Calculating Chainage of Transition Curve End

In surveying, particularly in railway or highway design, chainage refers to the distance measured along the center line from a fixed starting point. Curves often involve a transition curve between a tangent and a circular curve.

The question provides the following information:

• The chainage of PC is given as 40000 m.
• The length of the transition curve is given as 220 m.

We are asked to find the chainage of the junction of the transition curve. In the context of curve design involving transition curves, PC (Point of Curve) typically denotes the point where the transition curve meets the circular curve. However, given the options and the correct answer, the term 'PC' in this question is likely referring to the start of the transition curve from the tangent (often called T.S. or Tangent to Spiral), and the 'junction of transition curve' refers to the point where the transition curve ends and joins the circular curve (often called S.C. or Spiral to Curve).

Assuming this interpretation, to find the chainage of the end of the transition curve (S.C.) from the chainage of its start (T.S., referred to as PC in the question), we simply add the length of the transition curve to the starting chainage.

The formula for calculating the chainage at the end of the transition curve is:

\( \text{Chainage at End of Transition Curve} = \text{Chainage at Start of Transition Curve} + \text{Length of Transition Curve} \)

Let's substitute the given values into the formula:

\( \text{Chainage at Junction} = 40000 \text{ m} + 220 \text{ m} \)

Performing the addition:

\( \text{Chainage at Junction} = 40220 \text{ m} \)

Therefore, the chainage at the junction of the transition curve (where it meets the circular curve), assuming PC is the start of the transition curve, is 40220 m.

Let's check the options:

• Option 1: 40220 m
• Option 2: 39840 m
• Option 3: 39780 m (This would be 40000 - 220, representing the start if 40000 was the end)
• Option 4: 400420 m

Our calculated chainage matches Option 1.

The final answer is 40220 m.