II):

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The stiffness of the beams: The smaller the flexural stiffness of the beams, the larger the required transverse shear load (V) for guaranteeing compatibility, the larger the transverse distribution of the applied load, the smaller the transverse-distribution coefficients The smaller the second moment of inertia of the beams, the smaller the stiffness of the beams The larger the span, the smaller the stiffness of the beams The smaller the restriction to the longitudinal rotation of the beams, the smaller the stiffness of the beams Factors affecting the transverse distribution of longitudinal bending moments (III):

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Eccentricity of the point load: The larger the eccentricity of the point load, the smaller the transverse distribution of the load and the larger the transverse- distribution coefficients Width/Span ratio: The larger the width/span ratio, the smaller the transverse distribution of the load and the larger the transverse-distribution coefficients Factors affecting the transverse distribution of longitudinal bending moments(IV):

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Transverse structural behaviour under uniform load

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Transverse structural behaviour under eccentric point load

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(1) Transverse local bending (2.1) Transverse local bending (2.2) Longitudinal bending (2.3.1) Warping torsion (2.3.2) Distorsion

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Deformation and longitudinal normal stresses due to: a)Total b)Due to bending c)Due to torsion d)Due to transverse deformation and distorsion

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Deformed shape: Longitudinal normal stresses: Transverse bending moments: Transverse Shear forces: Horizontal Shear forces: Horizontal normal stresses:

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Deformed shape: Longitudinal normal stresses:

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Modelling beam decks

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One longitudinal member per beam plus additional beams representing the slab if this is required Transverse members located at diaphragms, mid-span section plus intermediate sections The ratio between the transverse spacing and the longitudinal spacing should not be larger than 2 and smaller than 0.5

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Second moment of inertia of the longitudinal members = Second moment of inertia of the corresponding beam, with respect of the centroid of the complete section, considering effective width (or the corresponding slab section in the case of intermediate/end longitudinal members) Torsional constant of the longitudinal members = Torsional constant of the corresponding beam + ½ Torsional constant of the corresponding slab section Second moment of inertia of the transverse members = Second moment of inertia of the corresponding slab section, with respect of the centroid of the slab Torsional constant of the transverse members = ½ Torsional constant of the corresponding slab section

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REFERENCES: CHEN, W. F. AND DUAN L. 2003. Bridge Engineering. CRC Press LLC HAMBLY, E.C. 1991. Bridge Deck Behaviour. Spon Press. PARKE G, HEWSON N. 2008. ICE manual of bridge engineering. ICE. MANTEROLA, J. BRIDGES. (6 Volumes, in Spanish). ETSICCP, Madrid

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