Advanced Course Course on Communication and Power Power Transmission Transmission Towers 6-8 Februa February ry 2013, CSIR-SERC, Chenn Chennai ai - 113, India. pp 323-371.
STEEL MONOPOLES
R. Balagopal Scientist, Tower Testing and Research Station, CSIR-Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai – 600113, INDIA. Email:
[email protected]
1. INTRODUCTION
Generally, the self supporting lattice type towers are most commonly used for power transmission. In a fast developing country faced with density of population in the urban areas, great difculties are experienced in nding corridor (land) for new transmission lines. It is very difcult to get land for installation of conventional lattice towers for power transmission. Power utilities utilit ies throughout the world are making diverse attempts to make compact lines. Compaction of a transmission line means reduction in the dimension of a line both in horizontal and vertical direction. By horizontal compaction power density over available corridors is increased by more efcient use of land and Right Of Way (ROW). Poles are suitable alternate supports to the conventional lattice towers. Steel poles have smaller plan dimension and are composed of only few pieces, compared to the lattice type towers. Poles are generally tapered and manufactured in number of pieces which can slip in to each other to form the entire pole structure. The pole circumference thickness is varied for each pole segment along the pole height to to obtain a lighter structure. The pole cross section may have a rectangular, circular or regular polygonal shape of 6, 8, 12, 16, and 24 sided. Pole structures having polygonal cross sections with larger number of sides have larger exural capacity for a specied circumference thickness. For pole structures of same exural capacity, ones having larger base diameter to circumference thickness ratios and designed to utilize the full yield strength of the material are lighter. The pole structures are either connected by a base plate and anchor bolts to the foundation or directly embedded in to the soil or into a drilled concrete foundation. Poles with direct embedment foundations might have smaller base diameter than those with traditional base plate - anchor bolt type foundations to reduce the negative effect of extra weight, resulting from the additional pole length used for embedment. 2.0 INITIAL DESIGN CONSIDEARIONS
Geometry: The basic pole structure conguration, conductor and shielding geometry insulation
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assembly length, swing angles, electrical clearances and shielding angles shall be determined. It is important to note that a critical loading condition may depend on the type of tubular pole structure conguration being considered.
Stress analysis: The structure designer will normally need to consider the effects of large deections during the design. A secondary secondary moment will develop when a structural member m ember having an axial force deects in a direction normal to the line of action of the force. The additional stress caused by this secondary moment is dependent on the magnitude of the axial force and the deected shape of the member.
Clearences: Clearances from conductors to supporting structures, ground or edge of right-of-way are usually not affected signicantly by deections except perhaps where special span and line angle conditions exist.
Appearance: Line angles and unbalanced phase arrangements create load situations which will cause a pole to appear bowed. There are several methods that can be used to minimize the appearance problem. One method is to camber the pole to offset the deection under this load so that it will appear straight and plumb. Another method is to rake the pole when setting it. The deection at the top t op is determined for everyday loading. A pole can be designed to limit deection by increasing its stiffness. stiffness.
Other considerations: Pole structures should be considered exible and relatively large deections can result due to loads. Deections can affect the magnitude of loads caused by an unbalanced longitudinal loading situation. The deection of the structure and the swing of suspension insulators can signicantly decrease wire tensions. Line spans, location of strain structures, structure exibility, wire tensions and insulator lengths are some of the variables needed in the analysis to determine equivalent static loads.
Construction, fnish and Transportation: The specication should include possible limits due to equipment, access limitations, methods of hauling, assembly, erection, stringing or one circuit installed for the present with provisions for future circuits. Rigging attachment points should be provided for lifting the structure, hoisting insulators and stringing blocks, stringing, clipping in, deadending and maintenance. Special consideration should be given in the structure design for helicopter erection. The type of corrosion protection may limit structure design concepts. As an example, the diameter, length or weight of a pole section may be limited to t available galvanizing kettle capabilities.
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assembly length, swing angles, electrical clearances and shielding angles shall be determined. It is important to note that a critical loading condition may depend on the type of tubular pole structure conguration being considered.
Stress analysis: The structure designer will normally need to consider the effects of large deections during the design. A secondary secondary moment will develop when a structural member m ember having an axial force deects in a direction normal to the line of action of the force. The additional stress caused by this secondary moment is dependent on the magnitude of the axial force and the deected shape of the member.
Clearences: Clearances from conductors to supporting structures, ground or edge of right-of-way are usually not affected signicantly by deections except perhaps where special span and line angle conditions exist.
Appearance: Line angles and unbalanced phase arrangements create load situations which will cause a pole to appear bowed. There are several methods that can be used to minimize the appearance problem. One method is to camber the pole to offset the deection under this load so that it will appear straight and plumb. Another method is to rake the pole when setting it. The deection at the top t op is determined for everyday loading. A pole can be designed to limit deection by increasing its stiffness. stiffness.
Other considerations: Pole structures should be considered exible and relatively large deections can result due to loads. Deections can affect the magnitude of loads caused by an unbalanced longitudinal loading situation. The deection of the structure and the swing of suspension insulators can signicantly decrease wire tensions. Line spans, location of strain structures, structure exibility, wire tensions and insulator lengths are some of the variables needed in the analysis to determine equivalent static loads.
Construction, fnish and Transportation: The specication should include possible limits due to equipment, access limitations, methods of hauling, assembly, erection, stringing or one circuit installed for the present with provisions for future circuits. Rigging attachment points should be provided for lifting the structure, hoisting insulators and stringing blocks, stringing, clipping in, deadending and maintenance. Special consideration should be given in the structure design for helicopter erection. The type of corrosion protection may limit structure design concepts. As an example, the diameter, length or weight of a pole section may be limited to t available galvanizing kettle capabilities.
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Climbing and maintenance: The line designer should identify climbing, working and hot line maintenance provisions required. Generally, provisions should be made so that all parts of pole structures and insulator and hardware assemblies can be reached for maintenance. Detachable ladders should be fabricated in lengths which can be handled by line maintenance personnel personnel on the structure.
Load testing : Consideration should be given to the full-scale structure testing which may be required. The necessity to perform a test may be to adequately verify the design concept, to verify connection details and to determine the level of reliability reliability..
Stability and Fatigue analysis: Stability should be provided for the structure as a whole and for each structural element. Consideration should be given to load effects resulting from the deected shape of the structure. Generally speaking, rigorous fatigue stress analyses of steel pole structure have proven unnecessary.
Modeling: It is important that the structure be accurately modeled for computer analyses. Finite element models should contain a sufcient number of elements to ensure that the curvature of members in the deected position is adequately represented and the point of maximum stress is adequately dened.
3.0 ASCE/SEI 48-05 DESIGN RECOMMENDATIONS The design stresses for members is based on ultimate strength methods using the factored loads. Material Stress: The yield stress F y, and the tensile stress, F u, shall be the specied minimum values specied in ASTM standard. The modulus of Elasticity of Steel is dened as, 200 GPa.
I) Tension: The tensile stress shall not exceed either of the following; P (a ) Ft ; where Ft F y ; or A g ( b)
P A g
Ft ;
wher e Ft 0.83F u
where F t is the permitted tensile stress; F y is the specied minimum yield stress; F u is the specied minimum tensile stress; P is is the axial tension force in the member; A g i iss the gross cross-sectional area; and An is the net cross-sectional area.
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II) COMPRESSION: The tubular members subjected to compressive forces shall be checked for general stability and local buckling. The compressive stresses shall not exceed the limiting stress values dened in the following sections.
a) Truss members with closed cross section: For truss members with closed cross section, the actual compressive stress, f stress, f a, shall not exceed the permissible compressive stress, F stress, F a, as determined by the following.
KL 2 r KL , when i) Fa F y1 0.5 C c C r c 2 E 2 E KL ii) F a , w h e n C , w h e r e C c c r F y KL 2 r where, F a is the permissible compressive stress; F y is the specied minimum yield stress; E is the modulus of elasticity; L L is the unbraced length; g is the radius of gyration; and K and K is the effective length factor. KL is the largest slenderness ratio of any r unbaked segment.
a) Beam Members: The limiting values of w/t and D and D0 /t specied specied in the following section may be exceeded without requiring a reduction in extreme bre stress if local buckling stability is demonstrated by adequate experimental test. i) Regular Polygonal Members: For formed, regular polygonal tubular members, the compressive stress P A Mc I , on the extreme ber shall not exceed the following;
Octagonal, hexagonal, or rectangular members (bent angle Fa F y , when
w t
260W F y
Fa 1.42 Fy1.0 0.00 0 0114
F a
1, 04, 980F
w 2 t
450)
, when
1
W
w t
F y
w 260W w 351W , when t t F y F y
351W F y
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Dodecagonal members (bent angle =30 o) w
Fa F y , when
t
260W F y
1 w 260W w 374W Fa 1.45 Fy1.0 0.00129 F y , when W t t F y F y F a
1, 04, 980F
w 2 t
, when
w t
374W F y
Hexdecagonal members (bent angle =22.5 o) w
Fa F y , when
t
215W F y
1 w 215W w 412W Fa 1.42 Fy1.0 0.00137 F y , when t t W F y F y F a
1, 04, 980F
w 2 t
, when
w t
412W F y
where, F y is the specied minimum yield stress; F a is the permitted compressive stress; w is the at width of a side; t is the wall thickness; W = 2.62 for F y or F a in MPa; and F = 6.90 for F a in MPa. ii) Rectangular Members: The permissible stress specied for octagonal, hexagonal members is used. If the permissible stress value exceeds 6.9 MPa, then the equations for dodecagonal members are used. iii) Polygonal Elliptical Members: The bend angle and at width associated with elliptical cross section are not constant. The smallest bend angle associated with a particular at shall be used to determine the compressive stress permitted. iv) Round Members: For round members or polygonal members with more than f a f b 1 ; sixteen sides, the compressive stress shall not exceed the following F a F b
Where f a is the compressive stress due to axial load; f b is the compressive stress due to bending; F a is the permitted compressive stress; and F b is the permissible bending stress. Permissible Compressive Stress: F a Fa F y when
DO t
3800F F y
; and
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Fa 0.75 F y
950F 3800F DO ; when DO F y t t
12, 000F F y
Permissible Bending Stress: Fb Fb F y when
DO t
6000F F y
; and
1600F 6000F DO 12, 000F ; when DO F y t F y t where D0 is the outside diameter of the tubular section (at to at outside diameter for polygonal members); t is the wall thickness; and F = 6.90 for F y , F b or F a is in MPa. Fa 0.70 F y
III) Shear: The shear stress resulting from applied shear forces, torsional shear, or a combination of the two shall not exceed the following:
VQ Ib
Tc J
Fv ; wher e Fv 0.58 F y
where, F y is the specied minimum yield stress; F y is the permitted shear stress; V is the shear force; Q is the moment of section about neutral axis; I is the moment of inertia; T is the torsional moment; J is the torsional moment of cross section; c is the distance from neutral axis to extreme ber; and b equals 2 times the wall thickness. IV) Bending: The stress resulting from bending shall not exceed either of the following; Mc Mc F t or F a I I
where F t is the permitted tensile stress; F a is the permitted compressive stress; L is the moment of inertia; M is the bending moment; and c is the distance from neutral axis to extreme ber. V) Combined Stresses: For a polygonal member, the combined stress at any point on the cross section shall not exceed the following; 1
P M c M c 2 VQ Tc 2 2 x y y x 3 Ft or F a A I It J I x y
For round members, the combined stress at any point on the cross section shall not exceed the following: 1
P M c M c VQ Tc 2 2 x y y x 3 Ft or F b A I It J I x y 2
where F t is the permitted tensile stress; F a is the permitted compressive stress; F b is the permitted bending stress; P is the axial force in the member; A is the cross sectional
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area; M x is the bending moment about X-X axis; M y is the bending moment about Y-Y axis; is the moment of inertia about X-X axis; I x is the moment of inertia about Y-Y axis; c x is the distance from Y-Y axis to the point where stress is checked; c y is the distance from X-X axis to the point where stress is checked; V is the shear force; Q is the moment of section about neutral axis; I is the moment of inertia; T is the torsional moment of cross section; J is the torsional moment of cross section; c is the distance from neutral axis to the point where stress is checked; and t equals wall thickness. VI) Slip Joint: Slip joint in poles shall be designed to resist maximum forces and moments in the connection. As a maximum, slip joints shall be designed to resist 50% of the moment capacity of the lower strength tube. The taper should be the same above and below the slip joint. VII) Base Plate and Flange Plate connections: Flexural stress in the base or ange plate shall not exceed the specied minimum yield stress, of the plate material. The base and ange plate connections shall be designed to resist 50% of the moment capacity of the lowest strength tube. VIII) Design of Anchor Bolts: The anchor bolts shall be designed to transfer the tensile, compressive, and shear loads to the concrete by adequate embedment length or by the end connection.
i) Bolts subject to tension: The bolts subject to designed to resist the sum of the tensile stresses caused by the external loads and any tensile stress resulting from prying action shall not exceed the permissible stress, F t , as ows: For bolts with specied proof –load stress, F t is the lowest of yield stress F y or 0.83 F u, where F u is the specied minimum tensile stress of the bolt. For bolts with no specied yield stress, F t = 0.83 F u; Thus
T s A s
F t ; where the stress area A s is given by;
where T s is the bolt tensile force; d is the nominal diameter of the bolt; and n is the number of threads per unit of length. ii) Shear Stress: The shear stress for anchor bolts shall be determined as follows: V Fv 0.65 F y A s 2 0.9743 , tensile stress of bolt; F where is the shear force on bolt; A s d y is the 4 n
shear stress permitted; F y is the specied minimum yield stress of bolt material; d is the nominal diameter of the bolt; and n is the number of threads per unit of length. iii) Combined Shear and Tension: For bolts subject to combined shear and tension, the permitted axial tensile stress in conjunction with shear stress, F t (v) shall be,
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f v 2 Ft ( v ) F t 1 ; F v where F v is the permitted shear stress; F t is the tensile stress permitted; and f v is the shear stress on effective area. The combined tensile and shear stress shall be taken at the same cross section in the bolt. iv) Development Length: The minimum clear cover for concrete is specied as 76mm. The development length for the threaded reinforcing bar used as anchor bolts shall be calculated as follows; L d l d . a. b.g where Ld is the minimum development length of anchor bolt; and l d is the basic development length for the bolt shall be taken as; For bars upto and including #11 (i.e upto 35.7 mm bar), use the larger of l d
1.27 A g F y ' y
f
or ld 0.400FdF y
For # 14 bars (43.7 mm bars), l d
2.69 F y f y'
For #18 and #18J bars (56.4 mm bars), l d
; 3.52 F y ' y
f
;
where A g is the gross area of anchor bolt; s ( req ' d ) is the required tensile stress of bolt; ' F y is the specied minimum yield stress of anchor bolt; f c is the specied compressive ' strength of concrete; d is the diameter of the bolt; =0.0150 for F y and f c in MPa and ' f A g in mm2, =9.67 for F and y y in 414 MPa or 1.2 if F y in 517 c in MPa; a =1.0 if F MPa; b =0.8 for bolt spacing upto and including 152 mm, or 1.0 for bolt spacing less than 152 mm; g A s ( req ' d ) Ag . IX) Stress concentrations:
Care must be taken to distribute loads sufciently to protect the pole wall against local failure. Slip joints, arm to pole connections and abrupt changes in member’s cross section or longitudinal axis are points of susceptibility. 4. ANALYSIS
Stress calculations for transmission structures have traditionally been based on elastic analysis. The design criteria presented in ASCE/SEI 48-05 is based on elastic stress analysis methods. Stability should be provided for the structure as a whole and for each structural element. The response of tubular transmission structures to applied loads is generally nonlinear in nature. The standard industrial practice in design is
Steel Monopoles
331
to use nonlinear nite element based computer programs. These computer programs consider the effects of large displacements and dependence of the structure’s stiffness on member stress levels and are capable of computing elastic stability phenomena. For pole structures the rened nite element models are necessary for the static and buckling analysis since a high level of accuracy is required at specic critical locations. For pole structures a seismic analysis produces no critical response. Analysis programs have virtually eliminated the use of linear analysis methods for most design work, However, some preliminary design and estimating work might still be accomplished by using linear analysis methods by assuming a deected position or by using amplication factors on moments. 5. TYPICAL FABRICATION AND ERECTION DETAILS:
Slip splices : Sections jointed by telescoping splices should be detailed for a nominal lap that will assure a minimum lap of 1.35 times the largest inside diameter. A commonly used practice is to specify a nominal lap 1.5 times the largest inside diameter of the female section and allow a 10% tolerance on the nal assembled lap length. Supplemental locking devices are needed if relative movement of the joint is critical or if the joint might be subjected to uplift forces. In resisting uplift forces, locking devices should be designed to resist 100% of the maximum uplift load. The female section longitudinal seam welds in the splice area should be complete penetration welds for at least a length equal to the maximum lap dimension.
Circumferential welded splices: Complete – penetration welds should be used for sections joined by circumferential welds. Longitudinal welds within 75mm of circumferential welds should also be complete – penetration welds.
Welded T joint connections: Pole shaft to base plate welds, pole shaft to ange plate welds and arm to arm bracket welds are quite commonly T joint connections. Where the primary loads carried by the pole or arm are exural, a groove weld with reinforcing llet is recommended to satisfy the requirements for through - thickness stresses in the attachment plate.
Hole size: Typically, holes 3mm larger than the nominal bolt diameter are used except for anchor bolt holes. Anchor bolt holes in the base plate are normally 10mm oversize.
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6. FOUNDATION TYPES:
Steel pole structures can be installed using drilled shaft, direct embedded pile or spread footings. The soil condition will often dictate the best type to install. The base size of the structure or the available equipment may limit the foundation type.
Caisson: Caisson foundations are particularly effective in areas where the augured holes collapse or soft cohesive soils tend to slump or squeeze inward and reduce the diameter of the hole. The caisson should be provided with adjusting bolts at the top to plumb the pole into place.
Direct embedment: The bottom portion of the pole becomes the foundation member reacting against the soil. The length of the section of the pole below the ground line should be determined using a lateral resistance approach.
Reinforced concrete drilled foundation: An anchor bolt cage set in a reinforced concrete drilled foundation is a very popular foundation. The minimum foundation diameter is determined by the diameter of the bolt circle.
Pile foundation: The purpose of the pile foundation is to transfer the loads from the pole down to the denser underlying soil or rock. The skin friction of the pile is used to resist uplift. The most common piles are steel H-piles, wood pile and prestressed concrete.
Stem and pad foundation (spread): The stem and pad foundation is a basic spread footing. It is used in areas where drilled holes cave easily. Spread footings are designed to resist compression from axial loads and overturning moment from horizontal loads.
Rock anchors: Rock anchors can be designed to resist uplift, compression, horizontal shear and in some cases, bending moments. 7.0 COMPARATIVE STUDY
To compare the structural behavior of lattice tower and pole structure, the static and dynamic performance of 30m and 40m Mw monopole is compared with corresponding 30m and 40m high square is considered in the present study.
Steel Monopoles
333
a) 30m and 40m high self supporting Mw monopole. The conguration, dimensions and load application details for 30m and 40m High Mw monopole is shown in Fig. 1 and Fig. 2. The main shaft of both 30m and 40m High Mw Monopole is of twenty sided polygonal (20 sided regular polygon) in shape and made of four segments with bottom two segments of 8mm thick and the top two segments are of 6mm thick. These segments are joined by telescopic slip splice joint with minimum lap length of 1.35 times the largest inside diameter of the pole [ASCE Manual No: 72]. The diameter of the shaft is 900mm at the bottom and 150mm at the top for 40m high self supporting monopole, while the diameter of the shaft is 800mm at the bottom and 150mm at the top for 30m high self supporting monopole. The base plate is of 48mm thick welded to the bottom of the shaft. The main shaft is made of material Fe-490 with 350 MPa yield stress and base plate with yield stress of 250 MPa. The pole has been designed for a wind speed of 33 m/s and Terrain Category -2. The wind load on 40m and 30m high monopole is calculated based on IS: 875 (Part 3): 1987. NE-NASTRAN, a non-linear FE software is used for modeling both 30m and 40m high Mw monopole. In the FE model, four noded plate shell elements are used for modeling the main shaft, stiffeners and base plate. The FE Model for 30m and 40m high self supporting pole is shown in Fig. 3 and Fig. 4 respectively. The elastic plastic material property of steel was represented by an elastic-plastic bi-linear model, with the modulus of elasticity as 2E5 upto yield and 2000 MPa above yield stress. Eigenvalue analysis for both the pole structures has been carried out and the deformed FE model of both the pole structures are shown in Fig 5 and Fig 6. Both the wind load the antennae loads has been applied on the pole structures at equi-distant intervals along the height of the pole and the deected FE model for both the pole structures is shown in Fig. 7 and Fig. 8 respectively. 500 4.89 kN
k t 6
4.80 kN 7270
2.53 kN k t 2 1
k t 6
k t 6 1
k t 8
1060 2.47 kN
6170
2.53 kN
2.54 kN
1070 30000
6130
C/S OF 20 SIDED
2.53 kN
POLYGONAL POLE
2.48 kN k t 6 1
1100 4.89 kN
k t 8
7200
2.37 kN
800 All dimensions a re in mm BASIC POLE CONFIGUR ATION
WIND LOAD + ANTENNAE LOAD
3 0 m MW M O N O P O L E
Fig. 1 General conguration of 30m High Mw Monopole
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500
5.75 kN
4000
k t 6
5.62 kN
7600
4000 k t
3.19 kN
600
2 1
4000 k t
3.33 kN
7600
6
4000 3.35 kN
k t
1200
2 1
4000
k t
3.31 kN 6600 40000
6
4000 C/S OF 20 SIDED k t
POLYGONAL POLE
1000
4 1
3.23 kN 4000
k t 8
3.13 kN
6600
4000 k t
3.02 kN
1200
6 1
4000 k t 8
2.91 kN 7600 4000 All dimensions a re in mm WIND LOAD +
900
ANTENNAE LOAD BASIC POLE CONFIGURATION
40m MW MONOPOLE
Fig. 2 General conguration of 40m High Mw Monopole
Fig. 3 FE Model (30m Mw Monopole)
Steel Monopoles
Fig. 4 FE Model (40m Mw Monopole)
Fig. 5 Deformed FE Model of 30m Mw Monopole (First Mode)
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Fig. 6 Deformed FE Model of 40m Mw Monopole (First Mode)
Fig. 7 Deected FE Model of 30m Mw Monopole
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Fig. 8 Deformed FE Model of 40m Mw Monopole
b) 30m and 40m high self supporting Mw lattice tower. The conguration, dimensions and load application details for 30m and 40m High Mw lattice tower is shown in Fig 9 and Fig. 10 Both the lattice towers have square conguration with two slopes. The bottom and top widths of 40m Mw tower are 4.5m and 1.5 m respectively. The 30m Mw tower has base width of 3.5m and top width of 1.5m . These lattice towers have been designed for a wind speed of 33 m/s and Terrain Category -2. The wind load on 40m and 30m high lattice Mw tower is calculated based on IS: 875 (Part 3): 1987 recommendations. NE-NASTRAN, a non-linear FE software is used for modeling both 30m and 40m high lattice tower. In the FE model, two noded beam column elements are used for modeling the main leg, bracing and tie members of the tower. The undeformed FE Model of 30m and 40m high lattice tower is shown in Fig. 11 and Fig. 12 respectively. The elastic plastic material property of steel was represented by an elastic-plastic bi-linear model, with the modulus of elasticity as 2E5 upto yield and 2000 MPa above yield stress. Eigenvalue analysis for both the lattice tower has been carried out and the deformed FE model is shown in Fig. 13 and Fig. 14 respectively. Both the wind load and the antennae loads are applied at four noded point load at the top of each panel. The static analysis has been carried out and the deected FE model for both the lattice towers are shown in Fig. 15 and Fig. 16. respectively.
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1500 4.92 kN
5 x 0 6 x 0 6
5 x 5 4 x 5 5 x 4 5 5 x 7 5 x 4 5 x 5 7 4 6 x 0 8 x 0 8
5 x 0 5 x 0 5
2500 4.84 kN 2500 2.56 kN 2500 2.48 kN 1500
2.64 kN 2500 2.56 kN 2500 2.64 kN
8 x 0 0 1 x 0 0 1 8 x 0 1 1 x 0 1 1 0 1 x 0 3 1 x 0 3 1
R E B M R E R E M E B B M G M N E I E M C M A G E I R E T B L
2500
30000
2500 2.72 kN 2500 2.84 kN 2500 3.92 kN 2500 3.16 kN 2500 3.24 kN 2500 3500 BASIC TOWER CONFIGURATION
WIND LOAD + ANTENNAE LOAD
All dimensions are in mm 30m MW TOWE R
Fig. 9 General conguration of 30m High Mw square lattice tower 1500 5.12 kN
5 x 0 6 x 0 6
5 x 5 4 x 5 5 5 x 4 x 5 5 7 x 4 5 x 5 7 4 6 x 0 8 x 0 8 8 x 0 0 1 x 0 0 1 8 x 0 1 1 x 0 1 1 0 1 x 5 0 x 3 0 1 5 x x 0 0 3 5 1
2500
5.08 kN 2500
2.72 kN 2500
2.72 kN 1500
2.92 kN 2500
2.84 kN 2500
2.96 kN 2500
3.08 kN 2500 40000
3.24 kN
2500
3.28 kN 2500
3.40 kN 2500
3.36 kN 2500
6.84 kN
2 1 x 0 3 1 x 0 3 1 R E B M R E R E M E B B M G M N E I E M C M A G E R E I T B L
2500
5000
7.36 kN 5000
4500
BASIC TOWER CONFIGURATION
WIND LOAD + ANTENNAE LOAD
All dimensions are in mm 40m MW TOWE R
Fig. 10 General conguration of 40m High Mw square lattice tower
Steel Monopoles
Fig. 11 FE Model (30m Mw lattice tower)
Fig. 12 FE Model (40m Mw lattice tower)
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Fig. 13 Deformed FE Model of 30m Mw lattice tower (First Mode)
Fig. 14 Deformed FE Model of 40m Mw lattice tower (First Mode)
Steel Monopoles
Fig. 15 Deected FE Model of 30m Mw Monopole
Fig. 16 Deformed FE Model of 40m Mw Monopole
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c) Wind and Antennae load calculation on Pole and lattice tower a. Wind Load The wind load on pole and lattice tower is calculated based on IS: 875 (Part 1)-1987.The following design parameters are used for calculating the wind loads. Basic Wind Speed: 33 m/s, Terrain Category: 2, Topography factor k3=1.0, Risk coefcient k1=1.05. The design wind speed is calculated taking into account the terrain type, height of the structure, topography, risk level for the structure. The wind load ( F p) on the lattice tower is calculated based on solidity ratio (ø), the geometry of the member sections and the wind ow regime through the force co-efcient method. The wind pressure and subsequent wind load calculation on pole structure depends upon the aerodynamic effects of the pole structure. The solidity ratio (ø) is dened as the ratio between the effective area ( Ae) of the panel (areas of all members of the panel) projected on a plane normal to the wind direction and the overall area ( At ) of the panel. The effective area ( Ae) does not include the projections of the bracing members from faces parallel to the wind direction, plan and hip bracings. The wind load ( F p) on the tower at height z is then computed using the relation, F p = C f
P z Ae
(1)
2 where C f = force coefcient; Ae = effective frontal area at height z ; P z = 0.6Vz design wind pressure in N/m 2 at height z and due to design wind velocity V z in m/sec. The calculation details for design wind velocity V z is given IS 875 (Part 3): 1987.
The additional loading effects due to wind turbulence and dynamic amplication in exible structures such as guyed towers and pole structures is calculated using gust factor ‘G’. When the fundamental frequency of the pole structure is less than 1Hz, then dynamic loading analysis of the structure is recommended in codes of practice. The IS code recommends simplied method to calculate the peak response of wind resistance structures. F = C f Ae P z G
(2)
The gust factor ‘G’ accounts for the dynamic effects of gust on wind response towers. The values of these gust factors lies in the range of 1.5 to 2.5.The values of these gust factors changes with wind speed, decreases with height and increases with increased terrain roughness. The frequency of the pole structures is almost less than 1Hz, the wind loads on these structures is calculated based on gust factor method. The wind loads calculated based on this gust factor method is 35-25-30% higher when compared to force-co-efcient method.
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b. Antennae Load Both the pole and lattice structures are subjected to same antennae loads and the deection behavior is compared. The loading details for antennae are as follows. There are 3 nos. of GSM antennae of size 2.6m 0.3m at tower top and 3 nos. of CDMA antennae of size 1.2m 0.3m at 3m down from tower top. The wind load due to these antennae on the pole and lattice structure is calculated based on the exposed area of the antennae.
d) Simplied Numerical Model for steel pole and lattice tower Generally, the lattice tower and pole structure represents a system with innite degrees of freedom. In this method, this structure is discretized into a simple model with multiple degrees of freedom, thereby the continuum model is reduced to lower order discrete mass model. The entire structure is discretized into ‘n’ number of nodes, with their masses lumped at these nodes. The free vibration equation of motion for an undamped mutli degree of system is represented as,
M x K x 0
(3)
where [ K ] is the stiffness matrix, [ M ] is the mass matrix, { x} denotes the displacement and x denotes the acceleration vectors of different degrees of freedom. The stiffness matrix is obtained by evaluating the exibility matrix, [ F ]. To obtain the exibility matrix, a unit horizontal load was applied at the node ‘i’ and the displacement at node ‘ j’, is calculated, which is the f ij element of the exibility matrix [ F ]. The stiffness matrix [ K ] is obtained by inverting the exibility matrix [ F ]. Equation (3) represents the eigenvalue or characteristic equation of the structural system. The natural frequencies and mode shapes are obtained by solving the eigenvalue equation. For the numerical modeling, the entire lattice mast are discretized into nite number of elements. For the formulation of exibility matrix , the average of combined moment of inertia of all four leg members at bottom and top of the lattice mast is considered. While formulating the mass matrix, uniform mass density and uniform combined area of all the four leg members are considered. The fundamental frequency and mode shape is obtained by solving the characteristic Eigenvalue equation. The pole mast is descritized into nite number of elements. The cross sectional area and moment of inertia of the polygonal pole at bottom and top of the pole mast is calculated based on ASCE Manual No: 72 formulae with average thickness is considered. In the exibility matrix formulation, the average moment of inertia at bottom and top of the pole is considered. For mass matrix formulation, average density and average cross sectional area at bottom and top of the pole is considered. The fundamental frequency and mode shape is obtained by solving the characteristic Eigen value equation.
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e) Deection Comparison. The maximum deection obtained from static analysis for both lattice tower and pole structures are tabulated in Table1. From the table, it can be observed that the deection of 40m Mw monopole is 6.5 times higher than the corresponding deection for 40m high Mw lattice tower. The deection of 30m Mw monopole is 5 times higher than deection for 30m high Mw lattice tower. Table 1: Deection Comparison of Mw Monopole and Mw lattice tower
S. No
Self supporting Monopole
Self Supporting Lattice Tower
Height (m)
Deection (mm)
Height (m)
Deection (mm)
1
30
532
30
103
2
40
1097
40
168
f) Weight Comparison. Both the Mw tower and Mw Monopole has been designed based on working stress method. The self weight of both lattice tower and monopole has been calculated and is tabulated in Table 2. Table 2: Weight Comparison of Mw Monopole and Mw lattice tower
S. No
Self Supporting Monopole Height (m)
Self Weight (kN)
Height (m)
Self Weight (kN)
1
30
35
30
28
2
40
48
40
38
g) Natural Frequency Comparison. The natural frequency for both pole and lattice structures are calculated based on FE analysis and simplied numerical model and the results are tabulated in Table 3. Table 3: Natural Frequency Comparison of Mw Monopole and Mw lattice tower
S. No
Self Supporting Monopole Height (m)
Natural Frequency (Hz) FE Model
Simplied Model
Self Supporting Lattice Tower Height (m)
Natural Frequency (Hz) FE Model
Simplied Model
1
30
1.012
1.034
30
3.11
3.40
2
40
0.606
0.654
40
2.45
2.40
The monopole structures are dynamically sensitive, since the natural frequencies of these structures are close to 1Hz, when compared to lattice towers, whose frequencies are higher than 2 Hz. The natural frequency predicted from FE model and simplied model
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345
varies within 1% and hence the simplied model can be used as better approximation to estimate the natural frequency of pole and lattice structures. The deection criteria is one of the most important aspect in communication towers. The deection sway limit should be within 0.5 degrees for Mw towers. The deection for pole structures exceeds this limit, but this will not cause a major problem for signal attenuation, because nowadays CDMA and GSM antenneas are used in signal communication. The self weight of monopole is 18 to 20% higher than the lattice towers. The self weight of monopoles can be further reduced by applying suitable optimization techniques. Considering all these aspects along with ease in transportation, erection, handling and reduction in land acquisition cost, these pole structures forms a suitable alternate for conventional lattice towers.
7. ANALYTICAL AND EXPERIMENTAL INVESTIGATION ON STEEL TRANSMISSION POLE STRUCTURES Analytical and experimental studies conducted on 400kV D/C, 0-2 degree line deviation suspension type and 132 / 220kV S/C 30o deviation self supporting mono pole structures are discussed in detail. Test results from full scale testing conducted at Tower Testing and Research Station, Chennai, India are compared with the analytical results.
7.1 400kv D/C Suspension Type Pole The conguration, dimensions and load application of 400kV D/C transmission line pole is shown in Fig.17. The pole is of tapered cross section with 1850mm at bottom and 500mm at top and made in to ve sections for easy transportation and erection. These sections are jointed by telescoping slip splices with minimum lap of 1.7 times the largest inside diameter. The main shaft is hex decagonal (16 sided regular polygon) in shape and made of 10mm thick sheet. The cross arms are of octagonal shape made of 6mm thickness. The cross arm ends are welded to a circular ange plate as shown in Fig.18. A separate collar of hex-decogonal in shape is used to x the cross arms. The collar is attached to the main shaft at the required height by means of bolts. A circular cantilever bracket is welded to the collar and stiffened with plate stiffeners. The cross arm is connected to the bracket by bolts. The collar is connected to the main shaft by bolts. Transfer of load from collar to the main shaft is by friction developed by tightening the column of bolts provided in two opposite sides of the collars. The bolts are pretensioned to about 60% to 70% of it tensile capacity. The rotation due to broken wire loads are resisted by friction developed due to tightening of bolts and interlocking of collars with main shaft due to polygonal shape. The ground wire peaks are of octagonal shape made from 6mm sheets. The peaks are directly welded to the collars and the collars are connected to the main shaft by bolts as shown in Fig.19. The base plate is of 48mm thick ring, welded to the bottom most segment of the main shaft with provision for xing 20nos. of 45mm dia. 12.9 grade anchor bolts. Template of 16mm thickness is
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used below the base plate. The main shaft, base plate, cross arms and peaks are made of material Fe - 490 with 350MPa Yield stress and 210kN/mm2 Elastic modulus. The pole is designed for basic wind speed - 47m/sec, Security Class - 1, Terrain Category – 2,Normal span of 300m, wind loads on conductor and ground wires are as per IS:802 part II Sec.2 – 1995, and wind loads on pole structure as per IS: 875(Part 3)-1987. Foundation:
In general, the monopole towers can not be accommodated in a regular test bed. The pole structures requires exclusively a special type of anchoring system since the extreme bolt carry maximum tension due to uplift force. A special circular foundation with rock anchors located in concentric circles to resist the uplift forces and to accommodate the pole with base plate was constructed as shown in Fig.20. The foundation bolts are tightened up to 60% of their tensile capacity. The foundation bolts likely to be subjected to maximum tension are identied prior to testing and instrumented with strain gauges. The shaft is erected using a mobile crane segment by segment (Fig.21). The cross arms and ground wire peaks are assembled to the brackets at ground levels itself and then xed to the shaft. The verticality is ensured by using theodolites on both the axes.
Fig. 17 Conguration of 400kV D/c Pole and load point details
Steel Monopoles
Bracket
Collar
Fig. 18 Assembly of cross arms
Fig.19 peak with collars and brackets
Rock Anchors
Instrumented bolt
Fig.20 Foundation showing rock anchors and instrumented anchor bolts
Fig. 21 Various stages of erection
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Analytical and Experimental Natural Frequency of Pole Field experiment to determine the natural frequency is conducted on the pole structure erected in the test bed. The theoretical natural frequency of the pole is determined from nite element analysis. The full pole along with cross arms, peaks etc., are modeled using plate elements in NE Nastran. In the collar locations, thickness of shaft is increased to account for the combined thickness of collar and the shaft. The theoretical frequency is found to be 1.017 and 1.0Hz in the rst mode, in transverse and longitudinal directions and 4.83Hz in torsional mode. The measured experimental frequencies are 0.87Hz in rst mode in both directions and 3.25Hz in torsional mode. The rst few mode shapes are shown in Fig.22. To account for the additional loading effects due to wind turbulence and dynamic amplication of exible structures like poles, gust factor G is used. When the fundamental frequency of the towers is less than 1Hz then most of the current wind loading standards recommend dynamic analysis for the structures. Certain simplied formulae were recommended in the codes to calculate the peak response of wind sensitive structures. In the present case the measured frequency of the pole structure is less than 1Hz, hence, the gust factor method given in IS:875, (Part 3) -1987 is used for determination of wind loads on the pole. The loads due to conductors, earth wires and insulators are determined as per IS: 802 (Part 1/Sec 1):1995.
Fig. 22 The rst three eigenmodes of monopole tower
Finite Element (FE) Modeling Plate shell elements are used for modeling the main shaft, cross arms, peaks, stiffeners and base plate. This element typically resists membrane shear and bending forces. The non-linear analysis capability of NE Nastran, accounting for the geometric and material
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349
non linearity, is used to analyse the model and to obtain the pre-ultimate behaviour. The elastic- plastic material property of steel is represented by a bi-linear model, having modulus of elasticity up to a yield stress equal to 2105 MPa and 2000 MPa beyond yield stress. The incremental load and predictor-corrector iteration under each load increment is used in the non linear range. The load is applied in 30 to 40 steps until the limit point is reached in the load deformation behaviour. Loads are dened to simulate the eld condition environment for which the structure is designed. The boundary conditions are specied for each degree of freedom of each grounded node. Collars, slip splices and ange plates in cross arms are not modeled separately. Instead, the thickness of the shaft at collar and slip splice locations are increased to account for the combined thicknesses. Both linear and non-linear static analysis has been carried out. The body wind loads are applied as distributed discrete nodal loads along the full height of the structure. The conductor and ground wire loads are applied as nodal loads at the appropriate locations. The nite element model is shown in Fig.23.
Fig. 23 Finite element model: various components
Comparison of Test Vs Analytical Results
a) Security condition In the present study, the pole is tested for single conductor broken at a time with 75% wind condition. These tests are conducted on right side ground wire peak, top, middle conductors and on left bottom conductor. During bottom and middle conductor broken condition tests, rotation of collar by about 40mm, 56mm respectively were noticed
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Advanced Course on Communication and Power Transmission Towers
(Fig.24) in the direction of loading while increasing the longitudinal load from 20% to 40%. No increase in rotation was noticed during further loading. The deformed FE model is shown in Fig.25. The test and analysis foundation bolt forces and shaft stresses in right ground wire broken case are given in Fig.26 and 27. The analysis deections are compared with test in Fig.28. During top conductor broken test, the collar along with cross arm assembly has slipped and started rotating like a free body with increase in longitudinal load as shown in Fig.29. It was noticed that the friction developed at the interface of collar and main shaft due to tightening of bolts and interlocking forces between the folded sides of the main shaft and collar was not sufcient to resist the longitudinal (twisting) load even though number of bolts provided are same in all collars. The rotation may be due to reduction in contact area (only 50%) between shaft and collar due to reduced diameter of main shaft at top cross arm level when compared to other cross arm levels. The reduced widths of polygonal shaft sides or faces are also one of the reasons for not developing the interlocking forces necessary for resisting the twisting force. In order to avoid the free body rotation, through bolts passing from one side of the shaft to diametrically opposite side is provided as shown in Fig.30.
Fig. 24 Rotation of collar
Fig. 25 Deformed FE models in right ground wire and middle conductor broken condition
351
Steel Monopoles 100 3T
2
2A
1
90 1A 80 D A O70 L F O60 E G A T50 N E C R40 E P
30
20
10
0 0
50
100
150
200
250
300
350
400
450
500
550
600
BOLT FORCE IN kN
Fig. 26 Foundation bolt force in right ground wire broken condition 100 0A 90
0T
1T 1A
9T
9A
2T
6A
3T
7T
4 T
6T 5T
8T
80 D A O L 70 F O E60 G A T N50 E C R40 E P 30 20 10 0 -300
-250
-200
-150
-100
-50
0
50
100
STRESS IN N/mm 2
Fig. 27 Shaft stresses in right ground wire broken
150
200
250
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100 LA
LT
TA
TT
90 80 D 70 A O L F 60 O E G 50 A T N E C 40 R E P
TT Transverse Test : TA Transverse Analytical
30 LT Longitudinal Test : LA Longitudinal Analytical 20 10 0 0
250
500
750
1000
1250
DEFLECTION IN mm
Fig. 28 Pole deection in right ground wire broken test
Fig. 29 Rotation of top cross arm
1500
Steel Monopoles
353
Fig. 30 Through bolts arresting rotation
b) Reliability condition In this case, the pole is subjected to transverse and vertical loads only. The loads resulting from wind on conductors, insulators etc. are applied at the cross arm tips. The wind load on pole shaft between the cross arms are lumped at collar levels in both test and analysis. The wind load on shaft below bottom cross arm level is lumped in to a single point. The forces measured in the foundation bolt during testing and analysis is shown in Fig.31. Stresses at the bottom segment of the shaft in FE analysis are compared with the test results in Fig.32. The deformation of the pole measured in test using theodolite and FE analysis are shown in Fig.33. Deformed FE model and stress pattern in the bottom segment of the pole are shown in Fig.34. 100 1T
2T
90
2A
80 D A O 70 L F O 60 E G A 50 T N E C 40 R E P 30
1A
20 10 T TEST A ANALYTICAL
0 0
100
200
300
400
500
600
700
800
900
BOLT FORCE IN kN
Fig. 31 Foundation bolt force in reliability test
1000
1100
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100 2
2A
4T
3T
6T
5T 5A
90 8
0A
D A O L F O E G A T N E C R E P
7T 8A
80 70
1T
60 1A 0T
50 40 30 20 10 A -
ANALYTICAL
T - TEST
0 -350
-300
-250
-200
-150
-100
-50
0
50
100
150
200
250
300
350
STRESS in N/mm
Fig. 32 Shaft stresses in Reliability test 100 TEST
90 ANALYTICAL 80 D A O70 L F O 60 E G A T 50 N E C40 R E P 30 20 10 0 0
250
500
750
1000
1250
1500
1750
2000
2250
DEFLECTION IN MM
Fig. 33 Pole deection in reliability test
2500
2750
3000
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Fig. 34 Deformed FE model and shaft stresses in N/mm2 at bottom in reliability test
7.2 132/220KV S/C 300 Deviation Pole
The pole is of tapered cross section with a diameter of 1200mm at bottom and 450mm at top and is made in to ve sections. The main shaft is hex decagonal (16 sided regular polygon) in shape and made of different thicknesses varying from 12mm to 6mm. The pole is without cross arms and peaks. The conductors are connected to the tension insulators on either side of the pole. Jumpers are used to connect the conductors. Supports are used for hanging the jumper insulators. The pole during erection and testing is shown in Fig.35. The foundation bolts and bottom portion of shaft were instrumented with strain gauges. Fig.36 shows the deformation of pole in FE analysis and during testing in Reliability and Dead end load cases. The measured stresses in shaft and foundation bolt forces are shown in Fig.37 and 38.
Fig. 35 Various stages of erection, rigging of 132/220kV 30O dev. Mono pole in Test pad
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Fig. 36 Instrumented foundation bolts and shaft, buckled stiffener and Deformed pole dur-
ing test and FE analysis 100 4
1
2
2
90
4
6
1
3 80 6
3T 70
60 5 50
40
30
20 A -
ANALYTICAL
T - TEST 10
0
-350
-300
-250
-200
-150
-100
-50
0
50
100
150
Fig. 37 Shaft stresses in dead end condition
200
250
300
350
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357
100 2A
2T
90
80
70
60
50
40
30
20
10 A ANALYTICAL T TEST
0 0
50
100
150
200
250
300
350
400
450
500
550
600
650
Fig. 38 Foundation bolt force in dead end condition
The mono pole structures are successfully tested for all load cases. The non linear FE model shaft stresses, deformations and foundation bolt forces are compared with the test results. The measured test deection at top of shaft is more by about 55% to 80% to that of analysis deection in reliability load condition. The measured force in the extreme foundation bolt is 10% more than the analytical force. The measured stresses at bottom of shaft are almost the same as that of analysis. Rotation of cross arms is noticed during broken conductor loads. This rotation is less at bottom conductor level when compared to middle conductor level. 8.0
EXPERIMENTAL
INVESTIGATION
ON
OCTAGONAL
LIGHTING POLE WITH ACCESS HOLE
Tubular steel poles are laterally exible and relatively large deection occurs due to lateral loads. Street lighting columns are usually made from thin walled tubes of circular or octagonal in cross section. These lighting columns will have an access hole in the region of high bending moment. The problem under investigation is the bending strength of thin walled octagonal tapered street lighting columns with access hole in the region of critical moment location. The lighting columns are of 8m and 12m high with uniform thickness of 4mm. The primary loads on the lighting columns are mainly from wind loads. The wind load acting on these columns causes large bending moment in the bottom locations and the situation is further complicated by the presence of the access
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hole. The critical case is when the wind acts a direction such that the access hole lies in the most highly compressed region of the octagonal cross section. Strength and stability assessment of these lighting columns becomes important, whenever they are subjected to extreme wind loads. Octagonal poles are usually designed within the elastic limit of the material. Under extreme wind load cases, the stress limits are allowed to exceed the elastic limit and a moderate amount of plastic yielding is allowed. Due to the presence of access hole, the bending moment capacity is not only reduced due to the reduced cross section, but also by local plate buckling in the region of hole edges. Stress concentration effect also intensify the effect of local buckling. Because of the interaction between yielding and local buckling, the local buckling stress in the region of access hole is usually higher. Full scale tests on the lighting pole has been conducted, loaded upto 100% design load and further increase upto local failure and the corresponding deections and strain responses are correlated in this paper. M. Dicleli has concluded that the pole structures with polygonal shape have larger exural capacity for a specied circumferential thickness. The number of sides in a polygon is determined by the specied circumferential thickness of the pole cross section and its diameter. The location of maximum stress along the height of the pole is a function of load distribution and the relative orientation of forces acting on the pole. S. A. Baban. et. al) conducted pure bending test on 12 specimens of both circular and octagonal cross sections both with and without the access hole at the position of extreme bre compression. The results gave a quantitative indication of the weakening effect of the access hole and have formed an essential basis for the development of design formulae later. G.H.Little) developed empirical formulae for generating design curves for the bending strength of thin walled non tapered steel tubes, both circular and octagonal in cross section, along with the allowance for the presence of access hole in the compression zone based on the test results conducted by S. A. Baban et. al.
Present Study In the present study, analytical and experimental studies conducted on 12m street lighting without access hole and 8m high octagonal with and without access hole is discussed in detail. Test results from full scale testing conducted at Tower Testing and Research Station, SERC, Chennai are compared with the analytical results. The conguration, dimensions and load application details for 12m octagonal pole is shown in Fig.39. The main shaft is octagonal (8 sided regular polygon) in shape and made of 4mm thick throughout the height. The diameter of the shaft is 200mm at bottom and 100mm at top. The base plate is of 16mm thick welded to the bottom of the shaft. In the access hole location the shaft is reinforced with 16mm square bars around the periphery. The main shaft is made of Fe-490 material with 350MPa Yield stress and base plate with yield stress of 210MPa.
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359
Fig.39. 12m Octagonal Pole basic confguration and load point details
Fig.40 8m Octagonal Pole basic confguration and load point details
The conguration, dimensions and load application details for 8m octagonal pole is shown in Fig.40. The main shaft is octagonal (8 sided regular polygon) in shape and made of 4mm thick throughout the height. The diameter of the shaft is 150mm at bottom and 75mm at top. The base plate is of 20mm thick welded to the bottom of the shaft. The location of access hole is 0.5m from bottom of the shaft. The main shaft is made of material Fe-490 with 350 MPa Yield stress and base plate with yield stress 210MPa. The design parameters are common for both the poles. They are as follows: Basic Wind Velocity – 47 m/s; Terrain Category – 2; Wind load on Pole Structure as per IS:875 (Part 3):1987.
Preliminary Analysis The selection of structural conguration of the street lighting column such as the pole dimension, number of sides of the polygon, material yield stress and plate thickness
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Advanced Course on Communication and Power Transmission Towers
is left to the design engineer. Street lighting columns with regular octagonal cross section will not be subjected to lateral buckling or lateral torsional buckling, because of their symmetry. The European standard EN 40-3-3 species the requirements for the verication of the design of the lighting columns by limit state principles, where the effects of factored load are compared with the relevant resistance of the structure. Of the two limit states, the ultimate limit state corresponds to the load carrying capacity of the lighting column, whereas the serviceability limit state corresponds to the deection the lighting column. For closed regular octagonal cross section as shown in Fig.41, the bending strength of the section shall be calculated from the equation, M ux M uy
where
f y 1Z p 3
10 g m
in Nm
(1)
f y is the characteristic strength of the material (in N/mm2); f1 is the value obtained from the curve appropriate to the cross section with value of R t f y E ; E ; is the modulus of elasticity of the material = 2105 N/mm2; R is the mean radius of the cross section (in mm); t is the wall thickness (in mm); gm is the partial material factor (1.15); Z p is the plastic modulus of the closed regular cross section (in mm3); where 2 Z p 4.32 R t for octagonal cross section.
Fig. 41 Cross sectional details of 12m, 8m poles
Fig. 42 Access hole detail for 12m, 8m poles
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Steel Monopoles
Similarly, the bending strength of the reinforced openings in regular cross section as shown in Fig.42. is calculated from the equation, M ux where
f y 6 Z pnr 3
10 g m
and M uy
f y 6 Z pyr 3
10 g m
f6 is a factor for reinforcement provided given by
in Nm
(2)
2t tw 2 E . 2 2t tw E 0.32 RLf y
Z pnr is the plastic modulus of the section including the effect of door reinforcement q 90 B x 2 sin q B x cos q about plastic neutral axis n-n (in mm3) = 2 R t 2 cos 2 with B x Ac Rt mex mx . Z pyr is the plastic modulus of the section including the effect of door reinforcement about plastic neutral axis y-y (in mm3). = 2 R 2t 1 cos q B y sin q with B y Ac Rt mey my .
q is the half of the angle of the opening in degrees. mex , mey , mx , my are the distance from the centroid of the door reinforcement to the corresponding x-x and y-y axes respectively. t w is the thickness of the reinforcement at the side of the door opening in (mm); is effective length of opening inn(mm); Ac is effective cross sectional area of door reinforcement in (mm2). Little el. al. has developed empirical formulae to nd the maximum sustainable moment ( M max) for a non tapered steel tube for an octagonal cross section with or without the access hole. The Moment can be found directly from the tabulated values[1] or it can be calculated form the equation given below,
M
p
M max M cr M max hM cr M max
(3)
where M max is the maximum sustainable moment. M p is the Plastic Moment from tabulated values[1]; M cr is the moment at buckling assuming elastic behaviour. M p cr z e for closed octagonal sections and Sin q 2 D ; cr ; is the M p cr z e / for sections with access hole, where 1.0
13
t
extreme bre compressive bending stress at elastic buckling; D is the Diameter of the inscribed circle of octagonal section.
q is the access hole size; t is the wall thickness; h is the Ayrton – Perry factor given in (1). z e is the elastic section modulus.
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Advanced Course on Communication and Power Transmission Towers
Finite Element (FE) Modeling Plate shell elements are used to model the shaft, stiffeners and base plate. This element typically resists membrane shear and bending forces. The non-linear analysis capability of NE-NASTRAN, accounting for geometric and material non-linearity, is used to analyse the model and to obtain the pre-yielding behavior. The elastic-plastic material property of steel is represented by a bi-linear model, having modulus of elasticity up to yield stress equal to 2E5MPa and 2000MPa beyond yield stress. The incremental load and predictor-corrector iteration under each load increment is used in the nonlinear range. The load is applied in 30 to 40 steps until the limit point is reached in the load deformation behavior. Loads are dened to simulate the eld condition environment for which the structure is designed. The boundary conditions are specied for each degree of freedom for each node. Both linear and non-linear static analysis has been carried out. The body wind loads are applied as discrete nodal loads along the height of the structure. The nite element model of both the poles is shown in Fig. 43.
Fig. 43 Finite Element Model of 12m and 8m Pole
Comparison of Test Vs Analytical Results The testing was performed in vertical position simulating the eld condition. All load measuring sensors and other instruments are located in such a manner loss of accuracy
Steel Monopoles
363
as a result of rigging is minimum. A digital control system with recently calibrated instruments was used for simultaneous smooth load application with precise servo controlled hydraulic actuators. The pole is instrumented on salient locations as shown in Fig.44 using electrical resistant foil type strain gauge.
Fig. 44 Location of Strain gauges for 12m and 8m Pole
For 12m street lighting pole with doors in closed condition, the load was incremented step by step and reached up to 100% load in both serviceability and ultimate limit state conditions and kept constant for 5minutes. The pole test was declared successful since the mast withstood the 100% load for 5minutes duration with the deection of 269mm and 425mm. The load was increased beyond 100% and reached up to 3 times above the required load. At this point of load, prying deformation was observed in the base plate indicating large deformation at constant load and hence concluded as failure. The deformed nite element model and tested pole is shown in Fig.45. The test and FE analysis shaft stresses is shown in Fig.46. It was observed up to 100% of design load, the actual stress and theoretical stresses are very close and within 10% and deviates when load reached 300% indicating large inelastic strains. The analysis deections are compared with the test as shown in Fig.47. The deections are direct response of the applied load which also indicated large deections at 300% of load. Non linearity in deections are observed beyond 50% of design load indicating the need for non - linear
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Advanced Course on Communication and Power Transmission Towers
analysis of monopole structures. The bending strength comparison was made with the codal provision and Little’s equation along with the test and analytical results as shown in Fig.48. The bending strength of the monopoles are conservatively estimated by European Code EN-40-3-3. The full scale experimental bending strength is marginally lower than previous researchers (Little’s) and un-conservative with analytical values.
Fig. 45 Deformed Pole in FE analysis and Test (8m) 300 275 250 225
D A O L F O E G A T N E C R E P
1A
5T
5A
3T 4T
2A
4A
2T
3A
1T
200 175 150 125 100 T- TEST
75
A- ANALYTICAL
50 25 0 -450 -400 -350 -300 -250 -200 -150 -100 -50
0
50
100 150 200 250 300 350 400 450
SHAFT STRESS in N/mm2
Fig. 46 Shaft Stresses of 12m Pole
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Fig. 47 Deection of 12m Pole
Fig. 48 Comparison of Bending Strength for 12m Pole
For 8m street lighting pole with access hole in closed condition, the load was incremented step by step and reached up to 100% load in both serviceability and ultimate limit state conditions and kept constant for 5minutes. The pole test was declared successful since the mast withstood the 100% load for 5minutes duration with the deection of 200mm and 336mm constant in both the tests. The load was increased beyond 100% and reached up to 2 times more than the required loads. The deection at this stage of loading was recorded as 488 mm and then off loaded. Then the test was continued with the access hole in open condition and the loads was incremented in steps of 25% up to 325% of load. At this stage of loading, local buckling was observed in the shaft above the access hole as shown in Fig.49 and concluded as failure. The deformed nite element model and tested pole is shown
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in Fig.50. The test and FE analysis shaft stresses is shown in Fig.51. The deection and strain responses are similar to the previous experiments indicating non-linear behavior of the mast. The analysis deections are compared with the test as shown in Fig.52. The bending comparison was made with the codal provision and Little’s equation along with the test and analytical results as shown in Fig.53. The behavior was similar to the previous experiments but the bending strength estimated by previous researcher (Little’s) was very un-conservative and much lower than European Code when compared with full scale testing.
Fig. 49 Local buckling of plate near access hole in analysis and test Remarks:
The non-linear nite element stresses, deformations are compared with the test results. The measured deformation at top is more compared to that of analytical deection. The measured shaft stresses are same as analysis stresses. For 8m Pole with the access hole in open condition, the measured shaft stresses and deformations are comparable with the analytical stresses. From the comparison with the codal values for 12m Pole, the EN 40-3-3 is always on the conservative side when compared with the analytical and experimental values. The lower experimental bending strength is due to the distress in the base plate. For 8m Pole, the experimental and analytical bending strength are almost equal and higher the strength according to codal regulations. The Little’s experimental values are highly unconservative because the specimens tested by the author were non-tapered and behavior of the pole as a whole structure is different from the component specimens.
Steel Monopoles
Fig. 50 Deformed FE Model and deected pole during test
Fig. 51 Shaft Stresses of 8m Pole.
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Fig. 52 Deection of 8m Pole
Fig. 53 Comparison of bending strength for 8m Pole.
Steel Monopoles APPENDIX: PROPERTIES OF VARIOUS TUBULAR SECTIONS
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9. ACKNOWLEDGEMENTS
The author is thankful to the Director, CSIR-Structural Engineering Research Centre, Chennai, India for the kind support and encouragement.
