\documentclass[11pt,twoside]{article}\makeatletter

\IfFileExists{xcolor.sty}%
  {\RequirePackage{xcolor}}%
  {\RequirePackage{color}}
\usepackage{colortbl}
\usepackage{wrapfig}
\usepackage{ifxetex}
\ifxetex
  \usepackage{fontspec}
  \usepackage{xunicode}
  \catcode`⃥=\active \def⃥{\textbackslash}
  \catcode`❴=\active \def❴{\{}
  \catcode`❵=\active \def❵{\}}
  \def\textJapanese{\fontspec{Noto Sans CJK JP}}
  \def\textChinese{\fontspec{Noto Sans CJK SC}}
  \def\textKorean{\fontspec{Noto Sans CJK KR}}
  \setmonofont{DejaVu Sans Mono}
  
\else
  \IfFileExists{utf8x.def}%
   {\usepackage[utf8x]{inputenc}
      \PrerenderUnicode{–}
    }%
   {\usepackage[utf8]{inputenc}}
  \usepackage[english]{babel}
  \usepackage[T1]{fontenc}
  \usepackage{float}
  \usepackage[]{ucs}
  \uc@dclc{8421}{default}{\textbackslash }
  \uc@dclc{10100}{default}{\{}
  \uc@dclc{10101}{default}{\}}
  \uc@dclc{8491}{default}{\AA{}}
  \uc@dclc{8239}{default}{\,}
  \uc@dclc{20154}{default}{ }
  \uc@dclc{10148}{default}{>}
  \def\textschwa{\rotatebox{-90}{e}}
  \def\textJapanese{}
  \def\textChinese{}
  \IfFileExists{tipa.sty}{\usepackage{tipa}}{}
\fi
\def\exampleFont{\ttfamily\small}
\DeclareTextSymbol{\textpi}{OML}{25}
\usepackage{relsize}
\RequirePackage{array}
\def\@testpach{\@chclass
 \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
  \ifnum \@lastchclass=7 5 \else
   \ifnum \@lastchclass=8 \tw@ \else
    \ifnum \@lastchclass=9 \thr@@
   \else \z@
   \ifnum \@lastchclass = 10 \else
   \edef\@nextchar{\expandafter\string\@nextchar}%
   \@chnum
   \if \@nextchar c\z@ \else
    \if \@nextchar l\@ne \else
     \if \@nextchar r\tw@ \else
   \z@ \@chclass
   \if\@nextchar |\@ne \else
    \if \@nextchar !6 \else
     \if \@nextchar @7 \else
      \if \@nextchar (8 \else
       \if \@nextchar )9 \else
  10
  \@chnum
  \if \@nextchar m\thr@@\else
   \if \@nextchar p4 \else
    \if \@nextchar b5 \else
   \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
   \fi \fi  \fi  \fi  \fi  \fi  \fi \fi \fi \fi \fi \fi}
\gdef\arraybackslash{\let\\=\@arraycr}
\def\@textsubscript#1{{\m@th\ensuremath{_{\mbox{\fontsize\sf@size\z@#1}}}}}
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\def\abbr{}
\def\corr{}
\def\expan{}
\def\gap{}
\def\orig{}
\def\reg{}
\def\ref{}
\def\sic{}
\def\persName{}\def\name{}
\def\placeName{}
\def\orgName{}
\def\textcal#1{{\fontspec{Lucida Calligraphy}#1}}
\def\textgothic#1{{\fontspec{Lucida Blackletter}#1}}
\def\textlarge#1{{\large #1}}
\def\textoverbar#1{\ensuremath{\overline{#1}}}
\def\textquoted#1{‘#1’}
\def\textsmall#1{{\small #1}}
\def\textsubscript#1{\@textsubscript{\selectfont#1}}
\def\textxi{\ensuremath{\xi}}
\def\titlem{\itshape}
\newenvironment{biblfree}{}{\ifvmode\par\fi }
\newenvironment{bibl}{}{}
\newenvironment{byline}{\vskip6pt\itshape\fontsize{16pt}{18pt}\selectfont}{\par }
\newenvironment{citbibl}{}{\ifvmode\par\fi }
\newenvironment{docAuthor}{\ifvmode\vskip4pt\fontsize{16pt}{18pt}\selectfont\fi\itshape}{\ifvmode\par\fi }
\newenvironment{docDate}{}{\ifvmode\par\fi }
\newenvironment{docImprint}{\vskip 6pt}{\ifvmode\par\fi }
\newenvironment{docTitle}{\vskip6pt\bfseries\fontsize{22pt}{25pt}\selectfont}{\par }
\newenvironment{msHead}{\vskip 6pt}{\par}
\newenvironment{msItem}{\vskip 6pt}{\par}
\newenvironment{rubric}{}{}
\newenvironment{titlePart}{}{\par }

\newcolumntype{L}[1]{){\raggedright\arraybackslash}p{#1}}
\newcolumntype{C}[1]{){\centering\arraybackslash}p{#1}}
\newcolumntype{R}[1]{){\raggedleft\arraybackslash}p{#1}}
\newcolumntype{P}[1]{){\arraybackslash}p{#1}}
\newcolumntype{B}[1]{){\arraybackslash}b{#1}}
\newcolumntype{M}[1]{){\arraybackslash}m{#1}}
\definecolor{label}{gray}{0.75}
\def\unusedattribute#1{\sout{\textcolor{label}{#1}}}
\DeclareRobustCommand*{\xref}{\hyper@normalise\xref@}
\def\xref@#1#2{\hyper@linkurl{#2}{#1}}
\begingroup
\catcode`\_=\active
\gdef_#1{\ensuremath{\sb{\mathrm{#1}}}}
\endgroup
\mathcode`\_=\string"8000
\catcode`\_=12\relax

\usepackage[a4paper,twoside,lmargin=1in,rmargin=1in,tmargin=1in,bmargin=1in,marginparwidth=0.75in]{geometry}
\usepackage{framed}

\definecolor{shadecolor}{gray}{0.95}
\usepackage{longtable}
\usepackage[normalem]{ulem}
\usepackage{fancyvrb}
\usepackage{fancyhdr}
\usepackage{graphicx}
\usepackage{marginnote}

\renewcommand{\@cite}[1]{#1}


\renewcommand*{\marginfont}{\itshape\footnotesize}

\def\Gin@extensions{.pdf,.png,.jpg,.mps,.tif}

  \pagestyle{fancy}

\usepackage[pdftitle={Evaluation of Seismic Performance Focusing on Increasing Response of Lead Rubber Bearing (LRB) and Over Strength of RC Pier During Earthquake},
 pdfauthor={}]{hyperref}
\hyperbaseurl{}

	 \paperwidth210mm
	 \paperheight297mm
              
\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}
\clubpenalty=8000
\emergencystretch 3em
\hbadness=4000
\hyphenpenalty=400
\pretolerance=750
\tolerance=2000
\vbadness=4000
\widowpenalty=10000

\renewcommand\section{\@startsection {section}{1}{\z@}%
     {-1.75ex \@plus -0.5ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large\bfseries}}
\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
     {-1.75ex\@plus -0.5ex \@minus- .2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\Large}}
\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
     {-1.5ex\@plus -0.35ex \@minus -.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\large}}
\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%
     {-1ex \@plus-0.35ex \@minus -0.2ex}%
     {0.5ex \@plus .2ex}%
     {\reset@font\normalsize}}
\renewcommand\subparagraph{\@startsection{subparagraph}{5}{\parindent}%
     {1.5ex \@plus1ex \@minus .2ex}%
     {-1em}%
     {\reset@font\normalsize\bfseries}}


\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}
 \@tempdima 1.5em \begingroup
 \parindent \z@ \rightskip \@pnumwidth 
 \parfillskip -\@pnumwidth 
 \bfseries \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}\par
 \endgroup}
\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\@ifundefined{c@section}{\newcounter{section}}{}
\@ifundefined{c@chapter}{\newcounter{chapter}}{}
\newif\if@mainmatter 
\@mainmattertrue
\def\chaptername{Chapter}
\def\frontmatter{%
  \pagenumbering{roman}
  \def\thechapter{\@roman\c@chapter}
  \def\theHchapter{\roman{chapter}}
  \def\thesection{\@roman\c@section}
  \def\theHsection{\roman{section}}
  \def\@chapapp{}%
}
\def\mainmatter{%
  \cleardoublepage
  \def\thechapter{\@arabic\c@chapter}
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \pagenumbering{arabic}
  \setcounter{secnumdepth}{6}
  \def\@chapapp{\chaptername}%
  \def\theHchapter{\arabic{chapter}}
  \def\thesection{\@arabic\c@section}
  \def\theHsection{\arabic{section}}
}
\def\backmatter{%
  \cleardoublepage
  \setcounter{chapter}{0}
  \setcounter{section}{0}
  \setcounter{secnumdepth}{2}
  \def\@chapapp{\appendixname}%
  \def\thechapter{\@Alph\c@chapter}
  \def\theHchapter{\Alph{chapter}}
  \appendix
}
\newenvironment{bibitemlist}[1]{%
   \list{\@biblabel{\@arabic\c@enumiv}}%
       {\settowidth\labelwidth{\@biblabel{#1}}%
        \leftmargin\labelwidth
        \advance\leftmargin\labelsep
        \@openbib@code
        \usecounter{enumiv}%
        \let\p@enumiv\@empty
        \renewcommand\theenumiv{\@arabic\c@enumiv}%
	}%
  \sloppy
  \clubpenalty4000
  \@clubpenalty \clubpenalty
  \widowpenalty4000%
  \sfcode`\.\@m}%
  {\def\@noitemerr
    {\@latex@warning{Empty `bibitemlist' environment}}%
    \endlist}

\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}
\parskip0pt
\parindent1em
\def\Panel#1#2#3#4{\multicolumn{#3}{){\columncolor{#2}}#4}{#1}}
\newenvironment{reflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemsep}{0pt}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\itshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{sansreflist}{%
  \begin{raggedright}\begin{list}{}
  {%
   \setlength{\topsep}{0pt}%
   \setlength{\rightmargin}{0.25in}%
   \setlength{\itemindent}{0pt}%
   \setlength{\parskip}{0pt}%
   \setlength{\itemsep}{0pt}%
   \setlength{\parsep}{2pt}%
   \def\makelabel##1{\upshape ##1}}%
  }
  {\end{list}\end{raggedright}}
\newenvironment{specHead}[2]%
 {\vspace{20pt}\hrule\vspace{10pt}%
  \phantomsection\label{#1}\markright{#2}%

  \pdfbookmark[2]{#2}{#1}%
  \hspace{-0.75in}{\bfseries\fontsize{16pt}{18pt}\selectfont#2}%
  }{}
      \def\TheFullDate{2020 2020-01-15 (revised: 33 Year 2020 15 January 2020)}
\def\TheID{\makeatother }
\def\TheDate{2020 2020-01-15}
\title{Evaluation of Seismic Performance Focusing on Increasing Response of Lead Rubber Bearing (LRB) and Over Strength of RC Pier During Earthquake}
\author{}\makeatletter 
\makeatletter
\newcommand*{\cleartoleftpage}{%
  \clearpage
    \if@twoside
    \ifodd\c@page
      \hbox{}\newpage
      \if@twocolumn
        \hbox{}\newpage
      \fi
    \fi
  \fi
}
\makeatother
\makeatletter
\thispagestyle{empty}
\markright{\@title}\markboth{\@title}{\@author}
\renewcommand\small{\@setfontsize\small{9pt}{11pt}\abovedisplayskip 8.5\p@ plus3\p@ minus4\p@
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip \z@ plus2\p@
\belowdisplayshortskip 4\p@ plus2\p@ minus2\p@
\def\@listi{\leftmargin\leftmargini
               \topsep 2\p@ plus1\p@ minus1\p@
               \parsep 2\p@ plus\p@ minus\p@
               \itemsep 1pt}
}
\makeatother
\fvset{frame=single,numberblanklines=false,xleftmargin=5mm,xrightmargin=5mm}
\fancyhf{} 
\setlength{\headheight}{14pt}
\fancyhead[LE]{\bfseries\leftmark} 
\fancyhead[RO]{\bfseries\rightmark} 
\fancyfoot[RO]{}
\fancyfoot[CO]{\thepage}
\fancyfoot[LO]{\TheID}
\fancyfoot[LE]{}
\fancyfoot[CE]{\thepage}
\fancyfoot[RE]{\TheID}
\hypersetup{citebordercolor=0.75 0.75 0.75,linkbordercolor=0.75 0.75 0.75,urlbordercolor=0.75 0.75 0.75,bookmarksnumbered=true}
\fancypagestyle{plain}{\fancyhead{}\renewcommand{\headrulewidth}{0pt}}

\date{}
\usepackage{authblk}

\providecommand{\keywords}[1]
{
\footnotesize
  \textbf{\textit{Index terms---}} #1
}

\usepackage{graphicx,xcolor}
\definecolor{GJBlue}{HTML}{273B81}
\definecolor{GJLightBlue}{HTML}{0A9DD9}
\definecolor{GJMediumGrey}{HTML}{6D6E70}
\definecolor{GJLightGrey}{HTML}{929497} 

\renewenvironment{abstract}{%
   \setlength{\parindent}{0pt}\raggedright
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
   \textcolor{GJBlue}{\large\bfseries\abstractname\space}
}{%   
   \vskip8pt
   \textcolor{GJMediumGrey}{\rule{\textwidth}{2pt}}
   \vskip16pt
}

\usepackage[absolute,overlay]{textpos}

\makeatother 
      \usepackage{lineno}
      \linenumbers
      
\begin{document}

             \author[1]{Park  Kyeonghoon}

             \author[2]{Naito  Nobuyuki}

             \author[3]{Mazda  Taiji}

             \author[4]{Uno  Hiroshige}

             \author[5]{Kawakami  Masahide}

             \affil[1]{  Kyushu University}

\renewcommand\Authands{ and }

\date{\small \em Received: 13 December 2019 Accepted: 2 January 2020 Published: 15 January 2020}

\maketitle


\begin{abstract}
        


The characteristics of the seismic bearing change depending on various factors. When an earthquake occurs, the behavior of the bridge may differ from the values expected in the structural design. The shear deformation of the seismic bearing may increase, but it is difficult to reach the fracture deformation. This paper studied the effect of the stiffness due to various dependency and durability on Lead Rubber Bearings (LRB) and the over strength of bridge piers on the bearing behavior when an earthquake occurred. As a result, if the stiffness of LRB reduces within the criteria, seismic performance can be expected safety even if the shear strain designed in the current design is greater than the allowable shear strain. The reason is that the hardening phenomenon in the high strain region of the laminated rubber bearing suppresses the displacement. Also, since the seismic bridges with over strength of the piers have come near elastic behavior when an earthquake occurs, shear strain is easy to be large.

\end{abstract}


\keywords{rubber bearing characteristic change, hardening, lead rubber bearing, pier ductility, non-linear time history analysis, over pier strength}

\begin{textblock*}{18cm}(1cm,1cm) % {block width} (coords) 
\textcolor{GJBlue}{\LARGE Global Journals \LaTeX\ JournalKaleidoscope\texttrademark}
\end{textblock*}

\begin{textblock*}{18cm}(1.4cm,1.5cm) % {block width} (coords) 
\textcolor{GJBlue}{\footnotesize \\ Artificial Intelligence formulated this projection for compatibility purposes from the original article published at Global Journals. However, this technology is currently in beta. \emph{Therefore, kindly ignore odd layouts, missed formulae, text, tables, or figures.}}
\end{textblock*}


\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
he factors for changing the response of LRB are shown in Tab. 1. The properties of LRB vary by several factors. The actual behavior of earthquakes may be different from the expected behavior of the structural design  {\ref [1]}. In Tab. 1, the length of the arrow indicates the change in response. The earthquake reduces the stiffness of laminated rubber bearings and causes large shear deformation. Eventually, fracture deformation occurs beyond the allowable shear deformation \hyperref[b0]{[2]}. However, since the hardening occurs in the high shear deformation region of the laminated rubber bearing, the resistance force is greater than when it is designed without hardening \hyperref[b1]{[3]}. The actual displacement of the laminated rubber bearing of the structure is suppressed than the designed displacement, and it has a result that it is difficult to reach the fracture deformation. Besides, the pier has over strength, and the yield load becomes larger than the expected design. Therefore, the resistance of the pier during an earthquake is strengthened, but a large inertia force acts on the laminated rubber bearing. Moreover, a factor that increases the shear deformation of the laminated rubber bearing during an earthquake is involved statically indeterminate force due to the expansion and contraction of the girder caused by Evaluation of Seismic Performance Focusing on Increasing Response of Lead Rubber Bearing  {\ref (LRB)} and Over Strength of RC Pier During Earthquake Abstract-The characteristics of the seismic bearing change depending on various factors. When an earthquake occurs, the behavior of the bridge may differ from the values expected in the structural design. The shear deformation of the seismic bearing may increase, but it is difficult to reach the fracture deformation. This paper studied the effect of the stiffness due to various dependency and durability on Lead Rubber Bearings (LRB) and the over strength of bridge piers on the bearing behavior when an earthquake occurred. As a result, if the stiffness of LRB reduces within the criteria, seismic performance can be expected safety even if the shear strain designed in the current design is greater than the allowable shear strain. The reason is that the hardening phenomenon in the high strain region of the laminated rubber bearing suppresses the displacement. Also, since the seismic bridges with over strength of the piers have come near elastic behavior when an earthquake occurs, shear strain is easy to be large.\par
temperature changes. This paper proposes that the elongation of girders caused by expansion and contraction cannot ignore the effects of statically indeterminate force on seismic performance \hyperref[b2]{[4,}\hyperref[b3]{5]}. Also, the temperature dependency of the laminated rubber bearing at low temperatures is large \hyperref[b4]{[6,}\hyperref[b5]{7]}. In continuous girder bridges, the performance of laminated rubber bearings installed in each pier differs from the design values by dispersion of inertia forces, and the inertia forces acting on specific bearings, and substructures change. For this reason, it is preferred that the laminated rubber bearing applied to the continuous girder bridges is manufactured in the same manufacturing process as possible so that there is little difference in performance among products \hyperref[b6]{[8]}. On the other hand, because the ground conditions are different from the design expectations, there is a possibility that the seismic performance of the bridge may be lost due to changes in the characteristics of the foundation. This paper focuses on bridges with LRB that increase shear strain during an earthquake, and various cases were analyzed for this examination bridge. The details can be divided into the effect of reducing the deformation of hardening due to the stiffness reduction of LRB during an earthquake, the effect of over strength RC column type pier on the response of LRB and the effect of LRB stiffness increase or decrease in continuous girder bridge. Besides, temperature change, which is a factor in which shear strain of LRB increases, has already been shown in past papers \hyperref[b2]{[4,}\hyperref[b3]{5]}. Also, since the quantified amount of change in the foundation is uncertain and the impact of the change in the condition of the foundation is not expected to be significant when the pier is plasticized, it is not considered in this paper. 
\section[{Overstrength of pier}]{Overstrength of pier}\par
Enhancement of yielding stiffness and yielding load of pier due to execution, aging etc. Non-static stability force due to temperature change Influence to initial load during earthquake due to non-static stability force Aging deterioration of rubber Hardening of rubber by aging Allotment of inertia force on continuous girder Variation of distribution of inertia force caused by bearing, substructure etc. 
\section[{Characteristics of foundation ground}]{Characteristics of foundation ground}\par
Ground property exceeding assumptions  
\section[{Consideration of Factors for Analysis a) Decrease the stiffness of LRB}]{Consideration of Factors for Analysis a) Decrease the stiffness of LRB}\par
In a bridge equipped with laminated rubber bearings such as isolating bearing, there is a possibility that stiffness may be reduced due to the performance differences, dependency, and durability for each product \hyperref[b7]{[9,}\hyperref[b8]{10]}. As a result, the strain of laminated rubber bearings during an earthquake is larger than expected in structural design. The East, Central, and West Nippon Expressway Co., Ltd. defined the limit value of the performance variation due to these factors as R k+ and R k? , and sets limits of +0.30 and -0.15 respectively \hyperref[b9]{[11]}.This value was based on the Standard Specifications for Structure Construction Management (Jul.2012) and was calculated using the formula in Appendix 1. This paper studied the case where the shear modulus of LRB decreased by 15\% as the maximum value and increased by 30\% as the minimum value of the expected stiffness in LRB. In the model of piers that assumed continuous girder bridges, the effect of dispersion was also analyzed by combining the case where the stiffness of LRB between piers was increased by 30\% and the rigidity of LRB was decreased by 15\%. 
\section[{b) Hardening of LRB}]{b) Hardening of LRB}\par
The equivalent shear modulus of elasticity ??(??) for shear cross-sectional deformation in consideration of hardening of LRB by Takahashi et al. is shown in equation (1) \hyperref[b10]{[12]}.The first term ?? ?? (??) in Eq. (1) includes the effect of stiffness increase due to hardening given in Tab. 2. Fig.  {\ref 1}. shows the relationship between ?? ?? (??) and shear strain. The ?? ?? (??) of LRB, G12 in this paper, becomes 1.17 at 250\% of shear strain.The second term used ??(??) in the Manual for Highway Bridges Bearings \hyperref[b0]{[2]}. The performance variation due to the over strength of the piers proposed by Adachi and Unjou et al. is shown in Tab. 3 \hyperref[b11]{[13]}.This table shows the yield stiffness of the pier, the average value of the yield load, and the coefficient of variation. Here, the over strength range was set to three cases: average??, average, and average +? , which has a relatively high incidence.In addition, the maximum, average and minimum values of yield stiffness and yield load occur at the same time, respectively. 
\section[{III.}]{III.} 
\section[{Bridge to be Reviewed}]{Bridge to be Reviewed}\par
The bridge to be reviewed is located on the Type II ground listed in the Reference Design Calculation Examples of Seismic Design for Highway Bridges \hyperref[b12]{[14]}. Fig.  {\ref 2 and 3} show five spans continuous non-composite steel girder bridge. Fig. \hyperref[fig_2]{4} shows the cross-section of the pier. This bridge is equipped with distributed rubber bearings (RB). This research replaces the bearing of the pier from RB to LRB. The crosssectional configuration of the pier was set by adjusting only the arrangement of the bar without changing the dimensions of the cross-section of the pier. The maximum shear strain of LRB is designed to 250\%, the Global Journal of Researches in Engineering ( ) Volume Xx X Issue III V ersion I allowable shear strain. Tab. 4 and 5 show the crosssection configuration of the pier and LRB. Also, Fig. \hyperref[fig_3]{5} shows the historical model of the pier. Tab. 6 shows the maximum shear strain of LRB and the maximum ductility factor of the pier.       
\section[{Review Conditions}]{Review Conditions}\par
In this paper, the purpose of this research is to understand the effect of LRB stiffness reduction on single pillar pier upporting superstructure and the effect for dispersion of inertia force by combined decrease and increase of LRB stiffness on multi-pier during an earthquake. For reference, column type piers and wall type piers are representative types of piers. In this research, the column type pier is used as an analysis model. Fig. \hyperref[fig_4]{6} shows the structural model for the analysis. This structural model is the single pillar supporting beam of the bridge under review in Fig.  {\ref 2}. The analysis method is a nonlinear time historical response analysis. The input seismic waves were three waves of each Type I and Type II seismic wave in the Design Specifications for Highway Bridges part 5, Seismic Design and evaluated by the average of the responses from the three different waves [1].\par
V. The analysis that applies the history set in manual for Highway Bridges Bearings to the hysteresis characteristic of LRB is called the current design. The stiffness, which was decreased by 15\% of LRB, was designed to 0.85 times the shear modulus of the rubber. The resistance force of the laminated rubber of G12 increased by hardening is 1.2 × 1.17 = 1.40 N/mm 2 calculated in Fig.  {\ref 1} with a shear strain of 250\%. The bilinear and trilinear models are typical models considering the hardening of laminated rubber bearings. The bilinear model has a history that LRB behaves as a secondary stiffness concerning a working load equal to or higher than the yield load in the same way as the current design. The trilinear model assumes that the hardening occurs when the shear strain of the bilinear model is 175\% or more, and the resistance is a history that increases linearly with respect to the shear strain. Also, comparison by analysis using the setting formula of LRB proposed by Takahashi et al. was also conducted \hyperref[b10]{[12]}. The Tab. 7 shows the combinations used for the review. The hysteresis characteristics of the increases linearly due to the shear elasticity of the laminated rubber. These hysteresis characteristics were designed in the form of bilinear or trilinear. Fig. \hyperref[fig_6]{7} shows a comparison of the history of LRB used in the analysis. The maximum shear strain was set at 250\%. Convergence analysis using the hysteresis of the maximum shear strain obtained in the analysis is not performed. (a) shows all the cases and (b), (c), (d), (e) show the case where there is no stiffness drop for each hysteresis characteristic and the case where the stiffness decreases by 15\%, respectively.  rubber and lead plugs, which are the results obtained from the analysis, are superimposed and shown in Fig.  {\ref 2}. That is, in the region where the deformation is small, the hysteresis of the lead plug is the main.After the lead plug yields, the resistance force 
\section[{Effect of Hysteresis}]{Effect of Hysteresis} 
\section[{b) Analysis results}]{b) Analysis results}\par
Fig.  {\ref 8} shows the maximum shear strain of LRB and the maximum ductility factor of the pier due to the difference in stiffness and hysteresis of LRB. Fig.  {\ref 9} and Fig.  {\ref 10} show the response history of LRB and the lower part of the pier by seismic waves II-II-1, respectively. 
\section[{c) Effect of the hardening on current design}]{c) Effect of the hardening on current design}\par
The maximum shear strain of LRB, the response history of LRB, and the response history of the lower part of the pier are shown in Fig.  {\ref 11}. To understand the effects of hardening, a bilinear model and a trilinear model considering current design and hardening design were applied. When the analysis is performed using a bilinear model in consideration of the hardening, the maximum shear strain is reduced to 200\%. In contrast, when analyzed using a trilinear model, it is as small as 230\%, which is larger than the bilinear model and smaller than the current design. In the response history, the resistance force of LRB is large in the order of current design, hardening of the bilinear model, and hardening of the trilinear model. Likewise, the curvature of the lower part of the pier shows the same order. 
\section[{d) Effect of the hardening on the current design and 15\% decrease in stiffness}]{d) Effect of the hardening on the current design and 15\% decrease in stiffness}\par
The cases where the stiffness is reduced by 15\%, current design, the maximum shear strain of LRB, the hysteresis of LRB response, and the response of the lower part of the pier in consideration of hardening are shown in Fig. \hyperref[fig_9]{12}. In the current design, the maximum shear strain of LRB is 250\%, but when the stiffness decreases by 15\%, the maximum shear strain may increase to 300\%, resulting in fracture deformation. However, because the shear strain of LRB is suppressed by hardening, the maximum shear strain in the bilinear model is 250\%, which is equivalent to the current design. In contrast, in the trilinear model, the  The comparison of the hardening model and the response of the current design is shown in Fig.  {\ref 13(a}). Fig.  {\ref 13(b}) and (c) show the maximum shear strain of LRB, response history of LRB, and response history of the lower part of the pier when stiffness drop occurs by 15\%. The maximum shear strain of LRB is 250\% in the current design and 300\% when the stiffness is reduced by 15\%. In this paper, the maximum shear strain and LRB response history are the same as those of the current design, but the curvature history of the lower part of the pier is slightly different. This is because the rubber dependence coefficient ?? ?? (??) applied in the process of setting the hardening of the current design is equal to the value set in this paper. However, since the coefficient ??(?) for the lead plugs in the current design uses the values given in Manual for Highway Bridges Bearings, it is considered that the response of this paper and the current design may differ depending on the lead area ratio setting of LRB. When the stiffness decreased by 15\%, it was confirmed that the shear deformation of LRB was larger, and the response period was longer. The maximum shear strain of LRB decreases due to the effect of hardening, but when the hardening is represented by the trilinear model, the maximum yielding load of the pier becomes large. In addition, at 175\% shear strain, the stiffness of the rubber changes rapidly in the trilinear model, but the shear strain of LRB is not large, and a slight change in curvature of the lower part of the pier can be seen. Fig. \hyperref[fig_4]{16} shows the Fourier spectrum due to the displacement of the superstructure to determine the period. Each earthquake waves are predominant during the same period regardless of LRB recording characteristics and reduction in stiffness. In II-II-1, there are three predominant period ranges, in II-II-2, two predominant period ranges, and in II-II-3, a single period range is widely distributed. The reason why the predominant period range is different for each wave is due to the characteristics of the input wave and the nonlinearity of LRB and the pier. Fig. \hyperref[fig_12]{17} shows the period with the maximum value of the Fourier spectrum in each predominant period region. In II-II-1 waves, the period is most predominant at approximately 1.241 seconds. On the contrary, the current design with the bilinear model, which is a model with hardening under constant stiffness, and in case there is a predominant as well at a shorter period of 1.024 seconds.In the II-II-2 wave, the predominant period appears at around 1.138 seconds, but in the current design that does not consider hardening at a stiffness drop of 15\%, the predominant period appears at 1.575 seconds. In the II-II-3 wave, the period is mostly same predominant in all cases at 1.280 seconds. This predominant response period should be considered based on not only the difference in seismic waves but also the difference in hysteresis due to stiffness reduction or hardening.   was a remarkable difference in the response history of LRB between the bilinear model and the trilinear model, and the trilinear model showed a larger shear strain than the bilinear model. This reason can be confirmed from each set history shown in Fig. \hyperref[fig_11]{18}. The resistance of LRB increases with increasing maximum shear strain. As shown in Fig. \hyperref[fig_11]{18}(b), when the maximum shear strain is less than 250\%, the resistance force of the trilinear model is less than that of the bilinear model when the shear strain is the same. This means that with the same resistance force, the shear deformation of the trilinear model becomes larger than that of the bilinear model. The maximum shear strain of the hysteresis set in this analysis is 250\%. Since this is different from the maximum shear strain in the results of the dynamic analysis, clearly the trilinear model cannot be a large response unless the maximum shear strain to determine the hysteresis converges. The maximum shear strain of the bilinear model is about 250\% of the response history of LRB with reduced stiffness of 15\% shown in Fig. \hyperref[fig_13]{18(c}). Since this shear strain is consistent with the value set in the analysis, there is no need to reset the hysteresis shape due to the maximum shear strain. On the contrary, since the response history of the trilinear model is larger than 250\%, it is necessary to converge the history shape to the response history. At this point, the response of the trilinear model is larger than that of the bilinear model. Likewise, it can be seen that the response of the trilinear model is greater for the curvature of the lower part of the pier in Fig.  {\ref 11}. 
\section[{g) The difference in response between the bilinear model and the trilinear model}]{g) The difference in response between the bilinear model and the trilinear model} 
\section[{h) Response waveform and predominant period}]{h) Response waveform and predominant period}\par
Tab. 8 shows the maximum values of displacement and resistance force at the time of maximum shear strain in Fig. \hyperref[fig_2]{14}. In addition, this table contains the equivalent damping ratio for the response history of the bilinear model and the trilinear model, and the correction factor for each equivalent damping ratio. The absorbed energy was calculated as the historic area of one cycle. Fig. \hyperref[fig_14]{19} shows the energy absorbed by LRB during inputting the seismic wave. When calculating the equivalent damping constant, the strain energy was adjusted to an average value so that the starting point and the ending point could be one cycle. The absorbed energy is large in the trilinear model, but the equivalent damping constant is large in the bilinear model. The reason is that the resistance force and theelastic energy of the trilinear model are relatively larger than the bilinear model in the same shear strain.  
\section[{i) Consideration of LRB stiffness drop and response history in design}]{i) Consideration of LRB stiffness drop and response history in design}\par
The average of three seismic waves was evaluated in the current design. Depending on the seismic wave, there were some cases where the shear strain was greater than 250\%. In particular, Fig.  {\ref 11-(a)} shows that the shear strain is about 290\% in II-II-3 of the current design. This means that the shear strain of LRB exceeds 250\% and approaches the fracture strain. On the contrary, when analyzed with a bilinear model considering hardening, the maximum shear strain among the three seismic waves is about 230\%. Since it is within 250\% of the allowable shear strain, the analysis results can be sufficiently reliable. Therefore, after analyzing the response of LRB in the current design, it is better to verify it using a bilinear model that considers the hardening and to confirm the fact that the shear strain of LRB is less than 250\%. On the other hand, the trilinear model can be used to analyze the hardening phenomenon, but before that, it is necessary to verify the validity of the tertiary stiffness of LRB in the shear strain exceeding 250\%. 
\section[{VI.}]{VI.}\par
The Impact  
\section[{a) Setting of the pier}]{a) Setting of the pier}\par
To confirm the impact of the over strength of the pier on the response during an earthquake, a pier with a small plasticization with a maximum ductility factor of 1.351 (abbreviation as pier with ?? = 1.351) used in Tab. 6 and two piers with a ductility factor of 2.005 and 3.316 (abbreviation as pier with ?? = 2.005 , ?? = 3.316 ) were added. Tab. 9 shows the conditions of these three piers and each set LRB. A pier with a high ductility factor was added to investigate the effect of plasticization due to over strength of piers on the behavior of LRB during an earthquake. The maximum ductility factor of the added pier does not satisfy the allowable ductility factor, but the purpose is to understand the effect of the high ductility factor due to over strength on the pier. In this paper, pier characteristics were determined based on the amount of change in over strength. The characteristics of the pier were divided into 4 cases: the 'standard value' without considering the over strength, the 'average value' with the over strength considered, and finally, the '±?' considering the standard deviation. Also, the yield stiffness and yield load of the pier were set in the order of standard value, ??, average value, and +?. The ratio of yield load was set to 1.00: 1.07: 1.14: 1.21. 
\section[{b) Analysis result}]{b) Analysis result}\par
The maximum shear strain of LRB and the maximum ductility factor of the pier with seismic waves of level 2 seismic Type I and Type II are shown in Fig.  {\ref 20}. The horizontal axis represents the yield stiffness and yield load of each pier. In addition, even when the pier has an elastic response, the value obtained by dividing the maximum displacement of the pier by the yield displacement was defined as the ductility factor. The over strength is evaluated as the average of the responses by three seismic waves.   
\section[{Fig. 20: Response including influence of over strength c) Effect on the maximum shear strain of LRB}]{Fig. 20: Response including influence of over strength c) Effect on the maximum shear strain of LRB}\par
As shown in Fig.  {\ref 20}, since the pier behaves elastically in Type I, the pier yield load does not affect the maximum shear strain of LRB. However, because the yield stiffness and over strength are increasing at the same time, the maximum shear strain of LRB changes slightly. The following is a review of the response of Type II. In Fig.  {\ref 20}, in the pier with ?? = 1.351 , the maximum shear strain of LRB increases as the yield load becomes ?? to the standard value, but at the average value, +? , the yield load increases and the shear strain decreases. In contrast, the ?? = 2.005 pier has an overall constant shear strain of LRB. Finally, for a pier with ?? = 3.316, the yield load and the maximum shear strain of LRB are proportional. In general, when the pier is plasticized, the maximum acting force of the rubber bearing becomes large, depending on the yield load of the pier. For this reason, the maximum shear strain of LRB of a pier with large plasticization and ?? = 3.316 is consistent with the general behavior. On the other hand, when the yield load of the pier increases, the maximum ductility factor of the pier necessarily decreases. As a result, the maximum ductility factor of pier with ?? = 3.316 at large plasticization decreases linearly due to the increase in the yield load of the pier. However, the trends of the pier with ?? = 1.351and pier with ?? = 2.005 are different. The reason is that at the pier with ?? = 1.351, the average yield load and the maximum ductility factor of +?are less than 1.0 and have the elastic response. That is, since the pier is not plasticized, the yield load of the pier does not directly affect the maximum shear strain of LRB. The pier with ?? = 2.005 is in a plasticized state due to over strength, but the maximum shear strain of LRB shows a different result from that of the pier with ?? = 3.316 because there is little change due to over strength. 
\section[{Fig. 21: Dynamic correction factor d) Dynamic correction factor}]{Fig. 21: Dynamic correction factor d) Dynamic correction factor}\par
The dynamic correction factor is calculated by dividing the maximum resistance force of LRB by the yield load of the pier. When the pier with ?? = 3.316in Fig.  {\ref 21(b}) is plasticized, the dynamic correction factor does not change significantly even if the yield load of the pier increases. In contrast, the dynamic correction factors for pier with ?? = 1.351 and ?? = 2.005 decrease with increasing yield load. In addition, when the yield load is the average value and +? , the dynamic correction factor is less than 1.0, which means that acting force is less than the yield load. In ?? = 1.351pier, the pier behaves elastically and ?? = 2.005 pier is plasticized, but the force acting on LRB is smaller than the yield load. For this reason, the increase in yield load did not significantly affect the maximum shear strain of LRB. This factor is considered to be caused by the inertia of the pier itself and the vibration mode of the second or higher order. 
\section[{e) Evaluation of LRB for over strength}]{e) Evaluation of LRB for over strength}\par
In the seismic isolation bridge, the plasticization of the lower part of the pier is suppressed. However, it was confirmed that the maximum shear strain of the bearing did not necessarily increase even if the yield load increased due to over strength. Since the specifications of the designed bridge are varied, the effects of over strength are different. Therefore, it is necessary to investigate the effect of over strength on the response for each bridge. Meanwhile, the dynamic correction factor in Fig.  {\ref 21(a}) is a vibration system using a pier with ?? = 1.351, and there is little change in the dynamic correction factor due to the elastic response of the seismic wave. On the contrary, when the hardening of LRB is analyzed with a trilinear model, the dynamic correction factor is increasing. This is because the force on the pier was increased by the trilinear model. As a result, it is larger than the case of applying the bilinear model. 
\section[{f) Effect of over strength to the lower part of the pier}]{f) Effect of over strength to the lower part of the pier}\par
In general, the yield load of the lower part of the pier is designed to be more than 1.1 times the yield load of the pier, so that the lower part of the pier does not yield before the pier. However, if the yield load of the lower part of the pier is exceeded due to over strength, there is a concern that the lower part of the pier will yield first. Fig. \hyperref[fig_17]{22} shows the relationship between the bending moment and the yield bending moment of the lower part of the pier considering the over strength of the pier. As a result, the bending moment of the lower part of the pier is difficult to increase and slightly exceeds 1.1 times the yield bending moment of the pier without the effect of over strength. Therefore, the maximum shear strain of LRB of the seismic isolation bridge, where plasticization of the pier is suppressed, is not affected by the overstrength, but it is necessary to consider the safety of the lower part of the pier separately. 
\section[{VII.}]{VII.} 
\section[{Influence of Dispersion in}]{Influence of Dispersion in}\par
Multi-Span Girders a) Pier model to be reviewed The framework of the girders of the two single column bridge piers and four single pillar pier supporting superstructure, which are the models to be  However, the shear strain of 0.85 does not increase in the case where the 1.30 model increases from the four pier models to three. This is considered to be because the inertia force of the superstructure is concentrated at 1.30. On the other hand, the response of the lower part of the pier is largely plasticized in the 1.30, but plasticization hardly occurs in the 0.85. In particular, in the case of one 1.30 among the four pier models, an extremely large plasticization occurs because most of the inertia force of the superstructure is concentrated only in this pier. However, the response change of LRB is not much different compared to the plasticization of the lower part of the pier. This means that it is difficult to concentrate the load on LRB due to the plasticization of the pier, but the seismic energy is largely consumed as the plasticization of the lower part of the pier proceeds. The time history response resistance waveform of LRB and the time history response curvature at the lower part of the pier are shown in Fig. \hyperref[fig_6]{27} and 28. In the time history response waveform, there is no significant difference in the resistance waveform of each model's LRB. In contrast, the curvature of the time history response at the lower part of the pier varies greatly for each pier. Particularly, when the residual variation at the 1.30 pier is large and there is only one 1.30 model, quite large residual variation occurs. The comparison of the shear strain of LRB, the bending moment of the lower part of the pier, and the ductility factor of the lower part of the pier between models are shown in Fig.  {\ref 29}, Fig.  {\ref 30} and Fig.  {\ref 31}, respectively. From this, it can be seen that when the rigidity of the 1.30 model and LRB is increased, the response of LRB decreases, but on the contrary, the plasticization of the lower part of the pier becomes large. In conclusion, if there is a difference in the performance of LRB for each pier, it gives a significant effect in the plasticization of LRB and the lower part of the pier, and has a greater effect on the pier. Although the results of this research are extreme cases, it is desirable to make LRB installed at each pier in the same manufacturing process as much as possible so that there is no difference in performance of LRB.  
\section[{Conclusion}]{Conclusion}\par
Based on the analysis results presented in this paper, the main conclusions are as follows:\par
1. Considering the hardening of LRB in the current design reduces the maximum shear strain of LRB. In the current design, the maximum shear strain is about 250\%, but in the bilinear model and the trilinear model considering hardening, it is reduced to 200\% and 230\%, respectively. In general, as in this paper, when considering hardening, the maximum shear strain of LRB is set to be larger for the trilinear model than for the bilinear model. 2. Suppose the maximum shear strain of LRB is designed to be 250\% according to the current design, considering the decrease in stiffness of 15\%, the maximum shear strain of LRB increases to about 300\%, so there is a risk of fracture. However, the hardening phenomenon must occur and it becomes difficult to fracture because the shear strain is reduced to about 250\% when considered in the bilinear model. In contrast, in the trilinear model, the shear strain is about 270\%, which is greater than the allowable shear strain 250\%. In conclusion, when designing in consideration of hardening, it is necessary to review the modeling method of hardening. 3. It is necessary to understand that in a seismic isolation bridge, the predominant period depends not only on the difference in seismic waves but also on LRB hysteresis setting and nonlinearity. 4. When the allowable ductility factor of the pier is set to be small, such as a seismic isolation bridge, it is expected that the effect of the over strength of the pier on the maximum shear strain of LRB is small. On the contrary, in the design of plasticizing piers largely, it is necessary to pay attention to the increase in the maximum shear strain of the bearings due to the over strength of the piers.\par
Based on the results presented in this paper, it was confirmed that LRB performance in the current design of LRB is difficult to become larger than the expected response in the design due to the hardening occurring in the high deformation region even if the stiffness decreases due to various dependencies or durability. In addition, in the seismic isolation design with limited plasticization of the pier, the effect of the over strength of the pier was found to be small. In conclusion, it means that when the seismic isolation design according to the current design is applied in the actual design, the response of LRB due to the performance change of the bearing (LRB) or the over strength of the pier does not significantly exceed the allowable shear deformation. 5. If the stiffness of LRB between piers is different from the design value, the response of LRB with small stiffness increases due to the difference, or the piers with LRB with high stiffness are large plasticized. This means that it is different from the expected value of the design. There are various factors for fluctuations in LRB between piers. Therefore, it is important to manufacture in the same manufacturing process as LRB used in the same pier in order not to cause a relative difference in LRB between piers. 
\section[{IX.}]{IX.} 
\section[{Afterword}]{Afterword}\par
In this paper, LRB seismic safety was evaluated in cases where the stiffness of LRB is smaller than the design stiffness and the yield load of the pier is increased by selecting a single column pier model in a bridge using LRB. In this regard, if the stiffness of LRB is greater than the design expected, there is a possibility that a large inertia force acts on the pier and the safety of the pier is lost when the earthquake occurs. However, in general, the design of piers has a greater allowance during an earthquake than LRB, and the yield load of piers due to over strength is greater than the value determined in the design. In addition, since the earthquake safety factor of the seismic isolation designed pier is twice that of the distributed bearing (RB), it is thought that there is a large allowance for the safety during an earthquake, but it is important to note that an earthquake behavior of the seismic isolation bridge is not necessarily guaranteed. For this reason, it is necessary to evaluate the safety of the pier by increasing the response of the pier of the seismic isolation bridge. In addition, a case study was conducted on the effect of the stiffness change of LRB between piers on the dispersion of the inertia force of the continuous girder. Depending on the pier, there are various factors that affect the stiffness of LRB. Therefore, it is important to manufacture LRB in the same manufacturing process so that stiffness does not change. In this paper, the statically indeterminate force due to temperature change and the characteristics of the foundation were not verified as factors that increase the response of the seismic isolation bearing. Among them, temperature change is a clearly occurring phenomenon, and if the length of the extension girder is long, like a multi-span continuous girder bridge, the effect on the earthquake response at low and high temperatures is clearly evident. Most of the statically indeterminate force is generated by plasticizing the pier, which increases the ductility factor and residual displacement of the pier, and also increases the response variation and residual displacement of the bearing. This means that bridges that are likely to have increased the statically indeterminate force need to check their behavior during an earthquake in the state of deformation when the temperature changes. In addition, since the temperature change affects the hysteresis characteristics of the bearing, it is preferable to use the hysteresis shape in consideration of these factors. However, in general, it is not necessary to consider a bridge that is not long because the temperature change has a small effect on the response during an earthquake. On the other hand, the variation in the dispersion of the inertia force of the continuous girder is likely to be influenced by the performance variation of the seismic isolation bearing of the pier. Therefore, in order to reduce the relative performance fluctuation between the seismic isolation bearings, it is necessary to make the manufacturing lot of the seismic isolation bearing used in the bridge almost identical. As a result, it can be expected that the effect on the horizontal force distribution of the continuous girder is reduced and the behavior is difficult to damage during an earthquake determined in the structural design \hyperref[b6]{[8]}. The influence of the characteristics of the foundation of the ground is expected to vary widely. Therefore, since it is difficult to set design conditions, it is necessary to prevent ground fluctuations from affecting the response during an earthquake through secondary plasticization of piers like a seismic isolation bridge. 
\section[{A ppendix}]{A ppendix}\par
Formula for R k in East, Central and West Japan Expressway co., Ltd. Construction Management Guidelines \hyperref[b9]{[11]} ?? ??+ = + ? ??? ??(?????????????? ) ? Where each R k is the ratio representing the change in various factors.\begin{figure}[htbp]
\noindent\textbf{3234}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Table 3 :?Fig. 2 :Fig. 3 :Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-3.png}
\caption{\label{fig_2}Fig. 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5}\includegraphics[]{image-4.png}
\caption{\label{fig_3}Fig. 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-5.png}
\caption{\label{fig_4}Fig. 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_5}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Fig. 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_7}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{89111314}\includegraphics[]{image-9.png}
\caption{\label{fig_8}Fig. 8 :Fig. 9 :Fig. 11 :Fig. 13 :Fig. 14 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{12}\includegraphics[]{image-10.png}
\caption{\label{fig_9}Fig. 12 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{15}\includegraphics[]{image-11.png}
\caption{\label{fig_10}Fig. 15 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{18}\includegraphics[]{image-12.png}
\caption{\label{fig_11}Fig. 18 (}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{17}\includegraphics[]{image-13.png}
\caption{\label{fig_12}Fig. 17 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{18}\includegraphics[]{image-14.png}
\caption{\label{fig_13}Fig. 18 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{19}\includegraphics[]{image-15.png}
\caption{\label{fig_14}Fig. 19 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-16.png}
\caption{\label{fig_15}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-17.png}
\caption{\label{fig_16}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{22}\includegraphics[]{image-18.png}
\caption{\label{fig_17}Fig. 22 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{23102427}\includegraphics[]{image-19.png}
\caption{\label{fig_18}Fig. 23 :Table 10 :Fig. 24 :Fig. 27 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.25625\textwidth}P{0.0875\textwidth}P{0.11875\textwidth}P{0.13125\textwidth}P{0.25625\textwidth}}
\multicolumn{2}{l}{Application condition}\tabcellsep a 0\tabcellsep a 1\tabcellsep a 2\\
??1.75\tabcellsep Common\tabcellsep 1\tabcellsep -\tabcellsep -\\
\tabcellsep G8\tabcellsep 0.905\tabcellsep 0.028\tabcellsep 0.015\\
1.75???2.50\tabcellsep G10\tabcellsep 1.046\tabcellsep -0.161\tabcellsep 0.077\\
\tabcellsep G12\tabcellsep 1.049\tabcellsep -0.203\tabcellsep 0.100\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep Fig. 1: Cr (?) for LRB\\
II.\tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_0}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.660875\textwidth}P{0.082875\textwidth}P{0.10625\textwidth}}
Item\tabcellsep Unit\tabcellsep Value\\
Usable dimension (bridge axial direction)\tabcellsep mm\tabcellsep 735\\
Usable dimension (bridge perpendicular direction)\tabcellsep mm\tabcellsep 735\\
Monostromatic thickness\tabcellsep mm\tabcellsep 32\\
Number of layers\tabcellsep Sheet\tabcellsep 4\\
Total thickness of rubber\tabcellsep mm\tabcellsep 128\\
Elastic shear modulus of rubber\tabcellsep N/mm2\tabcellsep 1.2\\
Diameter of lead plug\tabcellsep mm\tabcellsep 106\\
Number of lead plugs\tabcellsep number\tabcellsep 4\\
The first shape factor\tabcellsep -\tabcellsep 5.367\\
The second shape factor\tabcellsep -\tabcellsep 5.742\\
Modulus of longitudinal elasticity\tabcellsep N/mm2\tabcellsep 290\\
Effective area\tabcellsep mm2\tabcellsep 504926\\
Area of lead plugs\tabcellsep mm2\tabcellsep 35299\\
Occupation ratio of lead plugs\tabcellsep -\tabcellsep 0.070\\
Yielding load\tabcellsep kN\tabcellsep 294.3\\
Shear spring constant (horizontal rigidity)\tabcellsep kN/m\tabcellsep 4734\\
Pressure spring constant (vertical rigidity)\tabcellsep kN/m\tabcellsep 1143252\\
Shear stress of lead plug\tabcellsep N/mm2\tabcellsep 2.0\\
Design displacement\tabcellsep Mm\tabcellsep 320\\
Design strain\tabcellsep \%\tabcellsep 250\\
Horizontal force\tabcellsep kN\tabcellsep 1584\\
First rigidity\tabcellsep kN/m\tabcellsep 26198\\
Second rigidity\tabcellsep kN/m\tabcellsep 4030\\
Equivalent rigidity\tabcellsep kN/m\tabcellsep 4950\\
Equivalent damping coefficient\tabcellsep -\tabcellsep 0.113\end{longtable} \par
 
\caption{\label{tab_1}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.1877083333333333\textwidth}P{0.13458333333333333\textwidth}P{0.27979166666666666\textwidth}P{0.24791666666666667\textwidth}}
\tabcellsep \tabcellsep LRB\tabcellsep \\
Input\tabcellsep \tabcellsep maximum\tabcellsep Pier maximum\\
\multicolumn{2}{l}{seismic wave}\tabcellsep shear strain\tabcellsep ductility factor\\
\tabcellsep \tabcellsep (\%)\tabcellsep \\
\tabcellsep I-II-1\tabcellsep 128\tabcellsep 0.700\\
Type I\tabcellsep I-II-2 I-II-3\tabcellsep 119 110\tabcellsep 0.714 0.710\\
\multicolumn{2}{l}{Average}\tabcellsep 119\tabcellsep 0.708\\
\tabcellsep I-II-1\tabcellsep 241\tabcellsep 1.428\\
Type II\tabcellsep I-II-2 I-II-3\tabcellsep 215 289\tabcellsep 1.179 1.448\\
\multicolumn{2}{l}{Average}\tabcellsep 248\tabcellsep 1.351\\
\multicolumn{2}{l}{Allowable}\tabcellsep \multicolumn{2}{l}{250\%(320mm) 1.695(0.0449m)}\end{longtable} \par
 
\caption{\label{tab_2}Table 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{P{0.09391608391608391\textwidth}P{0.03923076923076923\textwidth}P{0.07132867132867134\textwidth}P{0.26986013986013985\textwidth}P{0.08916083916083915\textwidth}P{0.13314685314685315\textwidth}P{0.15335664335664337\textwidth}}
Application\tabcellsep High strain region\tabcellsep Hysteresis shape\tabcellsep Setting of shear modulus of rigidity (N/mm2)\tabcellsep Resistance 250\%(kN) force on\tabcellsep \multicolumn{2}{l}{Abbreviation}\\
Handbook of bearing Conformity to handbook\tabcellsep Linear\tabcellsep Bilinear model\tabcellsep 1.2 1.2×0.85=1.02 1.2×1.17=1.404 1.2×0.85×1.17=1.1934\tabcellsep 1,584 1,357 1,842 1,576\tabcellsep H-Li-Bi-1.0 H-Li-Bi-0.85 H-HD-Bi-1.0 H-HD-Bi-0.85\tabcellsep H: handbook L: literature Li: linear HD: hardening Bi: bilinear\\
of bearing ? Literature\tabcellsep Hardening\tabcellsep Trilinear model Bilinear model\tabcellsep 1.2×1.17=1.404 1.2×0.85×1.17=1.1934 1.2×1.17=1.404 1.2×0.85x1.17=1.1934\tabcellsep 1,842 1,576 1,836 1,571\tabcellsep H-HD-Tri-1.0 H-HD-Tri-0.85 L-HD-Bi-1.0 L-HD-Bi-0.85\tabcellsep Tri: trilinear 1.0: non-rigid reduction 0.85: rigid reduction-15\%\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{4}{l}{?Conformity means including hardening behavior for handbook}\\
IV.\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_3}Table 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{P{0.03296795952782462\textwidth}P{0.3698145025295109\textwidth}P{0.06306913996627318\textwidth}P{0.05016863406408094\textwidth}P{0.0745362563237774\textwidth}P{0.05160202360876897\textwidth}P{0.05733558178752107\textwidth}P{0.0802698145025295\textwidth}P{0.07023608768971332\textwidth}}
\tabcellsep \tabcellsep \multicolumn{2}{l}{Time Displacement}\tabcellsep Resistance force\tabcellsep Absorbed energy ?W\tabcellsep Equivalent damping constant, h\tabcellsep Correction factor based on damping\tabcellsep Equivalent damping constant at 250\%, h\\
\tabcellsep \tabcellsep sec\tabcellsep m\tabcellsep kN\tabcellsep kN?m\tabcellsep \%\tabcellsep constant, CD\tabcellsep \%\\
\tabcellsep Time on minimum\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep response just before\tabcellsep 5.95\tabcellsep -0.199\tabcellsep -6,286\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep maximum response\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
H-HD-Bi-1.0\tabcellsep Time on maximum displacement\tabcellsep 6.56\tabcellsep 0.257\tabcellsep 7,684\tabcellsep 1,335.2\tabcellsep 13.0\tabcellsep 0.743\tabcellsep 10.7\\
\tabcellsep Time on minimum\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep response just after\tabcellsep 7.16\tabcellsep -0.208\tabcellsep -6,502\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep maximum response\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep Time on minimum\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep response just before\tabcellsep 5.98\tabcellsep -0.231\tabcellsep -6,211\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep maximum response\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
H-HD-Tri-1.0\tabcellsep Time on maximum displacement\tabcellsep 6.57\tabcellsep 0.297\tabcellsep 8,436\tabcellsep 1,508.1\tabcellsep 12.1\tabcellsep 0.757\tabcellsep 10.2\\
\tabcellsep Time on minimum\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep response just after\tabcellsep 7.20\tabcellsep -0.235\tabcellsep -6,358\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep maximum response\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}Table 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.30122807017543857\textwidth}P{0.5487719298245614\textwidth}}
The correction factor for each equivalent damping\tabcellsep 0.014.Still it does not indicate a difference in the\\
constant is slightly larger in the bilinear model as\tabcellsep decrease in response due to the damping performance.\\
\tabcellsep ( ) Volume Xx X Issue III V ersion I E\\
\tabcellsep of Researches in Engineering\\
\tabcellsep Global Journal\end{longtable} \par
 
\caption{\label{tab_5}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9} \par 
\begin{longtable}{P{0.17\textwidth}P{0.357\textwidth}P{0.323\textwidth}}
Basis pier\tabcellsep Middle ductility pier\tabcellsep Much ductility pier\end{longtable} \par
 
\caption{\label{tab_6}Table 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
  {\small\itshape [Note: 2+??? ??(?????????????????????? ð??"ð??"??????ð??"ð??"???? ) ? + ??? ??(????????? ð??"ð??"??????ð??"ð??"???? ) ?? -0.1]} 
\caption{\label{tab_7}}\end{figure}
 			\footnote{Evaluation of Seismic Performance Focusing on Increasing Response of Lead Rubber Bearing (LRB) and Over Strength of RC Pier During Earthquake} 			\footnote{© 2020 Global Journals} 			\footnote{© 2020 Global Journals Evaluation of Seismic Performance Focusing on Increasing Response of Lead Rubber Bearing (LRB) and Over Strength of RC Pier During Earthquake} 		 		\backmatter  			 			 			  				\begin{bibitemlist}{1}
\bibitem[Nakamura K et al. ()]{b5}\label{b5} 	 		‘Characteristic Value at Ambient Temperature Considering Self-heating and Study of Temperature rise During Earthquake of High Damping Rubber Bearing’.  		 			Nakamura K 		,  		 			Imai T 		,  		 			Y Okui 		,  		 			Sato T 		.  	 	 		\textit{Proc. of the 71th JSCE Annual Meeting},  				 (of the 71th JSCE Annual Meeting)  		2016. p. 215.  	 
\bibitem[East et al. (2016)]{b9}\label{b9} 	 		 			Central East 		,  		 			West Japan Expressway Co 		,  		 			Ltd 		.  		\textit{Standard Specifications for Structure Construction Management},  				2016. Jul 12.  	 
\bibitem[Adachi Y ()]{b11}\label{b11} 	 		‘Effect of Variations in Equivalent Stiffness and Damping Coefficient of Isolation Bearing on Seismic Response Characteristics of Road Bridges’.  		 			Unjoh S Adachi Y 		.  	 	 		\textit{Proc. Of the 4th Symposium on Ductility Design Method for Bridges},  				 (Of the 4th Symposium on Ductility Design Method for Bridges)  		2000. JSCE.  	 
\bibitem[Mazda T et al. ()]{b2}\label{b2} 	 		‘Evaluation on dynamic response of bridges considering expansion and contraction of girder’.  		 			Mazda T 		,  		 			H Uno 		,  		 			Yunoki K Miyamoto H 		.  	 	 		\textit{Proc. of},  				 (of)  		2008. Japan Concrete Institute. p. .  	 	 (30?No.3? pp) 
\bibitem[Kosaka A et al. ()]{b7}\label{b7} 	 		‘Experimental Study on Durability of Lead Rubber Bearing for Road Bridges’.  		 			Kosaka A 		,  		 			Inoue K 		,  		 			Senda T 		,  		 			H Hichido 		,  		 			Imai T 		.  	 	 		\textit{Proc. of the 58th JSCE Annual Meeting},  				 (of the 58th JSCE Annual Meeting)  		2013. p. 371.  	 
\bibitem[Hichinohe H et al. ()]{b8}\label{b8} 	 		‘Experimental Study on Performance Stability of Lead Rubber Bearing for Road Bridges’.  		 			Hichinohe H 		,  		 			Kuji S 		,  		 			H Uno 		,  		 			Kosaka A 		,  		 			Imai T 		.  	 	 		\textit{Proc. Of the 58th JSCE Annual Meeting, I-370},  				 (Of the 58th JSCE Annual Meeting, I-370)  		2013.  	 
\bibitem[Handbook on Design and Execution of No-Joint construction Methods for existing bridges Road Management Technology Center ()]{b6}\label{b6} 	 		‘Handbook on Design and Execution of No-Joint construction Methods for existing bridges’.  	 	 		\textit{Road Management Technology Center}  		1995.  	 
\bibitem[Uno H et al. ()]{b3}\label{b3} 	 		‘Influences to Seismic Behavior for Isolation Bridge and Non-Isolation Bridge under Temperature Changes’.  		 			Uno H 		,  		 			Mazda T 		,  		 			H Miyamoto 		,  		 			Yunoki K Chou S 		,  		 			Shinoda R 		.  	 	 		\textit{Proc. of the 13th Symposium Tokyo, Japan Association for Earthquake Engineer},  				 (of the 13th Symposium Tokyo, Japan Association for Earthquake Engineer)  		2010.  	 
\bibitem[Manual for Highway Bridges Bearings ()]{b0}\label{b0} 	 	 	 		\textit{Manual for Highway Bridges Bearings},  				2004.  	 
\bibitem[Part1 Design and Construction, Design and Construction Guidelines for Steel Road Bridges in Hokkaido ()]{b4}\label{b4} 	 		\textit{Part1 Design and Construction, Design and Construction Guidelines for Steel Road Bridges in Hokkaido},  		2012.  		 			Steel Road Bridge Research Committee of Hokkaido Civil Engineering Society 		 	 
\bibitem[Reference for Highway Bridge Seismic Design Japan Road Association ()]{b12}\label{b12} 	 		‘Reference for Highway Bridge Seismic Design’.  	 	 		\textit{Japan Road Association}  		1997.  	 
\bibitem[Naito N et al. ()]{b1}\label{b1} 	 		‘Seismic Performance Evaluation of LRB Considering Mullins Effect and Hardening’.  		 			Naito N 		,  		 			Mazda T 		,  		 			H Uno 		,  		 			Kawakami M 		.  	 	 		\textit{Proc. Of JSCE},  				 (Of JSCE)  		2017. 73 p. .  	 
\bibitem[Takahashi Y and Shinohara S ()]{b10}\label{b10} 	 		‘Upgrading of Seismic Isolation Bearing Analysis Model’.  		 			Takahashi Y 		,  		 			Hosikuma J Shinohara S 		.  	 	 		\textit{Proc. ofthe17th Symposium on Performance-based Seismic Design Method for Bridges},  				 (ofthe17th Symposium on Performance-based Seismic Design Method for Bridges)  		2014.  	 
\end{bibitemlist}
 			 		 	 
\end{document}
