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Simple Curves

A simple curve is a horizontal curve formed by one continuous circle, used to change the direction of an alignment gradually instead of abruptly at an intersection of straight lines.

Problem: Situation Involving Multiple Unknowns and Given the Bearings of Two Tangent Lines

A simple curve connects two tangents, AB and BC, with bearings of N76ΒΊE and S63ΒΊE, respectively. If the stationing of the vertex is 3+988 and the stationing of PC is at 3+866, determine the stationing of a point on the curve which intersects with the line making a deflection angle of 6ΒΊ with the tangent passing through the PC.

Highway Engineering – Problem: Situation Involving Multiple Unknowns and Given the Bearings of Two Tangent Lines – Diagram
Highway Engineering – Problem: Situation Involving Multiple Unknowns and Given the Bearings of Two Tangent Lines – Diagram

Problem: Offset Distance

A simple curve connects two tangents, AB and BC, with bearings of N76ΒΊE and S63ΒΊE, respectively. If the stationing of the vertex is 3+988 and the stationing of PC is at 3+866, determine the offset distance of a point on the curve which intersects with the line making a deflection angle of 6ΒΊ with the tangent passing through the PC.

Highway Engineering – Problem: Offset Distance – Diagram
Highway Engineering – Problem: Offset Distance – Diagram

Problem: Arc Basis and Fillet of Curve

If the degree of simple curve whose central angle is 26ΒΊ is 6ΒΊ, determine the area of the fillet of curve in m2. Use arc basis and S.I. units.

Highway Engineering – Problem: Arc Basis and Fillet of Curve – Diagram
Highway Engineering – Problem: Arc Basis and Fillet of Curve – Diagram

Problem: Radius of Curve Given the Angle of Intersection and Middle Ordinate

A simple curve has an angle of intersection of 30ΒΊ. If the middle ordinate is 16m, determine the radius of the simple curve.

Highway Engineering – Problem: Radius of Curve Given the Angle of Intersection and Middle Ordinate – Diagram
Highway Engineering – Problem: Radius of Curve Given the Angle of Intersection and Middle Ordinate – Diagram

Problem: Chord Basis with English Units

A simple curve has a degree of curve of 5ΒΊ. If English Units are to be used, determine the length of chord (in ft) if I=36ΒΊ. Use chord basis.

Highway Engineering – Problem: Chord Basis with English Units – Diagram
Highway Engineering – Problem: Chord Basis with English Units – Diagram

Problem: Offset Distance from PT

The offset distance of the simple curve from the PT to the tangent line passing through the PC is equal to 126.2m. The stationing of PC is at 2+978. The simple curve has an angle of intersection of 26ΒΊ. Determine the stationing of PT.

Highway Engineering – Problem: Offset Distance from PT – Diagram
Highway Engineering – Problem: Offset Distance from PT – Diagram
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