A NÁLISIS

strength for tangent structures:

• Wind on the conductors and OHGW is the primary load. 75 to 90 percent of the horizontal span will be determined by this load.

• Wind on the structure will affect the horizontal span by 5 to 15 percent.

• Unbalanced vertical load will increase ground-line moments. For single circuit structures, one phase is usually left unbalanced. The vertical load from the conductor will induce moments at the groundline and will affect horizontal span lengths by 2 to 10 percent.

• P-delta (P-δ) moments will also increase induced ground line moments. As a transverse load is applied to a structure, the structure will deflect. This deflection will offset the vertical load an additional amount " δ " causing an additional moment of the vertical weight times this deflection. This additional moment due to deflection is a secondary effect. An approximate method for taking into account the p-δ moments is given in section 13.4.2.

For wood structures, depending on the taper of the pole, the maximum stress may theoretically occur above the ground level. The general rule of thumb is that if the diameter at ground level is greater than one and a half times the diameter where the net pull is applied, the maximum stress occurs above the ground level. Even if the point of maximum stress occurs above the groundline for single base wood pole structures, one can assume that spans are based on groundline

moments in accordance with Exception 1 in NESC Rule 261A.2. Exception 1 states: “When installed, naturally grown wood poles acting as single-based structures or unbraced multiple-pole structures, shall meet the requirements of Rule 261A.2a without exceeding the permitted stress level at the ground line for unguyed poles or at the points of attachment for guyed poles.”

The strength of the crossarm has to be checked to determine its ability to withstand all expected vertical and longitudinal loads. When determining bending stress in crossarms, moments are calculated at the through bolt, without considering the strength of the brace. The vertical force is determined by the vertical span under those conditions which yield the maximum vertical

weight. The strength of two crossarms will be twice the strength of one crossarm. When considering the strength of the crossarm to withstand longitudinal loadings, reduction in the moment capacity due to bolt holes should be taken into account.

Equation 13-1 is the general equation for determining the moment induced in the pole from the applied loads represented in Figure 13-3. This equation may be used to determine the maximum horizontal span as demonstrated in the example in Paragraph 13.4.2.

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φM_A =M_g = LF M_wp + LF M_wc+ LF M_vo+ LF M_p− Eq. 13-1 where:

φ = strength factor, see Chapter 11

M_A = F_bS, the ultimate groundline moment capacity of the pole, ft-lbs. For moment capacities of wood poles at the groundline, (see Appendix F);

F_b = designated ultimate bending stress (M.O.R.) S = section modulus of the pole at the groundline (see

Appendix H).

LF = load factor associated with the particular load M_g = induced moment at the ground line

Other symbols are defined by Equations 13-2, 13-3, 13-4, 13-5.

When estimating the load carrying capacity of a pole using manual methods, it is difficult to assess the additional moment due to deflection. Equations 13-5 and 13-6 provide an

approximate way to calculate the additional moment due to defection. Because M_p-δ is a function of the vertical span (VS), the engineer should make an assumption about the relationship between the vertical and horizontal span (HS). In Equations 13-4 and 13-5, the relationship used is: VS = 1.25HS.

FIGURE 13-3: TS TYPE STRUCTURE

Refer to Figure 13-3 when considering the equations and symbols that follow.

a. Mwp = groundline moment due to wind on the pole

( )( )( )

72 2d d h ²

M_wp = F ^t+ ^a Eq. 13-2

where:

F = wind pressure, psf

dt = diameter of pole at top, inches

da = diameter of pole at groundline, inches h = height of pole above groundline, feet

h

h h

h SPg

g

Sa Sb A

Sc

c g

l

h ,ahb Pc

Pt

b. Mwc = groundline moment due to wind on the wires c. Mvo = groundline moment due to unbalanced vertical load

Mvo = 1.25HS(wcst + wgsg) + Wist Eq. 13-4 where:

sg = Horizontal distance from center of pole to ground wire (positive value on one side of the pole, negative on the other), feet

st = sa + sb + sc , where sa , sb ,and sc are horizontal distances from center of pole to conductors (positive value on one side of the pole, negative on the other), wc = weight of the conductor per unit length, lbs./ft. feet wg = weight of overhead groundwire per unit length, lbs./ft.

Wi = weight of insulators, lbs.

d. Mp-δ = groundline moment due to pole deflection

Mp-δ = 1.25HS(wt)δimp Eq. 13-5

where:

wt = total weight per unit length of all wires, lbs./ft.

δimp = improved estimate of deflection of the structure, ft.

( )( )( )

da = diameter of pole at location "A" (groundline), inches d1 = diameter of pole at height "h1" inches

δmag = deflection magnifier, no units, (assume 1.15 initially) hc = effective height to the conductors, feet

HS = horizontal span, feet

pt = total transverse load per unit length of all wires, lbs./ft.

After substitutions of Mwp, Mwc,Mvo,and Mpδ have been made into Eq.13-1, the equation can be reduced to a quadratic equation (below) and solved for the horizontal span. (See Paragraph 13.4.2 for an example of how the calculation of HS is carried out.)

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Once “HS” has been calculated, check the assumption of δmag = 1.15:

( )

(See Chapter 14 for calculations of Pcr)

13.4.2 Example of Maximum Horizontal Spans: Determine the maximum horizontal span for the 69 kV TSS-1 wood structure (Figure 13-4). Terrain is predominantly level, flat, and open. ("sg" is

negligible; see Equation 13-4). Location and magnitude of resultant loads are indicated in Figure 13-5.

Given:

NESC Heavy Loading

Extreme wind 19 psf on the wires 22 psf on the structure Extreme Ice with 4 psf, 1 inch radial ice Concurrent Wind(EI&W)

Pole: Western red cedar

Conductor: 266.8 kcmil,

26/7 ACSR (Partridge) Ground wire: 3/8"

H.S.S.

Conductor loads, lbs./ft:

Heavy High Wind EI&W

Transverse 0.5473 1.0165 .8808

Vertical 1.0776 0.3673 2.402

Ground wire loads, lbs./ft: FIGURE 13-4: TSS-1 STRUCTURE

Heavy High Wind EI&W

Transverse 0.4533 0.5700 .7868

Vertical 0.8079 0.2730 1.9667

Other information:

APPLICATION OF FORCES (HEAVY LOADING)

Solution for Maximum Horizontal Span Considering P-δ moments: A comparison of unit loads with load factors indicates that the Heavy Loading District Loads control design. Therefore, for Heavy Loading, the moments for Equation 13-1 are calculated.

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h. Lateral Stability: The Equivalent load 2 feet from the top is approximately 4400 lbs.

From Figure 12-2 (average soil), the embedment depth for a 4400 lb. load 2 feet from the top is between 8 and 8.5 feet. Lines nearby have performed well with the standard embedment depths. Engineering judgment dictates that an 8 foot embedment depth for the 60 foot pole will be sufficient.

13.4.3 Maximum Vertical Span for TP and TS Pole Top Assemblies: To determine the