In the electrical utility industry, lines of voltages 35 kV and below are generally termed distribution lines. Cross arms are horizontal elements used on distribution line structures to support insulators and conductors of various configurations. Figs. (1a and 1b) show a typical tangent (suspension) and a dead end cross arm configuration, respectively. Wood cross arms are traditionally used by utilities, although during the past decade, composite (fiber-reinforced) poles and cross arms are increasingly becoming popular [1]. Some of the advantages of composite cross arms include lighter weight, excellent strength and stiffness, low conductivity, moisture and corrosion resistance, ease of installation, minimum maintenance and durability.

Wood distribution cross arm sizes and design are standardized by the Rural Utilities Service (RUS) of United States Department of Agriculture [2-4] on the basis of length and pattern/location of insulator attachments. RUS Bulletin 1724E-151 [5] discusses the structural loading and analysis of distribution cross arms. The design of composite utility poles and structures is governed by ASCE Manual 104 [6] and the NESC [7]; however, the Manual does not address cross arms specifically. NESC specifies load and strength factors required for design.

From strength perspectives, allowable loads per load point for wood arms are derived simply on the basis of designated ultimate bending stress and recommended strength reduction factors. For composite arms, allowable loads per load point are obtained on the basis of test loads and deflections. NESC recommends a strength factor of 1.00 for composite cross arms. Most composite materials possess high strength-to-stiffness ratios thus permitting poles to be designed to be as flexible as needed. However, there is no information available on this flexibility aspect as it refers to composite cross arms.

Fig. (1a). Typical tangent cross arm with 4 post insulator attachment points.

Fig. (1b). Typical dead end cross arm with 4 strain insulator attachment points.

To the best of our knowledge, there is little information in literature regarding the relative performance of wood and composite distribution cross arms. Parameters such as strength-to-stiffness ratios and weight-to-stiffness ratios are useful for engineers in making design choices. This study is a small step in this direction.

The objectives of this paper are to:

1. Derive relationship between wire loads and strength for wood cross arms based on ultimate design bending stress.
2. Derive relationship between wire loads and strength for composite cross arms based on test deflections.
3. Propose definitions of Strength-to-Stiffness and Weight-to-Stiffness ratios.
4. Evaluate the strength and stiffness performance of various wood and composite cross arms in both tangent and dead end configurations.
5. Compare Strength-to-Stiffness and Weight-to-Stiffness ratios of all study cases.

This study is limited to linear, elastic behavior of the structural elements. For tangent cross arms, only vertical or gravity loads are considered. For dead end cross arms, whose design is controlled by longitudinal loads, only wire tension loads are considered. Ice loads and transverse loads due to wind and line angles are not considered here but will be included in future studies.

The six (6) configurations of tangent and dead end distribution cross arms studied in this paper are shown in Figs. (2 and 3). The selected configurations are standard designs which are commonly used by utilities [8]. Both Douglas Fir and Southern Yellow Pine are popular materials for wood cross arms [4]; however, Douglas Fir is selected in this study for its superior strength in terms of Modulus of Elasticity.

Fig. (2a). Tangent cross arm 8T (2.44 m).

Fig. (2b). Tangent cross arm 10T (3.05 m).

Fig. (2c). Tangent cross arm 12T (3.66 m).

Composite cross arms are firmly attached to the pole with a metal mounting bracket and multiple bolts. This connection is almost a fixed joint. Wood cross arms are generally connected to the pole with a single machine bolt, washer and a lock nut. This situation is closer to a pinned joint than a fixed joint. In fact, wood cross arms often have V-braces underneath to provide additional support against bending. However, in order to have consistency and facilitate a one-on-one comparison in this study, the connection at pole in both cases is considered fixed thus enabling modeling as a simple cantilever in both.

For cross arms made of Douglas Fir material, the designated ultimate bending stress is 51 MPa (7.4 ksi). Modulus of Elasticity ‘E’ is 13.24 GPa (1920 ksi) [4]. The dressed sizes of wood cross arms used in the study are 88.9 mm x 114.3 mm (3½ in. x 4½ in.). Material dry density for calculation purposes is taken as 6.28 kN/m³ (40 pcf).

For cross arms made of composite materials, Table 1 gives the elastic properties used in the study [9]. Density of composites varies with type of manufacture but standard cross arms weigh about 0.0054 to 0.0068 kN/m (4 to 5 plf). Typical composite cross arms are similar to wood cross arms in cross sectional dimensions.

Fig. (3a). Dead end cross arm 8D (2.44 m).

Fig. (3b). Dead end cross arm 10D (3.05 m).

Fig. (3c). Dead end cross arm 12D (3.66 m).

Figs. (4a and 4b) show the cantilever models of the cross arms analyzed. Since symmetry is available, only one half of the total cross arm is modeled.

All loads used in the analyses include appropriate load factors. Capacities include recommended strength (reduction) factors. The values used in this study are given below [4].

Load Factor γ        Vertical Load        1.50

               Longitudinal Load        1.65 (Wire Tension)

Strength Factor ψ       Wood Cross Arm        0.65 (Applied to designated bending stress f_r)

               Composite Cross Arm     1.00

The derivation of the relationship between applied loads, insulator locations, deflections and cross arm bending strength is shown in Appendix A. The equations are applicable to both tangent and dead end cross arms.

Fig. (4a). Wood cross arm cantilever model with two (2) load points.

Fig. (4b). Composite cross arm cantilever model with two (2) load points.

Tables 2 and 3 show the results of application of the equations to various tangent cross arms. Three (3) wood cross arms and eleven (11) composite cross arms are studied.

The derivation of the relationship between test loads, insulator locations, deflections and cross arm bending strength is shown in Appendix B. The equations are applicable to both tangent and dead end cross arms.

Tables 4 and 5 show the results of application of the equations to various dead end cross arms. Three (3) wood cross arms and eight (8) composite cross arms are studied.

All four tables also show the relative weights and costs of the cross arms modeled.

We propose two (2) ratios here with reference to cross arm strength, stiffness and weight.

The lateral flexural stiffness k_L is given by finite element method as 12 EI / L³ where EI is the flexural rigidity of the cross section and L is the length of the element.

Evaluated lateral flexural stiffness of all cases are shown in the tables. The units of both R_SS and R_WS are 1/mm (1/in).

As seen in Table 1, average bending stress capacities for composites are 5 to 14 times than those of wood. The modulus of elasticity, E, which controls stiffness and thereby deflections, is about 1.9 to 2.9 times larger for composites than for wood. These two parameters govern the behavioral differences between the two materials.

Tables 2 to 5 show the main differences between wood and composite arms. While the composite arms exhibited larger strength-to-stiffness ratios, there is little difference between the two materials with reference to weight-to-stiffness ratios. However, from deformation point of view, composite arms sustained deflections 4 to 5 times larger than wood arms.

Tables 2 to 5 also show the allowable loads on cross arms computed considering nominal NESC load and strength factors. As expected, composite cross arms showed larger load bearing capacity than wood arms of the same length and configuration.

Cost-wise, composite cross arms are about 2 to 2¼ times costlier than wood arms based on nominal market prices. But, the additional cost is offset by superior load-deflection performance and flexibility while subject to large loads.

A total of 25 distribution cross arms made of wood and composites are analyzed. Both tangent and dead end configurations are studied using specially derived load-deflection relationships. Though the study comprised only of a small set of data, the following main conclusions can be drawn.

1. Composite arms consistently showed large strength-to-stiffness ratios relative to wood arms. On an average, the R_SS ratios of composite arms are over 4 times than those of wood.
2. Composite arms sustained deflections 4 to 5 times larger than wood arms at ultimate load levels.
3. Composite arms showed larger load carrying capacity than wood arms of similar configurations.
4. However, composite arms are more than twice as expensive as wood arms. This additional expense is however offset by their superior performance and flexibility at higher load levels.