Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
A conductor, due to sag between two supports, takes the form of
Catenary
Semi-circle
Triangle
Ellipse
Catenary
A transmission line conductor suspended between two supports hanging under its own weight assumes the mathematical shape of a catenary. This curve represents the equilibrium state where the gravitational force of the conductor's weight is balanced by the tension along its length.
A transmission line conductor suspended between two supports hanging under its own weight assumes the mathematical shape of a catenary. This curve represents the equilibrium state where the gravitational force of the conductor's weight is balanced by the tension along its length.
y=acosh(axтАЛ) тАФ Catenary equation
S=8TwL2тАЛ тАФ Parabolic approximation of sag
The shape is defined by the equilibrium of forces in a flexible, inextensible string of uniform density. Because the weight per unit length of the conductor acts vertically while the tension varies along the span, the curve satisfies the differential equation y=acosh(axтАЛ). In practical transmission engineering, for spans where the sag is small compared to the span length, the catenary is often approximated by a parabola to simplify calculations.
A catenary is the shape formed by a hanging flexible chain or wire under its own weight.
The tension in the wire is minimum at the lowest point (the center) and maximum at the supports.
For practical transmission lines, if the sag is less than 10% of the span, the catenary curve is nearly identical to a parabola.
Calculations for power lines are simplified using the parabolic approximation because it is mathematically easier to integrate.
Provides a balanced distribution of internal mechanical tension.
Allows for the determination of sag and clearance requirements.
Catenary math is computationally more complex than parabolic approximations.
Sag varies with temperature and ice loading, requiring dynamic structural analysis.
Transmission and distribution power lines
Suspension bridges and catenary-based railway overhead lines
The catenary curve depends on the ratio of tension to weight per unit length (T/w).
Options B, C, and D are geometric shapes (circle, triangle, ellipse) that do not represent the natural equilibrium of a hanging flexible conductor.
A is correct тАФ A conductor suspended between two supports under its own weight follows the shape of a catenary curve.
Always remember that while the true shape is a catenary, transmission line sag calculations for competitive exams often use the parabolic approximation (S=8TwL2тАЛ) for simplicity when the span length is small.