Koi Koi Grace
by on March 12, 2019

This section deals with the theoretical basis for analysis procedures for various transmission structure forms and types. Computer programs such as PLS-POLETM and TOWERTM are generally employed by most utilities; some utilities also have their own in-house programs for structural analysis, in addition to general purpose finite element programs. However, it is important to understand the underlying basis and limitations of these programs. The basics of analysis of various systems will be illustrated below. Equations governing design checks will be covered in Section 3.5.


1-) Single tangent poles

Kalaga, Sriram; Yenumula, Prasad. Design of Electrical Transmission Lines: Structures and Foundations: 1 (Page 99). CRC Press. Kindle Edition. 

The analysis of single, unguyed poles is governed by bending. The controlling flexural stress in the tangent pole is a result of the effects of factored transverse and vertical loading on the structure. Selection of the appropriate wood, concrete, steel or composite pole for a given design bending situation is also possible in other ways:

(a) Specifying the ultimate lateral load that can be applied 2 ft. below the pole tip

(b) Specifying the loading tree and load cases from which the manufacturer can deduce the size of pole needed (concrete, composite and steel only)

(c) Specifying the maximum horizontal wire span the pole can resist for a given conductor/ground wire/loading configuration (Allowable Spans)


2-) H-Frames

Section 13.5 of the RUS Bulletin 200 (2015) gives the governing design formulae for various wood H-Frame configurations. The equations are based on critical points of flexure at specified pole locations. Structure strength, expressed in allowable spans, refers to these points. The most general H-Frame assembly often encountered in practice is the braced frame shown below. The labels are self-explanatory; C is at the location of point of contraflexure (point where bending moment changes its sign) and G is the ground line. Governing Equations for Analysis. The point of contraflexure is calculated using the following equation:

3-) Angle Structures

The behavior of single-pole and three-pole guyed running angle structures is basically governed by interaction of guys and anchors and the design tensions transferred to the guy wires due to the line angles. For systems with multiple guy wires, it is also required to check buckling of the poles since the vertical component of the guy forces act on the poles axially. A typical guying guide is shown in later in Chapter 5 (see Figure 5.7); spreadsheets can be developed to calculate the allowable spans of a given pole-wire-guy-anchor system.


4-) Deadends

The behavior of single-pole guyed angle/deadend structures is also governed by interaction of guys and anchors and the line design tensions transferred to the guy wires due to the line angles. One additional load is the component of the guy force transferred to the pole axially. Therefore, for systems with multiple guy wires, it is also required to check buckling of the poles.

If the structure has more wire (conductor + shieldwire) attachments than guy wires, and the highest guy wire attachment is below the lower-most wire, then the pole needs to be analyzed and checked for both bending and buckling. However, if the structure has the same number of wires and guy wires, and the wire and guy wire attachments are more or less at the same elevation, then the pole just need to be checked for buckling.

4-a)  Wood pole buckling

Guyed angle and deadend poles, in addition to conductor and equipment weights, also carry vertical (axial) components of guy tensions. This axial force is directly dependent on the number of guy wires supporting the pole. Unlike concrete poles, wood poles are not strong in compression and are susceptible for buckling. Therefore, the buckling strength of guyed wood poles must be checked.

The RUS Bulletin 153 (2001) provides an equation for the critical vertical column load Pcr (in pounds) that can be imposed on a wood pole. The equation is derived from the theory of tapered columns.

When using the Gere-Carter formula for NESC District loads with load factors, strength factors between 0.50 and 0.65 are recommended. This gives a net safety factor of 3.3 to 2.5. For extreme wind loads, strength factors between 0.50 and 0.65 are suggested giving a net safety factor of 2.0 to 1.50. For full deadends, a much lower strength factor is recommended. Programs such as PLS-POLETM conduct buckling checks automatically while performing a non-linear structural analysis.


 5-)  Lattice Towers

Utilities impose rigorous design requirements on lattice towers for bigger safety margins under severe structural and environmental loadings. The goal is to see that no tower member suffers permanent, inelastic deformation and that foundations are capable of sustaining imposed compressive and uplift forces. While suspension (tangent) towers are relatively easier to design, towers used at angles and deadends demand higher strength. At deadends, one of the design conditions is the broken wire case (i.e.) all wires cut on one side of the tower, creating a highly imbalanced loading situation.

Lattice towers are generally analyzed as 3-dimensional space trusses made up of steel angle members connected by bolts. The members carry compressive or tensile loads; therefore effective slenderness ratio kL/r governs design in most cases. The following slenderness limits are usually adopted for towers:

Legs ≤ 150

Others ≤ 200

Redundant ≤ 250 T

ension only ≤ 500


L = length of the member

k = slenderness factor depending on restraint at the ends

r = radius of gyration of angle member about one of the axes.


5-a)  End restraints

The primary consideration in the design of individual members in a lattice tower is the amount and type of restraint offered by the bolted connections at the member ends. Increasing the number of bolts at an end will always increase the amount of rotational restraint; and increasing restraint will lessen the effects of load eccentricity. The relationship between end restraint and eccentricity is qualitatively understood; but it is very difficult to mathematically quantify the actual joint stiffness in 3-dimensional space.

Some simple assumptions may be used in routine designs without sacrificing accuracy. A single bolt is considered as a hinge not offering any restraint; 2 bolts offer partial restraint and any joint with 3 bolts and above approaches full fixity. This idealization can help determine the appropriate slenderness ratios of members. The other consideration is whether the angle member is connected by one leg or both legs. Obviously, an angle bolted on both the legs is doubly restrained against rotation and thereby negate the effects of eccentricity of load. Main leg members of a tower are a good example of this situation.

To ensure integrity of connections and prevent tear-outs, minimum end and edge distance – along and perpendicular to the line of force in an angle – must be maintained. Figure 3.20 shows the definitions of end, edge and gauge distances (e, f, g1 and g2, respectively) and bolt spacing ‘s’ associated with typical lattice tower angles.

 5-b)  Crossing Diagonals

Almost all transmission towers contain crossing diagonals – X-type members – with a bolt in the middle. Structurally, these diagonals are part of a tension-compression system where a crossing tension member provides out-of-plane bracing support for the compression member. This support helps in reducing the effective buckling length for the compression member but is dependent on the load level in the tension diagonal. Programs such as TOWERTM contain various provisions to define such diagonals.



6-) Substation structures


Outdoor electrical substations and switchyards are a collection of various equipment, structures and components where electrical energy (typically high voltage) is modified. These substation structures support above grade items such as switches, circuit breakers, insulators, arresters, rigid bus and transformers. In the USA, analysis and design of substation systems is governed by ASCE Substation Structure Design Guide 113 (2008), RUS Bulletin 300 (2001) for rural systems and IEEE Standard 693 (2005).

Substation structures are essentially classified into three types, based on function:

Line Support Structures (LSS) – These are also called take-off or strain structures, deadend or line termination structures and internal strain bus. These can be single or multi-bay, truss or steel pole type. Major forces sustained are conductor and ground wire tensions (full or slack) and wind. LSS are critical components of a substation and are designed to withstand large stresses although on a non-catastrophic failure basis.

Equipment Support Structures (ESS) – These are switch stands, bus support stands, lightning arrestor stands, and line trap stands etc. ESS are designed mainly as vertical cantilever beams for short circuit forces and wind. Stresses rarely control but deflections must be checked. Distribution Structures – Intended for low voltage applications, these are mostly comprised of steel beams and columns (truss or tube), may have multiple bays but are usually one-bay wide. They support switches and other equipment and are designed for rigidity at equipment location.

Distribution Structures – Intended for low voltage applications, these are mostly comprised of steel beams and columns (truss or tube), may have multiple bays but are usually one-bay wide. They support switches and other equipment and are designed for rigidity at equipment location.

Structural profile configurations in substations basically fall under three types: Lattice, Solid and Semi-Solid. Lattice-type systems consist of steel angles framing into a box truss, both vertically and horizontally. Solid-type systems are made of wide flange shapes, pipes, round or tapered poles or rectangular tubes. Connections are either bolted or welded. Solid- type configurations are widely used for LSS, in either an A-Frame setup or single pole. Cross arms may be square or rectangular tubes or round/tapered polygonal members. Semi-solid types are made from wide-flange shapes or pipes as main members and use steel angles as braces in-between.

Design loads depend on whether they are intended for LSS or ESS. All LSS and their components, however, must withstand stresses induced by factored loads. For LSS, design loading is similar to that of a transmission line structures. Load Factors (LF) are specified for vertical (V), wind (W) and wire tension (T) forces. For ESS, design loading includes all applicable wind, ice, short circuit and dead loads; wind plus short circuit loads, however, produce maximum stresses. Ice is not expected to control design. Since all loads contain load factors, Ultimate Strength Design (or USD) is appropriate for LSS. Stiffness is an important requirement for ESS and the goal is to limit deflection under wind. Sections a bit larger than necessary are usually specified. Allowable Stress Design (ASD) is appropriate for ESS, while conforming to NEMA-SG6 (2006) rules, per RUS Bulletin 300.


6-a) Semi Considirations

Seismic analysis may be necessary at places with high earthquake risk. Seismic loads are generally considered as environmental load situations and are not combined with ice or wind loads, but may be combined with short circuit loading or operational loading. Substation structures are divided into four types with references to seismic loading:


ST1 Single- or Multi-bay Rack (not supporting equipment)

ST2 Single- or Multi-bay Rack (supporting equipment and conductors)

ST3 Rigid Isolated Support (supporting equipment)

ST4 Flexible Isolated Support (supporting equipment)


ST3 and ST4, in voltage classes higher than 121 kV, and within seismic zones 3 and 4, should be designed as per IEEE 693. For other types of structures and situations, design procedures are outlined in ASCE Substation Guide 113.


6-b) Deflection Considirations

In addition to stresses, deflection limitations are imposed on ESS. Excessive movement or rotation of substation structures and components can affect mechanical/electrical operation of the equipment, reduce clearances, induce stresses in insulators/connectors etc. Disconnect switches are highly sensitive to deflections but overhead line deadends are not. Lattice-type systems, and A-Frames with solid sections, do not present any deflection problems. ASCE Guide 113 defines the following classes of substation structures for deflection purposes:

Class A – support equipment with mechanical mechanisms where structure deflection could impair or prevent proper operation. Examples: group switches, vertical switches, ground switches, circuit breaker supports and circuit interrupters.

Class B – support equipment without mechanical components but where excessive structure deflection could result in compromised phase-to-phase or phase-toground clearances, stresses in equipment, fittings or bus. Examples: support structures for rigid bus, surge arresters, metering devices, power transformers, hot-stick switches and fuses.

Class C – support equipment relatively insensitive to deflection or stand-alone structures that do not carry any equipment. Examples: support structures for flexible bus, masts for lightning shielding, deadend structures for incoming transmission lines. SG-6 does not give any specific limits but deflections here refer to limiting P −  stresses.

Multiple Class – Combination of any above classes


Tables 3.2, 3.3 and 3.4 show the basic load conditions, load cases for ultimate strength design (USD) and deflection limits for substation structures. Figure 3.21 from ASCE Guide 113 defines various structure classes and spans graphically for determining deflections.

Substation structures have a wide range of ground line reactions due to applied forces and therefore a wide variety of foundation types. These include drilled shafts, spread footings and slabs on grade, among others. Drilled shafts are typically used for LSS and steel poles while spread footings are used for circuit breakers and small

transformers. Heavy oil-filled transformers need slab-on-grade footings which are generally designed not to exceed the allowable bearing pressure at site as determined by the Geotechnical engineer.

If frost is present at substation location, then spread footings must be seated below frost depth or a minimum of 12 in. (30.5 cm), whichever is maximum. Design loads on most footings include axial compression, uplift, bending and shear. Most utilities



adopt the Ultimate Strength Design philosophy for structural design of foundations, often nominally increasing the ultimate reactions by 10% or so for additional margin of safety. RUS recommends that soil borings be taken at critical locations (i.e.) deadend structures and heavy transformers. Bearing capacity, ground water level and other soil parameters must be determined. Possibility of differential settlement in silts and silty sands must be checked.


7-) Special Structures

Special situations in transmission lines arise at locations such as river crossings, storm structures and air break switches. These are discussed briefly below.

7-a)  Anti-cascade structures


Overhead Transmission Lines often face extreme events such as severe ice or wind loads, which damage line sections and affect power supply to customers. Even when the best design criteria are employed, there is always a risk to overhead lines when extreme wind or ice storms exceed the design criteria. This damage can occur in poles or supporting structures, insulators or guy wires, depending on the weakest point. Utilities must therefore consider the possibilities of severe wind storms and icing while planning for High Voltage Lines.

Some approaches to limiting the impact of ice and wind loads on overhead lines include:

a) Better forecasting of maximum wind and ice loads

b) Careful design approaches to minimize the risk of failures, while simultaneously reducing the potential consequences of such events

One preferred way of reducing the chance of several miles of cascading line collapse (domino effect) is to install an in-line or tangent deadend or storm structure at chosen locations. Mitigation approaches also include strengthening existing deadends at critical locations by adding or using stronger guy wires and strain insulators along with better hardware.

Storm or damage mitigation structures are typically installed every 4 to 5 miles of a transmission line. Theoretical structure configuration is that of a guyed in-line deadend. This means, even if one section of the line is damaged, the other remains intact. The structure introduced in the line to prevent cascading failures is known as “Anti-Cascade Structure’’ or ACS. Figure 3.22 shows typical anti-cascade structure locations on a transmission line.

 7-b)  Long Span Systems

Figure 3.23 shows typical river crossing structures in a transmission line. Long span designs are very rare and make complex demands on various design-related items such as loadings, wire strengths and foundations as well as regulatory and environmental impacts. The design criteria fall outside the normal scope used on other routine cases; long spans mean much larger loads, larger tensions, increased scope for Aeolian vibration and larger foundation loads, not to mention custom design and installation of dampers on all wires. Galloping checks are therefore an important means of accepting a particular conductor or ground wire.

Not all conductors are amenable to a long span situation and special wires may be needed in the span. Special wires in turn demand special attachment hardware and handling. It is also difficult to choose an optimum optical ground wire given the demand for large tensions. The structures themselves at each end of the river (long) span are much taller than the others, requiring transition structures to gradually reduce the height to normal levels. It is common to design these transition structures as a full deadend capable of resisting either large tensions from the special wires or unbalanced tensions due to wire changes at the transition points.


Constructability, including access to large construction vehicles, is a very important issue after design. Communities living within the vicinity of such large structures often are known to express public opposition, mostly based on aesthetics. Other impediments include special markers, lighting beacons and height constraints if located within the proximity of an airport.

 7-c)  Air-break switches


Two-way and three-way phase-over-phase (vertical) and low-profile horizontal phase configuration switches are designed specifically for switching applications on transmission lines. They provide economical sectionalizing, and tap and tie switching points for circuit control. These phase-over-phase switches can be mounted on a single pole, minimizing ROW requirements. Installation on a single pole significantly reduces costs of land and equipment that a conventional switching substation requires. Switches rated 69 kV and below can be mounted on any suitable structure; for 115 kV and above, they need laminated wood, steel or concrete poles. For side-break style switches, the operating effort to open and close the switch is minimal even at high voltages.

Figure 3.24 shows a steel pole- mounted three-way air break switch (the framing drawing of a 161 kV switch structure is shown later in Section Analysis and design of switch structures is a specialized process. Briefly, the structures are designed as 3-way deadends with the third wire usually a slack span into another line or substation. Deflection is one of the design criteria and guying is often used for laminated wood poles, especially in the slack span plane.


7-d) Line Crossing

Figure 3.25 shows a situation where one line crosses another. Crossing clearances are defined on the assumption that the upper circuit is of higher voltage. In most cases, the lower line is a distribution (or another transmission) circuit. Depending on the voltages


involved, this situation demands taller structures due to extra clearance required. A special case arises when the two lines are owned by different utilities. Both the RUS Bulletin 200 and NESC provide guidance for wire and structure clearances for all these cases.


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