Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Learn it your way
A short class with Sarah and her students. The other ways are under More.
Sign up free to listen. Transcripts are free to read.
Today, we’re going to explore chainage and its importance in setting out circular curves. Students, what do you think chainage means?
Isn't it the distance along a path from a starting point?
Exactly! Chainage is the linear measure from a reference point. It's crucial when navigating curves. Now, can anyone tell me what the Point of Intersection or PI is?
I think it's where two tangents meet, right?
Spot on! The PI is essential for determining how to set out the curve. Remember the acronym 'TLC' - Tangent Length, Length of Curve, and Chainage, which are all interrelated in calculating PI.
How do we calculate the Tangent Length?
Great question! Tangent Length T is calculated using the formula T = R tan(Δ/2). Let’s practice: if R is 300 m and Δ is 36°, how would you find T?
I think T would be 300 tan(18°).
Correct! This fundamental understanding of T is vital for determining the chainage of the PI and other curve points. Today, remember the importance of each element in the context of setting out curves.
Now let’s discuss the Length of Curve. Can anyone tell me what the formula is?
Isn't it L = R * (Δπ/180)?
Exactly right! For example, if we have a radius R of 600 m and a deflection angle Δ of 36°, how would we compute L?
We'd multiply 600 times (36π/180).
Correct! And what does that yield?
It should give us the length of the curve.
Right! Understanding how to find the Length of Curve is pivotal not just for the calculations but for practical applications in road/rail design which we will cover next. Remember to always check the units and make necessary conversions!
Let’s apply these principles through an example where we're setting out a curve; we have Δ = 36° and R = 300m. Can anyone tell me the first step?
Calculate the Tangent Length first, right?
Absolutely! And what’s the formula for that?
It’s T = R * tan(Δ/2).
Great! Now, how do we calculate the Chainage for the next point, T?
I think we would subtract the Tangent Length from the initial chainage.
Exactly! So if PI is 1190m and we found T, what would the chainage of T be?
Chainage of T would be 1190 minus the Tangent Length.
Spot on! Remember, working backwards or forwards between points using chainage is a critical aspect in effectively managing construction projects.
To find the Length of Curve with ease, use R and Δ, it's a breeze!
Imagine two friends at a park, walking paths that meet where they start. They're trying to find out how far to go; just use chainage, and you'll surely know!
Remember 'TLC': Tangent Length, Length of Curve, Chainage.
R for Radius and D for Deflection - together they help in any direction.
Term
Tangent Length Formula
Click to flip
Term
Length of Curve Formula
Click to flip
The linear measurement from a specific point along a path, usually in meters or chains.
The point where two tangential paths meet in a circular curve.
The distance from the PI to the point where the tangent touches the circle.
The distance from the center of the circle to any point on the circumference.
The angle through which a tangent to a curve must turn to follow the curve.
This section covers the calculations and methodologies used to determine the chainage of points of intersection (PI) in circular curves.
The section details various methods for calculating the chainage of points of intersection in circular curves, focusing on concepts such as tangent lengths, curve lengths, and deflection angles. Key formulas, examples, and exercises are presented to solidify understanding.
In this section, we delve into the calculations necessary for determining the chainage of the Point of Intersection (PI) for circular curves. Chainage is crucial in civil engineering and surveying as it denotes the linear measure from a specified starting point along a path, typically expressed in meters or chains.
Tangent Length (T): The distance from the PI to the point where the tangent touches the curve. It is calculated as:
Length of Curve (L): The length of the circular arc between two points on the curve, determined by:
Chainage Calculation: Chainage at any point can be found using:
This section includes several worked-out examples, such as calculating chainage from specified parameters (like deflection angles and radii) as well as practical exercises that reinforce key concepts. Understanding these calculations is vital for the design and layout of roads, railway lines, and other civil engineering projects.