Valdebenito et al 2018a - Revision history

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Cinmemj moved page Draft Samper 432909089 to Valdebenito et al 2018a

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Cinmemj at 07:44, 29 May 2018

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@@ Line 1: / Line 1: @@
 ==Acknowledgments==
@@ Line 345: / Line 328: @@
 -->
-==Chapter 1==
+==Chapter 1. Introduction==
-−
-==Introduction==
 :<big>1.1 Cable-Stayed Bridges and Seismic Protection </big>
@@ Line 576: / Line 557: @@
 |}
-==Chapter 2==
+==Chapter 2. Fluid Viscous Damping Technology==
-−
-==Fluid Viscous Damping Technology==
 :<big>2.1 General Overview </big>
@@ Line 1,425: / Line 1,404: @@
 As a conclusion remark, it is clear that additional viscous damping to control the seismic response of cable-stayed bridges is beneficial, reducing the seismic forces on members as well as their displacements by increasing the structural damping.
-==Chapter 3==
+==Chapter 3. Seismic Response. Parametric Analysis==
-−
-==Seismic Response. Parametric Analysis==
 :<big>3.1 Introduction</big>
@@ Line 6,187: / Line 6,164: @@
 '''Fig. 3.77''' Average of the Maximum Bending Moments for ''AR4 ''Bridge</div>
-==Chapter 4==
+==Chapter 4. Seismic Protection. Application of Fluid Viscous Dampers==
-−
-==Seismic Protection. Application of Fluid Viscous Dampers==
 :<big>4.1 General Considerations</big>
@@ Line 8,755: / Line 8,730: @@
 As a general conclusion, very high energy dissipation rates are obtained, which confirms the important incidence of the addition of fluid viscous dampers as passive energy dissipation devices to reduce the seismic response of cable-stayed bridges.
-==Appendix A==
+==Appendix A. Step-by-Step Nonlinear Time History Analysis==
-−
-==Step-by-Step Nonlinear Time History Analysis==
 <big>A.1 General Considerations</big>
@@ Line 9,053: / Line 9,026: @@
 For analysis of large structural systems, it is not possible to store all information within high-speed storage. If data needs to be obtained from low-speed disk storage, the effective speed of a computer can be reduced significantly. For that reason, it is recommended the use of computer codes with the transfer data to and from disk storage conducted in large blocks to minimize disk access time, also called ''paging operating systems''.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+==References==
-<big>''' '''References</big></div>
 Abdel – Ghaffar, A.M. (1991), “Cable-Stayed Bridges under Seismic Action”, ''Proceedings of the Seminar Cable – Stayed Bridges: Recent Development and their Future'', Yokohama, Japan.

← Older revision		Revision as of 07:44, 29 May 2018
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	[[Image:draft_Samper_432909089-monograph-image409.png\|252px]] [Eq. A.4]		[[Image:draft_Samper_432909089-monograph-image409.png\|252px]] [Eq. A.4]
−	\|}
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−
	\|}		\|}

@@ Line 6,234: / Line 6,234: @@
 In order to investigate the best locations of the damper devices for this research, a brief study was conducted considering five analysis cases, all applied to the ''AB4'' model. The first case considered locations of the dampers at the deck-ends only, in the longitudinal direction. Case 2 considered longitudinal dampers at the deck-ends and at the tower-deck connections, in which the fixed-hinge of the tower-deck connections was changed by roller supports plus the dampers. Case 3 considered dampers at the deck-ends plus longitudinal damper in one of the tower-deck connections, and the replacement of the associated tower-deck connection by roller supports. Case 4 considered dampers at the deck-ends and transverse dampers plus roller supports at the tower-deck connections. Finally, case 5 considered dampers at the deck-ends and at the tower-deck connections for both directions, plus the corresponding replacement of the tower-deck connections by roller supports. It is obvious that cases 4 and 5 are an attempt of exploring the tri-dimensional response of the bridges in the presence of additional damping devices selected to control the longitudinal and transverse responses. Table 4.1 summarizes the five analysis cases.
-==Table 4.1 Layout of the Tower-Deck Connections and Dampers for the Analysis Cases==
+'''Table 4.1''' Layout of the Tower-Deck Connections and Dampers for the Analysis Cases
 {| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
@@ Line 6,952: / Line 6,952: @@
 {| style="width: 100%;border-collapse: collapse;"
 |-
-|  style="vertical-align: top;"|'''Table 4.7 '''Critical Damping Ratios – Damped Cases
+|  style="vertical-align: top;width: 40%;"|'''Table 4.7 '''Critical Damping Ratios – Damped Cases
 {| style="width: 50%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
@@ Line 6,977: / Line 6,977: @@
-|  style="vertical-align: top;"|Modal damping exposed in Table 4.7 was obtained applying the empirical formulation by Kawashima ''et al'' (1993). In general terms, critical damping ratios for the damped cases are different compared with the undamped cases, with the exception of damping associated with transverse bending vibrations.
+|  style="vertical-align: top;width: 60%;"|Modal damping exposed in Table 4.7 was obtained applying the empirical formulation by Kawashima ''et al'' (1993). In general terms, critical damping ratios for the damped cases are different compared with the undamped cases, with the exception of damping associated with transverse bending vibrations.
 |}
@@ Line 7,849: / Line 7,849: @@
 <span style="text-align: center; font-size: 75%;"><sup>a</sup> At the tower base <sup>c</sup> In-plane</span>
-<sup>b</sup> At the tower-deck connection <sup>d</sup> Out-of-plane
+<span style="text-align: center; font-size: 75%;"><sup>b</sup> At the tower-deck connection <sup>d</sup> Out-of-plane</span>
 The analysis of the maximum forces and velocities of the dampers can be appreciated in Table 4.11. For simplicity, response of the dampers is exposed in absolute values again. Almost the same results are observed for both structures, with insignificant differences between the seismic events. Important differences are observed comparing deck-end damper response with the tower damper response, in which average velocities of about 0.30 m/sec and 0.18 m/sec are obtained respectively. With regard to the average maximum damper forces, differences of about 20% are evaluated between both damper locations. Of course, maximum damper forces are obtained at the deck-ends, implying higher energy dissipation than that associated to the tower-deck connection.
@@ Line 8,382: / Line 8,382: @@
 <span style="text-align: center; font-size: 75%;"><sup>a</sup> At the tower base <sup>c</sup> In-plane</span>
-<sup>b</sup> At the tower-deck connection <sup>d</sup> Out-of-plane
+<span style="text-align: center; font-size: 75%;"><sup>b</sup> At the tower-deck connection <sup>d</sup> Out-of-plane</span>
 .Summarizing, the analysis considering near-fault ground motions shows that the largest seismic responses are obtained with events Gatos and Kobe. A similar situation occurs for the undamped bridges. Responses obtained for ''AB4 ''and ''AR4 ''models are similar, mainly for displacements and velocities. Most important differences are observed with the deck response for internal forces and cable forces, as long as the tower response is less sensitive. This behaviour is independent on the earthquake nature (far-fault – near-fault) or the damped or undamped condition of the bridges. As was concluded for the undamped condition, it is difficult to select the best stay cable layout in terms of the seismic response. There are not clear tendencies, and application of time-history analysis can be confused for this purpose.

@@ Line 1,529: / Line 1,529: @@
 |}
-==Fig. 3.5 Proposed Decks for the Analysis (dimensions in metres)==
+'''Fig. 3.5''' Proposed Decks for the Analysis (dimensions in metres)
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

@@ Line 1,470: / Line 1,470: @@
 |}
-==Fig. 3.1 Longitudinal Layouts for Fan Pattern (dimensions in metres)==
+'''Fig. 3.1'' Longitudinal Layouts for Fan Pattern (dimensions in metres)
 {| style="width: 100%;border-collapse: collapse;"

← Older revision	Revision as of 13:05, 29 May 2018
(No difference)

@@ Line 829: / Line 829: @@
 The control force ''u'' by non-linear viscous dampers with damping coefficient ''c<sub>d</sub>''  is expressed as
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image48.png|120px]] [Eq. 2.10]</div>
 In Eq. 2.10, the exponent ''N'' controls the damper nonlinearity and has typical values in the range of 0.10 to 1.0 for seismic applications. For the special case of ''N = 1'', Eq. 2.10 represents the force applied by linear viscous dampers. In the case of ''N = 0, ''Eq. 2.10 changes to a friction damper as follows:
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image49.png|90px]] [Eq. 2.11]</div>
@@ Line 873: / Line 873: @@
 :<big>2.3.2 Effect of the Damper Parameters</big>
-:''<sub>2.3.2.1 </sub>Damping coefficient c<sub>d</sub>''
+:''2.3.2.1 Damping coefficient c<sub>d</sub>''
 In general terms, for viscous dampers, ''c<sub>d</sub>'' does not affect the shape of the hysteretic force – displacement cycle; however, an increase of the value of this parameter increases the energy dissipation capacity and the maximum force in the device [Guerreiro, 2006]. In this sense, the work carried out by Virtuoso ''et al ''(2000) studies the modelling of the seismic behaviour of bridges with added viscous dampers, analyzing the effects of the constant ''c<sub>d</sub>'' (here called ''C'')''.'' To allow an analysis on the influence of that parameter on the structural response, values of the constant ''C ''between 0.10 and 10 were considered, since those values, together with the values considered for the parameter ''N ''(here called ''α''), will cover forces corresponding to seismic coefficient varying from 1% to 50% of the weight. In this study a set of five artificial accelerograms compatible with the response spectrum defined in Eurocode 8 – Part 2 [CEN, 1998b] with a peak ground acceleration of 0.30g, type B soil and 30 sec total duration of the series, were used. Two extreme cases were considered: a solution without elastic stiffness (deck totally free over the piers) and a solution with elastic stiffness (low stiffness elastic connection between the piers and the deck). Also, in this research the configurations of the force – velocity relation curves were presented for different values of ''α'', corresponding to the linear branch, which, were defined by the origin and the point corresponding to 10% of the maximum velocity and force corresponding to the defined seismic action and obtained without the consideration of the linear branch. Figs. 2.15 and 2.16 show maximum forces and displacements in the viscous damper without and with elastic stiffness respectively. They show that solution involving a higher displacement control always lead to higher force levels in the device. It is also possible to observe that the more efficient solutions, with better displacement control for the same force level, generally corresponds to low ''α'' values. Likewise, for device solutions with low values of the constant ''C'', the elastic stiffness of the structure has an important contribution on the displacement control. It is important to notice that the contribution of the elastic force is out of phase with the one transmitted by the devices, what means that, in a solution of this type there is always a force restraining the movement of the deck. The problem is that the forces transmitted to the structure must be controlled to limit the contribution of the piers to values lower than their elastic limit.
@@ Line 1,129: / Line 1,129: @@
 Soong and Constantinou (1994) have shown that the work done (dissipated energy) in one cycle of sinusoidal loading can be written as
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image79.png|84px]] [Eq. 2.14]</div>
@@ Line 1,136: / Line 1,136: @@
 Equation 2.14 can be integrated to give
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image81.png|228px]] [Eq. 2.15]</div>
@@ Line 1,143: / Line 1,143: @@
 The equivalent (added) damping is calculated by equating equation 2.15 and the energy dissipated in equivalent viscous damping:
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
-''4πξ<sub>d</sub>ω<sub>0</sub>E<sub>s</sub> = W<sub>d</sub>'' [Eq. 2.16]</div>
+'''4πξ<sub>d</sub>ω<sub>0</sub>E<sub>s</sub> = W<sub>d</sub>''' [Eq. 2.16]</div>
 in which strain energy ''E<sub>s</sub> = kx<sub>0</sub><sup>2</sup>/2. ''Solving Eq. 2.16 for equivalent damping ratio:
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image82.png|234px]] [Eq. 2.17]</div>
@@ Line 1,161: / Line 1,162: @@
 Pekcan ''et al ''(1999), proposed a simple method for making the transformation from the non-linear damper behaviour to equivalent viscous damping. They explain that for velocity-dependent systems such as viscous dampers, consideration of the ''rate'' of energy dissipation – that is power (rather than energy) – becomes more important in seeking the equivalent linear properties for these systems. The proposed equivalent damping is
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image84.png|126px]] [Eq. 2.19]</div>
 Given the customary definition of damping ratio (''ξ'') obtained from ''c = 2ξω<sub>0</sub>M'', equation 2.19 can be expressed as follows:
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image85.png|156px]] [Eq. 2.20]</div>
@@ Line 1,195: / Line 1,196: @@
 The peak force ''f<sub>D0</sub>(N)'' in the non-linear fluid viscous damper with known non-linear parameter ''N ''can be expressed as
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image86.png|168px]] [Eq. 2.21]</div>
 where ''V = ω<sub>0</sub>x<sub>0</sub>'' is the spectral pseudo-velocity for the SDF system; ''c<sub>1</sub>'' is the damping coefficient of the linear system and ''β<sub>N </sub>''is a constant defined as
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image87.png|156px]] [Eq. 2.22]</div>
 The non-linear damper force can be computed from Eq. 2.21 if ''x<sub>0</sub>'' and '' [[Image:draft_Samper_432909089-monograph-image88.png|18px]] ''are known. They can be estimated as the peak values of deformation and relative velocity of the corresponding linear system. Equation 2.21 is almost exact in the velocity-sensitive region of the spectrum, overestimates the damper force in the acceleration-sensitive region (by at most 15%); and underestimates in the displacement-sensitive region (by at most 7%). Moreover, the accuracy of Eq. 2.21 deteriorates slightly with the increase of the equivalent damping ''ξ<sub>d</sub>. ''However, the actual velocity '' [[Image:draft_Samper_432909089-monograph-image88.png|12px]] ''of the corresponding linear system required in Eq. 2.21 and to compute ''f<sub>D0 </sub>(N=1) = c<sub>1</sub> [[Image:draft_Samper_432909089-monograph-image88.png|12px]] ''is not readily available, because the velocity spectrum is not plotted routinely. If the velocity '' [[Image:draft_Samper_432909089-monograph-image88.png|18px]] ''is replaced by the pseudo-velocity, Eq. 2.21 changes to
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image89.png|186px]] [Eq. 2.23]</div>
@@ Line 1,212: / Line 1,213: @@
 Another important point regarding the design of non-linear fluid viscous dampers is how to select the properties ''c<sub>d</sub>'' and ''N'' to satisfy a design requirement. As was previously explained, the structural deformation is essentially unaffected by the damper non-linearity parameter ''N'' and it is essentially the same as that for the corresponding linear system. The total damping capacity that must be provided in the system to limit the deformation of a linear system to a design value can be determined directly from the design spectrum. Subtracting the inherent damping in the structure from the total damping required gives ''ξ<sub>d</sub>'', the necessary supplemental damping. Many different non-linear fluid viscous dampers can be chosen to provide the required supplemental damping ratio ''ξ<sub>d</sub>''. Thus, for a selected value of ''N:''
-<div style="text-align: right; direction: ltr; margin-left: 1em;">
+<div style="text-align: left; direction: ltr; margin-left: 1em;">
   [[Image:draft_Samper_432909089-monograph-image90.png|168px]] [Eq. 2.24]</div>

@@ Line 547: / Line 547: @@
 '''Fig. 1.16 '''Millau Bridge, France
-|  style="vertical-align: top;"|''' [[Image:draft_Samper_432909089-monograph-image18.jpeg|312px]] '''
+| style="vertical-align: top;width: 50%;"|[[Image:Draft_Samper_432909089_8898_monograph-image18.png|312px]]
 '''Fig. 1.17''' Sutong Bridge, Nantong, China
@@ Line 575: / Line 575: @@
 |}
 ==Chapter 2==