To find the stationing of the Point of Intersection (P.I.) of a simple curve, we need to apply a couple of basic concepts from surveying, specifically related to the curve geometry.

Given:

• The offset distance (from P.C. to P.T.) is 20 m.
• The angle of intersection (Δ) of the tangents is 32°.
• The stationing of P.T. is 10 + 256.32.

Formula for calculating the stationing of P.I.:

1. Formula for the length of the curve (L):
   $L = \frac{20}{\tan\left(\frac{\Delta}{2}\right)}$

2. Stationing of P.I. can be found by subtracting the length of the curve (L) from the stationing of P.T.: $\text{Stationing of P.I.} = \text{Stationing of P.T.} - L$

Step 1: Calculate the length of the curve (L):

$L = \frac{20}{\tan\left(\frac{32^\circ}{2}\right)} = \frac{20}{\tan(16^\circ)}$

First, calculate $\tan(16^\circ)$: $\tan(16^\circ) \approx 0.2867$

Thus: $L \approx \frac{20}{0.2867} \approx 69.7 \text{ m}$

Step 2: Calculate the stationing of P.I.:

Now, subtract the length of the curve (69.7 m) from the stationing of P.T.: $\text{Stationing of P.I.} = 10 + 256.32 - 69.7 = 10 + 186.62 = 10 + 186.62$

Final Answer:

The stationing of P.I. is 10 + 186.62.

Would you like a more detailed breakdown or have any other questions?

Related Questions:

1. How do you calculate the radius of a simple curve given the offset distance and angle of intersection?
2. What is the significance of the tangent points (P.C. and P.T.) in curve alignment?
3. How do you find the degree of a curve from the length and offset distance?
4. What is the formula for the central angle of a circular curve based on the radius?
5. How does the method of stationing apply to large-scale civil projects, such as highways?

Tip:

When working with curves, ensure all angle measures are converted to radians if needed for certain calculators or equations, as some use radians rather than degrees.