Name: calculating elevations on a vertical curve
Uploaded: 2025-03-26T15:36:53.000Z
Duration: 1 min 23 s
Channel: JoVE

يربط المنحنى الرأسي خطين للدرجة، مما يضمن انتقالا سلسا للطريق السريع. يتم توفير طول المنحنى والدرجات وموقع PVI والارتفاع لحساب ارتفاعات المنحنى في محطات محددة. يتم حساب محطات P.V.C. و P.V.T. ، التي تحدد بداية المنحنى ونهايته ، عن طريق طرح وإضافة نصف طول المنحنى إلى محطة PVI.باستخدام الدرجات المعطاة, P.V.I. الارتفاع, ونصف طول المنحنى, يتم تحديد الارتفاعات في P.V.C. و P.V.T. يتم تحديد.لكل محطة، يتم حساب ارتفاع خط التسوية من خلال الجمع بين الدرجة والمسافة الأفقية من P.V.C. أو P.V.T.بعد ذلك، يتم تحديد ارتفاع نقطة المنتصف للوتر الطويل وارتفاع نقطة منتصف المنحنى لحساب الإزاحة عند P.V.I.تستخدم هذه الإزاحة والمسافة الأفقية من P.V.C. أو P.V.T. لحساب إزاحات الظل لكل محطة بناء على طول المنحنى.أخيرا، يتم الحصول على ارتفاعات المنحنى في المحطات عن طريق طرح إزاحات الظل من ارتفاعات خط الصف.تمثل الارتفاعات المحسوبة المظهر الرأسي للمنحنى.

المنحنى العمودي: حل المشكلات

توفر المنحنيات الرأسية الانتقال بين درجتين من الطرق ، مما يضمن السلامة والراحة والوظائف. يتضمن حساب الارتفاعات في محطات محددة على طول المنحنى عدة خطوات منهجية بناء على هندسة المنحنى ومعلمات التصميم المقدمة. يتم تحديد المنحنى الرأسي من خلال طوله ودرجاته وموقع نقطة التقاطع الرأسي (PVI) وارتفاع PVI. يتم تحديد محطات نقطة الانحناء الرأسي (P.V.C.) ، حيث يبدأ المنحنى ، ونقطة الظل الرأسي (P.V.T.) ، حيث ينتهي المنحنى ، عن طريق طرح وإضافة نصف طول المنحنى إلى محطة PVI. يتم حساب الارتفاعات في P.V.C. و P.V.T. باستخدام الدرجات و P.V.I. الارتفاع. ويحسب ارتفاع خط التسوية لكل محطة على طول المنحنى باستخدام الدرجة عند P.V.C. أو P.V.T. والمسافة الأفقية إلى المحطة. يوفر هذا الحساب ملف تعريف الارتفاع الخطي قبل حساب الشكل المكافئ للمنحنى. يتم تحديد الارتفاع عند نقطة منتصف الوتر الطويل ونقطة منتصف المنحنى لحساب الإزاحة عند PI. يمثل هذا الإزاحة ، المشتق من الهندسة المكافئة للمنحنى ، المسافة الرأسية بين خط التسوية والمنحنى عند P.V.I. باستخدام إزاحة PVI والمسافة الأفقية من P.V.C. أو P.V.T. ، يتم حساب إزاحة المماس لكل محطة. تعكس هذه الإزاحات الانحراف عن خط التسوية الناجم عن انحناء الطريق. ثم يتم الحصول على ارتفاع المنحنى في كل محطة بطرح تخالف المماس من ارتفاع خط الانحدار. تشكل الارتفاعات المحسوبة في محطات محددة المظهر الرأسي للمنحنى ، وهو أمر بالغ الأهمية لتصميم التحولات السلسة ، وضمان الصرف المناسب ، والحفاظ على معايير السلامة. تمكن هذه الحسابات المهندسين من إنشاء طرق توازن بين الوظائف وراحة السائق.

Vertical curves provide the transition between two roadway grades, ensuring safety, comfort, and functionality. Calculating elevations at specific ...

Education

JoVE Core

Civil Engineering

الهندسة المدنية

Unit 1

الوحدة الأولى

Horizontal and Vertical Curves

المنحنيات الأفقية والرأسية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الرئيسية

Vertical Curve: Problem Solving

calculating elevations on a vertical curve

Vertical curves connect two roadway grades and help make the road safer, smoother, and more functional. To find the elevation at specific stations on the curve, engineers follow a set of steps based on the curve length, the grades, the Point of Vertical Intersection, or P.V.I., and the P.V.I. elevation.

The first step is to locate the Point of Vertical Curvature, or P.V.C., and the Point of Vertical Tangency, or P.V.T. The P.V.C. marks the start of the curve, and the P.V.T. marks the end. Their stations are found by subtracting and adding half the curve length from the P.V.I. station. The elevations at the P.V.C. and P.V.T. are then calculated from the grades and the P.V.I. elevation.

Next, the grade line elevation is found at each station along the curve. This uses the grade at the P.V.C. or P.V.T. and the horizontal distance to the station. The result gives the straight-line elevation profile before the parabolic curve shape is applied. Engineers then find the elevation at the midpoint of the long chord and the curve’s midpoint to determine the offset at the P.V.I.

That offset comes from the curve’s parabolic geometry. It is the vertical distance between the grade line and the actual curve at the P.V.I. Using the P.V.I. offset and the horizontal distance from the P.V.C. or P.V.T., tangent offsets are calculated for each station. These offsets show how far the roadway curve deviates from the grade line.

The final curve elevation at each station is found by subtracting the tangent offset from the grade line elevation. These station elevations form the vertical profile of the roadway. They are important for smooth transitions, proper drainage, and safety, while also helping the road remain comfortable for drivers.

Calculating Elevations on a Vertical Curve

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introduction to horizontal curves

Horizontal Curve Parts and Road Alignment

Horizontal curves connect straight road or railroad segments and help vehicles move safely through a change in direction. They are used in highway and railroad design to create smooth transitions between tangents, which are the straight path sections before and after the curve. By reducing abrupt changes, these curves can support steadier travel speed and help lower the chance of accidents. A simple horizontal curve is defined by its geometry around the intersection point, or P.I., where two...

degree of curvature and radius of curvature

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Curvature Measures in Civil Engineering Curves

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Curve Measurements and Arc Length

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Vertical curves are parabolic transitions that connect different grades on highways and railroads. They help create a smooth alignment between the back tangent and the forward tangent. The back tangent is the first grade, and the forward tangent is the next grade. These curves may be symmetrical or nonsymmetrical. In a symmetrical vertical curve, the tangent lengths are equal. In a nonsymmetrical curve, the tangent lengths are different. The main points used to describe the curve are the Point...

vertical curve: problem solving

Vertical curves connect two roadway grades and help make the road safer, smoother, and more functional. To find the elevation at specific stations on the curve, engineers follow a set of steps based on the curve length, the grades, the Point of Vertical Intersection, or P.V.I., and the P.V.I. elevation. The first step is to locate the Point of Vertical Curvature, or P.V.C., and the Point of Vertical Tangency, or P.V.T. The P.V.C. marks the start of the curve, and the P.V.T. marks the end.

elevation of intermediate points on vertical curves

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Finding High and Low Points on Vertical Curves

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key terms and concepts

Learn how to calculate elevations on a vertical curve using P.V.C., P.V.T., P.V.I., grade line elevation, and tangent offsets in roadway design.

Calculating Elevations on a Vertical Curve | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Calculating Elevations on a Vertical Curve

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