1. Mechanical Design of Transmission Lines PREPARED BY: SHAH RAHIL(130010109053) SONAL SHRIVASTAVA(130010109056) Guided by: DR.NILESH CHOTHANI

2. 2 Main Considerations in the Mechanical Design  The main considerations in the mechanical design of an overhead transmission line are:  Adequate clearance between conductor and ground  High mechanical strength of the conductors  Tension or working stress of the conductor < ultimate tensile strength Ultimate tensile strength = F.O.S Χ working stress

3. 3 Basic Design Considerations  While erecting an overhead line, it is important that conductors are under safe tension.  If the conductors are too much stretched between supports to save the conductor material, the stress in the conductor may reach unsafe value and in certain cases, the conductor may break due to excessive tension.  In order to permit safe tension in the conductors, they are not fully stretched but are allowed to have a dip.

4. 4 Few Important Terms in the Mechanical Design  TENSION, a force tending to stretch or elongate a conductor.  ULTIMATE TENSILE STRENGTH, maximum stress, which a conductor can withstand without failure.

5. 5 Few Important Terms in the Mechanical Design  SAG, the vertical distance (d) between the mid-point of a conductor to the line joining the two supports level.

6. 6 Few Important Terms in the Mechanical Design  CATENARY‘S CURVE, When the conductor is suspended between two supports at the same level, it takes the shape of catenary's curve. However, if the sag is very small as compared with the span, then sag-span curve is parabola.

7. 7 Few Important Terms in the Mechanical Design  SPAN, the horizontal distance (L) between the two adjacent supports.

8. 8 Points to Remember  The following points are to be noted,  The tension at any point on the conductor is tangent to that point  The horizontal component of the tension is constant throughout the length of wire.  The tension will be maximum at the supports and minimum at the lowest point of the curve.

9. 9 Factors affecting Sag  SAG plays a very important role in the mechanical design of an overhead line. It is not a good practice to provide either too high or too low sag.  It is always desired that tension and sag should be as low as possible, which is not possible simultaneously. Low Sag ------> tight wire & high tension High Sag ------> loose wire and low tension Therefore, a COMPROMISE is made between the two. Sag (Too Low)Sag (Too High) 1. Tension in the conductor is too high1. Tension in the conductor is too low 2. Less conductor length is required2. More conductor length is required 3. Lower supports are required3. Higher supports are required

10. 10 Factors affecting Sag  The factors affecting the sag of a conductor strung between supports are  Weight of conductor  Distance between the supports (span length)  Working tensile strength  Temperature

11. 11 Sag Calculations  A conductor AOB of length l’ is suspended at two towers A and B and are spaced L unit apart. Let O is the lowest point of the wire. Consider a length OP of the curve length s.  w = weight/unit length,  H = tension at point O  T = tension at point P, A x H

12. 12 Sag Calculations  Three forces are acting on it  Horizontal tension H at the lowest point  Weight ws of OP acting through its center of gravity  Tension T at point P along tangent to the curve at P. For equilibrium, horizontal forces in one direction must be balanced by horizontal forces in the other direction. Same is true for vertical forces.

13. 13 Sag Calculations T cos θ T sin θ ws Let θ be the angle which the tangent at P makes with the horizontal.

14. 14 Components of Tension ………(1) …….(2) Dividing equation 1 by 2 we get …….(3)

15. 15 Length …..(4)

16. 16 Length From equation 3 we have So eq. 4 becomes

17. 17 Length Integrating both sides, we have Where A is the integration constant

18. 18 Length Using intial values as x = 0 s = 0 we get A = 0, So we have,

19. 19 Length …….(5)

20. 20 Calculation of Sag As we know that So, Since

21. 21 Calculation of Sag or Integrating both sides we have

22. 22 Sag Calculations  Where B is the Integration constant  Using initial values  x = 0  y = 0 We get  B = -H/w So,

23. 23 Sag Calculations This equation is called the equation of catenary On Expanding we get

24. 24