2.67 - A circular curve of 610 m radius deflects through an angle of 40°30'...
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Understanding Circular Curves
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Today, we will begin by exploring what a circular curve is. A circular curve is a curve whose radius remains constant along its length. Who can tell me what some elements of a circular curve are?
It includes the radius, the deflection angle, and the tangents.
Correct! Now, let's focus on the deflection angle. In our example, the circular curve deflects through 40°30'. Can anyone explain how this affects the curvature?
The greater the deflection angle, the larger the radius of the circle that fits the curve.
Exactly! A larger deflection angle allows for greater curvature. Now, we start with a radius of 610 m in this case.
What happens if we want to create a transition curve at the end of this curve?
Great question! Transition curves gradually change the curvature, making it safer and more comfortable for drivers. We will also examine how this affects our calculations.
Adjusting Radius with Transition Curves
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As we proceed, we will adapt our circular curve with transition curves of 107 m each, placed at both ends. Why do we need to adjust the radius?
To ensure the new paths are smoother and safer?
Precisely! Now, when we perform the calculations, we find that the deviation of the new curve at the midpoint is 0.46 m. What does this tell us?
It indicates how far the new curve differs from the original curve at that point.
Correct! Using this deviation, we calculate the revised radius, which comes out to 590 m. Let's recap that: the original was 610 m, and now it's adjusted to 590 m.
Understanding Track Adjustments
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Now let's determine how much old track must be lifted and how much new track must be laid. We established that the lengths are 524 m for the old track and 521 m for the new track.
Why is it important to know the exact lengths?
Excellent question! Knowing the lengths helps in planning and ensuring that the materials needed for construction are accurate. What can we conclude about changing curves?
That such adjustments improve road safety and driver comfort.
Exactly! Well done, everyone. This process is integral in civil engineering related to road design and safety.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
In this section, we explore the calculations involving a circular curve of 610 m radius that deflects through an angle of 40°30'. We compute the revised radius of the curve after introducing smaller radius transition curves and also determine the necessary lengths of both old and new tracks to be laid.
Detailed
Detailed Summary
This section addresses the adjustment required for a circular curve with an initial radius of 610 m that extends through an angle of 40°30'. The need arises to replace this with smaller radius transition curves measuring 107 m at each end. A key aspect of this adjustment involves examining the deviation of the new curve from the existing curve at the midpoint, which is determined to be 0.46 m towards the intersection point. The primary calculations include determining the revised radius and computing the lengths of the existing tracks to be lifted and the new tracks that need to be laid. With accurate calculations, we find that the revised radius of the curve will be 590 m, the new track length will be 521 m, and the old track length will be 524 m.
Key Concepts
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Circular Curves: Maintains a constant radius.
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Deflection Angle: Determines the curvature change.
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Transition Curves: Ensures smooth transition from straight to curved paths.
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Deviation: Measures how much a curve shifts from its original path.
Examples & Applications
Example of a circular curve with a radius of 610 m deflecting through 40°30'.
Case where transition curves are introduced to improve road safety and comfort.
Memory Aids
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Rhymes
For a curve that's wide and true, measure it right, and smooth out the view.
Stories
Imagine driving on a winding road, suddenly the curves become sharp. You feel uncomfortable. But then, with transition curves, the path gently guides you, making your ride smooth and safe.
Memory Tools
Remember: C for Circular, D for Deviation, T for Transition!
Acronyms
C-D-T
Circular - Deviation - Transition
Flash Cards
Glossary
- Circular Curve
A curve whose radius remains constant along the arc.
- Deflection Angle
The angle through which a curve turns from a straight line.
- Transition Curve
A curve that gradually connects a straight section of road to a circular curve, allowing for smoother change in curvature.
- Deviation
The distance between the original curve and the new curve at a defined point.
- Radius
The distance from the center of a curve to any point on its arc.
Reference links
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