Advances in Steel Structures - part 58 ppt

550
X S. Li and Y. Goto
Figure 6 shows that the ductility factor/1
p
of the pier increases with the increase of yield force ratio
Qy/Py for most values of Kbl/Kp, while the ductility factor/1 b of the isolator decreases. A different
tendency, however, is observed for Model-2 with Kb~/Kp=0.7 as shown in Fig.6(c). In this case, the
maximum value of /.t p is obtained for the yield force ratio of Qy/Py=0.2 that is the smallest one. This
phenomenon is identical with that observed in Fig.5(c) and is also identical with those obtained for
concrete piers by Kawashima & Shoji (1998). It can be concluded that an isolator with a higer
stiffness and a smaller yield force may result in much damage of the pier when subjected to wave
Type 2- Ill.
Fig.7: Relations between Energy Ratio Ep/Ef and Period Ratio Tp/Tf
Effect of Elongation of Natural Period
The main difference between isolated bridges and conventional bridges is characterized by a
significant increase in the natural period of isolated bridges due to the introduction of the isolator that
may also effectively absorb energy. As a result, the inertia force induced by earthquake is considerably
reduced in isolated bridges. In order to find an appropriate period range for the isolated bridge, an
energy ratio Ep/Ef is used to evaluate the damage of the pier, where Ep = 4Ppdup and Ef = ~Pfduf
are the energy absorbed in the pier with the isolator and that without the isolator, respectively. And, a
period ratio Tp/Tf is used as the abscissa, where Tp = 2nx/m/K e and Tf 2nx/m/K p are the
fundamental periods of the isolated bridge and the conventional one, respectively. K e is the equivalent
stiffness of the isolated bridge and defined as Ke=KBKp/(KB+Kp), where KB is the equivalent stiffness
of the isolator as shown in Fig.2. Figure.7 shows the relations between the energy ratio Ep/Ef and the
period ratio Tp/Tf for Model-1 and Model-2. It can been seen from Fig.7 (a) that a general tendency is
that the energy ratio Ep/Ef decreases as the period ratio Tp/Tf increases, except for a few points. The
three points over 0.4 are corresponding to the cases: (Qy/Py=0.3, Kbl/Kp=0.8, 0.9) and (Qy/Py=0.2,
Kbl/Kp=0.7) for Model-2 subjected to wave Type 2-Ill. If both Qy/Py and Kbl/Kp are limited to the
Seismic Analysis of Isolated Steel Highway Bridge 551
range from 0.3 to 0.7 that are favorable in the practical design, the maximum value of Ep/Ef will be
less than 0.3 as shown in Fig.7 (b). This result implies that the range from 0.3 to 0.7 is appropriate for

both
Qy/Vy
and Kbl/Kp of the isolator. The corresponding period ratio
Tp/Tf
is between 2.1 and 3.7.
Furthermore, by noting that
Ep/Ef
approaches zero when
Tp/Tf > 3.0,
the range from 2.1 to 3.0 of the
period ratio
Tp/Tf may
be more appropriate. This is based on the fact that too much elongation of the
natural period may lead to an undesirable large displacement of the deck.
Application of 'Property of Displacement Conversation'
As previously described, the interaction between the pier and the isolator results in the computational
difficulty due to the nonlinearity that occurs in both the pier and the isolator. To avoid the difficulty,
some simple methods have been proposed for predicting the dynamic response of the pier, such as the
method based on the 'Energy Conservation Principle'. For the conventional bridge pier that has a
shorter fundamental period, the method has been verified applicable and widely used in practical
design. For the isolated bridge that has a longer fundamental period, however, it overestimates or
underestimates the response of the pier. Here, based on the 'Displacement Conservation Principle' that
states 'the maximum elasto-plastic deformation of a system with a long fundamental period is
approximately equal to the maximum elastic deformation of the same system', the maximum
responses of steel piers are predicted by elastic dynamic analysis. In this method, the maximum elastic
response displacements of both the pier and the isolator are first dynamically calculated for the
isolated bridge with the elastic stiffness Kp of the pier and the equivalent stiffness KB of the isolator.
Then, the maximum lateral force of the pier can be obtained by equating the elastic response
displacement to the static elasto-plastic response displacement.
Fig.8: Comparison of Maximum Responses of Piers Obtained

by Simple Method and Analytical Method
The comparison of the maximum responses of the piers obtained by the simple method and by the
elasto-plastic dynamic method are shown in Fig.8 (a), where RF and ~ are the maximum lateral
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X S. Li and Y. Goto
force and displacement of the pier, respectively. The subscripts e and p denote the elastic dynamic
response and the elasto-plastic dynamic response. It is observed that the maximum lateral force ratio
RFJRFp is closer to 1.0 when Tp/Tf is smaller than 3.0, whilst the maximum lateral displacement ratio
d d d p is in the range from 0.77 to 1.86. Similarly, if both
Qy/Py
and Kbl/K p are limited to the range
from 0.3 to 0.7, RFe/RF p and ~ o/~ p will take the values between 1.0 to 1.81. The approximate results
obtained by the 'Displacement Conservation Principle ' may be considered to be reasonably safe and
accurate for practical design of the isolated steel piers.
SUMMARY AND CONCLUDING REMARKS
From the above analysis, the following conclusions are obtained.
The response of an isolated bridge is greatly influenced by the initial stiffness and yield force of the
isolator. The both ductility factors for the pier and the isolator increase with the increase of the initial
stiffness ratio Kb~/I< v of the isolator. The maximum response displacement of the pier increases with
the increase of yield force ratio
Qy/Py
for most values of Kb~/l ~, while the ductility factor r b of the
isolator decreases. An isolator with a higher stiffness and a smaller yield force may result in much
damage of the pier when subjected to wave Type 2-m'.
As a general tendency, the energy ratio Ep/Ef decreases as the period ratio Tp/Tf increases. Within the
range from 0.3 to 0.7 for both Qy/Py and Kb~/Kp of the isolator, the energy ratio Ep/Ef will be less than
0.3. Furthermore, by noting that Ep/Ef approaches zero when Tp/Tf > 3.0, the range from 2.1 to 3.0 of
the period ratio Tp/Tf may be more appropriate.
The applicability of the 'Displacement Conservation Principle' for predicting the maximum responses
of steel piers of the isolated bridges is numerically confirmed. The numerical results show that both

RF~RFp and d d ~ p will take the values between 1.0 and 1.81 when
Qy/Py
and Kbl/Kp are limited to
the range from 0.3 to 0.7. The approximate results may be considered to be reasonably safe and
accurate for practical design of the isolated steel piers.
REFERENCE
Kawashima, K. and Shoji, G. (1998). Interaction of Hysteretic Behavior between Isolator/Damper and
Pier in an Isolated Bridge, J.
Struct. Engrg.
JSCE. Vol.44A, pp.733-741.
Li, X.S. and Goto, Y. (1998). A three-dimensional nonlinear seismic analysis of frames considering
panel zone deformation,
Struct. Eng.~Earthquake Eng.,
JSCE, Vol.15, No.2, pp.201-213, 1998, Oct.
Ministry of Construction (1992).
Manual of Menshin Design of Highway Bridges,
Civil Engineering
Research Center, Tokyo, Japan (In Japanese)
Shear analysis for asphalt concrete deck pavement of steel bridges
Xudong Zha 1 and Qiuming Xiao 2
1Department of Highway and Bridge Engineering, Changsha Communications University,
Changsha, 410076, PRC
2Department of Highway and Bridge Engineering, Changsha Communications University,
Changsha, 410076, PRC
ABSTRACT
This paper is based on the elastic layered theory of rigid support. The horizontal shear stresses between
the bridge deck pavement of asphalt concrete and steel box girders, the maximum principal stresses
and the maximum shear stresses at the bottom of the deck pavement layer has been analyzed under the
normal motion and the emergency break of motor vehicles. Based on this result, the shear resistance
index of binder course has been put forward so as to supply the binder course design of steel bridge

deck pavement with a scientific basis.
KEYWORDS
steel bridge, bridge deck pavement, asphaltconcrete, horizontal shoving, binder course, elastic layer,
principal stress, shear stress, shear strength, shear resistance index
PREFACE
In the late 70s, China started building steel bridges with orthotropic plate decks, and the relative
decking technology research has been done for 20 years. From Mafang Bridge to recently completed
Xiling Bridge, Humen Bridge and Qingma Bridge, the deck pavement technology has been
continuously improved and developed. However, up to now, bridge deck pavement engineering of steel
bridges in China has not achieved a complete success.
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X. Zha and Q. Xiao
There are three main reasons for the distresses of bridge deck pavement of Xiling Yangzi Bridge,
Chongqing Highway Scientific Research Institute (1998). The first is that the deck pavement system
was not perfect, the second the qualification of construction teams could not meet the requirement for
the works, and the third the influence of heavy truck vehicles used for the Three Gorges was not fully
estimated. The local temperature conditions was not completely occupied during the designing of
Humen Bridge, and the worse thing was that the deck pavement thickness and structure were changed
at the time of construction, thus reducing the material quality, and the thermal stability distress
appeared due to the poor construction control. Although Qingma Bridge built in accordance with the
English bridge deck pavement improved the softening point of hard asphalt to 70~ the deck failed
to pass the test of high temperature in Hong Kong. In the meantime, the use of Eliminator waterproof
adhesive agent left the hidden trouble of air bubbles.
Now, China is building a lot of steel bridges with orthotropic plate decks. The bridges under
construction are Jiangyin Yangzi Bridge, Xiamen Haicang Bridge, Nangjing Yangzi Bridge II,
Chongqing Egongyan Yangzi Bridge, and etc. The bridge deck pavement of asphalt concrete was
employed in most of bridge construction. Therefore, the bridge deck pavement technology should be
urgently solved for steel box girders. The paper has put forward the shear resistance index for asphalt
concrete bridge deck pavement through the theoretical analysis as far as the horizontal shoving

problem between asphalt concrete of the bridge deck pavement and the steel sheets are concerned. This
has provided the design of binder course for bridge deck pavement and program alternatives with a
scientific basis.
BASIC THEORY
Due to the strength and rigidity of asphalt concrete is far from those of the steel box girders, the
geometric sizes of the wheel load is much less than the length and width of the steel box girders. In the
meantime, under the wheel load, the reducing speed of the horizontal distribution of the asphalt
concrete stress is rapid. Therefore, the asphalt concrete deck pavement of steel bridges can be regarded
as a elastic layer, while the steel box girders can be simplified as rigid support. Thus, the theory of
elastic layers on the rigid support can be used for the stress analysis of deck pavement, while the motor
vehicle load simplified as the uniformly distributed loads of double vertical and horizontal circles,
I TM ~1~ ~1 TM ~1~" x ~1~ ~1
q~ o~/
y
Asphalt concrete deck |
pavment E, h, ~t 1 r/// Binder course
//,<\V/,,K\\ ~z Steel girder
Figure 1: Mechanical model of bridge deck pavement analysis
Shear Analysis for Asphalt Concrete Deck Pavement of Steel Bridges
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Highway Planning and Design Institute of Ministry of Communications (1997). The mechanical model
is seen in Figure 1, x showing the longitudinal direction and y the horizontal one.
SHEAR STRESS ANALYSIS
Nowadays there exits a trend to apply SMA material for bridge deck pavement of asphalt concrete in
China. The pavement will be built in two layers. The size of the aggregate for the upper layer is
2-5mm larger than that for the lower layer, the general thickness of the pavement 6cm and the
modulus value of SMA measured in laboratory 1400 1600MPa. Therefore, in Figure 1, when the
analysis is carried out, the layer thickness h = 6cm, the modulus E = 1500MPa, the Poisson's ratio ~t =
0.25. The load of motor vehicles will be the standard axle load of 100kN, and the radius 5 = 10.65cm,
the vertical load p = 0.7MPa. The horizontal load will be determined in accordance with the friction

coefficient f between wheel and deck pavement, i.e.:
q=f.p (1)
Where: q is the horizontal load (MPa); p the vertical load (MPa); f the friction coefficient,
0.2 represents normal motion of motor vehicles, and 0.5 accidental emergency break, Fang Fusen
(1993).
According to the elastic-layered theory and the above data chosen, this paper has analyzed the
maximum principal stress cr 1 at the bottom of the pavement (z = 6cm), the maximum shear stress Xmax
and the horizontal shear stress Xxz. The different stress distributions will be computed under normal
motion of motor vehicles and emergency conditions, as shown in Figure 2 Figure 7. The maximum
and minimum value of various kinds of stress will be seen in Table 1. From Figure 2-Figure 7, the
maximum and minimum value of various stress at the bottom of the deck pavement layer will always
appear on x-direction in the center of the singular wheel. The relevant profile distributions in x-
direction will be seen in Figure 8-Figure 10.
TABLE
1
MAXIMUM AND MINIMUM VALUE OF VARIOUS KINDS OF STRESS (MPa)
Items
Maximum value
Minimum value
f= 0.2
Gl "~m~x "l~xz
0.048 0.267 0.068
-0.215 0.000 -0.189
f=0.5
ffl "Cmax "l;xz
0.078 0.355 0.000
-0.153 0.000 -0.283
From the above figures and tables, the maximum principal stress is mostly under compressive
condition. The maximum tension stress under both conditions will often be less than 0.1MPa, while the
cleavage strength of SMA between 1.2-1.6MPa. This shows that the fatigue cracking will not

generally appear in the paving layer. The maximum value of the maximum shear stress will be less
than 0.40MPa. Since SMA is of excellent stability at high temperature. The test shows that the shear
strength is between 1.0-1.4MPa. Therefore, the fatigue shear distress will not normally occur inside
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X. Zha and Q. Xiao
Figure 2: Distribution of principal stress Cl (f = 0.2)
Figure 3: Distribution of maximum shear stress Xm~x (f = 0.2)
Figure 4: Distribution of horizontal shear stress Xx~ (f= 0.2)
Shear Analysis for Asphalt Concrete Deck Pavement of Steel Bridges
557
Figure 5: Distribution of principal stress c~ (f= 0.5)
Figure 6: Distribution of maximum shear stress Xm~x (f = 0.5)
Figure 7: Distribution of horizontal shear stress x= (f= 0.5)
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X. Zha and Q. Xiao
Figure 8: Distribution of principal stress t~ l at center of singular wheel in x-direction
Figure 9: Distribution of maximum shear stress "lTma x
at
center of singular wheel in x-direction
Figure 10: Distribution of horizontal shear stress Xxz at center of singular wheel in x-direction
Shear Analys& for Asphalt Concrete Deck Pavement of Steel Bridges
the paving layer.
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As to the horizontal shear stress between the paving layer and steel sheets, the maximum absolute
value will appear at the place of 9.585cm (0.95) from the center of singular wheel along the driving
direction. The relevant value of the normal motion and emergency break of motor vehicles will
separately be -0.189MPa and -0.283MPa. Under normal driving condition, the area of reverse
direction for the horizontal shear stress will happen at the bottom of the front edge of singular wheel
(Figure 10). The maximum value is 0.068MPa. Through analysis, the larger shear stress will produce
between the deck pavement layer at 0.96 from the center of singular wheel and the steel sheet under

wheel loads, and this will result in horizontal shoving. Therefore, the design of the binder course
should meet the requirement of the shear action. Because the deck pavement layer will bear the
repeated load of motor vehicles, with the consideration of overloads and heavy loads, the shear
resistance strength of the binder course should be of enough safety. The shear resistance index is as
follows, Fang Fusen (1993):
1;
1;a < 1;R =- (2)
K,
In which 1;a is the computed horizontal shear stress value (MPa) ; 1;R is the allowable horizontal shear
stress (MPa); 1; is the shear resistance strength (MPa); I~ the structural coefficient of the shear
resistance strength, this is related to the acting times of axle loads.
K~ should be determined in line with the traffic conditions, the application conditions and the
importance of the steel bridge through the fatigue shear tests. I~ will be 2-3 at the time of normal
driving, while I~ will be 1.5-2 when in emergency. From it, the shear resistance strength index of the
binder course will be 0.4-0.6MPa.
CONCLUSION
This paper analyzes the maximum principal stresses, the maximum shear stresses and the horizontal
shear stresses in the deck pavement layer of asphalt concrete for steel bridges under the load of motor
vehicles. The analyzing result shows that the fatigue tension cracks and fatigue shear distress within
the paving layer will not generally happen. However, the greater horizontal shear stresses will take
place between the deck pavement and the steel box girders. This is the main cause for the horizontal
shoving of the deck pavement of steel bridges. The maximum absolute value will appear at 0.98 from
the center of singular wheel. Therefore, in order to prevent larger horizontal shoving of the deck
pavement, the shear resistance in the binder course should be controlled. In consideration of the
material, the thickness of the deck pavement of asphalt concrete for steel bridges and the traffic and
application conditions in China, it is suggested that the shear strength of the binder course between the
deck pavement and steel sheets at high temperature season should not be less than 0.4-0.6MPa.