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Learn it your way
A short class with Sarah and her students. The other ways are under More.
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Today, we're discussing the method of setting out curves by ordinates from the long chord. This technique is fundamental to ensuring our curves are accurate. Can anyone tell me what we understand by a 'long chord'?
I think it's the straight line connecting two points on the curve.
Exactly! The long chord connects the endpoints of our curve. Now, what do we do with that chord to set out the curve?
We create offsets, right? Like perpendicular lines from the chord?
Correct! These offsets allow us to establish points along the curve. Now, can anyone summarize how we calculate those offsets?
We use formulas based on the radius, the length of the chord, and the distance from the midpoint.
Good job! Remember the equation O = √ (R² − x²) helps you find offsets accurately. Always visualize this relationship!
In summary, this method requires dividing the chord into equal sections, calculating offsets, and using them to establish points along the curve. Be sure to practice these calculations!
Now, let's look at the successive bisection of arcs. Who recalls what this method entails?
Isn't it about bisecting chords? We also use the versine to find offsets.
That's right! In this method, we bisect not just the chords but the arcs of the curve too. This aids in accurately plotting points even when the ground is difficult to measure. Can someone explain what a versine is?
It's the distance from the chord to the arc, right?
Yes, well done! As a helpful mnemonic, remember that 'versine' is 'vertical sine.' This makes it easier to connect the concept to the geometry involved. What are the steps you would take to apply this method?
We start by bisecting the initial chord, setting points using the versine value, then repeating this for subsequent segments.
Perfect! Make sure to practice these steps. To wrap up, remember that this method is beneficial when other ground measuring methods are impractical.
Next, let's explore setting out curves by offsets from the tangents. Can anyone explain what the two types of offsets are?
We have radial offsets and perpendicular offsets.
That's correct! Radial offsets are measured directly outward from the tangent, while perpendicular offsets are at right angles. What are some formulas we might use with these offsets?
For radial offsets, we can use PP = OP - OR where each is calculated based on the radius.
Exactly! And don't forget for large radii, approximation formulas can help simplify calculations too. Now, how do we implement these steps in a real-world scenario?
We need to locate tangent points, then measure distances and apply the formulas for offsets we've learned.
Well said! In summarizing this method, remember it is especially useful for sharp curves where measurements need to be precise. Always pay attention to the ground conditions!
Lastly, let's discuss setting out curves using offsets from chords that are produced. What do you think is meant by 'chords produced'?
I believe it means extending the chord beyond the curve to find offset points.
Exactly! This allows for greater flexibility when locating points on the curve. What are some considerations we should take into account with this method?
We need to ensure we properly calculate the angle subtended at the center to maintain accuracy.
That’s a great observation! And can anyone recap how to practically apply this method step by step?
First, locate the tangent points, then calculate the lengths of chords and their offsets, ensure to consider any angles involved, then complete the setup!
Wonderful! To conclude this session, remember that this method is beneficial when precise measurements are required across the curve.
A method to measure offsets for curve construction.
Successive bisection helps in accurate point placement.
Use of both radial and perpendicular offsets allows for flexibility.
Utilizing produced chords can aid in flexibility in design.
Chords are straight, curves are round, put them together, measurements abound!
Imagine a road lined with trees, where engineers must plan the curves around hills. They measure chords and calculate offsets, ensuring every turn is safe and smooth.
Use 'COVERS' to remember: Chord, Offsets, Versines, Engineering Road Safety.
R.O.C. for Radial, Offsets, and Chords to recall key methods of setting out curves.
Term
Long Chord
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Term
Offsets
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Term
Versine
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Term
Radial Offsets
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A straight line connecting the endpoints of a circular curve.
Perpendicular lines from the chord or tangent to establish points on the curve.
The distance from the chord to the arc of a circle.
Offsets measured radially outward from a point on a tangent.
Offsets taken at right angles from the tangent line to the curve.
This section covers the linear methods used to set out simple circular curves in construction, focusing on four key techniques.
The section discusses methods for setting out simple circular curves, emphasizing linear techniques such as ordinates from the long chord, successive bisection of arcs, offsets from tangents, and offsets from chords produced. Each method is explained with procedural steps and mathematical formulations.
This section explains four linear methods utilized for setting out simple circular curves in construction projects. Understanding these methods is crucial for engineers and surveyors when designing roadways, railways, and other infrastructure involving curves. The methods discussed include:
By Ordinates from the Long Chord: This method involves establishing points along a curve by erecting perpendicular offsets from a long chord, which allows for precise calculations when determining offsets and positions on the curve. The offsets can be accurately calculated using relationships derived from the properties of circles.
By Successive Bisection of Arcs (Versine Method): This technique entails bisecting the arcs of the curve to determine offset points. It is particularly useful when accurate measurements of the ground distance outside the curve are challenging to obtain.
By Offsets from the Tangents: This method utilizes radial or perpendicular offsets from the tangents of the curve to plot points accurately. Two approaches—radial offsets and perpendicular offsets—are detailed, with specific formulas for each scenario.
By Offsets from Chords Produced: This involves taking offsets from extended or produced chords to define the curve accurately and calculate offsets effectively.
Overall, these methods are essential for ensuring that curves in road construction are set out accurately, facilitating safe and efficient design.