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Determination of analysis loads on transmission structures involves the following:

1. Wire Loads – vertical, transverse and longitudinal loads on wires due to ice, wind, temperature

2. Structure Loads – vertical, transverse and longitudinal loads on structure due to wires, attachments and hardware

Secondary loads include those due to P-Delta (2nd Order) effects which will be discussed below.

**1-) Load Cases and Parameters**

The weather conditions considered for structural design were discussed earlier in Chapter 2 in Sections 2.1 and 2.4. Also, Table 2.16, Table 2.17 (a, b) and Table 2.18 contain the required load case information. Though climate-related loading parameters were covered in Chapter 2, they are briefly summarized here.

Wind: Wind pressure on transmission structures is defined as force resulting from exposure of structure surface to wind. These surfaces include both the surface of the wires as well as structural system (steel or wood or concrete poles or lattice towers).

Radial Ice: This is the thickness of ice applied about the circumference of conductors and ground wires. In routine transmission line design, ice is only applied to conductors and ground wires but not to the surface of the structure, insulators and other hardware.

Temperature: This is a design parameter needed for calculating conductor and static wire sags and tensions. For example: Maximum sags (and corresponding clearances) are often evaluated at a conductor temperature of 100◦C (212◦F) for ACSR wires. Uplift situations are generally referred to a “cold weather case’’ for low temperatures in the range of 0◦F to –20◦F.

**2-) Load and strength factors**

The Load and Strength (Reduction) Factors – from both NESC and RUS – are given earlier in Chapter 2 in Section 2.4.4 and in Tables 2.15a, 2.15b, and 2.15c.

**3-) Point Loads**

Transverse Load: This load is defined as force or pressure acting perpendicular to the direction of the line. For tangent structures, wind forces are usually applied as transverse loads on the structures. In angle structures and deadends located in angles, the transverse direction is parallel to the bi-sector of the line angle and the component of the wire tension acts in the transverse direction. All transverse loads are usually factored (i.e.) contain applicable Load Factors.

Vertical Load: This load is defined as force acting vertically due to gravity. For all structures, vertical forces usually include factored weight of wires (iced and noniced), insulators and hardware, along with the weight of various components defining the system. All vertical loads are multiplied by a specified load factor to obtain the design load. Uplift loads, which occur due to uneven terrain and cold temperatures, are another form of vertical loads, acting against gravity.

Longitudinal Load: This load is defined as force or pressure acting parallel to the direction of the line. In angle structures and deadends located in angles, the longitudinal direction is perpendicular to the bi-sector of the line angle and the component of the wire tension acts in the longitudinal direction. For deadends located in zero line angles, with wires on one side, this load is simply the wire tension with the appropriate tension load factor.

Figure 3.15 shows the wire scheme used to illustrate the calculation of point loads V, T and L for various line angles. The loads are computed with the equations given below:

Note that the equation for vertical loads includes weight of glazed ice at 57 pcf (8.95 kN/m3). For a case where line angle is zero, the equations reduce to the situation of a perfect tangent structure. The values obtained from these formulae depend on the parameters related to that specific load case. For example, for extreme wind case, all load factors are usually 1.0. Also, some utilities add the weight of workers to the vertical load component to account for construction-related loads.

The following Examples 3.2 and 3.2a illustrate the process of calculating point loads and ground line moments for an unguyed deadend pole.

**Example: 3.2**

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For the 2-span system, determine the point loads due to conductor for a line angle of 20◦ for the following situations:

(a) All Load Factors = 1.00

(b) Vertical LF = 1.50, Wind LF = 2.50 and Wire Tension LF = 1.65

(c) Determine the force in the guy wire supporting the transverse load for Case ‘b’ for a 45◦ guy angle.

Assume level ground and the following data:

Conductor tension Tw = 5,000 lbs. (22.25 kN)

Conductor diameter = 1 in. (2.54 cm)

Conductor weight = 1.0 plf. (14.59 N/m)

Wind pressure = 21 psf. (1.01 kPa)

No ice on wires. Guying is bi-sector type.

Solution:

For level ground span, with attachment points at the same elevation:

Wind span = Weight span = Average span

Average span = (500 + 600)/2 = 550 ft. (167.6 m).

Use Equations 3.2a and b

. (a) Vertical load V = (550) (1) (1) = 550 lbs. (2.45 kN)

Transverse load T = component due to wind + component due to wire tension

= (21) (550) (1/12) + (2) (Sin (10◦)) (5000)

= 2,699 lbs. (12.01 kN)

Since the conductor tension is same in both spans, net longitudinal load L is zero.

(b)

For the given load factors:

Vertical load V = (550) (1.50) = 825 lbs. (3.67 kN)

Transverse load T = component due to wind + component due to wire tension

= (2.5) (21) (550) (1/12) + (1.65) (2) (Sin (10◦)) (5000)

= 5,271 lbs. (23.46 kN)

Since the conductor tension is same in both spans, net longitudinal load L is zero.

(c) Guy force = (5271) [1/Cos (45◦)] = 5271/0.7071 = 7,455 lbs. (33.17 kN)

**Example 3.2a** Consider the 90◦, unguyed, single circuit, deadend transmission pole in the figure. Wire tensions for various weather cases and their load factors have been determined as follows (consider only cable tensions; neglect wind forces on wires and pole):

Determine the maximum ground line moment for the pole assuming 10% moment due to P − effects. The span in each direction is 330 ft. (100.6 m).

** Solution:**

The design ground line moment (GLM) will be determined using the factored tensions of the wires for each load case.

Resultant tensions for various load cases: The first four (4) are cases where all wires are intact. The last one has all wires cut on one side of the pole.

NESC Heavy TRC = √ (66002 + 66002) = 9,333 lbs. (41.5 kN) (see Note 1)

TRSW = √ (49502 + 49502) = 7,000 lbs. (31.2 kN)

NESC Ext Wind TRC = √ (37602 + 37602) = 5,317 lbs. (23.7 kN)

TRSW = √ (23902 + 23902) = 3,380 lbs. (15.0 kN)

Extreme ice TRC = √ (78802 + 78802) = 11,145 lbs. (49.6 kN) ← CONTROLS

TRSW = √ (56902 + 56902) = 8,047 lbs. (35.8 kN) ← CONTROLS

NESC Ext. Ice TRC = √ (60002 + 60002) = 8,485 lbs. (37.8 kN)

w/Conc. Wind TRSW = √ (43602 + 43602) = 6,166 lbs. (27.4 kN)

Broken Wires TRC = √ (44002 + 02) = 4,400 lbs. (19.6 kN)

TRSW = √ (33002 + 02) = 3,300 lbs. (31.2 kN)

Extreme Ice load case governs. This case is associated with no wind, either on wires or poles (see Table 2.17a).

Bending Moment at ground line due to resultant controlling design wire tensions is:

M = [(8,047) (70) + (11,145) (42 + 52 + 62)]/1000 = 2301.9 kip-ft. (3121.4 kN-m)

Wind on wires = 0

Wind on pole = 0

P − Moment = (0.10) (2301.9) = 230.2 kip-ft. (312.1 kN-m)

Total GLM = 2301.9 + 230.2 = 2532 kip-ft. (3433.5 kN-m) (see Note 2)

Note 1: In Equation (3.2b), if we neglect the first component due to wind pressure, the equation simplifies to 2 sin (90/2)(4000)(1.65) = 9,333 lbs. (41.5 kN). Note 2: The wire tensions contribute a major component of the load on the deadend poles. However, in real life, the reader must consider moment due to wind on wires and wind on pole in addition to the moments associated with wire tensions.

**4-) Loading Schedules**

The various loads applied on transmission structures are specified to the manufacturers/ vendors by means of Loading Schedules (also known as Loading Trees). Here the wire

loads – vertical, transverse and longitudinal, associated with different weather cases and determined by various methods – are listed in a tabular form. An outline of the structure and the insulator attachment points are also shown.

Loading Schedules (also called Loading Trees) can be determined by several means:

1. Spreadsheets (usually for tangent and angle structures on level terrains).

2. PLS-CADDTM or PLS-CADD/LITETM (for deadend and large angle structures on uneven, rolling terrains).

These Loading Trees constitute the most important communication between the engineer and the steel fabricator. Figures 3.16, 3.17 show commonly-used format of loading schedules for tangent lattice towers and H-Frames. Figure 3.18 refers to an angle/deadend steel pole; the loading table is left blank as an exercise for students. Only critical load cases are generally shown on these loading schedules; other additional cases (example: uplift case at sub-zero temperature) can be added at the discretion of the engineer. For angles and deadends, the loads generally refer to the bi-sector orientation (see below).

For strain and deadend structures, loading schedules often contain separate loads for the ‘back’ and ‘ahead’ spans if requested by the fabricator. If a full PLS-CADDTM model of a transmission line is available with all structures spotted and all wires strung, then the load trees for each structure can be extracted in print form from the line model in the required coordinate system. For greater control over design data, it is often preferred to use PLS-CADD/LITETM to model each individual structure using a bi-sector model (by importing the structure file from the project’s structure family library). Briefly, in the bi-sector format, the transverse axis is aligned with the line bisecting the line angle; the longitudinal axis is orthogonal to this transverse axis. These loads thus obtained are later converted to tabular form to be inserted onto the load schedule sheet.

With reference to Figures 3.16, 3.17 and 3.18, the loading trees include:

(a) NESC loading: Heavy (or Medium or Light), Extreme Wind, Extreme Ice with Concurrent Wind

(b) Others: Extreme Ice, Construction

(c) Broken Wire loading: wires cut, deadends

Broken Wire cases for angle/deadend structures usually consist of broken conductor(s), broken ground wire(s) or both, simulating a condition of unbalanced tension. For pure deadends or failure containment structures, this implies ALL wires cut on one side. Some utilities use a NESC Heavy weather condition for broken wires but with all load factors equal to 1.0.

*Loads due to snapped conductors*

ASCE Manual 74 (2010) recommends a procedure based on Residual Static Load (RSL) which is a final effective static tension in a wire after all the dynamic effects of a wire breakage have subsided. This RSL is a function of Span/Sag ratio and Span/Insulator ratio and is an unbalanced longitudinal load that acts on a support structure in a direction away from the initiating failure event. It is applied in one direction only and for lattice towers is given by RSL = Wire Tension ∗ Longitudinal Load Factor.

RSL is generally calculated for bare wire (i.e.) no ice, no wind loading condition at an average temperature. Effects of wind are not considered when using RSL. Some utilities specify NESC Heavy weather condition for tensions; however, the longitudinal load factors are generally taken as 1.0. For a single circuit structures, unbalanced longitudinal loads can be applied at any single conductor phase or any one ground wire support. For double circuit structures, unbalanced longitudinal loads could be applied to any two conductor phases or one or two ground wire supports or one conductor and one ground wire support.

** 5-) Deflection Limits**

Limits on free-standing pole/structure deflections are often prescribed for various reasons which include aesthetics, reducing P − effects (see below), maintaining the require phase clearances, maintaining conductor separation from structure surface and other objects. Some utilities also take into account the impact of structure deflection on vertical clearance to ground, typically in case of angle structures. These limits are defined by RUS for steel and concrete poles. Appendix 5 discusses these limitations in detail. For routine steel pole designs, engineers often limit the pole top movement to 1% to 2% of the pole heights for normal operating conditions. Specifying low deflection limits will result in a large, stiffer and more expensive structure. In a majority of the cases, the issue is left to the decision of the utilities and conveyed to structure designers at the fabricator. Some utilities request the manufacturer to camber the steel poles at angle locations so that the poles become straight and plumb after installation.

For concrete poles, the effects of deflections are more critical than steel; but owing to the difference in material behavior, the limits are different. ASCE Manual 123 (2012) requires appropriate concrete modulus be used in determining elastic (pre-cracking) and inelastic (post-crack) deflections.

For composite poles, tip deflection is a function of the materials used and the pole geometry. FRP (fiber-reinforced polymer) materials have a very high strength-tostiffness ratio and often transmission poles made from such materials can be designed to be flexible. ASCE Manual 104 (2003) provides guidance with reference to deflections permitted in composite poles.

**6-) P-Delta Analysis**

This refers to the secondary bending effects on a transmission pole due to lateral deflection ‘’ of the pole due to wind or other load actions. The movement of the vertical load application points produces small additional bending moments on the pole to add to those produced by wire and wind loads. Computer programs for transmission structure analysis include these effects. The exact magnitude of the secondary moments varies from structure to structure and can be determined only as a function of the geometry of the system. For quick manual calculations for preliminary pole sizing, it is sometimes assumed that P-Delta () moments are approximately 10% of the total moment on the pole. ASCE Manual 111 (2006) uses the Gere-Carter Method for estimating these P − loads for tapered poles. This method, in general, is conservative than other sophisticated methods such as the finite element analysis approach.

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