Vertical curves provide a smooth transition between roadway segments with different grades. They are usually parabolic in shape. The key steps in designing a vertical curve are to first calculate the sight distance based on design speed, then use this to calculate the minimum curve length. The location of the PVI, PVC, and PVT can then be determined based on the length and intersection of the tangent grades. Finally, the equation relating elevation to distance along the curve is used to develop the entire curve profile.
This document provides an overview of key components and considerations for railway engineering. It discusses:
- The definition of railway engineering as dealing with design, construction and maintenance of railway tracks.
- Key components of permanent way including rails, sleepers, ballast and track gauge.
- Selection and standard sizes of rails and factors that influence this like locomotive axle load.
- Common defects in rails like wear, creep, buckling and methods to prevent or address them.
- Importance of proper gauge, alignment, gradient and super elevation on curves for safety and efficiency of train movement.
Lec 05 Horizontal Alignment (Transportation Engineering Dr.Lina Shbeeb)Hossam Shafiq I
The document discusses horizontal alignment in transportation engineering. It defines horizontal alignment as straight segments connected by circular curves. It describes different types of curves like simple, compound, and reverse curves. It provides formulas to calculate curve length, radius, degree of curve, and sight distance. Examples are given to demonstrate calculating curve length, radius, and minimum sight distance around a curve. Methods for attaining superelevation on curves through pavement revolutions are also summarized.
This document provides a program of work and cost estimate for constructing a diversion works structure in Barangay Aslum, Leyte, Philippines. It includes a project description, duration, needed equipment, personnel, itemized scope of works, cost breakdown, funding sources, concrete and rebar estimates, and excavation details. The total estimated cost is PHP 687,964.80. It seeks to implement the sub-project through a KALAHI-CIDSS grant and contributions from community and local government units.
The overtaking sight distance or passing sight distance is measured along the center line of the road over which a driver with his eye level 1.2 m above the road surface can see the top of an object 1.2 m above the road surface.
passing sight distance formula
aashto intersection sight triangles
highway sight distance
stopping sight distance formula
stopping sight distance calculator
headlight sight distance equation
headlight sight distance
aashto sight triangle standards
stopping site distance
safe stopping sight distance
aashto stopping sight distance
sight distance in geometric design
stopping sight distance example
ssd stopping sight distance
stopping site distance calculation
headlight sight distance
A culvert is a small bridge, typically 6m or less in length, that allows water to flow underneath a road or railway. There are several types of culverts including pipe, box, arch, slab, and beam/slab culverts. The design of culverts considers factors like site selection, alignment, estimated discharge, number of spans, foundation, and clearance to ensure safety and stability.
Rail Gauges and Rail standards [Useful for Civil Engineering Students IECT SPPU]Tushar Sonawane
Useful for Third year Civil Engineering Students of Savitribai Phule Pune university, Pune (University of Pune)
This PPT shows the details regarding Rail gauges and Rail Standards used in Indian Railways.
Few more PPTs and Videos are available at my blog tusharhsonawane.wordpress.com
This document provides information on geometric design concepts for highways, with a focus on vertical alignment and vertical curves. It includes definitions of terms like gradient, ruling gradient, limiting gradient, minimum gradient, and critical length of grade. It describes factors that influence grades like vehicle speed, acceleration and comfort. It also covers vertical curve fundamentals, including equations for crest and sag vertical curves based on stopping sight distance and headlight sight distance. Examples are provided for calculating sight distances and lengths for different grade change scenarios.
This document discusses various aspects of railway track design including gradients, horizontal and vertical curves, super-elevation, and transition curves. It provides formulas for calculating ruling gradient, super-elevation, safe speeds on curves, and other key design elements. Track must be designed to suit the loads and speeds of trains based on safety and economic standards. Proper gradient, curvature, and super-elevation are necessary for smooth train operation.
This document provides an overview of key components and considerations for railway engineering. It discusses:
- The definition of railway engineering as dealing with design, construction and maintenance of railway tracks.
- Key components of permanent way including rails, sleepers, ballast and track gauge.
- Selection and standard sizes of rails and factors that influence this like locomotive axle load.
- Common defects in rails like wear, creep, buckling and methods to prevent or address them.
- Importance of proper gauge, alignment, gradient and super elevation on curves for safety and efficiency of train movement.
Lec 05 Horizontal Alignment (Transportation Engineering Dr.Lina Shbeeb)Hossam Shafiq I
The document discusses horizontal alignment in transportation engineering. It defines horizontal alignment as straight segments connected by circular curves. It describes different types of curves like simple, compound, and reverse curves. It provides formulas to calculate curve length, radius, degree of curve, and sight distance. Examples are given to demonstrate calculating curve length, radius, and minimum sight distance around a curve. Methods for attaining superelevation on curves through pavement revolutions are also summarized.
This document provides a program of work and cost estimate for constructing a diversion works structure in Barangay Aslum, Leyte, Philippines. It includes a project description, duration, needed equipment, personnel, itemized scope of works, cost breakdown, funding sources, concrete and rebar estimates, and excavation details. The total estimated cost is PHP 687,964.80. It seeks to implement the sub-project through a KALAHI-CIDSS grant and contributions from community and local government units.
The overtaking sight distance or passing sight distance is measured along the center line of the road over which a driver with his eye level 1.2 m above the road surface can see the top of an object 1.2 m above the road surface.
passing sight distance formula
aashto intersection sight triangles
highway sight distance
stopping sight distance formula
stopping sight distance calculator
headlight sight distance equation
headlight sight distance
aashto sight triangle standards
stopping site distance
safe stopping sight distance
aashto stopping sight distance
sight distance in geometric design
stopping sight distance example
ssd stopping sight distance
stopping site distance calculation
headlight sight distance
A culvert is a small bridge, typically 6m or less in length, that allows water to flow underneath a road or railway. There are several types of culverts including pipe, box, arch, slab, and beam/slab culverts. The design of culverts considers factors like site selection, alignment, estimated discharge, number of spans, foundation, and clearance to ensure safety and stability.
Rail Gauges and Rail standards [Useful for Civil Engineering Students IECT SPPU]Tushar Sonawane
Useful for Third year Civil Engineering Students of Savitribai Phule Pune university, Pune (University of Pune)
This PPT shows the details regarding Rail gauges and Rail Standards used in Indian Railways.
Few more PPTs and Videos are available at my blog tusharhsonawane.wordpress.com
This document provides information on geometric design concepts for highways, with a focus on vertical alignment and vertical curves. It includes definitions of terms like gradient, ruling gradient, limiting gradient, minimum gradient, and critical length of grade. It describes factors that influence grades like vehicle speed, acceleration and comfort. It also covers vertical curve fundamentals, including equations for crest and sag vertical curves based on stopping sight distance and headlight sight distance. Examples are provided for calculating sight distances and lengths for different grade change scenarios.
This document discusses various aspects of railway track design including gradients, horizontal and vertical curves, super-elevation, and transition curves. It provides formulas for calculating ruling gradient, super-elevation, safe speeds on curves, and other key design elements. Track must be designed to suit the loads and speeds of trains based on safety and economic standards. Proper gradient, curvature, and super-elevation are necessary for smooth train operation.
The document discusses the geometric design of roads, specifically horizontal curves. It covers key elements of geometric design like alignment, profile, and cross-section. Horizontal curve design is an important part that influences safety and efficiency. Parameters like design speed, superelevation, extra widening, and minimum radius are discussed in detail according to Indian Road Congress standards. Methods for building superelevation and effecting widening on curves are also summarized.
Chapter 6 concrete dam engineering with examplesMohsin Siddique
This document provides an overview of concrete dam engineering. It begins by outlining the key learning outcomes which are to understand dam classification, selection criteria, ancillary works, and forces acting on dams. It then defines what a dam is and discusses the types of dams including gravity, arch, buttress, and embankment dams. It describes the various components of dams such as spillways and outlets. It also covers the forces acting on dams including primary loads from water, self-weight, and seepage, as well as secondary loads from sediment, thermal effects, and seismic loads. It concludes by discussing the analysis of gravity dams and safety criteria for overturning, sliding, crushing, and tension.
Railway Engineering - Geometric design of trackMani Vel
This document discusses the importance of proper geometric design of railway tracks. It outlines key considerations for geometric design including gradients, curvature, and track alignment. Proper design is needed to ensure safe train operation at maximum speeds and loads. Specific geometric design elements are described, such as ruling gradients, helper gradients, momentum gradients, and standards for station yard gradients. Grade compensation is also outlined, where steeper gradients are allowed on curved tracks compared to straight tracks.
This document is a project report on the geometric design of railway tracks submitted by Mohit M. Jain to Gujarat Technological University in India. It introduces the topic of geometric design and its importance for ensuring safe and efficient train operation. The following chapters discuss geometric cross sections, gradients including different types, curves, superelevation, and gauge widening on curves. The report provides information on the key design considerations for railway tracks.
This document summarizes a presentation on highway failure and maintenance. It begins with an introduction to highways and highway pavements. It then discusses the main types of highway failures including cracking, surface deformation, disintegration, and surface defects. The document outlines the various maintenance activities needed to preserve highways, such as surface maintenance, drainage system upkeep, and rehabilitation. It emphasizes that regular maintenance is important to prevent pavement deterioration and ensure safe transportation.
This document discusses the key concepts of geometric design of highways. It defines geometric design as dealing with the visible dimensions and layout of a highway. The goals of geometric design are to maximize comfort, safety and economy while providing efficient traffic operation. Some key factors that influence geometric design are design speed, topography, traffic, environment and cost. The document outlines various elements of highway cross-sections including the carriageway, shoulders, roadway width, right of way and median. It also discusses horizontal and vertical alignment, types of alignment, and considerations for factors like gradient, sight distance and curves.
Freeway & Highway LOS (Transportation Engineering)Hossam Shafiq I
This document discusses methods for determining freeway and highway level of service (LOS). It defines key terms like free-flow speed, passenger car equivalents, and LOS criteria. The document outlines how to calculate the free-flow speed by measuring it or using a baseline adjusted for factors like lane width. It also explains how to determine the traffic flow rate and convert volumes to passenger cars per lane per hour. Finally, it shows how to use the speed-flow curve and density to establish the LOS for a basic freeway segment based on traffic conditions.
This document discusses various aspects of vertical alignment in transportation engineering. It describes how vertical alignment specifies the elevation of points along a roadway based on safety, comfort, drainage needs. Vertical curves are used to transition between different roadway grades and can be crest or sag curves. The coordination of vertical and horizontal alignment is also discussed to ensure driver safety and aesthetics. Maximum and minimum grades, as well as critical lengths of grades, are addressed based on truck performance.
Railway Track Components. A Railway Track has many Components in it. they are as follows, Rails; Sleepers; Ballast; Formations or subgrades; A good quality and strong aggregate materials, steel I section to use in the construction of railway tracks. 1. Rails. Rails are the first main element in the Railway Track Components. It is of an I section make with steel. Two rails fix opposite to each other.
components of a railroad track
rail track components
railroad components
parts of a railroad track
parts of a rail
parts of a railroad crossing
rail components
railroad switch part components
components of a railroad track
rail track components
railroad track switch components
railway track and structure
The document discusses bridge types, components, selection criteria, and design considerations. It begins by defining what a bridge is and its purpose in transportation systems. It then covers typical bridge components and various structural forms for bridges based on material, span length, and other factors. Key criteria for selecting bridge types include span length, site conditions, cost, and aesthetics. The document emphasizes that aesthetic design requires considering function, proportion, harmony, order/rhythm, and contrast/texture to create pleasing structures that blend with their environments.
The document discusses the reasons for and methods of calculating the widening of pavements on horizontal curves. There are two types of widening: mechanical widening to account for vehicle off-tracking due to rigid wheel bases, and psychological widening to allow for greater driver maneuverability at higher speeds. Mechanical widening is calculated based on number of lanes, vehicle wheel base length, and curve radius. Psychological widening is also based on design speed and curve radius. The total widening is the sum of mechanical and psychological widening. Tables from the Indian Road Congress provide extra width recommendations for single and double lane pavements on curves.
I'm Irfan Nasir. Currently studying Civil Engineering at Mehran University of Engineering and Technology. This is a slide made by me on Defects in rails from the subject Transportation Engineering.
Highway Materials: Desirable Properties, Testing Procedures, Standards, and standard values relating to Soil, Stone Aggregates, Bitumen and Tar, fly- ash/pond-ash. Role of filler in Bituminous mix, materials of filler.
Specifications of DLC and PQC for rigid pavement
The document discusses factors that affect the alignment of railway lines, including horizontal and vertical alignment. It describes the importance of proper alignment for reasons of cost, difficulty of changing alignment later, and fulfilling objectives. An ideal alignment considers purpose, integrated development, and economic factors like shortest route, construction/maintenance costs, operational expenses, safety, comfort, and aesthetics. Selection of alignment is based on gauge, obligatory points, topography, geometrical standards, geology, road crossings, labour/materials, station/yard placement, and political considerations.
This document discusses various aspects of airport engineering and design. It begins by outlining the history of air transport development in India. It then defines key terms like airport, airfield, aerodrome and describes important airport components such as runways, terminals, taxiways, and control towers. The document also discusses factors that influence airport site selection and layout, including aircraft characteristics, wind patterns, and safety. It provides examples of different types of airports and concludes by covering topics like runway orientation, design, lighting and signage.
This document discusses vertical curves used in transportation design. Vertical curves provide a smooth transition between different road or rail grades. They are designed using parabolic equations to maintain a constant rate of change in slope. The key points are:
- Vertical curves connect two different grades using a parabolic shape.
- Their design ensures a constant rate of change in slope for driver comfort.
- The general parabolic equation and methods for computing curve elements like high/low points and elevations at different points are presented.
Here are the key steps and calculations for the homework:
1. Use design speed of 55 mph, emax of 4%, and fmax of 0.12 from Green Book
2. Calculate minimum radius using formula: Rmin = V2/(15(e+f)) = 1,200 ft
3. Select radius of 1,400 ft
4. Given: PI station of 352+44.97, Δ of 35° 24' 55"
5. Calculate curve length using L = ΔR/5729.58 = 1,260 ft
6. Calculate tangent length using T = Rtan(Δ/2) = 630 ft
7. Calculate PC station: PC = PI - T
The clear distance ahead of vehicle which is visible to the driver is known as sight distance
The minimum distance within which a driver can safely stop his vehicle without any collision with some vehicle, animal or any other object is known as stopping sight distance.
Often changes in the direction are necessitated in highway alignment due to various reasons such as topographic considerations, obligatory points.
The geometric design elements pertaining to horizontal alignment of highway should consider safe and comfortable movement of vehicles at the given design speed of the highway.
It is therefore necessary to avoid sudden changes in direction with sharp curves or reverse curves which could not be safely and conveniently negotiated by the vehicles at design speed.
Improper design of horizontal alignment of roads would necessitate speed changes resulting m higher accident rate and increase in vehicle operation cost.
Vertical alignment refers to the vertical profile of a road, including any crests or sags. The two basic components are grade, which is the slope/incline of the road, and vertical curves, which provide a gradual transition between different grades. There are two types of vertical curves - sag curves for positive grade changes and crest curves for negative grade changes. Both are designed as parabolic curves defined by points of vertical curvature, intersection, and tangency. Grade changes of 1% or less may not require a vertical curve depending on design speed.
This document discusses vertical alignment in road design. It defines vertical alignment as the vertical aspect of the road profile, including crest and sag curves. It describes the basic components of vertical alignment as grade and vertical curves. Grade is the slope of the road expressed as a percentage, while vertical curves are parabolic curves that provide gradual transitions between different grades to allow comfortable driving. The document discusses types of vertical curves such as sag curves at the bottom of hills and crest curves at the tops of hills, as well as symmetrical and unsymmetrical curves. It provides the equations used to design different types of vertical curves.
The document discusses the geometric design of roads, specifically horizontal curves. It covers key elements of geometric design like alignment, profile, and cross-section. Horizontal curve design is an important part that influences safety and efficiency. Parameters like design speed, superelevation, extra widening, and minimum radius are discussed in detail according to Indian Road Congress standards. Methods for building superelevation and effecting widening on curves are also summarized.
Chapter 6 concrete dam engineering with examplesMohsin Siddique
This document provides an overview of concrete dam engineering. It begins by outlining the key learning outcomes which are to understand dam classification, selection criteria, ancillary works, and forces acting on dams. It then defines what a dam is and discusses the types of dams including gravity, arch, buttress, and embankment dams. It describes the various components of dams such as spillways and outlets. It also covers the forces acting on dams including primary loads from water, self-weight, and seepage, as well as secondary loads from sediment, thermal effects, and seismic loads. It concludes by discussing the analysis of gravity dams and safety criteria for overturning, sliding, crushing, and tension.
Railway Engineering - Geometric design of trackMani Vel
This document discusses the importance of proper geometric design of railway tracks. It outlines key considerations for geometric design including gradients, curvature, and track alignment. Proper design is needed to ensure safe train operation at maximum speeds and loads. Specific geometric design elements are described, such as ruling gradients, helper gradients, momentum gradients, and standards for station yard gradients. Grade compensation is also outlined, where steeper gradients are allowed on curved tracks compared to straight tracks.
This document is a project report on the geometric design of railway tracks submitted by Mohit M. Jain to Gujarat Technological University in India. It introduces the topic of geometric design and its importance for ensuring safe and efficient train operation. The following chapters discuss geometric cross sections, gradients including different types, curves, superelevation, and gauge widening on curves. The report provides information on the key design considerations for railway tracks.
This document summarizes a presentation on highway failure and maintenance. It begins with an introduction to highways and highway pavements. It then discusses the main types of highway failures including cracking, surface deformation, disintegration, and surface defects. The document outlines the various maintenance activities needed to preserve highways, such as surface maintenance, drainage system upkeep, and rehabilitation. It emphasizes that regular maintenance is important to prevent pavement deterioration and ensure safe transportation.
This document discusses the key concepts of geometric design of highways. It defines geometric design as dealing with the visible dimensions and layout of a highway. The goals of geometric design are to maximize comfort, safety and economy while providing efficient traffic operation. Some key factors that influence geometric design are design speed, topography, traffic, environment and cost. The document outlines various elements of highway cross-sections including the carriageway, shoulders, roadway width, right of way and median. It also discusses horizontal and vertical alignment, types of alignment, and considerations for factors like gradient, sight distance and curves.
Freeway & Highway LOS (Transportation Engineering)Hossam Shafiq I
This document discusses methods for determining freeway and highway level of service (LOS). It defines key terms like free-flow speed, passenger car equivalents, and LOS criteria. The document outlines how to calculate the free-flow speed by measuring it or using a baseline adjusted for factors like lane width. It also explains how to determine the traffic flow rate and convert volumes to passenger cars per lane per hour. Finally, it shows how to use the speed-flow curve and density to establish the LOS for a basic freeway segment based on traffic conditions.
This document discusses various aspects of vertical alignment in transportation engineering. It describes how vertical alignment specifies the elevation of points along a roadway based on safety, comfort, drainage needs. Vertical curves are used to transition between different roadway grades and can be crest or sag curves. The coordination of vertical and horizontal alignment is also discussed to ensure driver safety and aesthetics. Maximum and minimum grades, as well as critical lengths of grades, are addressed based on truck performance.
Railway Track Components. A Railway Track has many Components in it. they are as follows, Rails; Sleepers; Ballast; Formations or subgrades; A good quality and strong aggregate materials, steel I section to use in the construction of railway tracks. 1. Rails. Rails are the first main element in the Railway Track Components. It is of an I section make with steel. Two rails fix opposite to each other.
components of a railroad track
rail track components
railroad components
parts of a railroad track
parts of a rail
parts of a railroad crossing
rail components
railroad switch part components
components of a railroad track
rail track components
railroad track switch components
railway track and structure
The document discusses bridge types, components, selection criteria, and design considerations. It begins by defining what a bridge is and its purpose in transportation systems. It then covers typical bridge components and various structural forms for bridges based on material, span length, and other factors. Key criteria for selecting bridge types include span length, site conditions, cost, and aesthetics. The document emphasizes that aesthetic design requires considering function, proportion, harmony, order/rhythm, and contrast/texture to create pleasing structures that blend with their environments.
The document discusses the reasons for and methods of calculating the widening of pavements on horizontal curves. There are two types of widening: mechanical widening to account for vehicle off-tracking due to rigid wheel bases, and psychological widening to allow for greater driver maneuverability at higher speeds. Mechanical widening is calculated based on number of lanes, vehicle wheel base length, and curve radius. Psychological widening is also based on design speed and curve radius. The total widening is the sum of mechanical and psychological widening. Tables from the Indian Road Congress provide extra width recommendations for single and double lane pavements on curves.
I'm Irfan Nasir. Currently studying Civil Engineering at Mehran University of Engineering and Technology. This is a slide made by me on Defects in rails from the subject Transportation Engineering.
Highway Materials: Desirable Properties, Testing Procedures, Standards, and standard values relating to Soil, Stone Aggregates, Bitumen and Tar, fly- ash/pond-ash. Role of filler in Bituminous mix, materials of filler.
Specifications of DLC and PQC for rigid pavement
The document discusses factors that affect the alignment of railway lines, including horizontal and vertical alignment. It describes the importance of proper alignment for reasons of cost, difficulty of changing alignment later, and fulfilling objectives. An ideal alignment considers purpose, integrated development, and economic factors like shortest route, construction/maintenance costs, operational expenses, safety, comfort, and aesthetics. Selection of alignment is based on gauge, obligatory points, topography, geometrical standards, geology, road crossings, labour/materials, station/yard placement, and political considerations.
This document discusses various aspects of airport engineering and design. It begins by outlining the history of air transport development in India. It then defines key terms like airport, airfield, aerodrome and describes important airport components such as runways, terminals, taxiways, and control towers. The document also discusses factors that influence airport site selection and layout, including aircraft characteristics, wind patterns, and safety. It provides examples of different types of airports and concludes by covering topics like runway orientation, design, lighting and signage.
This document discusses vertical curves used in transportation design. Vertical curves provide a smooth transition between different road or rail grades. They are designed using parabolic equations to maintain a constant rate of change in slope. The key points are:
- Vertical curves connect two different grades using a parabolic shape.
- Their design ensures a constant rate of change in slope for driver comfort.
- The general parabolic equation and methods for computing curve elements like high/low points and elevations at different points are presented.
Here are the key steps and calculations for the homework:
1. Use design speed of 55 mph, emax of 4%, and fmax of 0.12 from Green Book
2. Calculate minimum radius using formula: Rmin = V2/(15(e+f)) = 1,200 ft
3. Select radius of 1,400 ft
4. Given: PI station of 352+44.97, Δ of 35° 24' 55"
5. Calculate curve length using L = ΔR/5729.58 = 1,260 ft
6. Calculate tangent length using T = Rtan(Δ/2) = 630 ft
7. Calculate PC station: PC = PI - T
The clear distance ahead of vehicle which is visible to the driver is known as sight distance
The minimum distance within which a driver can safely stop his vehicle without any collision with some vehicle, animal or any other object is known as stopping sight distance.
Often changes in the direction are necessitated in highway alignment due to various reasons such as topographic considerations, obligatory points.
The geometric design elements pertaining to horizontal alignment of highway should consider safe and comfortable movement of vehicles at the given design speed of the highway.
It is therefore necessary to avoid sudden changes in direction with sharp curves or reverse curves which could not be safely and conveniently negotiated by the vehicles at design speed.
Improper design of horizontal alignment of roads would necessitate speed changes resulting m higher accident rate and increase in vehicle operation cost.
Vertical alignment refers to the vertical profile of a road, including any crests or sags. The two basic components are grade, which is the slope/incline of the road, and vertical curves, which provide a gradual transition between different grades. There are two types of vertical curves - sag curves for positive grade changes and crest curves for negative grade changes. Both are designed as parabolic curves defined by points of vertical curvature, intersection, and tangency. Grade changes of 1% or less may not require a vertical curve depending on design speed.
This document discusses vertical alignment in road design. It defines vertical alignment as the vertical aspect of the road profile, including crest and sag curves. It describes the basic components of vertical alignment as grade and vertical curves. Grade is the slope of the road expressed as a percentage, while vertical curves are parabolic curves that provide gradual transitions between different grades to allow comfortable driving. The document discusses types of vertical curves such as sag curves at the bottom of hills and crest curves at the tops of hills, as well as symmetrical and unsymmetrical curves. It provides the equations used to design different types of vertical curves.
This document discusses the geometric design of highways, specifically focusing on vertical alignment. It defines vertical alignment as the elevation profile of the road's centerline. The objectives of vertical alignment are to ensure proper drainage, acceptable safety levels, and smooth transitions between grades. Vertical curves are used to transition between two grades and can be either crest or sag curves. Design considerations for vertical curves include gradients, maximum grades, curve types, controls for sight distance, driver comfort, drainage and appearance. Equations for determining length and elevations of vertical curve elements like PVI, PVC, PVT are provided. Examples demonstrate calculating length and locations for given design speed, grade changes and other parameters.
The document discusses vertical alignment design for roads. It covers topics such as vertical curve properties, offsets, K-values, stopping sight distance, minimum curve lengths, and coordination of horizontal and vertical alignment. Equations are provided for determining offsets, high/low points, minimum curve lengths for crest and sag vertical curves to meet sight distance requirements. Design standards from sources such as AASHTO and SATCC for selecting K-values based on design speed are also presented. Sample design problems are included at the end related to calculating curve elements, offsets, and minimum lengths.
Alighnment & horizontal alignment of highway (transportation engineering)Civil Zone
This document discusses the alignment of highways, including horizontal and vertical elements. It covers topics such as grade line, horizontal and vertical curves, sight distance requirements, and super elevation. The key points are:
- Highway alignment consists of horizontal and vertical elements, including tangents and curves. Curves can be simple, compound, spiral, or reverse.
- Grade line refers to the longitudinal slope/rise of the highway. Factors in selecting a grade line include earthwork, terrain, sight distance, flood levels, and groundwater.
- Horizontal alignment deals with tangents and circular curves that connect changes in direction. Vertical alignment includes highway grades and parabolic curves.
- Proper design of curves
Location horizontal and vertical curves Theory Bahzad5
Setting out of works
horizontal and vertical curves
Horizontal Alignment
ØAn introduction to horizontal curve &Vertical curve.
ØTypes of curves.
ØElements of horizontal circular curve.
ØGeometric of circular curve
Ø Methods of setting out circular curve
Ø Setting out of horizontal curve on ground
Ø Vertical curve Definition.
ØElements of the vertical curves.
ØAvailable methods for computing the elements of vertical curves
Types of Curves
1- Horizontal Curves
2- Vertical Curves
Horizontal Curves
are circular curves. They connect tangent lines around
obstacles, such as building, swamps, lakes, change
direction in rural areas, and intersections in urban areas.
-Compound Curve.
-Reverse curve.
-Transition or Spiral Curves.
-Horizontal Curve: Simple circular
curve
-Elements of horizontal curves.
-Formulas for simple circular
curves.
-Properties of circular curves.
example:A horizontal curve having R= 500m, ∆=40°, station P.I=
12+00 ,prepare a setting out table to set out the curve
using deflection angle from the tangent and chord length
method, dividing the arc into 50m stations.
:Example H.W
A Horizontal curve is designed with a 600m radius and is
known to have a tangent of 52 m the PI is Station
200+00 determent the Stationing of the PT?
-PROCEDURE SETTING OUT Practical .
Vertical Curves
Elevation and Stations of main points on the Vertical Curve .
Assumptions of vertical curve projection.
Example: A vertical parabola curve 400m long is to be set
between 2% (upgrade) and 1% (down grade), which meet
at chainage of 2000 m, the R.L of point of intersection of
the two gradients being (500.00 m). Calculate the R.L of
the tangent and at every (50m) parabola.
Thank you all
Prepared by:
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
3 vertical alignment of road by Malyar TalashMalyar Talash
This document discusses vertical road alignment and provides guidance on vertical curve design. It covers several key topics:
- The influence of topography on vertical alignment and how terrain is classified.
- The two main aspects of vertical alignment: vertical curvature and gradient.
- The two types of vertical curves: crest and sag curves.
- Design considerations for vertical grades and maximum grades based on vehicle type and speed.
- Equations for determining minimum vertical curve lengths to provide adequate sight distance and passenger comfort.
This document provides an introduction to different types of curves used in computer graphics. It discusses curve continuity, conic curves such as parabolas and hyperbolas, piecewise curves, parametric curves, spline curves, Bezier curves, B-spline curves, and applications of fractals. Key points covered include the four types of continuity, how conic curves are defined by discriminant functions, using control points to define piecewise, spline, Bezier and B-spline curves, and properties of Bezier curves such as passing through the first and last control points.
Overview:
The vertical alignment of a road consists of gradients(straight lines in a vertical plane) and vertical curves. The vertical alignment is usually drawn as a profile, which is a graph with elevation as vertical axis and the horizontal distance along the centre line of the road as the the horizontal axis.
This presentation constitutes an integral component of a designated course curriculum and is crafted and disseminated for its intended audience. None of the contents within this presentation should be construed as a formal publication on the subject matter. The author has extensively referenced published resources in the preparation of this presentation, and proper citations will be provided in the bibliography upon completion of its development.
The document discusses various aspects of highway engineering related to horizontal and vertical alignment of roads. It describes extra widening needed on curved sections of roads to accommodate vehicles. It discusses the analysis and formulas to calculate mechanical and psychological widening. It also covers horizontal transition curves, their objectives and methods to determine length. The document discusses setback distance for obstructions on curved sections and the formulas to calculate setback based on sight distance and curve length. It concludes with definitions of gradient, ruling gradient and other types for vertical alignment considerations.
This document discusses horizontal curves in surveying. It covers the objectives of learning about horizontal curve layout, types of curves like simple, compound, and reverse curves. It defines degree of curve and how it is calculated based on the arc or cord length. It describes the elements of a circular curve like point of curvature, point of tangency, radius, chord length, and central angle. Methods for laying out a circular curve are discussed, including linear methods using offsets and bisection, and angular methods like Rankine's method and two theodolite method. Key questions about why curves are needed and defining the degree of curve are also answered.
Curvature is inevitably provided on railway tracks to bypass obstacles, provide longer gradients, and pass lines through desirable locations. Horizontal curves change track direction, while vertical curves connect gradients or gradients to level ground. Curvature restricts speed and train length, increases maintenance costs, and risks accidents. Degree and radius describe curves, with smaller radii indicating sharper curves. Super-elevation/cant counters centrifugal force on curves, and is calculated using speed, weight, radius, and gauge. Cant deficiency occurs where full cant cannot be provided, like where lines branch, requiring speed restrictions.
This document discusses vertical curves and sight distance requirements for road design. It defines types of vertical curves (crest and sag) and provides equations to calculate the minimum length of vertical curves based on design speed to provide adequate sight distance. Sight distance must be considered to ensure drivers can safely stop sight lines are not obstructed by curves. Both crest and sag curves have different equations that factor in speed, grade, and eye heights to determine appropriate lengths.
The document discusses circular curves and their use in highway and railway alignment. It defines key terms related to circular curves like deflection angle, chord, radius, and introduces different types of horizontal curves - simple circular curves, compound curves, reverse curves, spiral curves, and lemniscate curves. It also discusses vertical curves like valley and summit curves. The document provides formulas to calculate length of tangent, external distance, middle ordinate, length of chord, length of curve, degree of curve, and minimum radius of curvature for circular curves. It includes examples of problems calculating radius, offset distance, and degree of curve given different curve elements.
This document provides information about curve ranging in surveying engineering. It begins with describing the expected learning outcomes of understanding how to calculate positions for horizontal and vertical curves. It then discusses different types of horizontal curves used in road and railway design, including simple, compound, transition and reverse curves. The key geometry and elements of circular curves like tangent length, external distance, mid-ordinate and curve length are defined. Several example problems are provided to show how to tabulate data and calculate values needed to lay out horizontal and vertical curves using surveying methods and tools. Vertical curves called summit and valley curves are also introduced to smoothly connect changes in roadway gradients.
This chapter discusses key concepts about straight lines including:
- Gradient is the ratio of vertical to horizontal distances between two points and represents the steepness of a line.
- The equation of a straight line can be written in slope-intercept form as y = mx + c or point-slope form.
- Parallel lines have the same gradient. An example shows that the lines 2x - y = 6 and 2y = 4x + 3 are parallel because they have the same gradient of 2.
Vertical alignment of highway (transportation engineering)Civil Zone
Vertical curves are used in highway design to gradually transition between two different slopes or grades. There are two main types - crest vertical curves, which are used on roadway tops, and sag vertical curves, which are used on dips. The minimum length of a vertical curve is determined based on providing the required stopping sight distance for a given design speed. Additional criteria like passenger comfort, drainage, and appearance may also influence the curve length selected. Longer vertical curves generally provide a smoother ride but require more construction costs.
This document discusses curves and surfaces. It begins by introducing parametric curves, which are defined by continuous functions of a parameter. Important properties of curves discussed include affine invariance and satisfying the convex hull property. Several interpolation techniques for constructing curves through given points are covered, including Lagrange interpolation and Bézier curves. Bézier curves are constructed using Bernstein polynomials and have desirable properties like the convex hull property. The document shows how to define piecewise continuous Bézier curves and discusses algorithms for evaluating and rendering Bézier curves.
The document discusses roll pass design for continuous bar mills. It defines basic terminology like roll pass and nominal roll gap. The goal of roll pass design is to produce the desired product shape with good internal structure, surface and lowest cost. There are definite, intermediate and combination pass shapes. A deformation changes one shape to another, while a sequence produces a definite shape. Roll pass design considers the starting material, mill layout, sizes, power and production needs to determine pass details, schedules and power requirements for each pass. It also discusses basic rolling laws and formulas for shapes like squares and ovals.
2. Vertical Curves
• Vertical curves provide a •" In highway design, the grades of
means to smoothly shift from the disjointed segments of
one tangent grade to another. roadway are normally known
They are usually parabolic in
before any vertical curve
shape. They are classified into
crest vertical curves and sag calculations are initiated.
vertical curves. •" In addition, the design speed of
the roadway, the stopping sight
• In highway design, most distance, and the decision sight
vertical curves are equal- distance are also well established.
tangent curves, which means
•" The first step in the design of a
that the horizontal distance
from the center of the curve vertical curve is the calculation
to the end of the curve is of the curve length, which is the
identical in both directions. length of the curve as it would
appear when projected on the x-
• (Unequal-tangent vertical axis.
curves, which are simply equal-
tangent curves that have been
attached to one another, are
seldom used. )
3. Stopping Sight Distance
and Vertical Curvature
• Because the stopping sight •" Let’s assume that you have
distance (S or ds) should always already calculated the appropriate
be adequate, the length of the length (L) for your curve.
curve depends on the stopping •" The first step in developing the
sight distance. profile for your curve is to find
the center of your curve. The
• Occasionally, as with any other location of the center-point is
section of a highway, the where the disjointed segments of
decision sight distance is a the roadway would have
more appropriate sight intersected, had they been
distance. In these instances, allowed to do so. In other words,
the decision sight distance draw lines tangent to your
governs the length of the roadway segments and see where
vertical curve. those lines intersect. This
intersection is normally called the
• The curve length calculations vertical point of intersection
are slightly different for sag (PVI).
and crest vertical curves, and
are covered separately.
4. PVC and PVT
• The vertical point of curvature (PVC ) and the vertical point of tangency (PVT) are located
a horizontal distance of L/2 from the PVI. The PVC is generally designated as the origin
for the curve and is located on the approaching roadway segment. The PVT serves as the
end of the vertical curve and is located at the point where the vertical curve connects
with the departing roadway segment. In other words, the PVC and PVT are the points
along the roadway where the vertical curve begins and ends.
• One you have located the PVI, PVC, and PVT, you are ready to develop the shape of your
curve. The equation that calculates the elevation at every point along an equal-tangent
parabolic vertical curve is shown below.
PVI
B
PVT
PVC
L/2 L/2
L
5. Equation of Elevation
y = ax 2 + bx + c
Where:
y = Elevation of the curve at a distance x meters
from the PVC (m)
c = elevation of PVC (m)
b=G1
a=(G2-G1)/2L
L = Length of the curve (m)
x = Horizontal distance from the PVC (m) (Varied from
0 to L for graphing.)
6. Example 1
A 150 m equal tangent crest-vertical curve has
the PVC at station 8+500 and elevation of 250
m.
The initial grade is +2.6% and the final grade is
-0.5%.
Determine the elevation and stationing of the
PVI, PVT and the highest point of the curve.
7. Solution 1
Because the curve is equal tangent,
•" Substituting
the PVI will be 75m from the PVC,
and the PVT will be 150 m from the
PVC. 0=2(-0.0001)x+0.026
The stationing is therefore at:
PVI: 8+575 & Stationing of max = 8+500 + 0+125.8 =
PVT: 8+650 8+625.8
The grade = +2.6% = .026 m/m
•" Elevation =y=ax2+bx+c
PVI elevation is thus 250 + 0.026*75
= 251.95m •" =(-0.0001)*125.82 +
PVT elevation is 251.95 - 0.005*75 = 0.026*125.8+250=-1.583+3.27+250=251
251.575m
.69
Maximum occurs when first derivative
=0 •" 251.69 < 251.95 (PVI) check
dy/dx = 2ax+b = 0
b= G1= 0.026
a=(G2-G1)/2L =(-0.005-0.026)/
(2*150)=-0.0001033
x=125.8m
8. Suppose G1=0
Suppose G1= 0
Maximum occurs when first derivative = 0
dy/dx = 2ax+b = 0
b= G1= 0
a=(G2-G1)/2L =(-0.005)/(2*150)=-0.0000167
x=0m
So maximum is at start of curve (x=0)
Suppose G2 =0
b=G1=0.026
a=(G2-G1)/2L=-0.026/300=0.0000867
dy/dx = 2ax+b = 0=-0.000173x+0.026=0
x=150 m
So maximum is at end of curve (x=150)
9. Crest Vertical Curves: Design
Crest vertical curves connect inclined sections of roadway,
forming a crest. Objective: find an appropriate length for
the curve that will accommodate the correct stopping sight
distance.
Sight Distance > h1
Curve Length h2
L
Sight Distance < h1
h2
Curve Length
L
10. Equations Relating Length of
Curve and Sight Distance
•" Where:
If S ≥ L then –" L = Length of the crest
( )
2
vertical curve (m)
200 h1 + h2
L = 2S − –" S = Sight distance (m)
A –" A = |G2-G1| = The absolute
value of change in grades
(as a percent)
If S ≤ L then
–" h1 = Height of the
AS 2 driver's eyes above the
L=
( )
2 ground (m)
200 h1 + h2 –" h2 = Height of the object
above the roadway (m)
11. Stopping Sight Distance and Length of Crest Vertical Curve
Length of
Vertical Curve
500
450
400
350
300
L (A=1)
250 L (A=2)
L (A=6)
200
150
100
50
0
0 50 100 150 200 250 300 350 400 450 500
Stopping Sight Distance
12. Comments
• The heights in the calculations above should be those that
correspond to the sight distance of interest.
• For the stopping sight distance, h1 = 1.1 m and h2 = 0.15 m.
• For the passing sight distance, h1 = 1.1 m and h2 = 1.3 m.
• While the sight distance has been portrayed as the only parameter
that affects the design of vertical curves, this isn't entirely
true. Vertical curves should also be comfortable for the driver,
aesthetically pleasing, safe, and capable of facilitating proper
drainage. In the special case of crest vertical curves, it just so
happens that a curve designed with adequate sight distances in
mind is usually aesthetically pleasing and comfortable for the
driver. In addition, drainage is rarely a special concern.
13. Example 2: Minimum
Length of Crest Vertical
Curve
A crest vertical curve is to be designed to join a
+3 percent grade with a -3 percent grade at a
section of a two lane highway,
Determine the minimum length of the curve if
the design speed (V) of the highway is 100 km/hr
and S < L.
Assume that f = 0.29 and PRT = 2.5 sec
14. Solution
Determine SSD (Since the grade is constantly
changing, the worst case value for G is used).
v2
S = ds = 0.278tr v +
254 f ± G ( )
1002
= 0.278 * 2.5 *100 + = 221m
254 0.29 − 0.03 ( )
Obtain minimum length of the vertical curve
AS 2 6 * 2212
L= = = 710m
( ) ( )
2 2
200 h1 + h2 200 1.1 + .15
15. Problem: Minimum Safe
Speed on a Crest Vertical
Curve
An existing vertical curve on a highway joins a +4
percent grade with a -4 percent grade.
If the length of the curve is 100 m, what is the
maximum safe speed on the curve.
Assume f=0.4 and PRT = 2.5 sec. Also S < L
16. Solution
First determine the safe stopping distance S (SSD) using the length of the
curve
AS 2 8 * S2
L= = 100 =
( ) ( )
2 2
200 h1 + h2 200 1.1 + .15
S = 71.7m
Now determine the maximum safe speed for this SSD
v2 v2
S = ds = 0.278tr v + = 71.7 = 0.278 * 2.5 * v +
254 f ± G ( ) 254 0.4 − 0.04 ( )
= 0.69 * v + 0.010936v 2
71.7 = 0.69 * v + 0.010936v 2
v 2 + 63.6v − 6556 = 0
v ≈ 55km / h
(Technically 55.2, but round down to nearest speed limit in 5 km/hr
increments)
17. Problem: Design of a
Crest Vertical Curve
A crest vertical curve joining a +4 percent and
-3 percent grade is designed for 120 km/hr. If
the tangents intersect at metric station 20 +
050.00 and at an elevation of 150 meters,
determine the stations and elevations for the
PVI and PVT. Also calculate the elevations of
intermediate points on the curve at the whole
stations.
From tables, f=0.28
18. Solution
Stopping Sight distance (G=0.04 is critical grade)
v2 120 2
S = ds = 0.278t r v + = 0.278 ( 2.5 )120 + = 320m
254 ( f ± G ) 254 ( 0.28 − 0.04 )
•" Length of Curve
AS 2 7 * 320 2
L= = = 1737.78m
( ) ( )
2 2
200 h1 + h2 200 1.1 + 0.15
•" Station of PVC = (20+050.00) - (1+737.78)/2 = (20+050.00) - (0+868.89) =19+181.11
•" Station of PVT = (20+050.00) + (1+737.78)/2 = 20+918.89
•" Elevation of PVC = PVIy-(G*L/2)=150 - (0.04*0.5*1737.78) = 115.24 m
•" Elevation of PVT = PVIy-(G*L/2)=150 - (0.03*0.5* 1737.78) = 123.93 m
20. Abbreviations
PVI - Point of Vertical Intersection (sometimes VPI)
PVC - Point of Vertical Curvature (sometimes VPC)
PVT - Point of Vertical Tangency (sometimes VPT)
SSD - Stopping sight distance (ds) or (S)
22. Variables
y = Elevation of the curve at a distance x meters from the PVC (m)
c = elevation of PVC (m)
b=G1
a=(G2-G1)/2L
L = Length of the crest vertical curve (m)
S = Sight distance (m)
A = The change in grades (|G2-G1| as a percent)
h1 = Height of the driver's eyes above the ground (m)
h2 = Height of the object above the roadway (m)