PART 1

Crossing Problem

 

The crossing diagram and dimensions are shown on the following page.  The primary data chosen for the crossing follow:

 

DATA OF CROSSING.

 

Number of Circuits, Voltage and Phase.    Two 3-phase 60,000-volt circuits.  One private telephone circuit.

 

Configuration.    Power conductors of each circuit in vertical plane on opposite ends of the crossarms.  Private telephone circuit in horizontal plane.

 

Conductors.    Power circuits-6 No. 00 A.W.G. copper, hard drawn, stranded, bare.  *Private telephone circuit-2 No. 8 A.W.G. copper, and 2 No. 6 A.W.G. copper, hard drawn, solid, bare.

 

Insulators.     Pin Type porcelain, to meet the requirements of the rules.

 

Ties.    Annealed copper wire to meet the requirements of Rule 49.3.

 

Pins.    Power Circuits.    Iron  (extra strong) 1 ½’’ (nominal) X 18 ½’’ – pins of each circuit metallically bonded together to conform to the requirements of Rule 53.4.

Communication Circuits.    1 ½’’ X 9’’ locust pin

 

Crossarms.    Power Circuits.    Douglas fir 5 ¾’’ X 5 ¾’’ X 12’-0’’, 1.9’’ pin holes –11/16’’ hole for pole bolt.

Communication Circuits.    Douglas fir 3 ¼’’ X 4 ½’’ X 42’’

 

Crossarm Braces.    To conform to Rule 52.9-B

 

Poles.    Western red cedar.

 

Pole Framing.    As per dimensional diagram.

 

Location of Poles.    As per dimensional diagram.

 

Length of Crossing Span.    200 feet

 

Length of Adjacent Spans.    150 feet

 

CONSTRUCTION REQUIREMTNS.

 

1.    Conductor Sags  (Normal Conditions, 60°F., no wind).

 

The required sags of power and telephone conductors are determined from the minimum requirements given in this order.  From the curve sheet shown here it is found that the correction factor for apparent sag is negligible and therefore normal sag values as shown below are used.

#00 A.W.G. copper wire    12 inches

#6 A.W.G. copper wire     13 inches

 

150 foot span:

#00 A.W.G. copper wire    6.9 inches

#8 A.W.G. copper wire     7.2 inches

 

2.    Conductor Sags (Light Loading 25° F., 8 pounds wind)

 

Since no ice loading is considered, the vertical sags under the light loading condition will be less than normal sags at 60°F. and no wind.  Consequently the clearances provided under light loading will be greater than normal conditions, and it is therefore only necessary to determine the elevations of supports to provide the required clearances under normal conditions, 60°F. and no wind.  The tensions in the conductors loaded are found from Tables 15 and 16, Appendix B, to be as follows:

 

3.    Horizontal Conductor Separation from Center Line of Pole

 

Table 1, case 7, the following minimum clearances under the most severe conditions apply:

 

4.    Vertical Conductor Separation.

 

From Rule 36 modifying the minimum vertical separation as given in Table 2, for conductors of 60,000 volts on the same pole, a minimum of 4 feet is allowed.  For this problem a 5’6’’ separation is used.

 

The minimum separation between the supply conductor on the lowest crossarm and the private telephone circuit is given by Table 2, as 6 feet.  For this problem an 8 foot separation is used.

 

5.    Clearances of Conductors Above Crossarms.

 

Table 1, case 9, column F, gives the minimum clearance of conductors in the 60,000 volt class above the supporting crossarms as 9 inches.  Since in this case a 18 ½’’ pin is employed, the clearance of the conductor above the crossarm is 14 inches, which is in excess of the minimum requirements.

 

6.    Vertical Clearance of Conductors Over Highway, Pole lines and Railroad Tracks.

 

The poles supporting the crossing span are 55 feet in length set 7 feet in the ground.  From the dimensions of the pole framing diagram, the distance from the conductors of the private telephone circuit to the ground is 28’4’'.  The ground level is given as the same elevation the as top of the rail.

 

The sag of the signal conductors in the crossing span is given above as 13 inches.  The plan on the following page gives the distances from supporting pole C to the various structures crossed over as follows:

 

Telephone pole line – 37’6’’

Highway (center) – 60’0’’

Telegraph pole line on R.R r/w – 97’6’’

Center railroad tracks – 138’9’’

Railroad signal pole line – 180’0’’

 

Total length of crossing span, 200 feet.

 

In the case of clearances of the private telephone circuit conductors above the crossed over telephone pole lead the following calculations are obtained:

 

Clearance point distance from C 37’6’’

37’6’’  = 61% of the center sag. 

.61 X 13 =  8.0’’ center sag

28’4’’ – (8.0’’ plus 24’)  = 3’8’’, clearance

 

The minimum required clearance, as given in Table 2, would be 2 feet.

 

In a like manner the clearances of the private telephone circuit conductors at the other points of crossing are as follows:

 

 

7.    Insulators.

 

In addition to the electrical requirements set forth in Rules 55, 104 and 114, the insulators supporting the supply and communication conductors shall have a safety factor (mechanical) of 3 and 2, respectively.

 

8.    Pins, Ties and Conductor Fastenings.

 

Pins, ties and conductor fastenings used in connection with pin type insulators shall conform to Rule 49.3.  In this problem a No. 2 and No. 8 annealed copper wire for the No. 00 and No. 8 circuits involved are used.

 

Pins used in connection with pin type insulators shall have sufficient strength to withstand the tension in the conductor.  In the case under discussion wrought iron pipe pins are to be employed for the power conductors and locust pins for the private telephone conductors of the dimensions and construction indicated below.

 

 

Bending moment (at crossarm) = M = 2960 X 15=44,440 inch-pounds

Moment of inertia    

 

Section modulus

Fiber stress    

 

Assume that the ultimate fiber stress for wrought iron is 45,000 pounds per square inch, a single pin is of this type is not sufficient, as it provides a safety factor of 45,000 divided by 107,500 or .418 for an assumed stress of 2960 pounds tension in the conductor.

 

Since a safety factor of unity is required, double crossarms, pins and insulators are used on the crossing structures.

 

Locust pins 1 ½’’ X 9’’ are employed for supporting the private telephone conductors except at the dead ends.  Since locust pins of these dimensions provide strength up to 1000 pounds tension in the conductor, with the conductor 3 ½ inches above the crossarm (Rule 49.2-C), and the maximum tension in the conductor is only 320 pounds, the required strength is amply met.

 

9.    Crossarms – Horizontal Load on Cross Arms.

 

The point of maximum bending moment will be at the cross arm through bolt attaching the arm to the pole, at which point the cross section of the arm is reduced by the amount of the bolt hole.  Crossarms supporting the 60 K.V. wires are to be of Douglas Fir, dimensions 5 ¾’’ X 5 ¾’’  12’, bored as illustrated below:

 

 

The section through a single arm and the method of computing the fiber stress is shown below.

 

 

Bending moment = 2960 X 66 =195,350 inch-pounds

 

 

d=5.75’’

R=2.531’’

S=0.6875’’

B= R plus R=5.06’’

 

As the allowable fiber stress is 6,800 pounds per square inch, a single crossarm of the size chosen provides a safety factor of only 0.97 for the assumed load.

 

Double arms used in this problem are spaced 8 inches apart, the separation being maintained by space blocks and bolts.  Crossarm construction of this type is assumed to have 40 percent of the strength of two crossarms of the same dimensions connected as a rigid truss.

 

Below is shown a single arm section through a double arm and method of computing the fiber stress.

 

 

 

P=5.75’’

Q=8’’

B=R+R=5.06’’

D³=(P+P+Q)³-Q³=6,903

Bending moment=195,360 inch pounds.

 

Allowable section modulus = 299 X .40 = 119.6 inches³

 

 

As this represents a safety factor of 4.17, double arms provide ample strength.

 

At the crossing span double cross arms are used for the communication on account of dead-end construction being employed due to change of conductor size.  Current practice provides for this class construction although a single arm has sufficient strength as is found from the following calculations of fiber stress.

 

d=3.25’’

b=r + r=3.56’’    Bending moment 18 X 640=11,520

s=.69’’

 

 

Ample strength is provided as a safety factor of 3.69 is obtained, but, conforming to standard practice, double arms are used at this dead end.

 

10.    Crossarms – Vertical Load on Crossarms.

 

The vertical load on double supply cross arms under maximum conditions of loading will, for the conductor, be equal to the weight per foot of wire (since no ice loading is considered) time one-half the sum of the length of the crossing and adjacent spans plus a dead weight of 200 pounds.

 

Thus-

 

 

The added weight due to increase of conductor length account of sag and 5 feet difference of elevation of supports is negligible and, accordingly, is not considered.  Due to the fact that no recognition of the effects of the crossarm braces is made, no allowances are included for the added weight due to pins, insulators and ties.

 

Bending moment = 272X 66=17,950 inch pounds.

 

The fiber stress calculations for the top arm computed below.  The stress on the second and third arms decreases for increase of pole diameters, on account of the taper of the pole.

 

b=P+P+Q                                                                       S=.69

b=19.50                                                                          P=5.75’’

                                                                                      Q=8’’

                                                                                      R=2.53’’

                                                                                      D³=(R+R+S)³-S³

                                                                                      D³=189.7

 

Moment of inertia I =