ESDEP LECTURE NOTE [WG15C] http://www.fgg.uni-lj.si/kmk/ESDEP/master/wg15c/l0300.htm#SEC_1 Previous | Next | Contents ESDEP WG 15C STRUCTURAL SYSTEMS: MISCELLANEOUS Lecture 15C.3: Lattice Towers and Masts OBJECTIVE/SCOPE To describe typical lattice tower design problems; to introduce the background for the load requirements; to emphasize the connection between basic functional requirements and overall structural design; to explain the principles of the structural analysis and the choice of structural details. The lecture is confined to the detailed description of the design of one particular type of tower, i.e. the high voltage transmission tower. PREREQUISITES None. RELATED LECTURES Lectures 4A: Protection: Corrosion Lectures 6: Applied Stability Lectures 7: Elements Lectures 11: Connection Design: Static Loading Lectures 13: Tubular Structures SUMMARY The common structural problems in the design of steel lattice towers for different purposes are outlined. The details of design are discussed in relation to a specific category of tower, the high voltage transmission tower. The influence on the tower design of the user's functional demands is explained and the background for the load assumptions is pointed out. Different aspects affecting the overall design and the detailing are discussed and problems connected with the structural analysis are explained. The effect of joint eccentricities is discussed on the basis of a very common design example using angle sections. The use of different detailing is mentioned. The need for erection joints is stated and the types of joints are discussed. Corrosion protection is briefly dealt with and its influence on the tower design is pointed out. Tower foundations are not treated in this lecture. 1. INTRODUCTION Towers or masts are built in order to fulfil the need for placing objects or persons at a certain level above the ground. Typical examples are: single towers for antennae, floodlight projectors or platforms for inspection, supervision or tourist purposes. systems of towers and wires serving transport purposes, such as ski lifts, ropeways, or power transmission lines. For all kinds of towers the designer should thoroughly study the user's functional requirements in order to reach the best possible design for the particular structure. For example, it is extremely important to keep the flexural and torsional rotations of an antenna tower within narrow limits in order to ensure the proper functioning of the equipment. The characteristic dimension of a tower is its height. It is usually several times larger than the horizontal dimensions. Frequently the area which may be occupied at ground level is very limited and, thus, rather slender structures are commonly used. Another characteristic feature is that a major part of the tower design load comes from the wind force on the tower itself and its equipment, including wires suspended by the tower. To provide the necessary flexural rigidity and, at the same time, keeping the area exposed to the wind as small as possible, lattice structures are frequently preferred to more compact 'solid' structures. Bearing in mind these circumstances, it is not surprising to find that the design problems are almost the same irrespective of the purpose to be served by the tower. Typical design problems are: 1 of 15 11/12/2010 3:26 PM i. 2 of 15 11/12/2010 3:26 PM .htm#SEC_1 establishment of load requirements. establishment of overall design. To provide safety against lightning.e. earthed conductors are placed at the top of the tower. towers for one particular purpose. consistency between overall design and detailing.1 Background The towers support one or more overhead lines serving the energy distribution. In this lecture. the high voltage transmission tower. see Figures 1 and 2. have been selected for discussion. sectioning of structure for transport and erection. detailing with or without node eccentricities.uni-lj. consistency between loads and tower design. HIGH VOLTAGE TRANSMISSION TOWERS 2.ESDEP LECTURE NOTE [WG15C] http://www. including choice of number of tower legs.fgg. Most frequently three-phase AC circuits are used requiring three live conductors each. 2.si/kmk/ESDEP/master/wg15c/l0300. 4. f. type of insulators. tracing of transmission line. c.ESDEP LECTURE NOTE [WG15C] http://www.fgg. To prevent short circuit between live and earthed parts. The route of the line has as few changes in direction as possible. the conductors behave like wires whose sag between their points of support depends on the temperature and the wire tension. As explained in Section 2. b. including the surrounding environment. (c) angle towers. 3 of 15 11/12/2010 3:26 PM . (d) tension towers and.si/kmk/ESDEP/master/wg15c/l0300. Depending on their position in the line various types of towers occur such as (a) suspension towers. voltage. the size of the tension forces in the conductor has a great effect upon the tower design. They are: a. type of conductors. the length of which increases with increasing voltage of the circuit. They may be designed to serve also as angle towers.2 Types of Towers An overhead transmission line connects two nodes of the power supply grid. 2.3 Functional Requirements Before starting the design of a particular tower. see Figure 1.uni-lj. number of circuits. e. Note similarities and mutual differences. the latter coming from the external loads and the pre-tensioning of the conductor. 2. (b) angle suspension towers. possible future addition of new circuits. In Figure 2 examples of suspension tower designs from four European countries are presented. minimum mutual clearances are prescribed. Tension towers serve as rigid points able to prevent progressive collapse of the entire line.htm#SEC_1 The live conductors are supported by insulators. a number of basic specifications are established. To the above-mentioned types should be added special towers required at the branching of two or more lines. d. Mechanically speaking. (e) terminal towers. The clearances and angles.si/kmk/ESDEP/master/wg15c/l0300. The tower designer should notice that the specifications reflect a number of choices. the designer is rarely in a position to bring about desirable changes in these specifications. selection of conductor configuration. 4 of 15 11/12/2010 3:26 PM . Safety against lightning is provided by prescribing a maximum value of the angle v. which naturally vary with the voltage. They are all hinged at the tower crossarm or bridge. selection of height for each tower. are embodied in national regulations. functional requirements are understood here as the electrical requirements which guide the tower design after establishment of the basic specifications. selection of rigid points.ESDEP LECTURE NOTE [WG15C] http://www.fgg. i. Figure 4 shows the clearances guiding the shape of a typical suspension tower. In Figure 3 three types of insulators are shown. h. j.htm#SEC_1 g. The maximum swing u of the insulators occurs at maximum load on the conductor. selection of tower sites. However.uni-lj. Therefore. The tower designer should be familiar with the main features of the different types of insulators. damage forces.htm#SEC_1 2. It is essential to realize that the major part of the load arises from the conductors. j. ice load. see Figure 5. c. loads from conductor tensile forces. 5 of 15 11/12/2010 3:26 PM . h. wind load on conductors and equipment. rime or wet snow on conductors and equipment.si/kmk/ESDEP/master/wg15c/l0300. dead load of tower. d. on the tower itself e. etc.4 Loads on Towers. the dead load from the conductors is calculated by using the so-called weight span. earthquake forces. g.fgg.ESDEP LECTURE NOTE [WG15C] http://www. f. erection and maintenance loads. which may be considerably different from the wind span used in connection with the wind load calculation. dead load from conductors and other equipment. i.uni-lj. b. and that the conductors behave like chains able to resist only tensile forces. wind load on tower. Consequently. Loading Cases The loads acting on a transmission tower are: a. load from ice. If they are balanced no longitudinal force acts on a tower suspending a straight line. The wind force is usually assumed to be acting horizontally. By far the most common structure is a four-legged tower body cantilevering from the foundation. The tensile forces in the conductors act on the two faces of the tower in the line direction(s). easily divisible in sections suitable for transport and erection. Underestimation of these circumstances has frequently led to damage and collapse. Statically speaking. However. durable when properly protected against corrosion. very important to choose the design data carefully.ESDEP LECTURE NOTE [WG15C] http://www. As the tensile forces vary with the external loads. It is. different wind directions (in the horizontal plane) must be taken into account for the conductors as well as for the tower itself. therefore. The advantages of this design are: 6 of 15 11/12/2010 3:26 PM . easy to repair. therefore. depending on local conditions. introduced in the calculation of the load transferred to the towers. strengthen and extend. as previously mentioned.uni-lj. The occurrence of ice. The size and distribution of the ice load depends on the climate and the local conditions. and the tower body. In general. evident that different load intensities are likely to occur in neighbouring spans. and for terminal towers they cause heavy longitudinal forces. Also.htm#SEC_1 The average span length is usually chosen between 300 and 450 metres. etc. For all types of towers the risk of mechanical failure of one or more of the conductors has to be considered.e.5 Overall Design and Truss Configuration The outline of the tower is influenced by the user's functional requirements. adds to the weight of the parts covered and it increases their area exposed to the wind. For transmission lines with 100 kV voltage or more. a sloping direction may have to be considered. However. see Figure 6. the towers usually behave like cantilevers or frames. even suspension towers on a straight line are affected by longitudinal forces. basically the same requirements may be met by quite different designs. the use of steel lattice structures is nearly always found advantageous because they are: easily adaptable to any shape or height of tower. the tower structure consists of three parts: the crossarms and/or bridges. It is. Such load differences produce longitudinal forces acting on the towers. in some cases with supplementary stays. acting in the line direction. For angle towers they result in forces in the angle bisector plane. The loads and loading cases to be considered in the design are usually laid down in national regulations. the peaks. 2. i. The ice load is often taken as a uniformly distributed load on all spans. The maximum wind velocity does not occur simultaneously along the entire span and reduction coefficients are.si/kmk/ESDEP/master/wg15c/l0300.fgg. however. possibly with redundant members reducing the buckling length of the leg members. the cross-section is very suitable for the use of angles.si/kmk/ESDEP/master/wg15c/l0300. as it reduces the design forces (except for torsional loads). many features also apply to other tower designs. For further study on this matter see [1].uni-lj. the same type of bracing is chosen for all four tower body faces. This arrangement provides better space for the connections. Its main advantage is that the buckling length of the brace member in compression is influenced positively by the brace member in tension. However.ESDEP LECTURE NOTE [WG15C] http://www. most frequently with a staggered arrangement of the nodes. and it may offer considerable advantage with respect to the buckling load of the leg members. for example see Figure 6. Generally. For a cantilever structure. The choice of bracing depends on the size of the load and the member lengths. The following remarks in this section relate mainly to a cantilever structure. 7 of 15 11/12/2010 3:26 PM . since it diminishes the buckling length for buckling about the 'weak' axis v-v. This advantage applies especially to angle sections when used as shown in Figures 10 and 11. The most common type is cross bracing. see Figure 7. as the connections can be made very simple. even with regard to deflection perpendicular to the tower face. the square or rectangular cross-section (four legs) is superior to a triangular tower body (three legs) for resisting torsion.htm#SEC_1 the tower occupies a relatively small area at ground level. two legs share the compression from both transverse and longitudinal loads. the tower legs are usually given a taper in both main directions enabling the designer to choose the same structural section on a considerable part of the tower height. The taper is also advantageous with regard to the bracing. The bracing of the tower faces is chosen either as a single lattice.fgg. a cross bracing or a K-bracing. htm#SEC_1 8 of 15 11/12/2010 3:26 PM .si/kmk/ESDEP/master/wg15c/l0300.ESDEP LECTURE NOTE [WG15C] http://www.uni-lj.fgg. For staggered bracings these members are necessary to 'turn' the leg forces. in principle. However.uni-lj. mostly acting at crossarm bottom levels. as the load on the cross arms rarely has an upward component.si/kmk/ESDEP/master/wg15c/l0300. 9 of 15 11/12/2010 3:26 PM . designed like the tower itself.fgg.ESDEP LECTURE NOTE [WG15C] http://www. the tower is generally equipped with horizontal members at levels where leg taper changes. see Figure 8. are distributed to the tower faces by means of horizontal bracings. Cross arms and earthwire peaks are. Torsional forces. cross arms are sometimes designed with two bottom chords and one upper chord and/or with single lattice bracings in the non-horizontal faces.htm#SEC_1 Irrespective of the type of bracing. The effect of eccentricities in the joints should also be taken into account. In addition.6 Structural Analysis Generally. 2. towers and conductors.ESDEP LECTURE NOTE [WG15C] http://www. see Section 2. b. particularly well. Generally speaking. bending moments in one of the main directions produce an equal compression in the two legs of one side.7 Detailing of Joints 10 of 15 11/12/2010 3:26 PM . the effect of fixed connections (as opposed to hinged connections) must be considered.e. Although this approach is satisfactory in most cases attention must be drawn to the function of redundant members. Finally. especially concerning the forces and moments in the brace members. the distribution of an eccentric horizontal load is studied.5. It is frequently modelled as a set of plane lattice structures. since they produce moments in the bracing members. The deflections of the plane lattice structures of the tower body deform the rectangle ABCD to a parallelogram A¢ B¢ C¢ D¢ . By adding member AC or BD this deformation is restricted and all four tower body planes participate in resisting the force H. the tower is designed for static or quasi-static loads only. i. i. a tower is a space structure. c. they provide a basis from simple calculations which have broadly led to satisfactory results. and equal tension in the two legs of the other side. which in some cases may change the load distribution considerably. The shear forces are resisted by the horizontal component of the leg forces and the brace forces (thus.si/kmk/ESDEP/master/wg15c/l0300. Without horizontal bracing in the tower.e. However. the leg taper has a significant influence on the design of the bracing). vertical loads are equally distributed between the four legs. the structural analysis is carried out on the basis of a few very rough assumptions: the tower structure behaves as a self-contained structure without support from any of the conductors. torsional moments broadly produce shear forces in the tower body faces.uni-lj.fgg. the effect of redundancies should be considered. In Figure 9 the force H is acting at the cross arm bottom level.htm#SEC_1 2. However. three tower body planes are affected by H. A classical analysis assuming hinges in all nodes leads to very simple calculations. These assumptions do not reflect the real behaviour of the total system.7. which are identical with the tower body planes together with the planes of the cross arms and the horizontal bracings mentioned in Section 2. In a simplified calculation a four-legged cantilevered structure is often assumed to take the loads as follows: a. in the braces. centrally acting. a resultant moment vector along axis v-v will be advantageous. The splice plates and the bolt connections must then be designed in accordance with this model. As the lower part of the leg usually is somewhat oversized at the joint . usually leaving the major part to the leg members. As an introductory example of design and calculation. such as: simple and uniform design of connections. This very simple design requiring a minimum of manufacturing work is attained by the choice and orientation of the leg and brace member sections. This is achieved. especially when only one bolt is used in the connection (eccentricities ec and et). let the lower part resist the eccentricity moment.that V cannot be transferred by the leg and. e2 must diminish. The connections are all bolted without the use of gussets. They arise from the fact that the axes of gravity of the truss members do not intersect at the theoretical nodes. details allowing for easy transportation and erection. As z-z is the 'strong' axis of the leg section. when eo=-e1¢ . bolted connections are generally preferred. For legs in compression the joint must be designed with some flexural rigidity to prevent unwanted action as a hinge. The use of gussets is shown in Figure 12. and they allow for the use of double angle sections. consequently.8. In the latter case out-of-plane eccentricities almost vanish. The joint eccentricities have to be carefully considered in the design. the reason for changing leg section at the joint .a suitable model would be to consider the upper part of the leg centrally loaded and thus. V = H´ e2. details allowing for proper corrosion protection. except for a spacer plate at the cross bracing interconnection. as they offer the opportunity to assemble the structural parts without damaging the corrosion protection.uni-lj. They provide better space for the bolts. simple shaping of structural components. Additional eccentricity problems occur when the bolts are not placed on the axis of gravity. However. According to the bending caused by the eccentricities they may be classified as in-plane or out-of-plane eccentricities. which may eliminate the in-plane eccentricities. By choosing the design described above. see Figure 10. the torsional stiffness of the leg member may be so moderate . In Figure 11. in fact.htm#SEC_1 The detailed design is governed by a number of factors influencing the structural costs once the overall design has been chosen. In this case C and T intersect approximately at the middle of the leg of the section. In this case there is a change of leg section. acting on the leg may be measured between the axes of gravity for the brace members (see Figure 11).si/kmk/ESDEP/master/wg15c/l0300. Nevertheless some additional comments should be added concerning the use of gussets and multiple angle sections.fgg.ESDEP LECTURE NOTE [WG15C] http://www. a segment of a four-legged tower body is discussed. some structural eccentricities have to be accepted. However. Usually this situation is not fully practicable without adding a gusset plate to the joint. The leg joint shown in Figure 10 is a splice joint in which an eccentricity e3 may occur.depending on its support conditions . 11 of 15 11/12/2010 3:26 PM . The bolted connections might easily be replaced by welded connections with no major changes of the design. These moments are distributed among the members meeting at the joint according to their flexural stiffness. except for small structures. the brace forces C and T meet at a distance eo from the axis of gravity. The out-of-plane eccentricity causing a torsional moment. see Section 2.this is. All members are made of angle sections with equal legs. or the gravity axis for the four (or two) splice plates in common does not coincide with the axis of the leg(s). This introductory example is very typical of the design with angle sections. The latter causes bending out-of-plane in the brace members. The resultant force DS produces two bending moments: Me = DS´ eo and Mf=DS´ e1. and stays. Thus a number of joints which are easy to assemble on the tower site. transportation and erection. The framed structure is divided into lattice structure bodies. In Figure 14 two examples of the joint positions are shown.uni-lj. circular sections may be more interesting because their better shape reduces wind action.htm#SEC_1 For heavily loaded towers it might be suitable to choose double or even quadruple angle sections for the legs. Towers designed with other profiles than angles In principle any of the commercially available sections could be used. Construction joints and erection joints The tower structure usually has to be subdivided into smaller sections for the sake of corrosion protection. e. So far only flat bars. 12 of 15 11/12/2010 3:26 PM . Two main problems have to be solved: the position and the detailing of the joints.fgg. The use is limited to small size towers for the corrosion reasons mentioned above. each of which may be fully welded.si/kmk/ESDEP/master/wg15c/l0300. In other contexts. Figure 13 shows some possibilities.ESDEP LECTURE NOTE [WG15C] http://www. mostly with welded connections.g. round bars and tubes have been used. However. The cantilevered structure usually is subdivided into single leg and web members. have to be arranged. they have to compete with the angle sections as regards the variety of sections available and the ease of designing and manufacturing simple connections. high rise TV towers. but is mostly used for joints in round tube or bar sections. The latter is used for all sections.htm#SEC_1 The two types of joints are lap (or splice) joints and butt plate joints.ESDEP LECTURE NOTE [WG15C] http://www. The former is very suitable for angle sections. 13 of 15 11/12/2010 3:26 PM .fgg.si/kmk/ESDEP/master/wg15c/l0300.uni-lj. Figure 15 shows some examples of the two types. The maximum size of parts to be galvanized is limited by the size of the available galvanic bath. For systems of interconnected towers it must be considered that the collapse of one tower may influence the stability of a neighbouring tower.uni-lj. K-bracings and/or staggered cross bracings are generally found advantageous.8 Corrosion Protection Today. The protection method influences the structural design. For towers supporting wires. possibly with an additional coating. A major part of the design loads on the tower results from the wind force on tower and equipment. No welding should be performed after galvanizing. The requirements must be studied carefully.htm#SEC_1 2.si/kmk/ESDEP/master/wg15c/l0300. The occurrence of an ice cover on the tower and equipment must be considered in the design. 14 of 15 11/12/2010 3:26 PM . 3. long lasting corrosion protection must be provided. as it damages the protection. Angle sections are widely used in towers with a square or rectangular base. CONCLUDING SUMMARY The overall design of a lattice tower is very closely connected with the user's functional requirements. corrosion protection of steel lattice towers is almost synonymous with hot-galvanising. In most cases a cantilevered tower with four legs is preferred. The type of bracing greatly affects the stability of both legs and braces.fgg. usually about 100 m m thick.ESDEP LECTURE NOTE [WG15C] http://www. differential loads in the wire direction must be taken into account. Both in-plane and out-of-plane eccentricities in the connections must be considered. as they permit very simple connection design. as it offers structural advantages and occupies a relatively small ground area. Horizontal braces at certain levels of the tower add considerably to its torsional rigidity. The process involves dipping the structural components into a galvanic bath to apply a zinc layer. A proper. si/kmk/ESDEP/master/wg15c/l0300. Fischer. December 1988).. design and calculation of towers. conductors. 1992.e. 5. foundation. International Electrotechnical Commission . REFERENCES [1] European Convention for Constructional Steelwork. insulators and other equipment. 4. CEN. CEN (in preparation) Definition of wind action. Ausführung".ESDEP LECTURE NOTE [WG15C] http://www.Planung.Technical Committee No 11.uni-lj. Eurocode 3: "Design of Steel Structures": ENV 1993-1-1: Part 1. 3.htm#SEC_1 4. "Recommendations for Overhead Lines" (Draft. corrosion protection and erection. 2. ECCS Technical Committee 8. R.1: General rules and rules for buildings. i. and Kiessling. "Recommendations for Angles in Lattice Transmission Towers". "Freileitungen . planning. ADDITIONAL READING 1. Recommendations concerning slenderness ratios and buckling curves from leg and web members taking into account redundancies and eccentricities. Previous | Next | Contents 15 of 15 11/12/2010 3:26 PM .fgg. F. Berechung. Eurocode 1: "Basis of Design and Actions on Structures". Brussels 1985. ECCS. Recommendations for establishing design criteria and loadings. Springer Verlag 1989 (In German) Comprehensive treatment of all aspects on high-voltage transmission lines.