METRIC BRIDGE GEOMETRYUSER’S MANUALbyProject Engineering Customer Support UnitRevised: December 15, 1995
Metric Bridge Geometry Table of ContentsTable of ContentsCHAPTER 1 - SYNOPSIS .1-1CHAPTER 2 - METRIC BRIDGE GEOMETRY OVERVIEW .2-1TERMINOLOGY . 2-1DECK ORGANIZATION. 2-4CHAPTER 3 - INPUT DATA.3-1DESCRIPTIVE DATA. 3-1STRUCTURE ID. 3-1DESCRIPTION . 3-1HORIZONTAL ALIGNMENT DATA. 3-2DELTA . 3-2P.I. STATION. 3-3DEGREE OF CURVE . 3-3SPIRAL LENGTHS . 3-3PROFILE OFFSET. 3-3RADIUS OF CURVE . 3-3STATION EQUATION. 3-3VERTICAL ALIGNMENT DATA . 3-5PERCENT GRADE . 3-5LENGTH OF VERTICAL CURVE IN . 3-5STATION OF P.I. . 3-5ELEVATION OF P.I. . 3-5LENGTH OF VERTICAL CURVE OUT . 3-6PERCENT GRADE . 3-612/15/95i
Metric Bridge GeometryCROWN AND SUPERELEVATION DATA .3-7CROWN TYPE. .3-7NOMINAL CROSS-SLOPE.3-8SUPER RATE (e) .3-8PIVOT OFFSET FROM PROFILE LINE .3-8TRANSITION LENGTH FOR SIMPLE CURVE.3-8PERCENT OF TRANSITION OUTSIDE SIMPLE CURVE .3-8MAXIMUM LENGTH OF TRANSITION VERTICAL CURVE .3-9PARABOLIC CROWN DATA (cols 57-80) .3-9OPTIONAL SUPERELEVATION OVERRIDE .3-11STATION . .3-12SLOPE LEFT/SLOPE RIGHT .3-12REFERENCE AND LAYOUT LINE DATA.3-13REFERENCE STATION.3-13STATION TYPE .3-13SKEW . .3-15DEFAULT SKEW .3-15LAYOUT LINE DEFINITION.3-15SEGMENTED GIRDER LINES TO BE BROKEN AT REFERENCE LINE .3-16SUPPRESS LISTING .3-16OFFSET OPTION FOR SEGMENTED GIRDER PATTERN SHIFT .3-17REVERSE LAYOUT LINE.3-17REQUEST X-0 POINTS .3-18EXTENDED PRINT CAPABILITY .3-18TRANSFORM CONSTANT FOR LAYOUT COORDINATES .3-18LIMITS OF VALID ELEVATION AND CROSS-SLOPE DATA .3-19GIRDER LINE DATA.3-20LINE TYPE .3-20Figure 5 : Segmented Girder Lines .3-23OFFSET DISTANCE .3-24ELEVATION SHIFT .3-26DESCRIPTION.3-26SEGMENTED GIRDER LINES ARE PARALLEL TO CHORDS ON THIS LINE.3-27LAYOUT LINE IS A CHORD ON THIS LINE .3-28X-TYPE FRACTIONAL POINTS .3-28MATCHING CHARACTER FOR DEAD LOAD DEFLECTIONS .3-29LINE OF CONSTANT OFFSET .3-29SUPPRESS LISTING .3-30BENT LINE DATA.3-33DISTANCE FROM PRIMARY OR SECONDARY REFERENCE LINE .3-33SKEW .3-34FRACTIONAL POINTS .3-35DESCRIPTION.3-37SEGMENTED GIRDER LINES TO BE BROKEN AT THIS BENT LINE .3-37BENT TO DEFINE OFFSETS FOR FLARED GIRDER LINES .3-37BENT TO DEFINE CHORD LAYOUT LINE .3-37SUPPRESS LISTING .3-38SELECTIVE INTERSECTIONS.3-38MATCHING CHARACTER FOR DEAD LOAD DEFLECTIONS .3-39SECONDARY REFERENCE LINES .3-39ii12/15/95
Metric Bridge Geometry Table of ContentsDEAD LOAD DEFLECTION DATA . 3-41Field 05/54 . . 3-41Field 06/44 . . 3-42M (METERS) . . 3-42DEFLECTION VALUES . 3-42ROADWAY APPROACHES . 3-44BEGIN STRUCTURE . 3-44END STRUCTURE . 3-44APPROACH LENGTH . 3-44OFFSETS FROM HORIZONTAL CONTROL . 3-44CHAPTER 4 - OUTPUT RESULTS .4-1DESCRIPTION . 4-1HORIZONTAL ALIGNMENT DATA . 4-2VERTICAL ALIGNMENT DATA . 4-2PARABOLIC CROWN DATA . 4-2TABLE OF ROADWAY CROSS-SLOPES. 4-3LIMITS OF VALID ELEVATION AND CROSS-SLOPE DATA. 4-5LAYOUT LINE DATA. 4-5BENTS TO DEFINE OFFSETS FOR FLARED GIRDER LINES . 4-5SEGMENTED GIRDER LINE DATA . 4-5DEAD LOAD DEFLECTION DATA. 4-6AVERAGE CROSS-SLOPE . 4-8GENERAL GIRDER LINE . 4-10BENT LINE. . 4-10STATION and OFFSET . 4-10ELEVATION. . 4-10ELEV DL. . 4-10OFFSET (X) and ORDINATE (Y) . 4-10BENT LENGTH . 4-11SKEW. 4-11GIRDER LENGTH. 4-11CROSS-SLOPE . 4-11ROADWAY APPROACHES .4-12CHAPTER 5 - FATAL ERROR MESSAGES.5-1CHAPTER 6 - CDOT FORMS .6-1INDENTIFICATION AND ALIGNMENT. 6-2SUPERELEVATION AND LAYOUT DATA . 6-3GIRDER LINE DATA . 6-4BENT LINE DATA . 6-5DEAD LOAD DEFLECTION DATA and ROADWAY APPROACHES . 6-612/15/95iii
Metric Bridge GeometryCHAPTER 7 - EXAMPLE. 7-1CHAPTER 8 - USE OF CARTESIAN SYSTEMS. 8-1iv12/15/95
Metric Bridge Geometry Index of FiguresIndex Of FiguresFIGURE 1 : SKEW CONVENTION . 2-3FIGURE 2 : PARABOLIC CROWN. 3-10FIGURE 3 : LAYOUT LINE . 3-14FIGURE 4 : GIRDER LINES. 3-21FIGURE 5 : SEGMENTED GIRDER LINES . 3-23FIGURE 6 : OFFSETS FOR TYPE 4 GIRDER LINES. 3-25FIGURE 7 : LINE OF CONSTANT OFFSET . 3-31FIGURE 8 : LINE OF CONSTANT OFFSET . 3-32FIGURE 9 : FRACTIONAL POINTS. 3-3612/15/95v
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Accessing Metric Bridge GeometryAccessing Metric Bridge GeometryFor CDOT - Staff Bridge EmployeesMetric Bridge Geometry is available on the VAX cluster computersystem at the Colorado Department of Transportation. At the main CDOTBridge menu, enter ‘GEOM’ as follows:Colorado Department of CPMISALL-IN-1 Office ApplicationsElectronic MessagingDirectory ServicesFile ServicesPrint file(s)User ServicesTK Solver (Equations)File archival systemBid Analysis Mgt SystemFinancial SubsystemsDOH Form 463GeoHwySNA link to uipment Management SystemEngineering Tools (MOSS, etc.)Kermit File TransferFile ViewerBridge design sub menu.Bridge design super menu.Bridge design misc. menu.Bridge geometry menu.Bridge rating menu.Bridge inventory menu.IRIS Beta testEnter option and press Return: GEOM Return EXit KP0 TOPmenu PF1 Help PF2 REFresh PF3 LOGout PF4 Enter ‘MBGM’ at the following Bridge Geometry menu:12/15/95vii
Metric Bridge GeometryBRIDGE GEOMETRY L-IN-1Electronic MessagingDirectory servicesFile servicesUser servicesKermit file transferBridge GeometryMetric Bridge GeometryCamber cutting diagramCoordinate GeometryDATENT bridge data entryPicasso IIGeom to stick figure data transGeom to Camber data transEnter option and press RETURN: MBGM Return EXit KP0 TOPmenu PF1 Help PF2 REFresh PF3 This gives you access to Metric Bridge Geometry.viii12/15/95LOGout PF4
Metric Bridge Geometry Index of FiguresAccessing Metric Bridge GeometryFor Consultant EmployeesMetric Bridge Geometry is available on the VAX cluster computersystem at the Colorado Department of Transportation. At the main CDOTConsultant menu, enter ‘GEOM’ as follows:Colorado Department of TEINVElectronic MessagingDirectory ServicesFile ServicesUser ServicesKermit File TransferEngineer’s Estimate TabulationEngineering Tools (MOSS, etc.)Consultant design sub menu.Consultant design super menu.Consultant design misc. menu.Consultant geometry menu.Consultant rating menu.Consultant inventory menu.Enter option and press Return: GEOM Return EXit KP0 TOPmenu PF1 Help PF2 REFresh PF3 LOGout PF4 Enter ‘MBGM’ at the following Bridge Geometry menu:12/15/95ix
Metric Bridge GeometryCONSULTANT GEOMETRY MENUEMDSFSUSKERBR2SBR2CBRGMMBGMCMBRCOGOElectronic MessagingDirectory servicesFile servicesUser servicesKermit file transferGeom to stick figure data transGeom to Camber data transBridge GeometryMetric Bridge GeometryCamber cutting diagramCoordinate GeometryEnter option and press RETURN: MBGM Return EXit KP0 TOPmenu PF1 Help PF2 REFresh PF3 This gives you access to Metric Bridge Geometry.x12/15/95LOGout PF4
Metric Bridge Geometry SynopsisChapter 1Chapter 1 - SynopsisThe bridge geometry program computes three-dimensional coordinates ofpoints on a structure and on the roadway approaches to a structure. Theinput data consists of eight essential items:1. Horizontal alignment data2. Vertical alignment data3. Superelevation and cross-slope data4. Reference line and layout data5. Girder/longitudinal lines6. Bent/transverse lines7. Dead load deflections8. Roadway approach dataThe surface deck of the structure is considered a grid ofintersecting girder lines and bent lines. Output results include thecoordinates of each intersection point, together with intermediate“fractional” points, printed sequentially along each girder line. Twoindependent coordinate systems locate the points in the horizontalplane: (1) the surveyor's station and offset from the horizontalcontrol line, and (2) a right-hand rectangular Cartesian coordinatesystem (X,Y) with respect to a selected layout line.Results printed for intersection and fractional points include:finished elevation, elevation adjusted for dead load deflection, girderline length, and roadway cross-slope (when continuous). Forintersection points, bent line length and the skew angle of the bentline (with respect to the girder line) are also printed.On roadway approaches, finished grade elevations and roadwaycross-slopes are printed at given stations for each designated offsetline.12/15/951-1
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Metric Bridge Geometry OverviewChapter 2Chapter 2 - Metric Bridge Geometry OverviewTERMINOLOGY“Col” means a column position (l to 80) of a Hollerith punch card.Every input card begins with a two col Card Type field, precoded onforms.“Default” value refers to the number, amount or option that willbe used if a field is blank. In many cases default and zero have thesame effect.Except in the instance of normal crown section, “normal” is usedin the sense of perpendicular (at right angles).Directions such as left/right, back/ahead, in/out, or begin/endare with respect to ahead station unless otherwise specified.Throughout this manual, the term “girder line” is used in ageneric sense to mean any longitudinal line; i.e., a line running thelength of the structure which intersects each bent line. Thus outsideedge of deck, gutter line, back tangent, layout line, horizontal controlline, and profile line are all examples of girder lines. Similarly,“bent line” is used generically to mean any transverse line (moreaccurately, a transverse vertical plane); i.e., a line running acrossthe structure which intersects each girder line. Thus splice line,diaphragm, centerline of bearing, face of cap, and back face of abutmentare all examples of bent lines. Girder lines have the attribute ofelevation; bent lines do not.A “straight” line means that its projection in the horizontalplane (disregarding elevation) is straight.Unless otherwise specified the terms “reference bent,” “referenceline,” or “reference bent line” mean the primary reference (bent) line.Each set of 04-07 cards is associated with a single primary referenceline; there may be many secondary reference lines or none in a set.12/15/952-1
Metric Bridge GeometryAfter the program has located all bent lines, they are sorted inorder of increasing station (at the point where they cross thehorizontal control line). This means that the order of 06 cards is notsignificant: a group of 06 cards may be shuffled in any order withoutsignificantly affecting output. References to order of bent lines (suchas “first,” “next” or “last”) refer to this sorted order, not to thesequence of 06 cards on input.Two girder lines are always known to the program: (l) The stationline controls horizontal alignment and is the line where, even through acurve, one station is equal to 1000 meters; it is commonly coincidentwith the profile (vertical control) line. (2) The layout line is astraight line determined by parameters on 04 card.The term “intersection point” is used for points at theintersection of a girder line and a bent line. “Intermediate points” or“fractional points” occur in a “span” between two (not necessarilyconsecutive) intersection points. A “span” of deflection pointscorresponds to a “span” of fractional points.The skew of a bent line, with respect to a girder line, is theangle measured from a normal on the girder line (drawn at the point ofintersection) to the bent line. When the angle turns to the right, theskew is positive; to the left is negative, as shown in Figure 1.“Finished” elevation does not necessarily mean finished grade. Thefinished surface of the deck means top of concrete, which may be belowfinished grade if, for example, a 50 mm asphalt overlay is to berequired. Finished elevation for a line representing bottom of girdermay be several hundred millimeters below finished grade.When reference is made to an option being “selected” (or a cardbeing “designated”), it is frequently to be inferred that the option isselected by coding ANY non-blank character in the indicated (single) colposition of the card.2-212/15/95
Metric Bridge Geometry Input DataFigure 1 : Skew Convention12/15/952-3
Metric Bridge GeometryDECK ORGANIZATIONThe input data deck consists of a set of 00 through 08 cards forone structure. Only one structure may be processed at a time.One data set for a structure consists of:a. at least one (or arbitrarily many) 00 card(s)b. optional 01 cardc. one 02 cardd. at least one (or up to 16) 03 card(s)e. at least one (or arbitrarily many) sequence(s) of:i. one 04 cardii. at least one (or up to 30) 05 card(s)iii. at least one (or up to 80) 06 card(s)iv. (up to 200) optional 07 cardsf. optional 08 cardCards with Card Type 99 are transparent to the program; they may beused for comments anywhere in the deck.If the program fails to find a required card in this sequence, itwill ignore the card read and continue reading and ignoring cards untilit finds the card type for which it is searching. In this case a fatalerror message, listing (at least some of) the cards that were ignored,will be printed at the end of the output.2-412/15/95
Metric Bridge Geometry Input DataChapter 3Chapter 3 - Input DataDESCRIPTIVE DATA00 CARDS (refer: “IDENTIFICATION AND ALIGNMENT” Form)STRUCTURE ID(cols 3-12, first card only)This field provides a ten character identification which willappear in the banner line at the top of each page of output.DESCRIPTION(cols 3-80)Provide a detailed description of the structure and its designincluding: project number, designer, detailer, location, method andmaterials of construction, span lengths, etc. An M in col 80 isrequired on the first 00 card to distinguish Metric input from Englishinput files. In unusual or complicated situations, also include remarksregarding special considerations made for the input data, such as:a. nonstandard treatment of superelevationb. station equations or curves resulting in begin or end stationcoded in 04 card, cols 59-80c. nonuniform elevation shifts on 05 cardsd. nominal offsets specified on 05 cards (line type 4)e. reasons for any adjustment to alignment data taken from linesheetsAn unlimited number of 00 cards may be used, so make remarksthorough, detailed and complete. If more than seven cards areneeded, eighty col forms may be used with first two cols blank.Formatting for double spaced lines may be accomplished byinserting blank cards as appropriate.The information on these cards will be printed on the first pageof output.4/16/963-1
Metric Bridge GeometryHORIZONTAL ALIGNMENT DATA01 CARD(refer: “IDENTIFICATION AND ALIGNMENT” Form)If the entire structure and roadway approaches lie on horizontaltangent at nominal cross-slope (no superelevation transitions orrun-out), cols 3-43 may be blank.When the entire structure and roadway approaches lie on horizontaltangent, the profile offset is zero, and no station equation is used,cols 3-80 may be blank. Equivalently, the card may be left outentirely.CAUTION: It is usually better to code a proximal horizontal(or vertical) curve than to assume it will not affect elevations.For example, a bridge begins at station 1 120.0, just after ahorizontal curve with P.T. at station 1 020.0 and with 50 metertransitions. The person coding the deck for a geometry runfigures that the end of transition (station 1 060.0) occurs beforethe beginning of the 50 meter roadway approach (station 1 070.0);so they omit the horizontal curve.Later, someone else wants to run the same deck for elevationsheet plots and decides to give 70 meter roadway approaches. Ifthey merely change the approach length on the 08 card to 70.0, thetranslucent output will have errors in elevation at the first sixstations (three-meter stations) of the approach.A similar problem can occur with vertical curves near thestructure. To prevent such problems, make full use of the Limitsof Valid Elevation and Cross-Slope Data field (04 card, cols59-80). If, in this example, the person originally coding thegeometry deck had coded the end of transition station in the BeginStation field (despite the fact that the P.T. is nearly 100 metersbefore the structure), no errors would have cropped up in thelater run.DELTA(cols 3-12)Code the central deflection angle (including spirals) in degrees,minutes and seconds and indicate whether deflection is to the left (L)or right (R). Equivalent to an L is a minus sign for left deflections;equivalent to an R is a plus, a blank or any character other than L orminus.Allowable range for delta is:0 00’ 04.13” DELTA 179 59’ 55.32”3-24/16/96
Metric Bridge Geometry Input DataP.I. STATION(cols 13-23)Code the station of the P.I. of the horizontal curve. This is atangent station, not a station on the horizontal control line.DEGREE OF CURVE(cols 24-31)Not used in the metric version.SPIRAL LENGTHS(cols 32-37 & 38-43)Code the length in meters of spiral transitions into and out ofthe curve. If spirals are not used (simple curve), leave this fieldblank; but see “Crown and Superelevation Data” (03 cards) regardingsmooth profiles.PROFILE OFFSET(cols 44-51)If the horizontal control line is also the profile line, leavethis field blank. If not, code the offset in meters from horizontalcontrol to profile line. Positive offset indicates profile line is tothe right of horizontal control; negative indicates offset is to theleft.RADIUS OF CURVE(cols 52-58)Code the radius in meters with EXPLICIT decimal point. The radiuswill be shown in the output under “Horizontal Alignment Data.”Allowable range for radius is: 43 m rad 30,784 mException: If spirals are not used (simple curve), a shorterradius may be used. The minimum radius permitted in this case is 3.1met
FS File Services US User Services KER Kermit File Transfer STAB Engineer’s Estimate Tabulation ENG Engineering Tools (MOSS, etc.) DSUB Consultant design sub menu. DSUP Consultant design super menu. DMSC Consultant design misc. menu. GEOM Consultant geometry menu. RA
D. Metric Jogging Meet 4 E. Your Metric Pace 5 F. Metric Estimation Olympics. 6 G: Metric Frisbee Olympics 7 H. Metric Spin Casting ,8 CHAPTER III. INDOOR ACTIVITIES 10 A. Meteic Confidence Course 10 B. Measuring Metric Me 11 C. Metric Bombardment 11 D. Metric
Button Socket Head Cap Screws- Metric 43 Flat Washers- Metric 18-8 44 Hex Head Cap Screws- Metric 18-8 43 Hex Nuts- Metric 18-8 44 Nylon Insert Lock Nuts- Metric 18-8 44 Socket Head Cap Screws- Metric 18-8 43 Split Lock Washers- Metric 18-8 44 Wing Nuts- Metric 18-8 44 THREADED ROD/D
Aluminum bridge crane isometric 11 Steel bridge crane plan view 12 Aluminum bridge crane plan view 13 Bridge Crane Systems & Dimensional Charts Installation Parameters 14 250 lb. capacity bridge cranes 15 - 17 500 lb. capacity bridge cranes 18 - 21 1000 lb. capacity bridge cranes 22 - 25 2000 lb. capacity bridge cranes 26 - 29 4000 lb. capacity .
metric units. During Year 3 familiar metric units are introduced for length, mass and capacity. Working with metric units is extended in Year 4 to include familiar metric units for area and volume. Familiar metric units are metric units that would most commonly be experienced by
THE METRIC SYSTEM The metric system is much easier. All metric units are related by factors of 10. Nearly the entire world (95%), except the United States, now uses the metric system. Metric is used exclusively in science
Hammersmith Bridge Suspension Bridge, 2 piers (1887) 210m 13m No, on road only Steps footway/ road Narrow traffic lanes, 20000 veh/day 3,872 1,923 5,795 Barnes Footbridge Deck arch bridge, 2 piers (1895) 124m 2.4m No, foot bridge only Steps Runs alongside railway bridge 1,223 256 1,479 Chiswick Bridge Deck arch bridge, 2 piers (1933) 185m 21m .
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somewhat more complicated geometry. Let S2 denote the upper half plane {(x,y) : y 0},equipped with the following metric g: g 1 p 1 ρ2 y2C(x)2 1 ρC(x) ρC(x) C(x)2 . This metric is a generalization of the Poincare metric: the case of ρ 0 and C(x) 1 reduces to the Poincare metric. The