Eurocodigo

BRITISH STANDARD

BS EN 1991-1-4:2005

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Eurocode 1: Actions on structures —
Part 1-4: General actions — Wind actions

The European Standard EN 1991-1-4:2005 has the status of a British Standard

ICS 91.010.30

12 &23 L1.

c) For three-span continuous bridges: K is obtained fromFigure F.2, using the appropriate curve for three-span bridges, where L1 L2 is the length of the longest side span is the length of the other side span and L > L1 > L2

This also applies to three-span bridges with a cantilevered/suspended main span. If L1 > L then K may be obtained from the curve for two span bridges, neglecting the shortest side span and treating the largest side span as the mainspan of an equivalent two-span bridge. d) For symmetrical four-span continuous bridges (i.e. bridges symmetrical about the central support): K may be obtained from the curve for two-span bridges in Figure F.2 treating each half of the bridge as an equivalent two-span bridge. e) For unsymmetrical four-span continuous bridges and continuous bridges with more than four spans: K may be obtained fromFigure F.2 using the appropriate curve for three-span bridges, choosing the main span as the greatest internal span.

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EN 1991-1-4:2005 (E)
EI b at the support exceeds twice the value at mid-span, or is less than 80 % of m

NOTE 1 If the value of

the mid-span value, then the Expression (F.6) should not be used unless very approximate values are sufficient.

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NOTE 2 A consistent set should be used to give n1,B in cycles per second.

(6) The fundamental torsional frequency of plate girder bridges is equal to the fundamental bending frequency calculated from Expression (F.6), provided the average longitudinal bending inertia per unit width is not less than 100 times theaverage transverse bending inertia per unit length. (7) The fundamental torsional frequency of a box girder bridge may be approximately derived from Expression (F.7):
n1,T = n1,B ⋅ P1 ⋅ (P2 + P3 )

(F.7)

with:
P1 = m ⋅ b2 Ip

(F.8)

P2 =

∑r
2

2 j

⋅Ij

b ⋅ Ip L2 ⋅ ∑ J j

(F.9)

P3 =

2 ⋅ K 2 ⋅ b 2 ⋅ I p ⋅ (1 + ν )

(F.10)

where: n1,B b m is the fundamental bendingfrequency in Hz is the total width of the bridge is the mass per unit length defined in F.2 (5) is Poisson´s ratio of girder material is the distance of individual box centre-line from centre-line of bridge is the second moment of mass per unit length of individual box for vertical bending at midspan, including an associated effective width of deck is the second moment of mass per unit length ofcross-section at mid-span. It is described by Expression (F.11).
Ip = md ⋅ b 2 + ∑ (I pj + m j ⋅ r j2 ) 12

ν
rj Ij Ip

(F.11)

where: md Ipj mj is the mass per unit length of the deck only, at mid-span is the mass moment of inertia of individual box at mid-span is the mass per unit length of individual box only, at mid-span, without associated portion of deck

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EN 1991-1-4:2005 (E)
Jjis the torsion constant of individual box at mid-span. It is described by Expression (F.12).
Jj = 4 ⋅ Aj2 ds # t ∫

(F.12)

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where: Aj is the enclosed cell area at mid-span
ds t

# ∫

is the integral around box perimeter of the ratio length/thickness for each portion of box wall atmid-span
NOTE Slight loss of accuracy may occur if the proposed Expression (F.12) is applied to multibox bridges whose plan aspect ratio (=span/width) exceeds 6.

140

EN 1991-1-4:2005 (E)

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Figure F.2 — Factor K used for the derivation of fundamental bending frequency

F.3 Fundamental mode...