Chapter 3: METHODOLOGY

Introduction

Depending on the geographical area, different standards are used for the design of
geotechnical and structural works. Thus, in the United States and Canada for example, the main
standard used is the one recommended by American Association of State Highway and
Transportation Officials (AASHTO), which uses lumped factors, whereas the norms used by
Western Europe are Eurocodes recommended by the European Committee for Standardization
which uses partial safety factors. These two standards used in the present work allow the
definition of the loads (variable loads, permanent loads ...) as well as the various verifications
to be carried out in order to ensure that the structure is without major risk. The various
combinations and verifications to be carried out can be implemented in software such as
CSIBridge in order to shorten the calculation times which can be very long if they are done
manually.

3.1. Design of a steel concrete composite roadway girder-bridge

This part consists in the presentation of the design process of a composite beams bridge
according to the European norms, the Eurocodes.

3.1.1. Actions on a roadway bridge

There exists several types of actions which can be applied on a roadway bridge and they
are usually classified in different categories.

3.1.1.1. Load categories

The main load categories applying on a roadway bridge are permanent loads, variable
loads, seismic loads and accidental loads but this part focus only on variable loads since
permanent loads have usually constant values.

Variable loads are actions acting on the structure with instantaneous values which can
be significantly different in time. For a concrete steel composite bridge, the usual variable loads
are the construction loads, the wind, the thermal actions, the shrinkage and the traffic loads.

a) Construction loads
They represent the possible actions during execution mainly the working personnel, the
staff and visitor, the possible hand tools. Usually, it’s represented by a uniform distributed load
of 1kN/m² for small bridges.
 b) Wind actions
It should be considered during two principal period of the bridge life: when there is
traffic and when there is no traffic (both in construction and service phase). It’s represented as
either a concentrated load or a distributed load acting transversally on a bridge. The value of
the force is given by the relation 3.1.

𝐹𝑤 = 𝑐𝑠 𝑐𝑑 c𝑓 𝑞𝑝 (z)𝐴𝑟𝑒𝑓 (3.1)

Where:
cscd is the structural factor whose value is usually taken as 1 when no dynamic response
are needed;

cf is the force coefficient whose value is found through a graph in EN-1991;

Aref is the reference area whose value depends on the geometry of the deck, the number
of parapet and safety barrier ;

qp(z) is the peak velocity pressure at elevation ze.

 Peak velocity pressure

The peak velocity pressure qp(z) at height z, includes the mean and the short-term
(turbulent) fluctuations and is expressed by the formula 3.2 while figure 3.1 explains
the calculation process.

1 2
𝑞𝑝 (𝑧) = (1 + 7𝐼𝑣 (𝑧)). 𝑣𝑚 (𝑧) (3.2)
2

Figure 3.1. Computation of the peak velocity pressure.

 vb is the fundamental basic wind velocity which can be observed in figure 3.2 for Africa.

Figure 3.2. Africa wind map (Syros, 1994)

 Reference Area
It corresponds to the transverse area “seen” by the wind and depends on many conditions
such as the presence of safety barrier or not and the presence of traffic on the bridge or
not. Its value is given by the product between total depth and the total length of the
bridge.

Figure 3.3. Total depth of the bridge (Malakatas, 2012)

But these values are the ones to consider when there is no traffic on the bridge, it should
be add to these 3m when the traffic is considered.
c) Shrinkage
Concrete shrinkage has 02 origins: the autogenous shrinkage ca and the drying
shrinkage cd. Taking place over the bridge life, the drying shrinkage starts as soon as the
concrete is poured. A total shrinkage cs = ca + cd will then be calculated for a bridge state
corresponding at infinite time. The relation (3.3) is the one to use for the computation of the
autogenous shrinkage while the relation (3.4) is the one to use for the computation of the drying
shrinkage.

𝜀𝑐𝑎 (∞) = 2.5(𝑓𝑐𝑘 − 10)10−6 (3.3)

𝜀𝑐𝑑 (∞) = 𝑘ℎ 𝜀𝑐𝑑,0 (3.4)

kh is a parameter taking into account the part of the section exposed to the environment
through the notional size ℎ0 and its value can be found through the table 3.1.
Table 3.1. Value of kh parameter

h0 = 2*Ac/u kh

1
100
0.85
200
0.75
300

≥500 0.7

Value of parameter cd, 0 is presented in expression (3.5)

𝑓𝑐𝑚 𝑅𝐻 3 (3.5)
𝜀𝑐𝑑,0 = 0.85((220 + 110. 𝛼𝑑𝑠1 ). exp (−𝛼𝑑𝑠2 ) 10−6 . 1.55(1 − ( ) )
10 100

Where  coefficients depend on the hardening speed of the concrete (type of cement used) and
RH is the relative humidity.
d) Temperature effect
Concrete and steel are sensitive to change in temperature. This is observed through a
dilation or contraction of the element. The temperature distribution within an individual
structural element may be split into the following four essential constituent components: a
uniform temperature component, ∆Tu, a linearly varying temperature difference component
about the z-z axis, ∆TMY, a linearly varying temperature difference component about the y-y
axis, ∆TMZ, a non-linear temperature difference component, ∆TE. This results in a system of
self-equilibrated stresses which produce no net load effect on the element.
e) Traffic loads
They represent the different types of moving load which can be on the bridge. Eurocode
defines 4 main models for vertical loads, 5 models for the assessment of the fatigue and one
model for the horizontal ones (acceleration or braking). For each of these models, the definition
of notional lanes is needed.
 Definition of the notional lane
The number and width of the notional is function of the width of the carriageway as
shown in table 3.2.
Table 3.2. Width and number of the notional lane

Carriageway Number of notional Notional lane Width of the

width lanes width remaining area

w < 5,4 m N=1 3m w–3m

5,4 m  w < 6 m N=2 w/2 0

6mw N=Ent (w/3) 3m w – 3N

The disposition of the notional lane should be the one that produces the most adverse
effect on the structural element under verification.
 Load Model N°1 (LM1)
It is the main model used for the global verification of the bridge. It’s constituted of a
tandem system (TS) with some uniform distributed loads (UDL). The values of these
loads are presented in table 3.3 with dynamic amplification already included and the
figure 3.4 shows the disposition of TS and the footprint of the wheel.
Table 3.3. Value of the TS and UDL for LM1

Tandem system TS UDL sytem

Location
Axle loads Qik (kN) qik (kN/m²)

300 9
Lane number 1

200 2.5
Lane number 2

100 2.5
Lane number 3

0 2.5
Other lanes

0 2.5
Remaining area (qrk)
 For the local verification the tandem should be positioned in order to obtain the most
adverse situation while for global verification they are positioned along the axis of the
lanes.

Figure 3.4. Footprint of TS wheel and position of axle on lanes (Malakatas, 2012)
 Load Model N°2 (LM2)
Load Model 2 consists of a single axle load βQQak with Qak equal to 400 kN, dynamic
amplification included, which should be applied at any location on the carriageway.
However, when relevant, only one wheel of 200 Q (kN) may be taken into account with
the dimensions prescribed in figure 3.5.

Figure 3.5. LM2 disposition (Malakatas, 2012)

 Load Model N°3 (LM3)

It corresponds to the case of special vehicles loading which will not be considered in
this design.
 Load Model N°4 (LM4)
Also known as crowd loading, it is represented by a uniform distributed load of 5kN/m²
for the characteristic value and 3kN/m² for the combination one dynamic amplification
included for both situations.
 Fatigue loads models
Eurocode defines 5 models of fatigue however, for road bridges, fatigue assessment may
be done by a simplified procedure that is based on a single model: the fatigue load model
3 (FLM3). For bridges longer than 40m a second vehicle running on the same lane may
be considered at a distance greater than 40m from the first vehicle. The vehicle moves
along the bridge to produce the maximum and the minimum effect (though Eurocode
accept a less severe disposition) and it’s placed centrally on the appropriate notional
lanes that are identified in the design.

Figure 3.6. FLM3 disposition (I. Vayas and A. Iliopoulos, 2014)

 Horizontal load Qlk

A characteristic braking force, Qlk is a longitudinal force acting at the surfacing level of
the carriageway. Qlk, limited to 900 kN for the total width of the bridge, is calculated as
a fraction of the total maximum vertical loads corresponding to Load Model 1 and
applied on lane number 1.
180kN < 𝑄𝑙𝑘 = 0.6(2𝑄1𝑘 ) + 0.1(𝑞1𝑘 𝑤1 L) < 900kN (3.6)

With L, the length of the deck or of the part of it under consideration.

 Groups of load
They represent the different cases to usually consider for the design of a roadway bridge
and they can be seen in figure 3.6.
 Figure 3.7. Groups of loads (Malakatas, 2012)
3.1.1.2. Combinations of loads
For each type of load Eurocode defines some partial safety factors in order to produce
the maximum effect on the structure. Thus, when the load tends to reduce the solicitations, it is
minimized while when it increases them, it is maximized. The main coefficients (considering
the limits states STR/GEO) are for permanent loads G,min=1.00 and G,max=1.35, for variable
loads excluding traffic Q,min=0.00 and Q,max=1.50, and for traffic Q,min=0.00 and Q,max=1.35.
Concerning the  factors, they are presented in figure 3.7 for different actions and group
of loads.

Figure 3.8.  factors for roadway bridge (Malakatas, 2012)

With these coefficients known the definition of combinations of loads can be done for
the ultimate limit state (relation 3.7) and the serviceability limit state (relations 3.8 to 3.10).
 ULS ∑ 𝐺𝑗 𝐺𝑘𝑗 + 𝑝 𝑃𝑘 + 𝑄1 𝑄𝑘1 + ∑ 𝑄𝑖 0𝑖 𝑄𝑘𝑖 (3.7)
𝑗≥1 𝑗≥1

∑ 𝐺𝑘𝑗 + 𝑃𝑘 + 𝑄𝑘1 + ∑ 0𝑖 𝑄𝑘𝑖 (3.8)

SLS
𝑗≥1 𝑗≥1

∑ 𝐺𝑘𝑗 + 𝑃𝑘 + 11 𝑄𝑘1 + ∑ 2𝑖 𝑄𝑘𝑖 (3.9)

𝑗≥1 𝑗≥1

∑ 𝐺𝑘𝑗 + 𝑃𝑘 + ∑ 2𝑖 𝑄𝑘𝑖 (3.10)

𝑗≥1 𝑗≥1

However the main cases to consider are the ones presented in figure 3.8 and 3.9.

Figure 3.9. Fundamental combinations for the ULS (Malakatas, 2012)

Figure 3.10. Fundamental combinations for the characteristic SLS (Malakatas, 2012)

3.1.2. Local verifications on the concrete slab

The local verifications to perform on the concrete slab are inter alia the minimum cover
which governs the position of the reinforcement, the minimum reinforcement ratio in the
transverse direction, the limitation of the stresses for the characteristic SLS combination of
action, control of cracking at quasi-permanent SLS combination, vertical shear resistance for
the ULS combination of action and punching shear.
3.1.2.1. Durability-Concrete cover requirement
One of the most dangerous events that can significantly reduce the durability of the
reinforced concrete structures is the corrosion of the reinforcement since it reduces the section
of steel bars. Corrosion protection of steel reinforcement and safe transmission of bond forces
are ensured by the concrete cover. The thickness of this one is governed by the structural class
of the structure and the exposure classes and its value is given by the relation:
cnom = cmin + c
With cmin=max (cmin,b; cmin,dur;10mm) and c=10mm
 cmin,b is the minimum cover to use in order to transfer safely the bond force and is equal
to the maximum size of the steel bars used.
 cmin,dur is the minimum cover to use in order to ensure good protection of steel bars. It
depends on the structural class and the exposure class shown in table 3.4. The
recommended structural is the class S4.

Table 3.4. Exposure class

Table 3.5. Structural class

 3.1.2.2. Transverse reinforcement verification
For the computation of the internal forces an equivalent beam model could be used.
However this should be limit only to the analysis for UDL while for the tandem, the 2-
dimensional behavior of the slab should be taken into account.

Internal forces known (bending moment in this case), the maximum resistant moment
of the section (considering 1m-width of the slab) should be greater and the computation of
required reinforcement can be done with an inferior limit As,min. In order to find As the position
of the neutral axis should be known by doing the equality 𝑀𝐸𝐷 = 𝑀𝑅𝐷 .

𝑀𝑅𝐷 = 0.8𝑏𝑋𝑙𝑖𝑚 𝑓𝑐𝑑 (𝑑 − 0.4𝑋𝑙𝑖𝑚 ) (3.11)

𝑐𝑢
𝑋𝑙𝑖𝑚 = 𝑑
𝑐𝑢 + 𝑦𝑑 (3.12)

𝑀𝑅𝐷
𝐴𝑠 = (3.13)
𝑠 (𝑑 − 0.4𝑋)

𝑓𝑐𝑡𝑚
𝐴𝑠,𝑚𝑖𝑛 = 0.26 𝑏𝑑 ≥ 0.0013𝑏𝑑 (3.14)
𝑓𝑦𝑘

3.1.2.3. Stress limitation for characteristic SLS combination of action

Stress limitations in concrete and reinforcements under characteristic combination are
checked to avoid inelastic deformation of the reinforcement and longitudinal cracks in concrete.
It is an irreversible limit state. The following limitations should be checked:

σs ≤ k3fyk σc ≤ k1fck (3.15)

Where k1 and k3 are defined by the national annex to EN-1992-1-1. The recommended values
are k1 = 0.6 and k3 = 0.8.

These checks have to be performed for both short and long terms since usually the stress
increases in the reinforcement while decreases in the concrete with time.

3.1.2.4. Control of cracking

According to EN-1992-2, the calculated crack width should not be greater than 0.3 mm
under quasi-permanent combination of actions, for reinforced concrete, whatever the exposure
class. It is important to notice that the limitation apply to calculated crack width, which can
differ notably from measured crack width in the real structure. But firstly the verification on
the apparition of cracks has to be done by checking that the tensile stress in the concrete is
2/3
greater than its mean tensile strength of the fctm= 0.3𝑓𝑐𝑘 .

3.1.2.5. Vertical shear force resistance

Knowing the vertical shear acting at slab supports, the verification of need of specific
reinforcement has to be done and if needed, the correct amount of steel should be determined.
Eurocode defines the resistance of concrete alone 𝑉𝑅𝐷,𝐶 , and the maximum shear capacity which
is the lower between 𝑉𝑅𝐷,𝑆 (steel tie strength) and 𝑉𝑅𝐷,𝑚𝑎𝑥 (concrete strut strength) when shear
reinforcements are used.

(3.16)
𝑉𝑅𝐷,𝑚𝑎𝑥 = 𝑐𝑤 . 𝑏𝑤 . 𝑧. 1 . 𝑓𝑐𝑑 (𝑐𝑜𝑡 + 𝑐𝑜𝑡)/(1 + 𝑐𝑜𝑡2)

1
(3.17)
𝑉𝑅𝐷,𝐶 = (𝐶𝑅𝐷,𝐶 𝑘(100𝑙 𝑓𝑐𝑘 )3 + 𝑘1 𝑐𝑝 ) 𝑏𝑤 𝑑 > (𝑚𝑖𝑛 + 𝑘1 𝑐𝑝 )𝑏𝑤 𝑑

𝐴𝑠𝑤 (3.18)
𝑉𝑅𝐷,𝑆 = ( ) 𝑧𝑓𝑦𝑤𝑑 (𝑐𝑜𝑡 + 𝑐𝑜𝑡)
𝑠

With
fck and fcd in MPa;
bw minimum width of the section;
z = 0.9 d for rectangular cross-sections;
α = angle between the shear reinforcement and the axis of the beam;
θ = inclination of the cracks or the concrete struts;
αcw = coefficient of interaction between compressive stresses which can be assumed equal to
1;
𝑓
𝑐𝑘
ν1 = reduction coefficient for shear cracked concrete, assumed equal to 0.6(1 − 250 );

CRdc = 0.18/γc;
γc = partial safety factor of concrete assumed to 1.5;
k = 1 + (200/d) 1/2 ≤ 2.0 with d in millimeters;
ρl = Asl / (bwd) ≤ 0.02 reinforcement ratio corresponding to Asl;
k1 = 0.15;
σcp = Nsd/Ac average stress (MPa) in the concrete due to the axial compressive force Nsd;
νmin = 0.035 k3/2 fck1/2 for beam element, but for the study of a slab, the national French annex
0.34 1/2
of Eurocode 2 recommends the use of νmin=( ) 𝑓𝑐𝑘 in order to take into account the 2-
𝑐

dimensional behavior of the slab in which transverse redistribution is possible;

fywd= design yield stress of the shear reinforcement;
Asw = area of the web reinforcement;
s = spacing of the shear reinforcement.
3.1.2.6. Punching shear
The punching shear verification is carried out at ULS. It involves verifying that the shear
stress caused by a concentrated vertical load applied on the deck remains acceptable for the
concrete slab. If appropriate, it could be necessary to add shear reinforcement in the concrete
slab. This verification is carried out by using the single wheel of the traffic load model LM2
which represents a much localized vertical load.
The definition of control perimeter u1 as shown in figure 3.9 has to be done in order to
compute the design shear stress 𝑣𝐸𝐷 and to compare it to the design shear strength of concrete
𝑣𝑅𝐷,𝐶 .

Figure 3.11. Reference control perimeter

𝑉𝐸𝐷
𝑣𝐸𝐷 = 𝛽 (3.19)
𝑢1 𝑑
1 (3.20)
𝑣𝑅𝐷,𝐶 = max(𝐶𝑅𝐷,𝐶 𝑘(100𝑙 𝑓𝑐𝑘 )3 + 𝑘1 𝑐𝑝 ); 𝑚𝑖𝑛 + 𝑘1 𝑐𝑝 )

Where
𝑉𝐸𝐷 is the punching shear force;
β is a factor representing the influence of an eventual load eccentricity on the pavement
(boundary effects); β = 1 is taken in case of a centered load;
𝐶𝑅𝐷,𝐶 = 0.15/γc;
𝑘1 = 0.12.
3.1.3. Global verification
This part concerns the verification of the girders which are considered in two different
states, the steel cross section only for the phase of construction when concrete is not yet hard
and the steel concrete composite section for the phase during traffic (concrete already hard).
There are different checks to carry out at ULS as well as SLS.
3.1.3.1. Section classes
First of all the class of each part of the steel cross section need to be determined. In fact,
formulas change when the class changes but usually for road bridge the section is of class 1 in
sagging area with the plastic neutral axis near or in the upper concrete slab, or at least in class
2, with only a small upper part of the compressed web. The classification of the web is done by
determining the position of the neutral axis comparing the design plastic resistance of concrete
to the sum of the design plastic resistance of some parts of steel section.
3.1.3.2. Bending resistance check
The bending moment capacity is given by the formulas 3.21 and 3.22 depending on if
the section is considered as composite or not (strength comes only from steel beam).
𝑀𝑃𝐿,𝑅𝐷 = 𝐹𝑐 . z (3.21)

𝑊𝑃𝐿 . 𝑓𝑦𝑘 (3.22)

𝑀𝑃𝐿,𝑅𝐷 =
𝑀

With Fc the design force of the compressed part (knowing the position of the neutral axis);
z the level arm between the center of gravity of the compressed part and the center of gravity
of steel cross section tensile part;
WPL the plastic modulus of the section (if classified classes 1 or 2).
3.1.3.3. Shear resistance check
For the determination of the shear capacity, the check of shear buckling has to be done
through the relation 3.23 where hw and tw are the height and thickness of the web while ,  and
k are parameters defined in table 3.6.
ℎ𝑤 31
≤ √𝑘 (3.23)
𝑡𝑤 

Table 3.6. Definition of some parameters

Designation Expression/Value

 √235⁄𝑓
𝑦𝑘

1

ℎ𝑤 2
𝑘 5.34 + 4. ( )
𝑎
𝑘 is the shear buckling coefficient with a the interaxis between transverse element.
The maximum design shear resistance is given by VRD = min (Vbw,RD; Vpl,a,RD), where
Vbw,Rd is the shear buckling resistance according to EN-1993 and Vpl,a,Rd is the resistance to
vertical shear according to EN-1993.
𝑤 𝑓𝑦𝑘,𝑤 ℎ𝑤 𝑡𝑤
𝑉𝑏𝑤,𝑅𝐷 = (3.24)
√3𝑀1

𝑓𝑦𝑘,𝑤 ℎ𝑤 𝑡𝑤 (3.25)
𝑉𝑃𝐿,𝑎,𝑅𝐷 =
√3𝑀1

Some of these parameters have already been defined except 𝑤 whose different expressions
are present in table 3.7.
Table 3.7. Value of 𝑤

Rigid end post Non-rigid end post

̅ 𝑤 < 0.83/  

0.83/̅ 𝑤 0.83/̅ 𝑤
0.83/ ≤ ̅ 𝑤 < 1.08

1.7/(0.7 + ̅ 𝑤 ) 0.83/̅ 𝑤
̅ 𝑤 ≥ 1.08

The slenderness parameter ̅ 𝑤 can be obtained with the relation (3.27) in which
2
𝑡𝑤
E=190000 2
(3.26)
ℎ𝑤

𝑓𝑦,𝑤 (3.27)
̅ 𝑤 = 0.76√
√3𝑘 𝐸

3.1.3.4. Bending and vertical shear interaction

If the vertical shear force is greater than half of the shear strength, there is an interaction
between the shear and the moment which usually results in a reduction of the moment capacity.
When this occurs, the relation 3.28 has to be fulfilled.
𝑀𝑓𝑙𝑎𝑛𝑔𝑒,𝑅𝐷

̅1 + [1 − ] [2
̅𝑠 − 1]² ≤ 1 (3.28)
𝑀𝑃𝐿,𝑅𝐷

𝑀𝐸𝐷 𝑉𝐸𝐷
Where 
̅1 = 𝑀 and 
̅𝑠 = 𝑉 .
𝑃𝐿,𝑅𝐷 𝑏𝑤,𝑅𝐷
 3.1.3.5. Stresses control at Serviceability Limit States
a) Concrete and Reinforcement
EN-1994-2 establishes that the excessive creep and microcracking of concrete shall be
avoided by limiting the compressive stress in concrete. EN-1994-2 refers to EN-1992-1-1 and
EN-1992-2, for that limitation which recommends to limit the compressive stress in concrete
under the characteristic combination to a value of k1·fck (k1 is a nationally determined
parameter, and the recommended value is 0.60) so as to control the longitudinal cracking of
concrete.
Unacceptable cracking or deformation may be assumed to be avoided if, under the
characteristic combination of loads, the tensile stress in the reinforcement does not exceed k3·fyk
where k3 is a nationally determined parameter, and the recommended values is k3= 0.8.

b) Structural steel
For the characteristic SLS combination of actions, considering the effect of shear lag in
flanges and the secondary effects caused by deflections (if applicable), the following criteria
for the normal and shear stresses in the structural steel should be verified.
𝑓𝑦𝑘
𝐸𝑑,𝑠𝑒𝑟 ≤ (3.29)
𝑀,𝑠𝑒𝑟

𝑓𝑦𝑘
𝐸𝑑,𝑠𝑒𝑟 ≤ (3.30)
√3𝑀,𝑠𝑒𝑟

𝑓𝑦𝑘 (3.31)
√𝐸𝑑,𝑠𝑒𝑟 2 + 3𝐸𝑑,𝑠𝑒𝑟 2 ≤
𝑀,𝑠𝑒𝑟

The partial safety factor 𝑀,𝑠𝑒𝑟 is a national parameter, and the recommended value is 1
according to EN-1993-2.

3.1.3.5. Web breathing

Slender webs may slightly buckle each time traffic passes over the bridge. These cyclic
out of-plane deformations, which are similar to the chests’ movements during breathing, result
in secondary bending stresses that may lead to fatigue cracks in the flange–web or in the web-
to-transverse stiffener junction. Instead of calculating these deformations and the corresponding
stresses and performing a fatigue analysis, detailing rules limiting the web slenderness are given
and the following limitations must be examined according to EN-1993 for web without
longitudinal stiffeners.
 ℎ𝑤
≤ 30 + 40𝐿 ≤ 300 (3.32)
𝑡𝑤

Where L is the span and should not be less than 20m.

3.1.3.6. Control of cracking in longitudinal direction
As explained in section 3.1.2.4 Eurocode limits the opening of cracks to maximum
values wk=0.2mm, wk=0.3mm and wk=0.4mm depending on the exposure classes considered
for the design. But again, this verification need to be done only if cracks could appear (tensile
stress in concrete greater than the mean tensile strength).
3.1.4. Fatigue
Fatigue is a process in which damage is accumulated in the material undergoing
fluctuating loading. Damage takes the form of cracks in the material that develop slowly at
early stages of loading and accelerate very quickly toward the end. Microcracks start to develop
at points of stress concentration at nominal stresses that may be well below the
elastic limit. Fatigue is a local phenomenon that takes place at regions of stress concentration
such as rapid changes of cross sections, at section reductions due to bolted connections or in
welding regions, where the material undergoes metallurgic changes
3.1.4.1. Detail categories
As said before, fatigue is a local phenomenon that depends on stress concentrations and
therefore on the shape of the construction detail. Accordingly, the fatigue resistance depends
on the detail category. Each detail category is associated with a figure that gives the fatigue
resistance at NC= 2.106 (2 million cycles). In the figure 3.12 is presented the detail categories
for built up sections. For transverse butt welds, there is an important size effect for plate
thicknesses t > 25 mm, expressed by the reduction factor ks = (25/t) 0.2.

Figure 3.12. Detail categories (I. Vayas and A. Iliopoulos, 2014)

 Each value represent the resistance of the part studied in MPa. The headed stud
connectors have a resistance of 90MPa while the concrete present a resistance fcd,fat whose
expression is given in Eurocode 2.
3.1.4.2. Stress range and fatigue check
Internal forces extreme values are determined by adding the values due to all actions
except fatigue loads, to the minimum and maximum values due to fatigue loads. The stress
ranges at a point are determined as the difference between maximum and minimum stresses and
are multiplied for road bridges with the damage equivalent factor λ which depends on the length
of the critical influence line, the traffic volume, the design period life of the bridge and the
traffic in lanes other than the slow lanes. Its expression is different depending on the check on
structural steel or shear connectors and can be found in the corresponding parts of Eurocode.
In order to check the fatigue, some relations need to be satisfied:
𝑘𝑠 ∆𝜎𝑅
𝛾𝐹,𝑓𝑎𝑡 𝜆∆𝜎 ≤ For structural steel (3.33)
𝛾𝑀,𝑓

∆𝜏𝑐 (3.34)
𝛾𝐹,𝑓𝑎𝑡 𝜆∆𝜏 ≤ For shear connectors
𝛾𝑀,𝑓

𝜎𝑐,𝑚𝑎𝑥 𝜎𝑐,𝑚𝑖𝑛 (3.35)

≤ 0.5 + 0.45 For concrete
𝑓𝑐𝑑,𝑓𝑎𝑡 𝑓𝑐𝑑,𝑓𝑎𝑡

𝑆𝑖𝑑 𝑒𝐿
With ∆𝜏 = ∆𝑉 𝐼 , 𝛾𝐹,𝑓𝑎𝑡 = 1, 𝛾𝑀,𝑓 = 1.35 and 𝑓𝑐𝑑,𝑓𝑎𝑡 the design fatigue strength of
𝑖𝑑 𝑛𝐴𝑑

concrete;
Where ∆𝑉 is the shear force range due to fatigue, Sid the static moment of the concrete slab in
respect to centroid of uncracked composite section, eL the longitudinal spacing of connectors,
n the number of shear connectors in one section (row) and Ad the area of the connector shank.

3.1.5. Shear connection at steel-concrete interface

When a concrete slab rests on a steel girder without any connection, it deflects like the
girder but has its own neutral axis so that its top fibers shorten while its bottom fibers elongate.
The fibers of the steel girder are also subject to similar displacements in longitudinal direction,
so a differential displacement appears at the concrete–steel interface. If the differential
displacements at the interface are restraint, the slab and the girder behave as a composite girder
with a single neutral axis. The restraint is provided by shear connectors, while any natural bond
between concrete and steel is ignored. The shear connectors transfer a longitudinal shear that
develops due to vertical shear.
Among the various types of shear connectors, EN 1994-2 provides design rules only for
headed studs welded to the steel girder but gives the possibility to use other types if relevant
information is given in national annexes.
3.1.5.1. Geometry
There exists of different dimensions but they should always fulfill the requirements
presented in figure 3.10.

Figure 3.13. Minimum dimensions of headed studs

Usually, their height h is comprised between 0.5 to 0.7 times the height of the concrete
slab while the diameter d varies between 16mm, 19mm, 22mm and 25mm.

3.1.5.2. Resistance of headed studs

The design shear strength of one headed stud connector according to EN-1994 is
(1) (2) (1)
𝑃𝑅𝐷 = min(𝑃𝑅𝐷 ; 𝑃𝑅𝐷 ) with 𝑃𝑅𝐷 the design resistance when the failure is due to the shear of
(2)
the steel shank toe of the stud and 𝑃𝑅𝐷 the design resistance when the failure is due to the
concrete crushing around the shank of the stud.
(1) 0.8𝑓𝑢 𝜋𝑑 2 /4 (3.36)
𝑃𝑅𝐷 =
𝛾𝑀2

(2) 0.29𝛼𝑑2 √𝐸𝑐𝑚 𝑓𝑐𝑘 (3.37)

𝑃𝑅𝐷 =
𝛾𝑀2

With
ℎ𝑠𝑐 ℎ𝑠𝑐
0.2 ( + 1) if 3 ≤ ≤4
𝛼={ 𝑑 𝑑 (3.38)
ℎ𝑠𝑐
1 for ≥4
𝑑

Where:
M2 is a partial safety factor with 1.25 as recommended value;
fu is ultimate tensile strength of the stud material but has to be less than 500 MPa;
d is the diameter of the shank of the headed stud;
hsc is the overall nominal length of the stud.;
𝑓𝑐𝑚 1/3
Ecm=22000 ( ) is the secant modulus of elasticity of concrete in MPa.
10

These expressions refer to the maximum design shear strength at ULS but under the
SLS characteristic combination of actions the maximum longitudinal shear force per connector
should not exceed ks·PRd (the recommended value for ks=0.75).

3.1.5.3. Detailing of shear connections

According to EN-1994-2, to ensure a composite behavior of the main girder, the
maximum longitudinal center to center spacing (s) between two successive rows of connectors
is limited to smax ≤ min (800 mm; 4 hc), with hc the concrete slab thickness while the minimum
longitudinal spacing corresponds to smin=5.d. Concerning the transverse direction (orthogonal
to the direction of shear stress), the minimum spacing is equal to 2.5d.

3.1.6. Substructure verification

Abutments are the shore elements whose first role is to support loads coming from the
bridge (for passing abutment) and second role is to retain the backfill. So it behaves as a
retaining wall with an axial force acting on its top.
3.1.6.1. Geotechnical verification
For the ULS there exists 05 limits states to consider concerning the geotechnical
verification. These ones are loss of equilibrium of the structure or the soil (EQU), internal
failure or excessive deformation of the structure (STR), failure and excessive deformation of
the ground (GEO), loss of equilibrium of the structure or the ground due to uplift water pressure
(UPL), hydraulic heave and internal erosion caused by hydraulic gradients (HYD). But this part
is only focused on the 03 first verifications aforementioned.
a) EQU verification
It consists mainly in the evaluation of the stabilizing and the destabilizing moments
around the more possible toppling point. In order to ensure the stability of the structure, the
stabilizing moment should be greater than the destabilizing one considering the partial factors
presented in table 3.8.
 Table 3.8. Partial factors on actions (a) and for soil parameters (b)
(a) (b)

b) STR/GEO verification
This part presents the different partial factors needed to check the structural resistance
of the structure (determination of reinforcement) and the geotechnical aspect which are the
sliding verification and the bearing capacity verification with respect to Design Approach 2
(A1 “+” M1 “+” R2).
Table 3.9. Partial factors on actions (a), for spread foundations (b) and for soil parameters (c)
(a)

(b)
 (c)

3.1.6.2. Structural verification

Concerning the determination of the reinforcement, Eurocode 2 gives the different
relations to use for the part under compressive axial loads (if reinforcement needed) using the
M-N interaction diagram. By inputting the value of the design moment and the value of the
design axial force, the M-N diagram allows to find the corresponding reinforcement knowing
the cover-height ratio. In case of concentrated loads, Eurocode recommends to assume a
dispersion angle of 45° in the concrete.

3.1.7. Model, analysis and design in CSIBridge V20

CSIBridge is an American software specialized in the design of many types of bridges.
It allows the verification of most of the criterions required by code such as Eurocode. It is used
in this work to perform the analysis and global design of the bridge according to what seen in
section 3.1.3.
3.1.7.1. Model
When modeling a bridge in CSIBridge, the bridge axis needs to be define, specifically
the length of the bridge using the beginning and the end stations, and the horizontal and vertical
layouts of the bridge (straight or curved). The axis created, the lanes need to be defined; these
ones represent the lanes that will be loaded by the traffic loads of the code used for the design.
All of this can be done through the Layout tab.
 Figure 3.14. Bridge layout line data
Depending on the regions (China, Europe, US) the materials used for the design can be
found in the Components tab. On this tab, the different sections of girders, transverse
diaphragm… can be specified. Also, on a subgroup panel of component tab, some
superstructure elements can be specified like the type of the deck chosen as shown in figure
4.19 and its characteristics such as the width, the thickness of the concrete slab, the number of
girders… After defined the bridge deck characteristics, the properties of some substructure
elements could be specified as the properties of bearings, the properties of the foundations
spring, the properties of bents and abutments.

Figure 3.15. Bridge deck section type

This defined, the loads can be created. The traffic are considered through the vehicles
subgroup in the Load tab. There, different kinds of traffic loads depending on the world region
(codes) can be considered. Load patterns can be created and concentrated, linear, or distributed
loads assigned to each load pattern.
The creation of different components of the bridge done, its mounting can be established
with the Bridge tab. In this tab, all the elements present in the bridge should be characterized
considering this time, interaction between each other. As example, position of transverses
should be defined, the assignment of each kind of bearing at each abutment, the application of
other loads as thermal load can be also done in this tab as shown in figure 3.13.

Figure 3.16. Bridge object data

3.1.7.2. Analysis and design

The process of design in CSIBridge is simple and presented in the figure 3.14. It
consists in analysis the structure, design the structure and optimize.

Figure 3.17. Design process in CSIBridge

In fact, the bridge assembled, the definition of the type of loads (static, moving load…)
acting on it should be done before the analysis be launched using the Analysis tab as shown
figure 3.15. Different kinds of analysis can be realized like linear analysis, nonlinear analysis,
and nonlinear staged construction analysis depending on what are the results researched.

Figure 3.18. Load cases to run

Once the analysis performed for each load cases, combination can be realized depending
on which code is used for the design. For the Eurocode, the following combinations presented
in figure 3.16 are available. The code and combination’s choice is done in the Design/Rating
tab, subgroup Load combinations.
The combinations realized, the analysis should be run again and the response
(deformations, stresses or solicitations) of each load case or load combinations could be
observed in the Home tab, subgroup display as presented in figure 3.17.

Figure 3.19. Code-Generated load combinations

 Figure 3.20. Bridge Object Response
After the analysis, the design begins by defining the Design Requests which are the load
cases/load combinations for which the bridge has to be checked. CSIBridge allows the
definition of different types of check as the global resisting force or the verification of stresses
inter alia, this for the two main phases namely, before and after the hardening of concrete.

3.2. Design of a suspension footbridge

In this work, the design of suspension footbridge is done according to the standards used
by the non-profit organization Bridge to Prosperity which adopted the use of Allowable Stress
Design (ASD), also known as “working stress design” or “service load design,” for designing
suspension cable bridges. ASD methodology (recommended by AASHTO) is based on a
principle that stresses developed in a structural component under normal service loading
conditions do not exceed a predetermined limit. But Bridge to Prosperity (B2P) limits the use
of its suspension bridge to a maximum span of 84m in order to avoid the use of wind guys.
3.2.1. Terminology and information to know
The different information to known concerning the B2P suspension footbridge concern
the bridge components and the environmental conditions. These ones are presented in figure
3.18 where the part (a) concerns the vertical layout while the part (b) concerns the horizontal
layout of the bridge.
 (a)

(b)
Figure 3.21. Suspension footbridge layout
The anchor system is comprised of a concrete anchor blocks, transition arms, and anchor
beam. The anchor blocks contain a steel pipe for securing the ends of the cables. The transition
arms transfer the entire load from the anchor block to the anchor beam. The anchor beam is the
primary means of resistance by engaging passive earth pressures and utilizing a large mass of
soil as overburden. Behind the tower, suspension bridge anchors are located approximately 15
to 25 meters back.
The towers are the elements supporting the main cables which are the ones supporting
the walkway on which people will pass. This one is composed of crossbeam associated to a
decking board that are in turn supported by suspenders. These suspenders main function is to
transfer load from the steel crossbeams into the main cables. Towers lay on a foundation blocks
which should be at least 3 meters from the edge of riverbank for soil conditions and 1.5 meters
for rock in order to prevent slope instability.
Freeboard is the clear distance from the bottom of the bridge walkway to the high water
level. The high water level is the absolute highest point the river level has reached as noted by
the community, including such cases as a hurricane or other large flood events. Maintaining a
proper freeboard is important to prevent the bridge from damage during high water events from
logs or other debris floating down the river. The topography of the area will dictate the
magnitude of required freeboard. For flatter areas with substantial floodplains, a freeboard value
of two meters may be acceptable because increased volume of water flow results in nominal
increases in water level. In locations with steeper slopes, a minimum freeboard of three meters
is required because channelized water flow can rise rapidly with increased flow.
3.2.2. Loads and load combinations
This section describes loads and load combinations that should be used for bridge design
along with their appropriate application.
3.2.2.1. Loads
During the analysis and design process, various loads affecting the bridge need to be
considered. There are two primary types of loads that must be considered: Permanent Loads
and Transient Loads. Each type of load has various contributors that together define the
magnitude of the Permanent Loads and Transient Loads.
a) Permanent loads
Permanent Loads are the ones that remain relatively constant over time and include the
weight of the structure itself and earth pressures constantly in contact with the bridge structure.
 Dead Load (DL)
The Dead Load includes the weight of all permanent components of the bridge structure.
For cable suspension bridges, 1.0 kN/m is a conservative assumption for the dead load
of the cables and walkway surface including the suspenders and fencing for a bridge
with a one meter wide walkway. The dead load of each tower, foundation, and anchor,
shall be calculated based on actual volumes and materials used.
 Lateral Earth Pressure (EH)
Lateral Earth Pressure is the pressure a soil exerts in the horizontal direction and should
be included with abutment, wall, and retaining structure designs. Two types of lateral
earth pressures to be considered are at-rest and active.
b) Transient loads
Transient Loads include any temporary or brief forces that act on the bridge structure.
Transient Loads include people, vehicles, wind, earthquakes, and anything that can be moved
along the walkway.
 Wind load (WL)
The design Wind Load is taken as a uniformly distributed load based on a wind speed
of 160 km/h acting horizontally on the walkway. This corresponds to a wind pressure
of 1.3 kN/m2 acting on the lateral bridge area of 0.3 m2 per meter span. Using a wind
drag coefficient of 1.30, the lateral design wind load is 0.50 kN/m span. Wind Load
 affects the dynamic behavior of the bridge however, practical experience has proven
that bridges of up to 84m span show no significant dynamic effects due to wind load.
For special cases with spans greater than 84 meters or extremely windy areas where
wind speeds exceed 160 kilometers per hour, a wind guy system for lateral stabilization
should be designed.
 Distributed Live Loads (LL)
A Distributed Live Load is a uniform force applied to the full length of the walkway
surface, representing people, animals, or motorbikes. Primary load carrying structural
components, including cables and foundations, shall be designed for a distributed live
load of 4.07 kN/m2 of bridge walkway area. If the bridge walkway area exceeds 37
square meters (400 ft^2), the distributed live load may be reduced by the following
equation:
4.57
3.14 ≤ 𝑤 = 4.07(0.25 + ) ≤ 4.07 (3.39)
√𝐴1

Where w is the distributed live load in kN/m² and A1 the walkway area in m².
 Point Live Loads (PL)
A Point Live Load is a singular force acting on any structural component. For the
cases of rural pedestrian bridges, loads such as livestock, horses, and motorbikes may
be larger in magnitude than the calculated Distributed Live Load and may act on a
smaller area. The walkway system, including decking and crossbeams, shall support a
point load of 2.22 kN anywhere between suspenders.

3.2.2.2. Combinations of loads

It is not probable for all of the potential load effects on a bridge to occur simultaneously.
As a result, it is necessary for an engineer to consider different combinations of loads that may
occur at the same time to ensure the bridge can withstand various loading scenarios that it may
experience throughout its lifespan. The following load combinations account for the practical
combinations of loads that may be applied: for standard cable suspension bridges:
DL + EH + LL (3.40)

DL + EH + LL + 0.3*WL
(3.41)

DL + EH + WL
(3.42)
 3.2.3. Structural Analysis of components
3.2.3.1. Cable analysis
A cable hanging between two supports and carrying a uniformly distributed load along
the true horizontal (as opposed to along its length) forms a parabola as opposed to a catenary.
The maximum deflection of a cable relative to a chord connecting the support points is called
the cable sag. There are three sag values to consider when designing the main cables for a
suspension bridge: Hoisting Sag hHoist which is the resting position of the cable when only
supporting its own weight (can be approximate to 7.50% the length of the cable), Dead Load
Sag hDL which is the cable’s position under full dead load (7.85% the length of the cable), and
Live Load Sag hLL which is the cable’s position under full dead load plus full live load (9.09%
the length of the cable).
a) Geometry and forces
The figures 3.19 and 3.20 presents the situation of the cable and the forces acting on it.

Figure 3.22. Cable Geometry and Forces for a Cable Subjected to a Uniform Distributed
Load

Figure 3.23. Backstay and Tower Cable Geometry and Forces

Each parameters on these graphs have their relations written on equation 3.40 and
table 3.10.
𝑤𝑐 . 𝐿2
𝑃ℎ = (3.43)
8. ℎ𝑠𝑎𝑔

Where wc is the distributed load, L the length of the cable and hsag the cable sag.
 Table 3.10. Parameter’s expression

Designation Expression
4ℎ𝑠𝑎𝑔 + ∆𝐻
Angle to Horizontal (High Side) 𝜃𝐻𝑖𝑔ℎ 𝜃𝐻𝑖𝑔ℎ =tan−1( )
𝐿

𝑃𝑣ℎ𝑖𝑔ℎ = 𝑃ℎ . tan 𝜃𝐻𝑖𝑔ℎ

Vertical Tension (High Side) 𝑃𝑣ℎ𝑖𝑔ℎ
𝑃ℎ
𝑃𝑡ℎ𝑖𝑔ℎ = ⁄cos 𝜃
Total Tension (High Side) 𝑃𝑡ℎ𝑖𝑔ℎ 𝐻𝑖𝑔ℎ

4ℎ𝑠𝑎𝑔 − ∆𝐻
Angle to Horizontal (High Side) 𝜃𝐿𝑜𝑤 𝜃𝐿𝑜𝑤 =tan−1 ( )
𝐿

𝑃𝑣ℎ𝑖𝑔ℎ = 𝑃ℎ . tan 𝜃𝐿𝑜𝑤

Vertical Tension (High Side) 𝑃𝑣𝐿𝑜𝑤
𝑃ℎ
𝑃𝑡ℎ𝑖𝑔ℎ = ⁄cos 𝜃
Total tension (High Side) 𝑃𝑡𝐿𝑜𝑤 𝐿𝑜𝑤

𝑃ℎ⁄
Total Backstay Tension 𝑃𝑡𝐵𝑎𝑐𝑘 𝑃𝑡𝐵𝑎𝑐𝑘 = cos α

Vertical Backstay Tension 𝑃𝑣𝐵𝑎𝑐𝑘 𝑃𝑣𝐵𝑎𝑐𝑘 = 𝑃𝑡𝐵𝑎𝑐𝑘 sin 𝛼

𝑃𝑡𝑀𝑎𝑖𝑛 = 𝑃𝑡ℎ𝑖𝑔ℎ 𝑜𝑟 𝑃𝑡𝐿𝑜𝑤

Total Main Span Tension 𝑃𝑡𝑀𝑎𝑖𝑛

Vertical Main Span Tension 𝑃𝑣𝑀𝑎𝑖𝑛 𝑃𝑣𝑀𝑎𝑖𝑛 = 𝑃𝑡𝑀𝑎𝑖𝑛 sin 𝜃

Total Vertical Reaction at Tower 𝑅𝑇𝑜𝑤𝑒𝑟 𝑅𝑇𝑜𝑤𝑒𝑟 = 𝑃𝑣𝐵𝑎𝑐𝑘 + 𝑃𝑣𝑀𝑎𝑖𝑛

b) Cable Design
Cable design shall satisfy the Load and Resistance Factor Design (LRFD) relation
𝑃
given by 𝑃𝑠 < 𝐹𝑆𝑢 where Ps is the maximum axial tension in cable, Pu is the ultimate breaking

strength (must be greater than 240MPa according to B2P) of cable and FS is the safety factor
equal to 3.
3.2.3.2. Walkway analysis
Each timber element shall be checked for both flexure and shear. Decking boards are a
minimum of two meters long spanning between three crossbeams, but are conservatively
analyzed as a simply supported member with a one-meter span. Typically, the point load case
will govern and B2P suggests minimum dimensions for decking boards of 5cm x 20cm.
The B2P standard crossbeam is comprised of two small steel angles that are either
welded or bolted together back-to-back. The standard steel crossbeams are supported at the
ends by the suspenders. As such, the crossbeam design loads are determined using basic statics
equations assuming a simply supported beam carrying a distributed load over the width of the
timber nailer. The steel crossbeams shall be checked for both flexure and shear.
3.2.3.3. Suspender analysis
The suspenders function to transfer load from the steel crossbeams into the main cables.
The suspenders are subjected to environmental factors and cyclical bending within the flexible
structure. As a result, Bridges to Prosperity uses a factor of safety of 5.0 to account for the
likelihood of potential fatigue failure and corrosion of the steel over time. Even though smaller
bars or wires may be used, B2P recommends using not less than a 10 mm deformed reinforcing
bar, with a minimum yield strength of 275 MPa.
For the axial design check of suspenders, the calculated stress in the member due to the
maximum axial load must be less than or equal to the yield stress divided by a factor of safety.
𝑓𝑦
Axial stress shall satisfy 𝑓𝑠 < 𝐹𝑆 where 𝑓𝑠 the stress inside the suspender and FS the safety factor

is equal to 5.
3.2.3.4. Steel tower analysis
This section briefly describes the design of the steel towers which are made of steel
round pipe sections. Also note that the steel towers have a hinge at the base. The hinge
permits the tower to rotate slightly towards the river when the bridge is fully loaded and rotate
back when the load is removed.
The tower is analyzed for combined bending and axial loads resulting from the vertical
cable load along with horizontal wind load. Using the appropriate code equations, the steel pipe
capacity can be calculated. Note that for the steel tower frames used in the B2P standard
designs, the pipes should be checked for each segment between brace points as well as about
each axis. Using the calculated forces and capacity of each tower section, the appropriate
Allowable Stress Design equations for axial load, moment, and combined axial load and
moment can be applied to verify the safety of the tower design.
3.2.3.5. Concrete pedestal analysis
This section describes the design of the pedestals that support the steel towers at the
base. The pedestals can be used to minimize height differential from one side to the other by
varying the height.
Design of cross sections subject to compression shall be based on equation 3.41.
𝑃𝑛 (3.44)
𝑃𝑢 ≤
𝐹𝑆

In which
 𝑙𝑐 2 (3.45)
𝑃𝑛 = 0.6𝑓′𝑐 [1 − ( ) ] 𝐴1
32ℎ

Where lc is the height of pedestal, h is the minimum dimension of pedestal, A1 is the loaded area
f’c is the compressive strength of concrete, assumed to 15MPa if drum mixer is used or 10MPa
if not and FS is the safety factor equal to 2.
Although the pedestals are sufficient to take the load without reinforcing steel, a minimal
amount is added. B2P adds one half of one percent (0.5%) of the area of concrete for added
durability (13 mm stirrups are placed at 300 mm spacing).
3.2.3.6. Concrete footing analysis
All of the vertical forces generated in the cables are transferred through the towers and
pedestal into the footing. Additional vertical load is also generated from the self-weight of the
towers, pedestal, and portions of the ramp directly above the footing. To perform satisfactorily,
the maximum bearing pressure generated must not exceed the bearing capacity of the soil.
Furthermore, the resultant cable force, considering the backstay and main span components of
the cable’s influence on the tower saddle, must not cause overturning.
The load per unit area of the foundation at which shear failure in soil occurs is called
the ultimate bearing capacity. The allowable soil bearing capacity is the ultimate bearing
capacity divided by a factor of safety. Specific values for the ultimate bearing pressure should
be determined for the soil found at the bridge site but B2P assumes ultimate soil bearing
pressure of 286 kPa for unsaturated soil conditions. Bearing pressure shall satisfies :
𝑞𝒖
𝑞𝒔 < (3.46)
𝐹𝑆

Where qs is the maximum bearing pressure, qu is the ultimate bearing pressure and FS=2.0.
Due to the unbalanced tower reactions from the load case including wind, the bearing
pressure beneath the footing is not uniform. The maximum bearing pressure can be calculated
using the equivalent width method as shown in the figure 3.22.

Figure 3.24. Distribution of pressure under foundation

 𝑃𝒕𝒐𝒕 (3.47)
𝑞𝒔 =
𝐵∗𝐿
2𝑀 (3.48)
𝐵∗ =
𝑃𝒕𝒐𝒕

Where l is the length of foundation, B* is the effective width of the foundation, M is the total
overturning moment about base caused by eccentricity of the total vertical force 𝑃𝒕𝒐𝒕 .

3.2.3.7. Anchor analysis

The suspension bridge anchor system resists vertical and horizontal forces induced by
the cables. The figure 3.23 give a schematization of the anchor system for a B2P suspension
footbridge.

Figure 3.25. Anchor system

a) Design of anchor block
The anchor block is the above ground portion of the anchor system that encases the steel
pipe that the cables wrap around. The reinforcing steel bars connecting the anchor beam to the
anchor block through the transition arm are also looped around the embedded steel pipe. The
pipe must be checked for shear and bending capacity. However, for the purposes of B2P
designs, the factor of safety for this pipe shall be 3.0 due to the importance of this component.
The anchor block should be designed for minimum reinforcing steel to control cracking and
increase durability.
b) Design of transition arm
The transition arms are heavily reinforced concrete beams primarily in tension. Since
they serve such an important role in connecting the anchor beam to the above-ground transition
block where the cables will attach, the safety factor is also set at 3. For a number of bars n of
yielding stress fy with Ab the area of reinforcing bar, axial stress shall satisfy:
𝑃 𝑓𝒚
< (3.49)
𝐴𝑏 𝑛 𝐹𝑆
 c) Design of anchor beam
Concrete anchor beams are used in soil conditions where the sliding resistance is
provided by the soil. B2P considers for the design that, soil wall friction is neglected as a
conservative simplification, soil is cohesionless (i.e. c = 0) and backfill is required above the
anchor beam to provide the necessary resistance.
In order for the passive resistance from the soil to be engaged, the soil must first deform
from the beam moving forward a small amount. When this happens, it causes a lateral active
earth pressure to develop behind the beam as it slides forward (i.e. the earth exerts a force on
the anchor in the same direction as the cable force). The anchor beam also resists sliding through
friction with the soil along each interface. The self-weight of the anchor beam along with the
soil above it contribute to the total vertical load used for determining the friction resistance.
The total horizontal driving force is a summation of the horizontal cable force and the active
earth pressure. The total horizontal resistance is a summation of the friction and passive
resistance of the soil. The safety factor consider for the sliding check is equal to 1.5.
The anchor itself is designed as a concrete beam. Since the forces applied to it are
relatively low compared to the size of the beam, minimum reinforcement per AASHTO is added
for resistance in bending. This states that the factored nominal resistance is greater than 1.2
times the cracking moment. Reinforcement was also added for shear resistance in the form of
stirrups, which are also helpful for construction purposes and increased durability

Conclusion
The main objective of a design, whatever the standard used, is to ensure the viability of
the structure; that is, the actions are everywhere below the allowable resistance threshold for
the structure. This chapter has had to present two standards used for designing two types of
short span bridges specifically a composite roadway girder bridge and a suspension footbridge.
The checks to carry out can often be numerous and in this case the use of software is advised.
Thus, it was presented the operation of the software CSIBridge V20 which was used in the case
of this project. The methodology used for the design of these bridges can be applied to local
cases in Cameroon insofar as some regions are often totally or partially (presence of long
detours) isolated because of the presence of gap. This situation, which is generally found in
rural areas, can be resolved by adopting a type of bridge appropriate to the local context and
thus greatly improving the living situation of local populations.