STRUCTURAL DESIGN - PART 04

English

The load conditions and combinations were defined according to Eurocode 1, in particular to Part 3 (ENV 1991-3: 1994) which refers to the definition of the pedestrian, cycle action and other actions specifically for footbridges. Eurocode 8 was referred to for the definition of the earthquake actions.

In Eurocode 1 footbridges are categorised as:

1. those on which pedestrian – and cycle traffic is not protected, or not fully protected, from all types of bad weather, and
2. those on which traffic is fully protected

Stari Most is of the first category.

For footbridges, wind and thermal actions are not taken into account as simultaneous.

For the first category of footbridges (like Stari Most), the traffic is considered incompatible with significant wind and/or snow.

PARTIAL FACTORS, TABLE C.1 ENV 1991-3: 1994

 SYMBOL P/T A permanent actions gg 1,35 1,00 traffic loads gq 1,35 1,00 other variable actions (snow, wind, temperature effect) gq 1,5 1,00 accidental actions ga --- 1,00

y FACTORS FOR FOOTBRIDGES

 y 0 y 1’ y 1 y 2 traffic loads 0,40 0,80 0,40 0 wind 0 0,6 0,5 0 temperature effect 0 0,8 0,6 0,5

NB: y 1’ to define infrequent loads

The following load combinations were defined, for the ultimate limit states.

PERSISTENT / TRANSIENT DESIGN SITUATIONS

 PERMANENT LOADS TRAFFIC LOADS (*) SNOW WIND THERMAL EFFECT 1,35 1,35 incompatible 0 x 1,5 = 0 0 x 1,5 = 0 1,35 0,40 x 1,35 = 0,54 incompatible 1,5 0 x 1,5 = 0 1,35 0,40 x 1,35 = 0,54 incompatible 0 x 1,5 = 0 1,5

(*) to be considered on the entire bridge and on half the bridge

ACCIDENTAL DESIGN SITUATIONS

 PERMANENT LOADS FLOOD TRAFFIC LOADS WIND TEMPERATURE EFFECT 1,35 1,0 0,40 0 0,5 1,35 1,0 0 0,5 0,5 1,35 1,0 0 0 0,6

(wind and thermal loads have not to be simultaneous)

SEISMIC DESIGN SITUATION

 PERMANENT LOADS EARTHQUAKE TRAFFIC LOADS WIND TEMPERATURE EFFECT 1,00 g I 0 0 0,5

The load combinations with the wind loads were not taken into account, as the bridge was checked against the accidental loads due to the flood and the earthquake, which are more onerous.

The following load conditions were considered:

2. live load uniformly distributed over the whole bridge
3. live load uniformly distributed over half the bridge
4. uniform thermal load +15 °C
5. uniform thermal load -15 °C

The dead weight adopted for the masonry of the various structural elements are listed in the following table.

 type of stone used in the old bridge quality g kg/mc 1 Load-bearing arch TeneIija Cvrsta Excellent 2200 2 Filling wedge TeneIija Mekša Ordinary 2000 3 stiffening ribs TeneIija Mekša Ordinary 2000 4 spandrels TeneIija Mekša Good 2100 5 Additional masonry layer TeneIija Mekša Inferior 1800 6 Horiz. stone slabs Krecnjak Good 2100 7 Parapet TeneIija Mekša Good* 2100 8 Filling material Variable Scarce** 1600 9 abutments TeneIija Mekša Good 2100

fig. 15 - Ruins of the bridge arch: location of the main elements

b – Live load uniformly distributed over the bridge

A uniformly distributed load of 5 kN / m2 was put on the whole bridge. EC1 allows for a reduction of this load for L > 10 m, but in safety no reduction was applied even if the bridge span is about 30 m.

c - Live load uniformly distributed over half the bridge

A uniformly distributed load of 5 kN / m2 was put on half the bridge.

d – Thermal loads (+ 15 °C)

A uniform thermal load variation of +15 °C was applied to the whole structure.

e - Thermal loads (- 15 °C)

A uniform thermal load variation of -15 °C was applied to the whole structure.

f – Flood (2500 m3 / s)

The actions due to the flood have been analysed assuming a discharge between 1500 m3/sec and 2500 m3/sec, with step of 250 m3/sec.

The discharge of 2500 m3/sec is the maximum allowed between the abutments of the arch; the line of the specific loads is tangent to the crown of the bridge itself.

fig. 16 - Assonometric view of the hydraulic sections used in the calculations

fig. 17 - Plan view of the hydraulic sections used in the calculations

The hydraulic sections were obtained starting from the five available sections (101, 102, 103, 104, 105, in black). The deck of the bridge is included between the sections 103 and 104, while the abutments lay between the sections 102 and 105.

The bed profile of the river was drawn, allowing for the evaluation of the mean slope.

The flow is slow, the motion in the section no. 101 is assumed as uniform with a mean slope of the riverbed if = 8.5 * 10-5.

A Manning coefficient of roughness n=0.03 s/m1/3 has been used, being the riverbed characterised by gravel and cobbles.

The following figures show the results of the performed simulations, with the following list of the symbols used:

• the discharges associated to the profiles are indicated as:
 Profile PF1 PF2 PF3 PF4 PF5 Q (m3/s) 1500 1750 2000 2250 2500
• the water surface level WS corresponds to the blue line,
• the specific energy EG is represented in green,
• the talweg profile is in black and the red circles indicate the maximum height of the lateral banks,
• D, H represent the coordinate system, measured from the mean sea level and from the first left point of each cross section, respectively.

The following figures show the result as the rate of the discharge varies. The profiles are also reported in correspondence of the same values of the discharge.

• the water level is shown in blue and indicated with the symbol WS,
• the specific energy in terms of height is represented in green and indicated with the symbol EG,
• the specific force, force divided by the specific weigth of the water [m3] is represented in red and indicated with the symbol Specif Force,

The force between the section no. 105 and the section no. 103 is computed applying the momentum theorem to the control volume bounded by these sections, neglecting the shear stresses:

R = Su – Sd

where R is the resultant action, S is the total force, the pedices u and d means the upstream and downstream section, respectively. The total force can be written:

S = g A yb + g Q2 / (g A)

where

• g is the specific weight of the water,
• A is the wetted area of the section,
• Yb is the depth of the barycenter of the section,
• Q is the discharge,
• g is the acceleration due to the gravity.

The pressure resultant on the bridge is calculated, in safety, as the difference of the total pressure of the flow (specific force multiplied by the specific weight of the water) between the sections 105 (immediately upstream of the lateral abutments) and 103 (immediately downstream of the bridge deck).

Such a resultant has been considered acting uniformly on the surfaces of the wetted portion of the abutments and of the bridge.

 Q (m3/s) 1500 1750 2000 2250 2500 Force 105 (ton) 3368 4069 4816 5608 6449 Force 103 (ton) 2874 3458 4074 4719 5393 Force on the bridge ton)

Pressure forces

g - Earthquake actions

The structural behaviour of the bridge under the seismic actions has been studied taking into account the non-linear behaviour of the masonry, as it was done for the flood force.

A simplified modal response spectrum analysis has been performed; this type of analysis can be used strictly speaking only to structures whose response is not significantly affected by contributions from higher modes of vibration.

In the analysis the X-axis coincides with the longitudinal axis of the bridge, the Z-axis is in the transversal direction and the Y-axis is vertical.

For each direction the mode of vibration considered is the mode corresponding to the maximum participation factor.

Moreover the seismic actions of each direction have been applied contemporarily on the F.E. model using the combination factors of Eurocode 8.

CREDITS:

Intellectual property of this report and of the design drawings is owned by the University of Florence - Department of Civil Engineering

author of the text: Prof.Eng. Andrea Vignoli – other contributes have been mentioned in related paragraphs

© - General Engineering Workgroup -

SOURCE:

Final Design Report