Prefabrike öngermeli ve betonarme kirişli karayolu köprülerinin bilgisayar yardımıyla boyutlandırılması

Abstract

Bu çalışmada, Prefabrike Öngermeli ve Betonarme Kirişli karayolu köprülerinin bilgisayar yardımıyla projelendirilmesi için bir algoritma geliştirilmiştir. Çalışma beş bölümden oluşmaktadır. Birinci bölümde çalışmanın gerekçeleri ve kullanılan şartname hakkında bilgi verilmiş, çalışmanın sınırları belirtilmiştir. İkinci bölümde araştırmaya esas şartnamenin bir özeti verilerek dayandığı temel ilkelerden bahsedilmiştir. Üçüncü bölümde geliştirilen programın esasları, giriş-çıkış bilgileri ve formatları ile ayrıntılı akış diyagramları verilmiştir. Dördüncü bölümde geliştirilen program kullanılarak çözülmüş iki adet örnek verilmiştir. Son bölümde ise elde edilen sonuçlar verilmiştir.

in this study, a computer program had been developed for the bridges which have prefabricated prestressed ör reinforced concrete girders on the highways.This study consists of five parts; in the fırst part, aim of this study and the provisions are explained. in the second part, the specifications in the many of countries are discussed. in the third part, the principle of the developed program, input data, outputs and the flow chart of the program are given. in the fourth part, two examples are solved by using the developed program and in the conclusions the final results are discussed. At recent years, in our country many higvvays are erecting. There are many bridges on these highways. These bridge must be designed and built as soon as possible to solve the transportation difficulties. in this study, it is developed a computer program that is provide fast and reliable solutions for the bridges include prestressed ör reinforced concrete girders. This program contains of 8 main and 5 auxiliary programs. The main program names are Prokesit, Proger, Cam, Kesme, Ultimate, Proayk, Ayak and auxiliary are programs are Mxmy, Çiz, Kesitciz, Donat, Editac. Specifications using in this study are AASTHO (American Association of State Highway and Transportation Officials) [1] and Guide Specifications for Seismic Design of Highways Bridges [2]. This specifications can be used for bridges with conventional steel, concrete girders and box section that is notexceed 150 m. Some basic assumptions are;. Strains vary linearly. Before cracking stress is proportional to strain. After cracking, tension in concrete is neglected. in general, it can be said that this program has a modular system that we can run each program separately ör ali program can be run via the main menu. This program needs 3 input data files to obtain ali of the results. Öne of them contains of bridge and girders general knowledge's. For example girder span length, road width, girder spacing, asphalt, girder concrete and slap concrete density, dead ör live loads, prestress steel knowledge's e.g. This data file is the main file that has DAT extention and uses ali of the other programs. Other two data files contain foundation and xiv abutments knovvledge's for seismic design. We 'II define these data file discussing Proayk and Ayak Programs. Before the explaining of the programs, it will be discussed some general things used in ali of the programs. Two files called Key.lnı and Color.Dat must be on working directory. If the programs don't find the above files gives the error message and create the default files. Now, we shall clarify main 8 programs. The first program is Prokesit.Exe that provides girder and composite section geometric properties and dead loads consist of girder, slab, asphalt and the other things that we can define freely. We find geometrical properties using following formulas. This program knows three type sections given in figüre 1., 0.0 0.0 "-0 l T f h y.. ^ ^ LJ i , Figüre. 1 Typical sections using the program Girder section area is found in the following formula using section corner coordinates; M\X(.I,J).Y(I,J + V)-Y(I,J).X(I,J+\)~ Area(I)=f4 - . Sy(l) = -[T Z. X(W).Y(U + 1)-Y(U).X(U + 1) )(X(U) + X(I,J + 1)) 6[vJ=1 / J Sx(l) = -[f T. X(U).Y(U + 1)-Y(U).X(U + 1)|(Y(U) + Y(I,J + 1)) 6 [\J=1 J J Moments of inertia about x and y axis are found in the follovving formulas lx(l) = - [f v X(I,J).Y(I,J + 1)-Y(I,J).X(I,J + 1)Y(Y(I,J) + Y(I,J + 1))2-Y(I,J).Y(I,J + 1)>) 12|_vJ=1 A 'J ly(l) = - [f Z X(I,J).Y(I,J + 1)-Y(!,J).X(I,J + 1)Y(X(I,J) + X(I,J + 1))2-X(I,J).X(I,J + 1)J XV 1 Ff M \ v * lxys(l) = - ZX(l,J).Y(l,J +1) - Y(l,J).X(l,J +1) (X(l,J) + X(l, J + 1))(Y(I,J) + Y(I,J +1)} 12LU = 1 i --(X(!,J).Y(I,J + 1) + Y(I,J).X(I,J + 1)) Section's center of gravity about x and y axis are found in the follovving formulas, Xc(n sy(D Xs(l)-Alan(l) Ysfl)- Sx^ YS(I) - Alan(l) Moments of inertia about principal axis are found in the following formulas lys(l) = ly(l) - Alan(l). Xs(l)2 lxs(l) = lx(l)-Alan(I).Ys(l)2 The sections modulus are; wDs«(,,=^a wal»(l)=5^L in this formulas, 'T shows secîion number which defined main data file. We can find öne ör more section's geometrical properties writing data files. An example for only section data is given in table.A. Table.A Section input data table "SECTION CORNER COORDINATES KESİT, 2. 14,4, 60...50 1,1,0,0,22,0,22,6,18,8,14,10,14,40,20,40,20,60,2,60,2,40,8,40,8,10,4,8,0.6 M,D.O,0,0.40,.0,0.40,0.50,0,0.50 in table.A, first line is the comment row, second line defines section number and according to this number, comer number and section height. XVI in this data there are two type sections and the first section's corner number is 14 other section's is 4, the last 2 number are the first section height and the other section height. After these 3 line we write lines include these sections corner coordinates. in the beginning of the lines include comer coordinates, there are two letter that öne of them defınes section type (I,T ör rectangular sections) and the other defines unit (l inch, M meter). Geometric properties of the composite section are found using girder section and effective slab width (b). This width ıs calculated following formula according to figüre 2, f b + \ | t* -'.. '- t bf * \- -ı Figüre 2. Flanged section b=bf|^ ^girder ^siab," Modulus of elasticity of slab concrete Egbder;Modulus of elasticity of girder concrete As the result, program of Prokesit.Exe generates fıles called KST, PRN MKV, BYT and YÜK. KST file includes girders geometrical properties, PRN file is only to print, in MKV file, there is composite section geometrical properties. YÜK file includes G1.G2.G3,... dead loads where discussed above. Finally, in BYT file, there are dimensions ali of the defined section. KST, MKV,YÜK, BYT and KST data files are used the other programs, so if we want to make some improvement in these data files after running of the Prokesit.Exe we can make it. Promax.Exe program genaretes MAX files that include in which section is critic from the point of view of moments of live loads. The highway live loading on the roadways of bridges shall consist of standard trucks ör iane loads that are equivalent to truck trains. Two systems of loading are provided, the H loading and the HS loading (HS is heavier than H loading). xvii There are four standard classes of highway loading; H20, H15, HS20, HS15. We must write this truck loads type and iane loads value in the main data file to find where the maximum moment exists. This program creates MAX files and this files numbers depend on sections defined by user. For example, if we look for moment to be at fıve meters from the support we must input 5 m running program. The program vvants data until you input nothing and after nothing begins calculation to maximum moments place and value on the girder. it writes them in MAX files when it finished calculation. This file is data file for the other programs. Truck loads and iane loads data table are like that table.B; Table.B. Live loads data table YUKES l NO l l l _J Q O O O 2 g a O O YÜK NO D1 D2 D3 Dn S1 l S2 j 53 l j S4 in the first tine, YUKES mean that begins iane loads values, NO defines how many types load there are. The second line and third line include load types and their values and place on the girders. 1 mean that there is uniform load (Q) on the girders and 2 means that concentrated load on the girder (q) and this loads place is (a) meter distance from support. Term of YÜK in data file defines truck loads, their place and values. D1.D2.D3 are truck loads coming öne vvheel on the ali axes. S1.S2.S3 are distances betvveen axes. After running Promax.Exe program, we obtain MAX files and use these files to find moments and section stress due to the dead load and live load at sections we want. We use Proger.Exe program to obtain moments and stress. Proger.Exe uses files created by above programsand main data file. Firstly, it reads Max files and calculates moments consist of live loads at ali defined sections. Secondly, it reads YÜK file and calculates moments consist of dead loads at ali defined sections. After it finds moments, ali moments are written in file called MOM. Highvvay live loads must be increased to allow for dynamic, vibratory, and impact effects, so the program determines impact fraction value. The amount of impact increment is expressed as a fraction of live load stress, and shall be determined by the formula: ı-*- L + 37 in which xviii Hmpact fraction (maximum 30 percent); L- length in meter of portion of span that is loaded to produce the maximum stress in the girder. The impact value is calculated and stored in file DAGITMA.SAY. it reads KST, MKV and MOM files to determine the total moments and section stressed. Maximum moments at ali sections are found and Moment.Dat file is created. it writes stress values at ali sections a file called GRL. Table.C shows GRL file; Table.C GRL File SECTlON NO l SPAN l KIRUST1 KIRALT1 KIRUST2 KIRALT2 KOMORTA1 KOMALT1 KOMÜST1 KOMORTA2 KOMALT2 KOMÜST2 TOPUST l TOPALT | TOPDÖSEME Table.D shows that which loads makes stress, and explains words in table.C. After we obtain GRL file, we can begin to determine prestressing force. Prestressing is applied to eliminate ör reduce tensile stress (to avoid cracking). There are two methods of prestressing concrete components:. Pre- tensioned, stress is applied before concrete hardens.. Post - tensioned, stress is applied after concrete hardens. Table. D Load Stresses LOADS l GİRDER S LA B TOP l BOTTOM l VVEİGHT OF GİRDER KIRUST1 KIRALT1 VVEİGHT OF SLAB & KIRUST2 KIRALT2 DİAPHRAGM WEİGHTOF KOMORTA1 KOMALT1 KOMÜST1 ASPHALT & OTHER LİVE LOAD KOMORTA2 KOMALT2 KOMÜST2 y TOPUST TOPALT TOPDÖSEME Prestressing can be applied internally ör externally. Following figüre shows that prestressing and other loads stressing combination. xix Prestressing Dead load Live load T t, stress stress stress fi t?ou c^ooiı ıy strands No tension, ör very little tension stress Figüre. 3 Load süperposition in this study, two stages are examined, öne of them is initial stage that prestressing force is transferred to concrete, no external loads except of weight of member. Other stage is final stage that ali service loads are applied, ali prestress losses have occurred vvhich composite sections are used. in AASTHO generally followıng design formula is used [1] ; ISMo+ZITM^^M^ where: <|>=1 forfactory produced precast prestressed concrete members <|>=0.95 for post-tensioned cast in place concrete members. (j>=0.90forshear Mult= ultimate moment carrying capacity. Howewer, AASTHO also requires checking of stress, and in most cases, the allowable stresses gövem the design. Program Cam.Exe makes prestrssing calculations. Firstly it reads presstressing strands knowledge's from the main file. Table.E shows strands knowledge's in the main file. CAM word in the first line indicates that the strands knowledge's begin. Fy is ultimate strength of prestressing steel, S1,S2,..Sn are strands number on the each row, and M1,M2,..Mn are distances to edge bottom of the girder for each row. l means that we shall write data as inch. We assume total prestressing loss before transfer and we find initial prestressing force and effective steel prestress after losses. The distance E from center of gravity for the girders section to center of gravity of prestressing steel is found. After we determine E distance, we can calculate prestrssing stress at the section. This stress is added ali other stresses and compare with AASTHO. We can compare ali of the result with AASTHO allowable values. İf we compare prestrssing stress we can use Cam.Exe program. If we want to compare ultimate strength and cracking load, we can use Ultimate.Exe TCK program and we can compare shear capacity and deflections using Kesme. Exe program. After we determined ali of the prestressing calculations, Cam.Exe program checks assumed prestress losses. There are following 4 types prestress losses in this study; 1. Relaxation of prestressing steel 2. Shrinkage of concrete 3. Creep of concrete 4. Elastic shortening of concrete. Table.E Presstressing^strands data table CAM I.Strands type no, Fy,Area,Strands row no 1 I.Strands type no, Fy,Area,Strands row no 2 I.Strands type no, Fy,Area,Strands row no 3 S1.S2.S3.S4 Sn M1.M2.M3.M4 Mn S1,S2,S3,S4, Sn M1,M2,M3,M4, Mn S1,S2,S3,S4 Sn M1.M2.M3.M4, Mn Proayk.Exe and Ayak.Exe programs solve abutments and foundations. This two programs reads two data files. Proayk.Exe makes seismic design and reads *A. Dat files give table.F. Table.F *A.Dat Data file ^AYAK.4 SYSTEM K,W,L.H,I,E.F 0,W,L,H,I,E.F 0,W,L.H,I,E,F K,W,L,H,I,E,F **** LİVE LOADS MH.O A.0.3 S.1.2 DEPLASMAN .000005785 .000009785 xxi Dynamic analysis methods using this study is Single-Mode Spectral Method [2]. This method is used to calculate the seismic design forces for bridges that respond predominantly in the first mode of vibration. The method, although completely rigorous from a structural dynamics point of view, reduces to a problem in static's after the introduction of inertia forces. Tablo.G Ayak.Dat file for Ayak.Exe XXll The system is conveniently formulated using energy principles. The principle of virtual displacements are used to formulate a generalized parameter model of a continuous system in a manner which approximates the overall behavior of the system. Ayak.Exe program reads AYAK.Dat file given table.G and finds abutment and foundation moments from the all dead and live loads.