Surveying Undergraduate Programmes

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Transverse schemes for bridge decks. Part 1
Beams
Dr Ana M. Ruiz-Teran
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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
Composite deck with steel girders
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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Factors affecting the transverse distribution of
longitudinal bending moments (I)

• 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

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Factors affecting the transverse distribution of
longitudinal bending moments (II)

• 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

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Factors affecting the transverse distribution of
longitudinal bending moments (III)

• 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

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Factors affecting the transverse distribution of
longitudinal bending moments(IV)

• 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-distributio
  n coefficients

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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
• Total
• Due to bending
• Due to torsion
• Due to transverse deformation and distorsion

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