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WG 15C : STRUCTURAL SYSTEMS: MISCELLANEOUS

Lecture 15C.1 : Design of Tanks for the Storage of Oil and Water

Lecture 15C.2 : Structural Design of Bins

Lecture 15C.3 : Lattice Towers and Masts

Lecture 15C.4 : Guyed Masts

Lecture 15C.5 : Chimneys

ESDEP WG 15

STRUCTURAL SYSTEMS: MISCELLANEOUS

Lecture 15C.1: Design of Tanks for the

Storage of Oil and WaterOBJECTIVE/SCOPE:

The lecture describes the basic principles used in the design of tanks for the storage of oil or water. It covers the design of vertical cylindrical tanks, and reference is made to the British Standard BS 2654 [1] and to the American Petroleum Industry Standard API650 [2].

PREREQUISITES

None.

RELATED LECTURES

Lecture 8.6: Introduction to Shell Structures

Lecture 8.8: Design of Unstiffened Cylinders

SUMMARY

Welded cylindrical tanks are commonly used to store oil products or water.

The principal structural element of these tanks is a vertical steel cylinder, or shell, which is made by welding together a series of rectangular plates and which restrains the hydrostatic pressures by hoop tension forces. The tank is normally provided with a flat steel plated bottom which sits on a prepared foundation, and with a fixed roof attached to the top of the shell wall.

This lecture explains the design basis for the structural elements of cylindrical tanks and illustrates the arrangements and the key details involved.

1. DESIGN OF WELDED CYLINDRICAL TANKS

1.1 General

Oil and oil products are most commonly stored in cylindrical steel tanks at atmospheric pressure or at low pressure. The tanks are flat bottomed and are provided with a roof which is of conical or domed shape.

Water is also sometimes stored in cylindrical steel tanks. When used to store potable water they are of a size suitable to act as a service reservoir for a local community; they have a roof to prevent contamination of the water. Cylindrical tanks are also used in sewage treatment works for settlement and holding tanks; they are usually without a roof.

The sizes of cylindrical tanks range from a modest 3m diameter up to about 100m diameter, and up to 25m in height. They consist of three principal structural elements - bottom, shell and roof.

For petroleum storage, the bottom is formed of steel sheets, laid on a prepared base. Some tanks for water storage use a reinforced concrete slab as the base of the tank, instead of steel sheets.

The shell, or cylindrical wall, is made up of steel sheets and is largely unstiffened.

The roof of the tank is usually fixed to the top of the shell, though floating roofs are provided in some circumstances. A fixed roof may be self supporting or partially supported through membrane action, though generally the roof plate is supported on radial beams or trusses.

1.2 Design Standards

Clearly, common standards are generally applicable whether a tank holds oil or water, though it is the petroleum industry which has been responsible for the development of many of the design procedures and standards.

The two standards applied most widely are British Standard BS 2654 [1] and the American Petroleum Institute Standard API 650 [2]. These two Standards have much in common, although there are some significant differences (see Appendix A). Other standards, American and European, are not applied much outside their respective countries.

This lecture will generally follow the requirements of BS 2654 [1]. This standard is both a design code and a construction specification. The design code is based on allowable stress principles, not on a limit state basis.

1.3 Design Pressure and Temperature

Tanks designed for storage at nominally atmospheric pressure must be suitable for modest internal vacuum (negative pressure). Tanks may also be designed to work at relatively small positive internal pressures (up to 56 mbar (5,6 kN/m2), according to BS2654.

Non-refrigerated tanks are designed for a minimum metal temperature which is based on the lowest ambient air temperature (typically, ambient plus 10oC) or the lowest temperature of the contents, whichever is the lower. No maximum service temperature is normally specified.

1.4 Material

Tanks are usually manufactured from plain carbon steel plate (traditionally referred to as mild steel) of grades S235 or S275 (to EN 10 025 [3]), or equivalent. Such material is readily weldable. The use of higher strength grades of low alloy steel (e.g. Grade S355) is less common, though its use is developing.

Notch ductility at the lowest service temperature is obtained for thicker materials (> 13 mm) by specifying minimum requirements for impact tests. This is normally achieved by specifying an appropriate sub-grade to EN 10 025 [3].

Internally, oil tanks are normally unpainted. Water tanks may be given a coating (provided it is suitably inert, where the water is potable), or may be given cathodic protection. Externally, tanks are normally protected. Where any steel is used uncoated, an allowance must be made in the design for loss of thickness due to corrosion.

2. DESIGN LOADING

A tank is designed for the most severe combination of the various possible loadings.

2.1 Dead Load

The dead load is that due to the weight of all the parts of the tank.

2.2 Superimposed Load

A minimum superimposed load of 1,2 kN/m2 (over the horizontal projected area) is applied to the roof of the tank. This load is commonly known as the 'snow load', but in fact represents, as well as a nominal snow load, any other imposed loads, such as maintenance equipment, which might be applied to the roof, and it includes the internal vacuum load. It is therefore applicable even in locations where snow is not experienced.

Non-pressure tanks are often fitted with valves which do not open until the vacuum reaches a value of 2,5 mbar, to contain vapour losses. By the time a valve is fully open, a vacuum of 5 mbar (0,5 kN/m2) may have developed. Even without valves a tank should be designed for a vacuum of 5 mbar, to cater for differential pressure under wind loads. In pressure tanks the valves may be set to 6 mbar vacuum, in which case a pressure difference of 8,5 mbar (0,85 kN/m2) may develop.

Actual predicted snow load or other superimposed load, plus appropriate vacuum pressure, should be used when it is greater than the specified minimum.

2.3 Contents

The weight and hydrostatic pressure of the contents, up to the full capacity of the tank, should be applied. Full capacity is usually determined by an overflow near the top of the tank; for a tank without any overflow, the contents should be taken to fill the tank to the top of the shell.

For oil and oil products, the relative density of the contents is less than 1.0, but tanks for such liquids are normally tested by filling with water. A density of 1000 kg/m3 should therefore be taken as a minimum.

2.4 Wind Loads

Wind loads are determined on the basis of a design wind speed. Maximum wind speed depends on the area in which the tank is to be built; typically a value of 45 m/s is taken as the design wind speed, representing the maximum 3-second gust speed which is exceeded, on average, only once every 50 years.

2.5 Seismic Loads

In some areas, a tank must be designed to withstand seismic loads. Whilst some guidance is given in BS 2654 [1] and API650 [2] on the design of the tank, specialised knowledge should be applied in determining seismic loads.

3. BOTTOM DESIGN

For petroleum storage tanks, steel bottom plates are specified, laid and fully supported on a prepared foundation.

The steel plates are directly supported on a bitumen-sand layer on top of a foundation, usually of compacted fill or, if the subsoil is weak, possibly a reinforced concrete raft. A typical foundation pad is shown in Figure 1 and a detailed description of the formation of this example is given in Appendix A of BS 2654 [1].

The bottom is made up of a number of rectangular plates, surrounded by a set of shaped plates, called sketch plates, to give a circular shape, as shown in Figure 2. The plates slightly overlap each other and are pressed locally at the corners where three plates meet (see Figure 3). Lapped and fillet welded joints are preferred to butt welded joints (which must be welded onto a backing strip below the joint) because they are easier and cheaper to make.

For larger tanks (over 12,5 m diameter, according to BS 2654) a ring of annular plates is provided around the group of rectangular plates. The radial joints between the annular plates are butt welded, rather than lapped, because of the ring stiffening which the plates provide to the bottom of the shell. A typical arrangement is shown in Figure 4.

The shell sits on the sketch or annular plates, just inside the perimeter and is fillet welded to them (see Figure 5).

The bottom plates act principally as a seal to the tank. The only load they carry, apart from local stiffening to the bottom of the shell, is the pressure from the contents, which is then transmitted directly to the base. Stress calculations are not normally required for the base, though BS 2654 sets out minimum thicknesses of plate depending on the size of the tank.

Water tanks may also have a steel bottom. In some circumstances a reinforced concrete slab is specified instead. There are no standard details for the connection between a shell and a concrete slab, though a simple arrangement of an angle welded to the bottom edge of the shell and bolted to the slab will usually suffice.

4. SHELL DESIGN

4.1 Circumferential Stresses

Vertical cylinder tanks carry the hydrostatic pressures by simple hoop tension. No circumferential stiffening is needed for this action. The circumferential tension in the shell will vary directly, in a vertical direction, according to the head of fluid at any given level. For a uniform shell thickness, the calculation of stresses is therefore straightforward. At a water depth H, the stress is given by:

where D is the diameter of the tank

t is the thickness of the plate

is the density of the fluid

g is the gravity constant

For practical reasons, it is necessary to build up the shell from a number of fairly small rectangular pieces of plate, butt welded together. Each piece will be cylindrically curved and it is convenient to build up the shell in a number of rings, or courses, one on top of the other. This technique provides, at least for deeper tanks, a convenient opportunity to use thicker plates in the lower rings and thinner plates in the upper rings.

The lowest course of plates is fully welded to the bottom plate of the tank providing radial restraint to the bottom edge of the plate. Similarly, the bottom edge of any course which sits on top of a thicker course is somewhat

restrained because the thicker plate is stiffer. The effect of this on the hoop stresses is illustrated in Figure 6.

Consequently, because of these restraints, an empirical adjustment is introduced into the design rules which effectively requires that any course is simply designed for the pressure 300mm above the bottom edge of the course, rather than the greater pressure at the bottom edge. (This is known as the 'one foot rule' in API 650 [2].)

When the load due to internal pressure is taken into account and an allowance for corrosion loss is introduced, the resulting design equation is of the form in BS 2654:

where t is the calculated minimum thickness (mm)

w is the maximum density of the fluid (kg/l)

H is the height of fluid above the bottom of the course being designed (m)

S is the allowable design stress (N/mm2)

p is the design pressure (pressure tanks only) (mbar)

c is the corrosion allowance (mm)

The allowable design stress in tension in the shell is generally taken to be a suitable fraction of the material yield stress. BS 2654 defines it as two-thirds of the yield stress, thus giving an overall factor of 1,5 on the plastic strength of the plate. API650 also uses two-thirds of the yield stress, but additionally limits the design stress to a smaller fraction of the ultimate strength; for higher strength steels, this is slightly more restrictive. Further, API650 allows a slightly higher stress during the hydrostatic test than the allowable design stress for service conditions when the relative density is less than 1,0.

Each course is made of a number of plates, butt welded along the vertical join between the plates. Each course is butt welded to the course below along a circumferential line. Good weld procedures can minimise the distortions or deviations from the ideal flat or curved line of the surface across the weld, but some imperfection is inevitable, especially with thin material. Consequently the rules call for the vertical seams to be staggered from one course to the next - at least one third of the length of the individual plates, if possible.

Holes in the shell for inlet/outlet nozzles or access manholes cause a local increase in circumferential stresses. This increase is catered for by requiring the provision of reinforcing plates. These plates may take the form of a circular doubling plate welded around the hole or of an inset piece of thicker plate. The nozzle provides some stiffening to the edge of the hole; it may also be made of sufficient size that shell reinforcement can be omitted.

4.2 Axial Stresses in the Shell

The cylindrical shell has to carry its weight, and the weight of the roof which it supports, as an axial stress. In addition, wind loading on the tank contributes tensile axial stress on one side of the tank and compressive stress on the other.

A thin-walled cylinder under a sufficient axial load will of course buckle locally, or wrinkle. The critical value of this stress, for a perfect cylinder, can be obtained from classical theory and, for steel, has the value:

In practice, imperfect shells buckle at a much lower stress; an allowable stress level of as little as a tenth of the above might be more appropriate. However, in normal service the axial stresses in shells suitable to carry the circumferential loads for the size of tank used for oil and water storage are much smaller than even this level of stress. The calculation of axial stress is therefore not even called for in codes, such as BS 2654 and API650, for the service conditions.

But under seismic conditions, larger stresses result because of the large overturning moment when the tank is full. In that case the axial stresses must be calculated. Axial stress due to overturning moment, M, is given simply by the expression:

a = 4M/tD2

In BS 2654 the axial stress under seismic conditions is limited to 0.20Et/R, which is considered a reasonable value when the cylinder is also under internal hydrostatic pressure. API650 uses a similar value, provided that the internal pressure exceeds a value which depends on the tank size.

Although axial stresses do not need to be calculated for service conditions, the tank does have to be checked for uplift when it is empty and subject to wind loading. If necessary, anchorages must be provided; a typical example is shown in Figure 7.

4.3 Primary Wind Girders

A tank with a fixed roof is considered to be adequately restrained in its cylindrical shape by the roof; no additional stiffening is needed at the top of

the shell, except possibly as part of an effective compression ring (see Section 5.2).

At the top of an open tank (or one with a floating roof), circumferential stiffening is needed to maintain the roundness of the tank when it is subject to wind load. This stiffening is particularly necessary when the tank is empty.

The calculation of the stability of stiffened tanks is a complex matter. Fortunately, investigations into the subject have led to an empirical formula, based on work by De Wit, which is easily applied in design. In BS 2654 this formula is expressed as a required minimum section modulus given by:

Z = 0,058 D2 H

where Z is the (elastic) section modulus (cm3) of the effective section of the ring girder, including a width of shell plate acting with the added stiffener

D is the tank diameter (m)

H is the height of the tank (m)

The formula presumes a design wind speed of 45 m/s. For other wind speeds it may be modified by multiplying by the ratio of the basic wind pressure at the design speed to that at 45 m/s, i.e. by (V/45)2.

Wind girders are usually formed by welding an angle or a channel around the top edge of the shell. Examples are shown in Figure 8. Note that continuous fillet welds should always be used on the upper edge of the connection, to avoid a corrosion trap.

It is recognised that application of the above formula to tanks over 60 m diameter leads to unnecessarily large wind girders; the code allows the size to be limited to that needed for a 60 m tank.

Primary wind girders are normally external to the tank. Settlement tanks usually require a gutter around the inside edge of the tank, into which the water spills and passes to the outlet. Although this detail is not covered in the code, a suitable gutter detail can participate as a primary wind girder, provided it is relatively close to the top of the tank. In that event a kerb angle is also required at the free edge; the arrangement of a low ring girder and a kerb angle is covered by the design rules.

4.4 Secondary Wind Girders

Although the primary wind girder or the roof will stabilise the tank over its full height, local buckling can occur in empty tall tanks between the top of the tank and its base. To prevent this local buckling, secondary wind girders are introduced at intervals in the height of the tank. The determination of the number and position of these secondary wind girders is dealt with in BS 2654 (but not in API 650).

The procedure is based on determining the length of tube for which, with the ends held circular, the elastic critical buckling will occur at a given uniform external pressure. Such buckling would also occur in a longer tube which is restrained at intervals equal to that length.

The critical stress for a length of tube, l, of radius R and thickness t, is given in Roark [4] by the formula:

Using values of E and for steel, rearranging and simplifying, this reduces approximately to the expression in the code:

where D is the diameter of the shell (m)

Hp is the maximum permitted spacing of rings (m)

(equivalent to critical length, l)

tmin is the thickness of the shell plate (mm)

Vw is the design wind speed (m/s)

va is the vacuum (mbar)

However, tank shells in practice are made up of courses, and the thickness of the plating increases from the top to the bottom. Fortunately, this non-uniform situation can be converted into an equivalent uniform situation by noting that the critical length l (or maximum spacing Hp) is proportional to t5/2. Taking the thinnest plate (the top course) as reference (tmin), courses of height h and thickness t can be converted to an equivalent height of a tube of the thin plate which has the same effective slenderness by applying the correction:

where t is the thickness of each course in turn

He is the equivalent height of each course at a thickness of tmin

The equivalent heights of all the courses are added to give the total equivalent height (length of tube) and divided by the critical length Hp to determine the minimum number of intervals and thus the number of intermediate rings. The positions of the intermediate rings, which are equally spaced on the equivalent tube, must be established by converting positions on the tube back to positions on the tank, by the reverse of the above procedure.

The whole process is illustrated by an example in BS 2654.

The stiffening is achieved by welding an angle to the surface of the shell plate in the same manner as for the primary wind girder. Minimum sizes for this angle are given in the code [1].

5. FIXED ROOF DESIGN

5.1 General

Fixed roofs of cylindrical tanks are formed of steel plate and are of either conical or domed (spherically curved) configuration. The steel plates can be entirely self supporting (by 'membrane' action), or they may rest on top of some form of support structure.

Membrane roofs are more difficult to erect - they require some temporary support during placing and welding - and are usually found only on smaller tanks.

Permanent support steelwork for the roof plate may either span the complete diameter of the tank or may in turn be supported on columns inside the tank. The use of a single central column is particularly effective in relatively small tanks (15-20 m diameter), for example.

The main members of the support steelwork are, naturally, radial to the tank. They can be simple rolled beam sections or, for larger tanks, they can be fabricated trusses.

Roof plates are usually lapped and fillet welded to one another. For low pressure tanks, they do not need to be welded to any structure which supports them, but they must normally be welded to the top of the shell.

5.2 Membrane Roofs

In a membrane roof, the forces from dead and imposed loads are resisted by compressive radial stresses. The net upward forces from internal pressure minus dead load are resisted by tensile radial stresses.

Conical roofs usually have a slope of 1:5. Spherical roofs usually have a radius of curvature between 0,8 and 1,5 times the diameter of the tank.

Limitations on buckling under radial compression are expressed in BS2654 as:

where R1 is the radius of curvature of the roof (m)

Pe is the external loading plus self weight (kN/m2)

E is Young's modulus (N/mm2)

tr is the roof plate thickness (mm)

For conical roofs, R1 is taken as the radius of the shell divided by the sine of the angle between the roof and the horizontal, i.e. R1 = R/sin .

Using a value of Pe = 1,7 kN/m2, i.e. 1,2 kN/m2, superimposed load plus 0,5kN/m2 for dead load, (equivalent to about 6 mm plate thickness) and the E value for steel, gives:

tr = 0,36 R1

A similar expression is given in API650, expressed in imperial units and for a loading of 45lb/ft2 (= 2,2 kN/m2).

For tensile forces, stresses are limited to:

(for spherical roofs)

(for conical roofs)

where is the joint efficiency factor

S is the allowable design stress (in N/mm2)

p is the internal pressure (in mbar)

Although lapped and double fillet welded joints are acceptable, they have a joint efficiency factor of only 0,5; butt welded joints have a factor of 1,0.

For downward loads, the radial compression is complemented by ring tension.

For upward loads, i.e. under internal pressure, the radial tension has to be complemented by a circumferential compression. This compression can only be provided by the junction section between roof and shell. This is expressed as a requirement for a minimum area of the effective section, as shown in Figure 9:

where Sc is the allowable compressive stress (in N/mm2)

R is the radius of the tank (in m)

is the slope of the roof at roof-shell connection

The allowable compressive stress for this region is taken to be 120 N/mm2 in BS2654 [1].

5.3 Supported Roofs

Radial members supporting the roof plate permit the plate thickness to be kept to a minimum. They greatly facilitate the construction of the roof.

Radial beams are arranged such that the span of the plate between them is kept down to a minimum of about 2 m. This limit allows the use of 5 mm plate for the roof. The plate simply lies on the beams and is not connected to them.

Supported roofs are most commonly of conical shape, although spherical roofs can be used if the radial beams are curved.

The roof support structure can either be self supporting or be supported on internal columns. Typical arrangements are shown in section in Figures 10 and 11. Self supporting roofs are essential when there is an internal floating cover.

When columns are used to support the roof, the slope may be as low as 1:16. When the roof is self supporting it may be more economic to use a steeper roof.

Not all radial members continue to the centre of the tank. Those that do may be considered as main support beams; the secondary radial members may be considered as rafters - they are supported at their inner ends on ring beams between the main support members. Where internal columns are used they will be beneath the main support members. Typical plan arrangements are shown in Figure 11.

The main support members need to be restrained at intervals to stabilise them against lateral-torsional buckling. Cross bracing is provided in selected bays.

In API650 it is permitted to assume that friction between the roof plate and the beam is adequate to restrain the compression flange of the secondary rafter beams, provided that they are not too deep; such restraint cannot be assumed for the main beams, however.

The main support members may be subject to bending and axial load. Where they are designed for axial thrust, the central ring must be designed as a compression ring; the top of the shell must be designed for the hoop forces associated with the axial forces in the support members.

Design of beams and support columns may generally follow conventional building code rules, though it must be noted that both BS 2654 and API650 are allowable stress codes. In the British code reference is therefore made to BS449 [5], rather than to a limit state code.

The shell/roof junction zone must be designed for compression, in the same way as described above for membrane roofs.

5.4 Venting

Venting has to be provided to cater for movement of the contents into and out of the tank and for temperature change of the air in the tank. Venting can be provided by pressure relief valves or by open vents.

For storage of petroleum products, emergency pressure relief has to be provided to cater for heating due to an external fire. Pressure relief can be achieved either by additional emergency venting or by designing the roof to shell joint as frangible (this means, principally, that the size of the fillet weld between the roof and the shell is limited in size - a limit of 5 mm is typical).

6. DESIGN OF FLOATING ROOFS AND COVERS

6.1 Use of Floating Roofs and Covers

As mentioned in Section 5.4, tanks need to be vented to cater for the expansion and contraction of the air. In petroleum tanks, the free space above the contents contains an air/vapour mixture. When the mixture expands in the heat of the day, venting expels some of this vapour. At night, when the temperature drops, fresh air is drawn in and more of the contents evaporates to saturate the air. The continued breathing can result in substantial evaporation losses. Measures are needed to minimise these losses; floating roofs and covers are commonly used for this purpose.

6.2 Floating Roofs

A floating roof is sometimes provided instead of a fixed roof. The shell is then effectively open at the top and is designed accordingly.

During service, a floating roof is completely supported on the liquid and must therefore be sufficiently buoyant; buoyancy is achieved by providing liquid-tight compartments in one of two forms of roof - pontoon type and double deck type.

A pontoon roof has an annular compartment, divided by bulkheads, and a central single skin diaphragm. The central diaphragm may need to be stiffened by radial beams.

A double deck roof is effectively a complete set of compartments over the whole diameter of the tank; two circular skins are joined to circumferential plates and bulkheads to form a disk or piston.

Both types of roof must remain buoyant even if some compartments are punctured (typically two compartments). The central deck of a pontoon roof should also be presumed to be punctured for this design condition.

Because the roof is open to the environment, it catches rain, which must be drained off. Drainage is achieved by a system on the roof which connects to flexible pipework inside the tank and thence through the shell or bottom plates to a discharge. The design is required to ensure that the roof continues to float in the event of a block in the drainage system which results in a surcharge of water on the roof (usually 250 mm of water).

When the tank is emptied, the roof cannot normally be allowed to fall to the bottom of the tank, because there is internal pipework; the roof is therefore fitted with legs which keep it clear of the bottom. At this stage the roof must

be able to carry a superimposed load (1,2 kN/m2) plus any accumulated rainwater.

For maintenance of the drainage system and for access to nozzles through the roof for various purposes, maintenance personnel need access from the top of the shell to the roof whatever the level of contents in the tank. Access is usually achieved by a movable ladder or stairway, pinned to the shell and resting on the roof. For maintenance of the tank when it is empty, an access manhole must be provided through the roof.

A typical arrangement of a pontoon type roof is shown in Figure 12.

6.3 Floating Covers

Where a cover to the contents is provided inside a fixed roof tank, to reduce evaporation or ingress of contaminants (e.g. water or sand), a much lighter cover or screen can be provided.

Such a cover is likely to be manufactured from lighter materials than steel, though a shallow steel pan can sometimes be provided. The cover does not need to be provided with access ladders, nor to be designed for surcharge. It does have to be designed to be supported at low level when the tank is empty and to carry a small live load in that condition.

Detailed recommendations for the design of internal floating covers are given in Appendix E of BS 2654 [1].

7. MANHOLES, NOZZLES AND OPENINGS

7.1 Manholes

Access is required inside fixed roof tanks for maintenance and inspection purposes. Such access can be provided through the roof or through the shell wall. Manholes through the roof have the advantage that they are always accessible, even when the tank is full. Access through the shell wall is more convenient for cleaning out (some access holes are D-shaped and flush with the bottom for cleaning out purposes).

A manhole through a roof should be at least 500 mm diameter. Stiffening arrangements around the hole in the roof plate, and the type of cover, depend on the design of the roof. Access to the roof manhole must be provided by ladders, with suitable handrails and walkways on the roof.

A manhole through the shell wall should be at least 600 mm diameter and is normally positioned just above the bottom of the tank. A typical detail is shown in section in Figure 13. Further details of this example, and details of clean-out openings, are given in BS2654 [1].

Clearly, the cutting of an opening in the shell interferes with the structural action of the shell. The loss of section of shell plate is compensated by providing additional cross-section area equal to 75% of that lost. The area must be provided within a circular region around the hole, though the actual reinforcement should extend beyond that region. Reinforcement can be provided in one of three ways:

(i) a reinforcing plate welded onto the shell plate (similar to the section in Figure 13)

(ii) an insert of thicker plate locally (in which the manhole is cut)

(iii) a thicker shell plate than that required for that course of the shell

7.2 Nozzles

As well as manholes for access and cleaning out, nozzles are required through the shell roof and bottom for inlet, outlet, and drainage pipes, and for vents in the roof. They are normally made by welding a cylindrical section of plate into a circular hole in the structural plate. For small nozzles, no reinforcement is necessary, the extra material is considered sufficient. Larger holes must be reinforced in the same way as manholes. An example of a roof nozzle detail is shown in Figure 14.

8. CONCLUDING SUMMARY

Oil and oil products are most commonly stored in cylindrical steel tanks at atmospheric pressure or at low pressure. Water is also sometimes stored in cylindrical steel tanks.

The two design standards applied most widely to the design of welded cylindrical tanks are BS2654 and API 650.

Tanks are usually manufactured from plain carbon steel plate. It is readily weldable.

A tank is designed for the most severe combination of the various possible loadings.

For petroleum storage tanks, steel bottom plates are specified, laid and fully supported on a prepared foundation. Water tanks may also have a steel bottom or a reinforced concrete slab may be specified.

Vertical cylindrical tanks carry the hydrostatic pressure by simple hoop tension. The cylindrical shell has to carry both its own weight and the

weight of the supported roof by axial stresses. Wind loading on the tank influences the axial stress.

For open tanks, primary wind girders are required to maintain the roundness of the tank when it is subject to wind load. Secondary wind girders are needed in tall tanks.

Roofs may be fixed or floating. A cover to the contents of a fixed roof tank may be provided to reduce evaporation or ingress of contaminants.

Manholes are provided for access and nozzles allow inlet, outlet and drainage, and venting of the space under the roof.

9. REFERENCES

[1] BS 2654: 1984, Specification for manufacture of vertical steel welded storage tanks with butt-welded shells for the petroleum industry, British Standards Institution, London.

[2] API 650, Welded Steel Tanks for Oil Storage, 8th Edition, November 1988, API.

[3] BS EN 10025, 1990, Hot Rolled Products of Non-alloy Structural Steels and their Technical Delivery Conditions, British Standards Institution, London.

[4] Young, W. C., Roark's Formulas for Stress and Strain, McGraw Hill, 1989.

[5] BS 449: Part 2: 1969, Specification for the Use of Structural Steel in Building, British Standards Institution, London.

Appendix A Differences between BS 2654 and API 650

The following are the principal differences between the British Standard, BS 2654 [1] and the American Petroleum Institute Standard, API650 [2]:

(a) API 650 specifies different allowable stresses for service and water testing. BS 2654 specifies an allowable stress for water testing only, which will allow oils with any specific gravity up to 1 to be stored in the tank.

(b) The allowable design stresses of BS 2654 are based on guaranteed minimum yield strength whereas the design stresses of API 650 are based on the guaranteed minimum ultimate tensile strength.

(c) BS 2654 specifies more stringent requirements for the weldability of the shell plates.

(d) The notch ductility requirements of BS 2654 are based on the results of a great number of wide plate tests. This system considers a steel acceptable if, for the required thickness, the test plate does not fail at test temperature before it has yielded at least 0,5%. This system gives the same safety factor for all thicknesses.

In API 650 a fixed value and test temperature is given for the impact tests for all thicknesses. As the tendency to brittle fracture increases with increasing plate thickness it means that API 650 in fact allows a lower safety factor for large tanks than for smaller ones.

(e) The steels specified by API 650 guarantee their notch ductility by chemical analysis but without guaranteed impact values. BS 2654 requires guaranteed impact values where necessary.

(f) BS 2654 gives a clearer picture of how to determine the size and location of secondary wind girders.

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ESDEP WG 15C

STRUCTURAL SYSTEMS: MISCELLANEOUS

Lecture 15C.2: Structural Design of BinsOBJECTIVE/SCOPE

To explain the calculation of loads on steel bins arising from stored materials. To describe the structural design of common types of bin.

PREREQUISITES

None.

RELATED LECTURES

None.

SUMMARY

This lecture explains how to calculate loads on steel bins from the stored material and describes the structural design of common types of bin. The methods for the calculation of loads are based on rules given in Eurocode 1 [1] and the guidelines for structural design have been compiled from numerous publications. Bin design is a complicated subject covering the analysis of thin shells and stiffened plate structures with uncertain load distributions. This lecture is necessarily limited to an overall view of simple and practical methods for the design of common bin types.

NOTATION

a, b plate dimensions

A cross-sectional area of vertical walled section

C wall load magnifier, buckling constant

Cb bottom load magnifier

Ch horizontal load magnifier

Cw wall frictional pressure magnifier

dc characteristic cross-section dimension (Figure 5)

E modulus of elasticity

e the larger of ei and eo

ei eccentricity due to filling (Figure 5)

eo eccentricity of the centre of the outlet (Figure 5)

fcr critical buckling stress

Fp total horizontal force due to patch load on a thin walled circular (membrane) silo

Frb ring beam force

h distance from outlet to equivalent surface (Figure 5)

k plate buckling factor

Ks horizontal to vertical pressure ratio

lh hopper wall length (Figure 8)

ph horizontal pressure due to stored material (Figure 5)

ph0 horizontal pressure after filling at the base of the vertical walled section (Figure 8)

pn pressure normal to inclined hopper wall (Figures 5 & 8)

pp patch pressure

pps patch pressure (unstiffened steel silos)

ps kick pressure (Figure 8)

pt hopper friction pressure (Figures 5 & 8)

pv vertical pressure due to stored material (Figure 5)

pvf vertical pressure after filling

pv0 vertical pressure after filling at the base of the vertical walled section

pw wall frictional pressure on the vertical section (Figure 5)

r radius

s length along the surface of the zone affected by the patch load (s = 0,2 dc)

t wall thickness

th hoop tension

U internal perimeter of the vertical walled section

W weight of hopper contents

z depth below the equivalent surface at maximum filling

zo parameter used to calculate loads

mean angle of inclination of hopper wall measured from the horizontal (Figure 5)

circumferential angular coordinate

patch load magnifier

bulk weight density of liquid or stored material

coefficient of wall friction for pressure calculation

effective angle of internal friction

w angle of hopper wall friction for flow evaluation

DEFINITIONS

Bin   (Figure 1) Any form of containment structure used to store particulate materials (i.e. bunker, bins, and silos).

Slender Silo  A silo where h/dc 1,5.Squat Silo  A silo where h/dc 1,5.Vertical Walled Section  The part of a silo or a tank with vertical walls.Hopper  A silo bottom with inclined walls where > 20 .Transition  The intersection of the hopper and the vertical walled

section.Flat Bottom  A flat silo bottom or a silo bottom with inclined walls

where 20 .Equivalent Surface  (Figure 5) Level surface giving the same volume of

stored material as the actual surface.Flow Pattern  (Figure 2) There are three flow patterns: mass flow,

funnel flow and internal flow.Mass Flow  (Figure 2) A flow pattern in which all the stored

particles are mobilised during discharge.Funnel Flow (or Core Flow)  (Figure 2) A flow pattern in which a channel of flowing

material develops within a confined zone above the outlet, and the material adjacent to the wall near the outlet remains stationary. The flow channel can intersect the vertical walled section or extend to the surface of the stored material.

Internal Flow  (Figure 2) A funnel flow pattern in which the flow channel extends to the surface of the stored material.

Kick Load  A local load that occurs at the transition during discharge.

Patch Load  A local load taken to act over a specified zone on any part of a silo wall.

1. INTRODUCTION

Bins are used by a wide range of industries throughout Europe to store bulk solids in quantities ranging from a few tonnes to over one hundred thousand tonnes. Bins are also called bunkers and silos. They can be constructed of steel or reinforced concrete and may discharge by gravity flow or by

mechanical means. Steel bins range from heavily stiffened flat plate structures to efficient unstiffened shell structures. They can be supported on columns, load bearing skirts, or they may be hung from floors. Flat bottom bins are usually supported directly on foundations.

For structural design, it is convenient to classify bins using the BMHB system [2] into the following four categories:

Class 1 Small bins holding less than 100 tonnes, are simply and robustly constructed often with substantial reserves of strength.

Class 2 Intermediate bins, between 100 and 1000 tonnes, can be designed using simple hand calculations. Care is required to ensure reliable flow and predictable wall pressures.

Class 3 Large bins, over 1000 tonnes. Specialist knowledge of bins is required to prevent problems due to uncertainties of flow, pressure and structural behaviour. Sophisticated finite element analyses of the structure may be justified.

Class 4 Eccentrically discharging bins where the eccentricity of the outlet eo is greater than 0,25 times the silo diameter, dc.

This lecture concentrates on the design of Class 1 and 2 bins although the design checks are also applicable to Class 3 bins.

Bin design procedures consists of four parts as follows:

i. Determine the strength and flow properties of the bulk solid.

ii. Determine the bin geometry to give the desired capacity, to provide a flow pattern with acceptable flow characteristics and to ensure that discharge is reliable and predictable. Specialised mechanical feeder design may be required.

iii. Estimate the bin wall loads from the stored material and other loads such as wind, ancillary equipment, thermal, etc.

iv. Design and detail the bin structure.

Before the structural design can be carried out, the loads on the bin must be evaluated. Loads from the stored material are dependent, amongst other things, on the flow pattern, the properties of the stored material and the bin geometry while the methods of structural analysis and design depend upon the bin geometry and the flow pattern. The importance of Stages i and ii of the design should not be underestimated. Simplified rules for the functional

design of bins and for estimating wall loads are given in Eurocode 1: Part 4 [1], and are discussed in Section 3 of this lecture. Detailed rules for the structural design of steel bins will be given in Eurocode 3, Part 4 [3]. This code has not yet been completed. However some design guidance is available in journal publications and elsewhere [2, 4-16]. Sections 4 and 5 of this lecture summarise existing structural design practice and give guidance for common types of bin.

2. BIN CLASSIFICATION

For design purposes, bins are classified by their size, geometry, the type of flow during discharge of the contents, and the structural material of the wall. The importance of each of these parameters in design is discussed below.

2.1 Bin Size and Geometry

The bin size and geometry depend on the functional requirements such as the storage volume and the method and rate of discharge, the properties of the stored material, available space and economic considerations. Bins usually consist of a vertical sided section with a flat bottom or a bottom with inclined sides, known as the hopper. They are usually circular, square or rectangular in cross-section and may be arranged singly or in groups. Typical bin geometries are shown in Figure 1.

 

Circular bins are more efficient structures than square or rectangular bins, leading to lower material costs. For the same height, a square bin provides 27% more storage than a circular bin whose diameter equals the length of the side of the square bin. Flat-bottom bins require less height for a given volume of stored material.

The bin size is determined by feeding and discharge rates and the maximum quantity of material to be stored. High discharge rates require deep hoppers with steep walls. Flat bottomed bins usually have low discharge rates and

are used when the storage time is long, the discharge is infrequent and the storage volume is high.

The ratio of bin height to diameter influences the loads from the stored material and hence the structural design. Eurocode 1 classifies bins as either squat or slender [1]. Squat bins are defined as those where the height does not exceed 1,5 times the diameter or smallest side length. Slender bins have a height to diameter ratio greater than 1,5.

Hoppers are usually conical, pyramidal or wedge shaped. Pyramidal hoppers have the advantage of being simple to manufacture although they may lead to flow problems due to the building up of stored material in the corners. Outlets may be either concentric or eccentric to the centre of the bin. Eccentric outlets should be avoided because the pressure distribution is difficult to predict and there may be problems due to segregation of the stored material. The angle of inclination of the hopper sides is selected to ensure continuous discharge with the required flow pattern.

2.2 Type of Flow

Two types of flow are described in Eurocode 1 and shown in Figure 2. They are mass flow and funnel flow. Discharge pressure is influenced by the flow pattern and so the flow assessment must be made before the calculation of loads from the stored material. In mass flow bins, all the contents of the bin flow as a single mass and flow is on a first-in first-out basis. The stored material in funnel flow bins flows down a central core of stationary stored material and flow is on a last-in, first-out basis.

 

The flow type depends on the inclination of the hopper walls and the coefficient of wall friction. Mass flow occurs in deep bins with steep hopper walls whereas funnel flow occurs in squat bins with shallow hopper walls. Eurocode 1 gives a graphical method (shown in Figure 3) for determining the flow pattern in conical and wedge shaped hoppers for the purpose of structural design only. Bins with hoppers between the boundaries of both the mass and the funnel flows should be designed for both situations.

2.3 Structural Material of the Bin Wall

Most bins are constructed from steel or reinforced concrete. The economic choice depends upon the material costs as well as the costs of fabrication and erection. Other factors such as available space also influence the selection. The main advantages of steel bins over cost in-situ concrete bins are:

small and medium sized steel bins and bunkers can be prefabricated and, therefore, their erection time is considerably shorter;

bolted bins are relatively easy to disassemble, move, and rebuild in another location;

The main disadvantages of steel bins are the necessity of maintenance to prevent corrosion, the steel walls may require lining to prevent excessive

wear, and the steel walls are prone to condensation which may damage stored products such as grain and sugar, etc. which are moisture sensitive.

The selection of structural material for the wall may depend upon the bin geometry. A bin wall is subject to both vertical and horizontal forces. The vertical forces are due to friction between the wall and stored materials, while the horizontal forces are due to lateral thrust from the stored materials. Reinforced concrete bins carry vertical compressive forces with ease and so tend to fail in tension due to the high lateral thrusts. Steel bins, circular in plan, usually carry the lateral forces by hoop tension. They are more prone to failure by buckling under excessive vertical forces. The increase of horizontal and vertical pressure with depth is shown in Figure 4. Increases in horizontal pressure are negligible beyond a certain depth and therefore concrete bins are more efficient if they are tall, whereas steel bins tend to be shallower structures.

3. CALCULATION OF PRESSURES ON BIN WALLS

3.1 General

Most existing theories for the calculation of loads from the stored material in bins assume that the pressure distribution around the perimeter of a bin is uniform at any given depth. In reality, there is always a non-uniformity of loading. This may arise from imperfections in the bin walls, non-concentric filling techniques, or discharge outlets positioned eccentrically to the centre of a bin.

The pressure exerted on the bin wall by the stored material is different when the material is flowing and when it is stationary. The stress state within a stored material changes as flow commences and the bin walls are subjected to high localised pressures of short duration. Research studies have identified two types of high pressure during discharge. The first is known as the kick load which occurs at the start of flow and is only significant in the hopper. The second high pressure is attributed to a local stress re-distribution within the flowing material as it passes the imperfections of the bin walls.

The neglect of the non-uniform loading in design results in more bin failures than any other causes. It leads to particular problems with circular bins which are designed to resist membrane forces only. Pressures due to eccentric discharge are erratic and may be higher or lower than the uniform pressure predicted using most existing theories.

Although high discharge pressures and their fundamental causes have been identified, they are difficult to quantify. It is common practice therefore for designers to multiply the calculated static pressure by a constant derived from experimental data. The empirical factor has traditionally been applied to the static pressure without any regard to the structural response of the bin. Since the high discharge pressures only affect local areas, variation of the pressure may result in a worse stress state in the bin wall than a high uniform pressure. Therefore the assumption of a high but constant pressure at any level is not necessarily safe.

3.2 Eurocode 1 - Rules for the Calculation of Loads from the Stored Material

Eurocode 1 [1] gives detailed rules for the calculation of loads from the stored material on bins subject to the following limitations:

The eccentricity of inlet and outlet is limited to 0,25 dc where dc is the bin diameter or shortest side length.

Impact loads during filling are small. Discharge devices do not influence the pressure distribution. The stored material is free flowing and has low cohesion.

Rules are given for calculating loads on slender, squat and homogeneous bins. The following four loads are specified and may be defined using the notation shown in Figure 5.

horizontal wall load and wall friction patch load hopper load kick load.

The initial horizontal (phf) and wall friction (pwf) loads are uniform at any depth in the bin. They are multiplied by a constant factor to allow for pressure variations during discharge. A patch load is added to the symmetric load to allow for the effects of non-symmetric loading. Due to the complexities of structural analysis of shells incorporating a patch load, Eurocode 1 permits the use of a symmetrical pressure distribution for the design of all bins with diameters less than 5m. The symmetrical pressure is increased to compensate for the patch pressure. This gives bins that are safe but more conservative than those bins designed for the patch pressure and the lower symmetrical pressure.

The hopper loads consist of a linear pressure distribution and a kick load. The kick load is applied at the junction of the transition of mass flow hoppers only.

3.2.1 Horizontal pressure and wall frictional pressure

The horizontal pressure at any depth in the bin is calculated using the classical Janssen theory. Janssen considered the vertical equilibrium of a horizontal slice through the stored material in a bin (Figure 6) and obtained the following relationship:

A(v + dv) + U Ks v dz = Adz + A v (1)

Rearranging and solving the first order differential equation gives the Janssen equation for vertical pressure pv at depth z, the horizontal pressure phf and the wall frictional pressure pwf:

pv = [A/UKs][1 - e-KszU/A]                (2)

phf = Ks pv (3)

pwf = phf (4)

The accuracy of the method depends on the selection of a value for the ratio of horizontal to vertical pressure Ks and the coefficient of wall friction .

Most bin wall pressures vary because the bins are filled with materials of different properties at different times. Other pressure changes may occur as the bin becomes polished or roughened by stored solids. Bins should therefore be designed with a variety of conditions in mind. Eurocode 1 recognises this situation and gives a range of properties for common stored materials. Material properties are selected to give the most adverse loading condition. The most adverse horizontal pressure occurs when Ks is at its maximum value and is at its minimum. The most adverse wall friction load arises when and Ks are both at maximum values. Material properties may be determined by testing or by taking values from Table 4.1 of Eurocode 1.

For bins with corrugated walls, allowance must be made for higher values of due to the effect of the stored material within the corrugations.

For convenience Eurocode 1 gives a formula for the calculation of the axial compression force due to the wall friction pressure at any depth in a bin. The axial compression per unit perimeter at depth z is equal to the integral of the wall friction pressures on the wall above and is obtained as below:

The Reimbert method [6] is a suitable alternative to the Janssen method for the calculation of static pressures. However, it has not been included in Eurocode 1.

3.2.2 Pressure increase for filling and discharge

The pressures calculated using the Janssen theory are multiplied by empirical factors to give filling and discharge pressures for the following conditions:

i. Patch load for filling.

ii. Uniform pressure increase for discharge.

iii. Patch load for discharge.

iv. For simplicity of structural design, Eurocode 1 also includes a simplified alternative rule to the patch load for filling and discharge.

i. a. The patch load for filling: non-membrane bins

Pressures determined using the Janssen equation are increased by a localised load or 'patch' load to allow for unsymmetrical pressure distributions. The patch load is prescribed to account for unsymmetrical pressures which experiments have shown occur in all bins. The non-uniformity of pressure depends mainly upon the eccentricity of the bin inlet, the method of filling and the anisotropy of the stored material. The patch load increases with the eccentricity of filling. The eccentricity of filling is shown in Figure 5 and results from the horizontal velocity of the stored material. It depends upon the type of filling device and must be estimated before calculating the patch load.

The patch load is different for unstiffened steel (membrane) and stiffened steel and concrete (non-membrane) bins to allow for the differences in the response of these structures to loading. The maximum stress in the walls of

non-membrane bins depends upon the magnitude of the pressure whereas membrane steel bins are more sensitive to the rate of change of pressure. For stiffened steel bins, two patch loads are applied on diametrically opposite square areas of wall, each with side length s = 0,2dc (Figures 7a and 7b). The loads are symmetrical and allow a relatively simple calculation of the bending moments induced in the structure.

The patch pressure is calculated as follows:

pp = 0,2 phf (5)

The pressure acts over a height s, where:

s = 0,2dc (6)

= 1 + 0.2 e

The patch should be applied at different levels on the bin wall to find the worst loading case resulting in the highest wall stress. For simplicity, Eurocode 1 allows the patch load in non-membrane bins to be applied at the mid-height of the vertical walled section and uses the percentage increase in the wall stresses at that level to increase the wall stresses throughout the silo. The simplified rule does not apply to groups of silos.

i. b. The patch load for filling: membrane bins

Membrane steel bins are sensitive to the rate of change of the patch pressure and so a cosine pressure distribution is specified. The pressure pattern shown in Figure 7c extends all around the bin. Pressure is outward on one side and inward on the other.

The most important influence of the patch is the increase in axial compression at the base of the bin. The increased axial compressive force can easily be calculated using beam bending theory and assuming global bending of the bin. In order to calculate the axial compressive force, the total horizontal force from the patch load should be calculated from:

(7)

where

pps = pp cos

and pp and s are calculated using Equations (5) and (6) respectively.

The patch should be taken to act at a depth z0 below the equivalent surface or at the mid-height of the vertical walled section, whichever gives the higher position of the load, where

zo =

The patch pressure introduces local bending stresses in the bin at the level of the patch. These bending stresses are difficult to calculate and a finite element analysis of the structure is required. To simplify the calculation it is easier to design using the increased pressure distribution described in iv. below as an alternative to the patch pressure.

ii. Uniform pressure increase for discharge

The static pressures are multiplied by two constant coefficients (Cw and Ch) to design for uniform discharge pressures. Ch increases the horizontal pressure and Cw increases the vertical pressure. Ch varies depending upon the stored material and Eurocode 1 gives a value that ranges from 1,3 for wheat to 1,45 for flour and fly ash. Cw is taken as 1,1 for all stored materials. These factors were selected from experience gained from satisfactory bin design and test results.

iii. Patch load for discharge

The patch load for discharge is calculated in the same way as the patch load for filling. Horizontal pressures calculated for discharge (described in ii.) are used to calculate the patch load. In addition, the eccentricity e, is taken as the greater of the eccentricities of the filling and the outlet (see Figure 5).

iv. Increased uniform load - an alternative to the patch for filling and discharge

For simplicity in structural design, Eurocode 1 permits the use of another constant factor on the uniform discharge pressures to allow for stress increases due to unsymmetrical pressure. The factor is calculated from the patch load magnifier and results in a simple but conservative rule which may be used instead of the patch pressure. For filling and discharge the normal wall pressure calculated using Equation (3) is multiplied by 1 + 0,4 and the wall friction is multiplied by 1 + 0,3 .

3.2.3 Hopper and bottom loads

Flat bottoms are defined as bin bottoms where < 20. The vertical pressure pvf varies across the bottom but for slender bins it is safe to assume that the pressure is constant and equal to:

pvf = 1,2 pv (8)

where:

pv is calculated using Equation (2).

It should be noted that for squat bins, the pressure variation at the bin bottom may influence the design and so flat bottomed squat bins may be designed for non-uniform pressures.

Loads on slopping walls of hopper

Eurocode 1 considers the sloping wall (where > 20) to be subject to both normal pressure, pn, and friction force per unit area pt. The hopper walls carry all the weight of the stored material in the bin other than that carried by wall friction in the vertical section. Knowledge of the vertical pressure at the transition between the vertical walled section and the hopper is required to define the loading on the hopper. Empirical formulae have been adopted in Eurocode 1 for the calculation of normal and frictional wall pressures on the hopper wall following a series of tests on pyramidal hoppers. The tests showed that it was sufficient to assume that the pressure distribution upon a hopper wall subjected to surcharge from the vertical walled section decreases linearly from the transition to the outlet. The pressure normal to the hopper wall, pn, as shown in Figure 8 may be obtained as follows:

pn = pn3 + pn2 + (pn1 - pn2) (9)

where

x is a distance measured from the edge (0 Lh) between 0, and lh

pn1 = pvo (Cb cos2 + 1,5 sin2 ) (10)

pn2 = Cb pvo cos2 (11)

pn3 = 3,0 (12)

where

Cb is a constant and is equal to 1,2

pv0 is the vertical pressure acting at the transition calculated using the Janssen equation.

The value of the wall frictional pressure pt, is given by:

pt = pn (13)

Kick load

High pressures have been measured in mass flow hoppers at the start of discharge due to a change in the stress state of the stored material. The change is often referred to as the 'switch' and results in a 'kick load' at the transition. It occurs when the material moves from a static (active pressure) to a dynamic (passive pressure) state. An empirical and approximate value for the kick load, ps, in Eurocode 1 is given as follows:

ps = 2 ph0 (14)

where

ph0 is the horizontal pressure at the base of the vertical walled section (see Figure 8)

ps is taken to act normal to the hopper wall at a distance equal to 0,2 dc down the hopper wall.

The kick load is only applied to mass flow bins. This is because it will be partially or totally absorbed by the layer of stationary material in funnel flow hoppers. The transition between the hopper, and the vertical section is subjected to a compressive inward force from the inclined hopper. The kick load acts against this compressive force and so, it may actually increase the outward load from the stored material (pn) which may be carried by the hopper during discharge (although the kick cannot be guaranteed and should not be used to reduce the design stresses).

3.3 Other Loading Considerations

Pressure distributions can be affected by factors which may either increase or decrease wall loads. Such factors are difficult to quantify, and are more significant in some bins than others. A limited list is given below.

Temperature variation

Thermal contraction of a bin wall is restrained by the stored material. The magnitude of the resulting increase in lateral pressure depends upon the temperature drop, the difference between the temperature coefficients of the wall and the stored material, the occurrence of temperature changes, the stiffness of the stored material and the stiffness of the bin wall.

Consolidation

Consolidation of the stored material may occur due to release of air causing particles to compact (a particular problem with powders), physical instability caused by changes in surface moisture and temperature, chemical instability caused by chemical changes at the face of the particles, or vibration of the

bin contents. The accurate determination of wall pressures requires a knowledge of the variation with depth of bulk density and the angle of internal friction.

Moisture Content

An increase in the moisture content of the stored material can increase cohesive forces or form links between the particles of water soluble substances. The angle of wall friction for pressure calculations should be determined using both the driest and wettest material likely to be encountered.

Increased moisture can result in swelling of the stored solid and should be considered in design.

Segregation

For stored material with a wide range of density, size and shape, the particles tend to segregate. The greater the height of free fall on filling, the greater the segregation. Segregation may create areas of dense material. More seriously, coarse particles may flow to one side of the bin while fine cohesive particles remain on the opposite side. An eccentric flow channel may occur, leading to unsymmetrical loads on the wall. The concentration of fine particles may also lead to flow blockages.

Degradation

A solid may degrade on filling. Particles may be broken or reduced in size due to impact, agitation and attrition. This problem is particularly relevant in bins for the storage of silage where material degradation may result in a changing pressure field which tends to hydrostatic.

Corrosion

Stored material may attack the storage structure chemically, affecting the angle of wall friction and wall flexibility. Corrosion depends on the chemical characteristics of the stored material and also the moisture content. Typically, the design wall thickness may be increased to allow for corrosion and the increase depends upon the design life of the bin.

Abrasion

Large granular particles such as mineral ores can wear the wall surface resulting in problems similar to those described for corrosion. A lining may be provided to the structural wall, but care should be taken to ensure that

wall deformation does not cause damage to the lining. The linings are usually manufactured from materials such as stainless steel or polypropylene.

Impact Pressures

The charging of large rocks can lead to high impact pressures. Unless there is sufficient material to cushion the impact, special protection must be given to the hopper walls. The collapse of natural arches which may form within the stored material and hold up flow, can also lead to severe impact pressures. In this case, a preventative solution is required at the geometric design stage.

Rapid Filling and Discharge

The rapid discharge of bulk solids having relatively low permeability to gasses can induce negative air pressures (internal suction) in the bin. Rapid filling can lead to greater consolidation, and the effects are discussed above.

Powders

The rapid filling of powders can aerate the material and lead to a temporary decrease in bulk density, cohesiveness, internal friction and wall friction. In an extreme case, the pressure from an aerated stored material can be hydrostatic.

Wind Loading

Methods for the calculation of wind loads on bins are given in Eurocode 1, Part 2 [17] and are not repeated in this lecture. Design against wind loads is especially critical during bin construction.

Dust Explosions

Eurocode 1, Part 4 [1] recommends that bins storing materials that may explode should either be designed to resist the explosion or should have sufficient pressure relief area. Table 1 of the Eurocode lists materials that may lead to explosions. Other general design guidance is available [14].

Eurocode 1 recommends proper maintenance and cleaning, and the exclusion of sources of ignition to prevent explosions.

Differential Settlements

Large settlements often occur as bins are filled, particularly the first time. The effects of differential settlement of groups of bins should be considered. Differential settlements may lead to buckling failure of membrane steel bins.

Seismic Actions

Provisional rules for seismic design are given in Eurocode 1. These rules are beyond the scope of this lecture.

Mechanical Discharge Equipment

Mechanical discharge equipment can lead to unsymmetrical pressure distributions even when it is considered to withdraw the stored material uniformly. The influence of mechanical discharge equipment on wall pressures should be considered during design.

Roof Loads

Bin roofs impose an outward thrust and axial compression on bin walls and should be considered during wall design. The design of bin roofs is beyond the scope of this lecture.

Load Combinations

Many bins are filled to their full design loads for most of their life. Eurocode 1 states that 100% of the predominant load should be added to 90% or 0% of other loads to give the most onerous design load at both ultimate and serviceability limit states respectively.

4. STRUCTURAL ANALYSIS AND DESIGN

4.1 Selection of the Bin Form

At the conceptual stage of design, the geometry of the bin is selected and consideration is given to the relative economy of different structural forms. The costs of materials, fabrication, erection and transport all influence the selection of the structural form. Steel bins usually have rectangular or circular cross-section shapes. Circular bins are usually more economical than rectangular bins because the circular walls carry loads in membrane tension whereas rectangular bins carry load less efficiently in bending. Rectangular bins typically require 2,5 times the material required for circular bins of the same capacity.

Rectangular bins tend to be heavily stiffened structures whereas circular bins are often unstiffened except at the top and the transition of the vertical walled section and the hopper. Rectangular bins tend to have large reserves of strength. This is not generally the case with circular bins for which care is needed in design to prevent overstress or buckling of the bin wall.

4.2 Design of Non-Circular Bins

A typical non-circular bin is shown in Figure 9. The structural design consists of the following main procedures:

select the support layout, stiffener layout and connections, design the wall plates, design the vertical and horizontal stiffeners including the transition

ring beam, design the supports.

The pressures on the vertical and inclined walls are calculated using the rules outlined in Section 3. The structural design is discussed below.

4.2.1 Wall plates

Non-circular bins tend to be heavily stiffened structures as shown in Figure 9. Material loads in the bin are applied directly to the wall plate, and transferred via the plate to the stiffeners. The walls are subject to bending and tensile membrane stresses. Frictional forces result in vertical compression of the wall and, because of the stiff cores and column supports, cause in-plane bending of the wall.

There are two main approaches to model the structural system. Either the bin is analysed as many isolated components or it is considered as a continuous folded plate structure. Most existing guides recommend the first approach. The walls are designed with assumed boundary conditions and interaction between individual plates is ignored. The guidance given is for flat plated bins. A more economical solution may be to use corrugated wall plates. In this case the bin wall is designed using the section properties of the corrugated sheet.

Wall pressure is carried partly by flexural action of the plate in bending and partly by membrane action. Bin walls are generally analysed using small deflection theory. The wall deflections are small (less than the thickness of the plate) and so for design purposes it is acceptable to assume that the load is carried entirely by plate bending. Three methods of analysis are commonly used. Wall plates between stiffeners with an aspect ratio greater than two to one are analysed as beams bending in one direction only. The beam is assumed to span continuously over stiffeners and may be fully fixed at the ends.

Plates with an aspect ratio less than two to one are designed with tabular data. The maximum bending moment for plates with simply supported or fixed edges is given by:

Mmax = pa2 b (15)

where

a and b are the shorter and longer plate dimensions respectively

p is the average normal pressure

is given in Tables 1 and 2.

b/a 1,0 1,2 1,4 1,6 1,8 2,0 3,0 4,0 >5,0

0,048 0,063 0,075 0,086 0,095 0,108 0,119 0,123 0,125

Table 1 for plates with simply supported edges

b/a 1,0 1,25 1,5 1,75 2,0 >2,5

0,0513 0,0665 0,0757 0,0817 0,0829 0,0833

Table 2 for plates with fixed edges

Tabulated data is not available for the analysis of trapezoidal plates and so the hopper wall is analysed as an idealised rectangular plate. The dimensions may be calculated from formulae given in Figure 10.

Both of the methods described lead to conservative designs due to the assumed plate geometry and boundary conditions. Higher accuracy can be achieved using numerical techniques, such as the finite element method, to

analyse the interaction of the various plate members subjected to in-plane and out-of-plane loads.

4.2.2 Plate Instability

Buckling is unlikely to control the design of the wall thickness of plates analysed using small deflection theory. Thus a conservative stability analysis is usually adopted and the critical elastic buckling load is calculated assuming that the loads are acting in the plane of the plate. The elastic critical buckling load can be calculated from the following equation:

fcr = (16)

The plate is assumed to be simply supported on all four edges and subject to a uniform or linearly increasing load. If necessary, the buckling resistance of a flat plate can be calculated allowing for additional strength due to lateral pressure from the stored material and post buckling strength [5].

4.2.3 Stiffener design

A typical stiffened arrangement is shown in Figure 9. It consists primarily of vertical stiffeners but with horizontal stiffeners at the transition and at the top of the bin. Vertical stiffeners in the vertical walled section are simply designed to carry horizontal and vertical wall friction loads from the adjoining wall plates. Stiffeners in the hopper are designed as beams with end reactions and loads normal to the wall from the stored material as shown in Figure 11. Tension forces along the beam may also need to be considered.

The horizontal stiffener at the top of the bin is designed to carry the reaction at A from the horizontal loads on the vertical wall. Horizontal loads include those from the stored material and the wind loads.

Hopper loads are usually carried by a ring beam at the transition. The ring beam has to carry the hopper weight and distribute the bin loads to the supports. At the start of filling the ring beam acts as a compression frame. It resists inward forces from the suspended hopper. As filling continues, the compressive forces are offset by tension from the lateral pressure exerted by the stored material in the bin. Figure 11 shows the load resultants. The ring beam force is found by taking moments about point O.

Frb = (17)

ph2 and ph3 are the horizontal components of pressure calculated normal to the hopper wall using Equation (9). The ring beam may also have to carry loads from the following:

Vertical load from wall friction in the bin.

Axial compressive forces that arise from in-plane bending of the wall plates.

Axial tension due to forces from adjacent walls. Torsion due to eccentricity of any of the above forces.

4.2.4 Support structure

The support structure for small bins is usually terminated at the ring beam. The walls of the structure above carry all the loads from the bin. This form of support is common in circular bins but in square bins the supports are usually continued from the transition ring beam to the top of the structure. Their function is to carry the vertical loads in the bin and provide resistance to buckling. A small ring beam is often positioned at the top of the bin to give additional restraint against horizontal forces. The support structure is braced to provide stability against externally applied lateral forces or non-symmetrical internal forces.

4.3 Design of Circular Bins

4.3.1 Introduction

The wall thickness of circular bins is selected after checks to prevent yielding due to circumferential tension forces and buckling. The wall thickness of most bins is governed by buckling although hoop tension controls the design of very shallow bins. Most cylindrical bins have only two stiffeners, one at the transition and one at the top of the vertical walled section. Additional stiffeners may be used to resist wind loads. Conical hoppers are usually unstiffened.

This section describes the basic design procedure and discusses the design of critical components. The main elements of design are:

Preliminary sizing of bin and hopper walls. Bin wall buckling. Stiffener design considering the influence on wall stresses and

buckling. Support design considering the influence on wall stresses and buckling.

Recent research has investigated the limitations of simplified design rules and highlighted areas of design which may require careful consideration. These areas include high localised stresses around bin supports and boundaries, and the influence of unsymmetrical loads on wall stress. For very large bins a detailed finite element analysis of the structure is recommended. For most bin designs this may not be possible due to economic restrictions and so the design is carried out using simplified

procedures. In many cases these procedures do not model the bin behaviour accurately and careful design is required to prevent failure.

4.3.2 Cylinder wall stress

The circumferential wall stresses in bins less than 5 m diameter can be first estimated simply but conservatively using the symmetrical pressure distribution alternative to the patch load discussed in Section 3.2.2 and the membrane theory of shells. Membrane theory assumes that the bin wall is subject to tensile forces only. The 'hoop' tension should be calculated at the bottom of the cylinder as follows:

th = phe r (18)

The resulting wall thickness may have to be increased to ensure adequate connection strength, corrosion and wear resistance and to prevent buckling. (Joint efficiency factors for welded connections are given in Lecture 15C.1.)

Membrane theory is only accurate for the predication of wall stresses away from discontinuities such as changes in wall thickness, supports and stiffeners. Particular precautions are required depending upon the type of support. These precautions are discussed in Sections 4.3.4 to 4.3.6.

4.3.3 Wall buckling

The most common failure mode of cylindrical steel bins is the buckling of the bin wall under axial compression. Axial compression may be due to combined loads of wall friction, roof loads and loads from attached equipment. The elastic buckling stress of a bin wall is influenced by the following:

magnitude and shape of wall imperfections; distribution of the wall friction load; magnitude of internal pressure; elastic properties of the stored material; connections; bin supports.

Buckling can be prevented using simple hand calculation methods provided that the bin walls, supports and connections are detailed carefully to prevent significant out-of-plane displacements.

Many methods have been proposed for the calculation of the critical elastic buckling stress and they are reviewed by Rotter [13]. A simple and conservative approach is to adopt the classical elastic critical stress multiplied by an empirical safety factor .

fcr = 0,605 (19)

where = 0,15

The influence of lateral pressure is ignored and the shell is assumed to be uniformly axially compressed.

Equation (19) may be used safely provided that the load distribution is uniform (i.e. the conservative pressure distribution in Eurocode 1 is used) and the supports are designed to prevent significant out-of-plane stresses and deflections in the shell. The following points should be considered when designing cylindrical bin walls to prevent buckling.

Bins can be designed less conservatively using the patch pressure distribution. The patch load results in an unsymmetrical pressure distribution around the bin wall corresponding to rapid circumferential changes in stress. A rigorous shell analysis of the bin wall is required as simple hand calculation methods are not available for an accurate analysis.

Further economy may result from utilising the increased strength of the bin wall due to lateral pressure from the stored material. Hoop tension resulting from lateral pressure reduces the imperfection sensitivity of buckling under axial compression and increases the buckling strength. Methods have been developed to include the influence of internal pressure on the buckling strength [15]. Designers have been reluctant to use the rules because of the high number of buckling failures of steel bins and the need to ensure that the stationery layer of stored material adjacent to the bin wall has adequate thickness. In eccentrically discharged bins, the lateral support cannot be guaranteed over the entire wall and so there may not be any increase in buckling strength.

Cylindrical walls are not normally stiffened with vertical stiffeners. The physical size of local buckles is small and so longitudinal stiffeners would need to be closely spaced to prevent buckling. Circumferential stiffeners serve no useful purpose in resisting buckling under axial compression.

The critical buckling stress is reduced by surface imperfections. The number and size of imperfections is influenced by the fabrication process. Apparently identical cylinders fabricated using different processes may have very different buckling strengths. The critical stress should be reduced for bins with large imperfections. The ECCS recommendations [15] give rules for the strength reduction depending upon the type and size of imperfection.

Where bolted construction is used on bins and the plates are lapped together, the buckling strength is reduced below the value for butt jointed construction. Circumferential joints lead to eccentricities in the line of axial thrust resulting in destabilizing axisymmetric deflections, compressive circumferential membrane stresses and local bending stresses.

Column supports can induce high bending stresses in the bin wall. They can influence stresses up to a distance equal to many times the diameter from the support. The problem can be alleviated by extending the columns to the full height of the bin (the columns can then carry the roof loads directly). If the columns are not continued to the top of the bin, a shell bending analysis could be used to determine the stresses induced in the shell wall and associated ring beams and stiffeners.

Buckling from Wind Loads

The ECCS [15] and BS 2654 [16] give recommendations for the design of cylinders to resist external pressure. Generally, restraint to the top of the bin is provided either by a fixed roof or a stiffener at the top of the cylinder. In large bins, it may be economical to stiffen the sheeting of circular bins. Stiffening generally increases the resistance to wind buckling, but not to circumferential tension or meridional compression, except locally. Circumferential stiffeners should be placed on the outside of a bin to avoid flow restrictions. Steel bins are more susceptible to wind buckling during construction than in service because restraint is provided by the roof and ring beam in service.

4.3.4 Bottom and hopper

High stresses occur near the base of a bin wall if it is rigidly connected to a flat floor. They may be reduced by detailing a suitable movement joint or by design of the bin wall to prevent overstress. Flat bottoms should be designed to carry the vertical pressure calculated from Equation (8).

Conical hoppers are designed as membrane structures in tension. For the calculation of the hopper wall thickness and connection detailing, it is necessary to calculate the meridional tensile stress and the circumferential hoop stress. The meridional tension, tm, is calculated from the resultant of the vertical discharge pressure pv at the transition and the combined weight of the material in the hopper and the hopper wall, W.

tm = (20)

The hoop tension th is calculated from the pressure normal to the hopper wall during discharge and is equal to:

th = (21)

The effects of mechanical discharge aids or column supports on the hopper wall stress should be considered. Again reliable hand methods for the calculation of stresses due to column supports are not available and so an accurate prediction is only possible using a finite element analysis.

4.3.5 Transition ring beam

The transition between the cylinder and the cone may be made using a variety of connection details (some are shown in Figure 12). The hopper applies an inward and downward force on the transition which induces a circumferential compression in the ring beam. The ring beam should be checked to prevent plastic collapse and buckling. It is a usual practice to design continuously supported rings to resist the horizontal components of the hopper meridional tension tm. This may be reduced to allow for hoop tension from the horizontal pressure in the cylinder. The ring beam may also have to carry vertical loads for column supports.

A summary of forces on the ring beam is as follows:

vertical load from wall friction in the cylinder; outward load from horizontal pressure in the cylinder; membrane forces from the hopper; torsion due to eccentricity of any of the above forces; upward load from the supports.

These forces result in:

axial compression from net outward and inward forces; shear and bending between support columns; local shell bending; torsion due to eccentricity of shell and column loads.

Circumferential compressive stresses in the ring beam at the transition of the mass flow hoppers is relieved by the kick load. Due to uncertainty of the exact magnitude of the kick load, the beneficial effects should not be used in design.

For many ring beam details, part of the hopper and the cylinder walls are effective in carrying the ring beam forces and should be designed accordingly. For skirt supported bins, the shell provides sufficient strength and a ring beam is not usually required.

4.3.6 Supports

Different types of bin support are shown in Figure 13. Column supported bins result in a complicated stress pattern in the bin wall around the column. The stress pattern is less complicated when the columns are continued to the top of the bin. Increased stresses in the shell wall can be reduced by sensible design of the column support. The distance of the column from the bin wall should be kept to a minimum and loads from the column supports can be distributed by stiffeners.

In the case of small-diameter bins and bunkers (dc < 7m), the metal walls may extend down to the foundation and support the entire structure.

4.3.7 Connections

Sheeting may be connected by welding or bolting. When bolted connections are used, designers should be aware of the reduced buckling strength of the bin wall due to lap joints. Connections are designed to carry the meridional and circumferential stresses in the cylinder and the hopper as described above.

5. CONCLUDING SUMMARY

Eurocode 1 gives simplified rules for the calculation of loads and the structural design of common bin types.

Non-uniform loading needs to be carefully considered in design. Non-circular bins are heavily stiffened structures designed to carry

loads in bending. In general, they are designed conservatively. The design of circular bins is usually governed by the buckling of the

bin wall.

Circular and non-circular bins may be designed conservatively using simple hand calculation methods.

Supports, connections, stiffeners and fittings should be detailed to minimise out-of-plane stresses and deflections.

6. REFERENCES

[1] Eurocode 1: "Basis of design and actions on structures, Part 4, Actions in silos and tanks", ENV 1991-4, CEN (in press).

[2] British Materials Handling Board, "Silos - Draft design code", 1987.

[3] Eurocode 3: "Design of steel structures": Part 4, Tanks, Silos and Pipelines, CEN (in preparation).

[4] National Coal Board, "The design of coal preparation plants", UK National Coal Board Code of Practice, 1970.

[5] Gaylord, E. H. and Gaylord, C. N., "Design of steel bins for storage of bulk solids", Prentice Hall, Englewood Cliffs, 1984.

[6] Reimbert, M. and Reimbert, A., "Silos: Theory and practice", Trans Tech Publications, 1987.

[7] Troitsky, M. S., "On the structural analysis of rectangular steel bins", Powder and Bulk Solids Technology, Vol 4, No. 4, 1980, pp 19-25.

[8] Trahair, N. S. et al, "Structural design of steel bins for bulk solids", Australian Institute of Steel Construction, 1983.

[9] The University of Sydney, "Design of steel bins for the storage of bulk solids", Postgraduate professional development course, 1985.

[10] Lambert, F. W., "The theory and practical design of bunkers", The British Construction Steelwork Association Limited, 1968.

[11] Safarian, S. S. and Harris, E. C., "Handbook of concrete engineering - Silos and Bunkers", Van Nostrand Reinhold Co., New York, 1974.

[12] Wozniak, S., "Silo design" in Structural Engineers Handbook.

[13] Rotter, J. M. et al, "A survey of recent buckling research on steel silos". Steel structures - recent research advances and their applications to design, ed M. Pavlovic, Elsevier applied science, London, 1986.

[14] Building Research Establishment, "Dust Explosions", BRE TIL 613, 1984.

[15] European Convention of Constructional Steelwork (ECCS), European recommendations for steel construction: Buckling of shells, 4th edn.

[16] BS 2654: 1989, "Manufacture of vertical steel welded non-refrigerated storage tanks with butt-welded shells for the petroleum industry". British Standards Institution, London, 1989.

[17] Eurocode 1: "Basis of design and actions on structures, Part 2, Wind loads on buildings", ENV 1991-2-1, CEN (in preparation).

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ESDEP WG 15C

STRUCTURAL SYSTEMS: MISCELLANEOUS

Lecture 15C.3: Lattice Towers and MastsOBJECTIVE/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:

establishment of load requirements. consistency between loads and tower design. establishment of overall design, including choice of number of tower

legs. consistency between overall design and detailing. detailing with or without node eccentricities. sectioning of structure for transport and erection.

In this lecture, towers for one particular purpose, i.e. the high voltage transmission tower, have been selected for discussion.

2. HIGH VOLTAGE TRANSMISSION TOWERS

2.1 Background

The towers support one or more overhead lines serving the energy distribution. Most frequently three-phase AC circuits are used requiring three live conductors each. To provide safety against lightning, earthed conductors are placed at the top of the tower, see Figures 1 and 2.

The live conductors are supported by insulators, the length of which increases with increasing voltage of the circuit. To prevent short circuit between live and earthed parts, including the surrounding environment, minimum mutual clearances are prescribed.

Mechanically speaking, the conductors behave like wires whose sag between their points of support depends on the temperature and the wire tension, the latter coming from the external loads and the pre-tensioning of the

conductor. As explained in Section 2.4, the size of the tension forces in the conductor has a great effect upon the tower design.

2.2 Types of Towers

An overhead transmission line connects two nodes of the power supply grid. The route of the line has as few changes in direction as possible. Depending on their position in the line various types of towers occur such as (a) suspension towers, (b) angle suspension towers, (c) angle towers, (d) tension towers and, (e) terminal towers, see Figure 1. Tension towers serve as rigid points able to prevent progressive collapse of the entire line. They may be designed to serve also as angle towers.

To the above-mentioned types should be added special towers required at the branching of two or more lines.

In Figure 2 examples of suspension tower designs from four European countries are presented. Note similarities and mutual differences.

2.3 Functional Requirements

Before starting the design of a particular tower, a number of basic specifications are established. They are:

a. voltage.

b. number of circuits.

c. type of conductors.

d. type of insulators.

e. possible future addition of new circuits.

f. tracing of transmission line.

g. selection of tower sites.

h. selection of rigid points.

i. selection of conductor configuration.

j. selection of height for each tower.

The tower designer should notice that the specifications reflect a number of choices. However, the designer is rarely in a position to bring about desirable

changes in these specifications. Therefore, functional requirements are understood here as the electrical requirements which guide the tower design after establishment of the basic specifications.

The tower designer should be familiar with the main features of the different types of insulators. In Figure 3 three types of insulators are shown. They are all hinged at the tower crossarm or bridge.

Figure 4 shows the clearances guiding the shape of a typical suspension tower. The clearances and angles, which naturally vary with the voltage, are embodied in national regulations. Safety against lightning is provided by prescribing a maximum value of the angle v. The maximum swing u of the insulators occurs at maximum load on the conductor.

2.4 Loads on Towers, Loading Cases

The loads acting on a transmission tower are:

a. dead load of tower.

b. dead load from conductors and other equipment.

c. load from ice, rime or wet snow on conductors and equipment.

d. ice load, etc. on the tower itself

e. erection and maintenance loads.

f. wind load on tower.

g. wind load on conductors and equipment.

h. loads from conductor tensile forces.

i. damage forces.

j. earthquake forces.

It is essential to realize that the major part of the load arises from the conductors, and that the conductors behave like chains able to resist only tensile forces. Consequently, the dead load from the conductors is calculated by using the so-called weight span, which may be considerably different from the wind span used in connection with the wind load calculation, see Figure 5.

The average span length is usually chosen between 300 and 450 metres.

The occurrence of ice, etc. adds to the weight of the parts covered and it increases their area exposed to the wind. Underestimation of these circumstances has frequently led to damage and collapse. It is, therefore, very important to choose the design data carefully. The size and distribution of the ice load depends on the climate and the local conditions. The ice load is often taken as a uniformly distributed load on all spans. It is, however, evident that different load intensities are likely to occur in neighbouring spans. Such load differences produce longitudinal forces acting on the towers, i.e. acting in the line direction.

The wind force is usually assumed to be acting horizontally. However, depending on local conditions, a sloping direction may have to be considered. Also, different wind directions (in the horizontal plane) must be

taken into account for the conductors as well as for the tower itself. The maximum wind velocity does not occur simultaneously along the entire span and reduction coefficients are, therefore, introduced in the calculation of the load transferred to the towers.

The tensile forces in the conductors act on the two faces of the tower in the line direction(s). If they are balanced no longitudinal force acts on a tower suspending a straight line. For angle towers they result in forces in the angle bisector plane, and for terminal towers they cause heavy longitudinal forces. As the tensile forces vary with the external loads, as previously mentioned, even suspension towers on a straight line are affected by longitudinal forces. For all types of towers the risk of mechanical failure of one or more of the conductors has to be considered.

The loads and loading cases to be considered in the design are usually laid down in national regulations.

2.5 Overall Design and Truss Configuration

The outline of the tower is influenced by the user's functional requirements. However, basically the same requirements may be met by quite different designs. In general, the tower structure consists of three parts: the crossarms and/or bridges, the peaks, and the tower body.

Statically speaking, the towers usually behave like cantilevers or frames, in some cases with supplementary stays. For transmission lines with 100 kV voltage or more, the use of steel lattice structures is nearly always found advantageous because they are:

easily adaptable to any shape or height of tower. easily divisible in sections suitable for transport and erection. easy to repair, strengthen and extend. durable when properly protected against corrosion.

By far the most common structure is a four-legged tower body cantilevering from the foundation, see Figure 6. The advantages of this design are:

the tower occupies a relatively small area at ground level. two legs share the compression from both transverse and longitudinal

loads. the square or rectangular cross-section (four legs) is superior to a

triangular tower body (three legs) for resisting torsion. the cross-section is very suitable for the use of angles, as the

connections can be made very simple.

The following remarks in this section relate mainly to a cantilever structure. However, many features also apply to other tower designs.

For a cantilever structure, 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, as it reduces the design forces (except for torsional loads).

The bracing of the tower faces is chosen either as a single lattice, a cross bracing or a K-bracing, possibly with redundant members reducing the buckling length of the leg members, for example see Figure 6. The choice of bracing depends on the size of the load and the member lengths. The most common type is cross bracing. Its main advantage is that the buckling length of the brace member in compression is influenced positively by the brace member in tension, even with regard to deflection perpendicular to the tower face.

Generally, the same type of bracing is chosen for all four tower body faces, most frequently with a staggered arrangement of the nodes, see Figure 7. This arrangement provides better space for the connections, and it may offer considerable advantage with respect to the buckling load of the leg members. This advantage applies especially to angle sections when used as shown in Figures 10 and 11, since it diminishes the buckling length for buckling about the 'weak' axis v-v. For further study on this matter see [1].

Irrespective of the type of bracing, the tower is generally equipped with horizontal members at levels where leg taper changes. For staggered bracings these members are necessary to 'turn' the leg forces. Torsional forces, mostly acting at crossarm bottom levels, are distributed to the tower faces by means of horizontal bracings, see Figure 8.

Cross arms and earthwire peaks are, in principle, designed like the tower itself. However, as the load on the cross arms rarely has an upward component, cross arms are sometimes designed with two bottom chords and one upper chord and/or with single lattice bracings in the non-horizontal faces.

2.6 Structural Analysis

Generally, 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.

the tower is designed for static or quasi-static loads only.

These assumptions do not reflect the real behaviour of the total system, i.e. towers and conductors, particularly well. However, they provide a basis from simple calculations which have broadly led to satisfactory results.

Generally speaking, a tower is a space structure. It is frequently modelled as a set of plane lattice structures, which are identical with the tower body

planes together with the planes of the cross arms and the horizontal bracings mentioned in Section 2.5.

In a simplified calculation a four-legged cantilevered structure is often assumed to take the loads as follows:

a. centrally acting, vertical loads are equally distributed between the four legs.

b. bending moments in one of the main directions produce an equal compression in the two legs of one side, and equal tension in the two legs of the other side. The shear forces are resisted by the horizontal component of the leg forces and the brace forces (thus, the leg taper has a significant influence on the design of the bracing).

c. torsional moments broadly produce shear forces in the tower body faces, i.e. in the braces.

A classical analysis assuming hinges in all nodes leads to very simple calculations. However, the effect of redundancies should be considered, especially concerning the forces and moments in the brace members.

Although this approach is satisfactory in most cases attention must be drawn to the function of redundant members, which in some cases may change the load distribution considerably. In addition, the effect of fixed connections (as opposed to hinged connections) must be considered, since they produce moments in the bracing members. The effect of eccentricities in the joints should also be taken into account, see Section 2.7.

Finally, the distribution of an eccentric horizontal load is studied. In Figure 9 the force H is acting at the cross arm bottom level. Without horizontal bracing in the tower, three tower body planes are affected by H. 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.

2.7 Detailing of Joints

The detailed design is governed by a number of factors influencing the structural costs once the overall design has been chosen, such as:

simple and uniform design of connections. simple shaping of structural components. details allowing for easy transportation and erection. details allowing for proper corrosion protection.

As an introductory example of design and calculation, a segment of a four-legged tower body is discussed, see Figure 10. All members are made of angle sections with equal legs. The connections are all bolted without the use of gussets, except for a spacer plate at the cross bracing interconnection. This very simple design requiring a minimum of manufacturing work is attained by the choice and orientation of the leg and brace member sections.

By choosing the design described above, some structural eccentricities have to be accepted. They arise from the fact that the axes of gravity of the truss members do not intersect at the theoretical nodes. According to the bending caused by the eccentricities they may be classified as in-plane or out-of-plane eccentricities. In Figure 11, the brace forces C and T meet at a distance eo from the axis of gravity. The resultant force S produces two bending moments: Me = S eo and Mf=S e1. These moments are distributed among the members meeting at the joint according to their flexural stiffness, usually leaving the major part to the leg members. As z-z is the 'strong' axis of the leg section, a resultant moment vector along axis v-v will be advantageous. This is achieved, when eo=-e1 . In this case C and T intersect approximately at the middle of the leg of the section. Usually this situation is not fully practicable without adding a gusset plate to the joint.

Additional eccentricity problems occur when the bolts are not placed on the axis of gravity, especially when only one bolt is used in the connection (eccentricities ec and et).

The out-of-plane eccentricity causing a torsional moment, V = H e2, acting on the leg may be measured between the axes of gravity for the brace members (see Figure 11). However, the torsional stiffness of the leg member may be so moderate - depending on its support conditions - that V cannot be transferred by the leg and, consequently, e2 must diminish. The latter causes bending out-of-plane in the brace members.

The leg joint shown in Figure 10 is a splice joint in which an eccentricity e3 may occur. In this case there is a change of leg section, or the gravity axis for the four (or two) splice plates in common does not coincide with the axis of the leg(s). For legs in compression the joint must be designed with some flexural rigidity to prevent unwanted action as a hinge.

The joint eccentricities have to be carefully considered in the design. As the lower part of the leg usually is somewhat oversized at the joint - this is, in fact, 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, let the lower part resist the eccentricity moment. The splice plates and the bolt connections must then be designed in accordance with this model.

The bolted connections might easily be replaced by welded connections with no major changes of the design. However, except for small structures, bolted connections are generally preferred, as they offer the opportunity to assemble the structural parts without damaging the corrosion protection, see Section 2.8.

This introductory example is very typical of the design with angle sections. Nevertheless some additional comments should be added concerning the use of gussets and multiple angle sections.

The use of gussets is shown in Figure 12. They provide better space for the bolts, which may eliminate the in-plane eccentricities, and they allow for the use of double angle sections. In the latter case out-of-plane eccentricities almost vanish.

For heavily loaded towers it might be suitable to choose double or even quadruple angle sections for the legs. Figure 13 shows some possibilities.

Towers designed with other profiles than angles

In principle any of the commercially available sections could be used. However, they have to compete with the angle sections as regards the variety of sections available and the ease of designing and manufacturing simple connections. So far only flat bars, round bars and tubes have been used, mostly with welded connections. The use is limited to small size towers for the corrosion reasons mentioned above.

In other contexts, e.g. high rise TV towers, circular sections may be more interesting because their better shape reduces wind action.

Construction joints and erection joints

The tower structure usually has to be subdivided into smaller sections for the sake of corrosion protection, transportation and erection. Thus a number of joints which are easy to assemble on the tower site, have to be arranged. Two main problems have to be solved: the position and the detailing of the joints.

In Figure 14 two examples of the joint positions are shown. The framed structure is divided into lattice structure bodies, each of which may be fully welded, and stays. The cantilevered structure usually is subdivided into single leg and web members.

The two types of joints are lap (or splice) joints and butt plate joints. The former is very suitable for angle sections. The latter is used for all sections, but is mostly used for joints in round tube or bar sections. Figure 15 shows some examples of the two types.

2.8 Corrosion Protection

Today, corrosion protection of steel lattice towers is almost synonymous with hot-galvanising, possibly with an additional coating. The process involves dipping the structural components into a galvanic bath to apply a zinc layer, usually about 100 m thick.

No welding should be performed after galvanizing, as it damages the protection. The maximum size of parts to be galvanized is limited by the size of the available galvanic bath.

3. CONCLUDING SUMMARY

The overall design of a lattice tower is very closely connected with the user's functional requirements. The requirements must be studied carefully.

A major part of the design loads on the tower results from the wind force on tower and equipment.

The occurrence of an ice cover on the tower and equipment must be considered in the design.

For towers supporting wires, differential loads in the wire direction must be taken into account.

For systems of interconnected towers it must be considered that the collapse of one tower may influence the stability of a neighbouring tower.

In most cases a cantilevered tower with four legs is preferred, as it offers structural advantages and occupies a relatively small ground area.

The type of bracing greatly affects the stability of both legs and braces. K-bracings and/or staggered cross bracings are generally found advantageous.

Horizontal braces at certain levels of the tower add considerably to its torsional rigidity.

Angle sections are widely used in towers with a square or rectangular base, as they permit very simple connection design.

Both in-plane and out-of-plane eccentricities in the connections must be considered.

A proper, long lasting corrosion protection must be provided. The protection method influences the structural design.

4. REFERENCES

[1] European Convention for Constructional Steelwork, ECCS, "Recommendations for Angles in Lattice Transmission Towers", ECCS Technical Committee 8, Brussels 1985.

Recommendations concerning slenderness ratios and buckling curves from leg and web members taking into account redundancies and eccentricities.

5. ADDITIONAL READING

1. Fischer, R. and Kiessling, F., "Freileitungen - Planung, Berechung, Ausführung", Springer Verlag 1989 (In German)

Comprehensive treatment of all aspects on high-voltage transmission lines, i.e. planning, conductors, insulators and other equipment, design and calculation of towers, foundation, corrosion protection and erection.

2. International Electrotechnical Commission - Technical Committee No 11, "Recommendations for Overhead Lines" (Draft, December 1988).

Recommendations for establishing design criteria and loadings.

3. Eurocode 1: "Basis of Design and Actions on Structures", CEN (in preparation)

Definition of wind action.

4. Eurocode 3: "Design of Steel Structures": ENV 1993-1-1: Part 1.1: General rules and rules for buildings, CEN, 1992.

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ESDEP WG 15C

STRUCTURAL SYSTEMS: MISCELLANEOUS

Lecture 15C.4: Guyed MastsOBJECTIVE/SCOPE

To outline calculation methods for guyed masts, in particular manual calculation of erection tensions in guy ropes, and computer calculation of forces in non-linear mode; to explain the main principles of non-linear calculation; to cover erection methods.

RELATED LECTURES

Lecture 15C.3: Lattice Towers and Masts

SUMMARY

The components of a guyed mast are described, i.e. mast, guy ropes, accessories, equipment.

Specific items of the calculation of guyed masts are introduced. The definition and manual calculation of erection tensions in guy ropes is described together with the principles and computer calculation of forces and strains.

The fabrication and erection of guyed masts are briefly discussed.

1. INTRODUCTION

The permanent development of regional, national and international communications requires very high structures.

These structures are generally designed for the following purposes:

to support small antennae, such as TV or FM antennae: they consist of a series of panels, the height of which relates to the required area of reception.

feeding cables which connect the panels to the transmitter at ground level.

to support antenna curtains: the antenna components are supported by a net of cables which is connected at the top of two towers; they are fed by a parallel feeding curtain. These antennae are used for short

wave transmission and their current dimensions are about 100m x 100m.

to constitute an antenna by themselves for long wave transmission; the height of the radiating structure is equal to a half or a quarter of the wave length.

Steel guyed masts may be designed specifically to meet the above needs since very high structures (up to 600 metres high) which are both light and stiff can be designed and built in steel.

The present lecture does not give:

the detailed constitution of the different antenna types. methods to improve the quality of the transmission (simultaneous use

of several antennae).

2. THE DESCRIPTION OF A GUYED MAST

The component parts of a guyed mast are:

the foundations the steel mast, which generally has a pinned foot the guy ropes the structural accessories the equipment.

2.1 The Foundations

It is not the purpose of the present lecture to describe the foundations in a detailed way. It is only indicated that:

the foundation under the foot of the mast is calculated to support a very big compression force. A moment is considered in addition for the rare cases where the mast feet are fixed.

the foundations in which guy ropes are anchored are calculated to support the sloping tension force.

2.2 The Steel Mast

The mast may be considered as a continuous beam on elastic supports which are provided by the guy ropes. In most cases, it is a lattice column with a square or equilateral triangle cross-section. It is also possible to design masts with a round tubular section.

For the masts with 3 faces, the most adequate section of the legs is a round hollow section or a round solid section. A circular flange is welded onto each end of each leg element. The leg elements are connected by bolting the flanges one to the other. The truss bars are bolted onto gusset plates which are welded on the legs. The section of the truss bars consists of one or two connected angles or of a circular tube. Where circular tubes are used, they are slotted and pressed at their ends in order to allow the bolted connection.

For masts with 4 faces, the same design can be used as for masts with 3 faces. Single angle legs or two cross-connected angle legs can also be used.

Where angle legs are used, the leg elements are connected together with bolted cover-plates. The truss bars are bolted onto the legs, either directly or by bolted gusset plates. For this type of mast, there is no welding work.

A mast structure with 4 faces must have horizontal bracings which prevent deformation of the cross-section.

In general in the few cases where the mast has a round tubular section, the mast has a fixed foot. It is very difficult to make a pinned foot for a mast with a tubular section. The mast elements are connected together by welded hollow flanges with external bolts.

2.3 The Guy Ropes

The guy ropes create elastic bearings with horizontal action on the mast. Where the mast has three truss faces, each bearing consists of three guy ropes situated in the medium plane of the angle of two adjacent truss faces. Where the mast has four truss faces, each bearing consists of four guy ropes each situated in a diagonal plane. Where the mast has a round hollow section, each bearing has three 120 spaced guy ropes or four 90 spaced guy ropes.

All the guy ropes (3 or 4) of a bearing form the same angle with the horizontal plane of between 30 and 60 .

The guy ropes are generally steel cables. In special cases where a guy rope enters the transmission field, cables of synthetic materials can be used. The three or four guy ropes which constitute a bearing must be of the same material.

The criteria for choosing cables are as follows:

high strength high Young's modulus no rotation around the cable axis when tension varies

ability to be easily protected from corrosion ability to be rolled for transportation.

It is always necessary to find the best compromise between the two first criteria and the fifth. The above analysis generally leads to the use of all-steel cables with large diameter wires, mainly one twist cables.

Guy ropes are provided with a socket at each end. The sockets are cast steel pieces of a conical shape and two parallel flanges which receive a connecting pin. The cable is entered in the hollow conical part of the socket, the wires constituting the cable are separated and bent to form a regular "flower" which is introduced into the socket. The socket cavity is then filled with a molten alloy. At one of the cable ends, the pin perpendicular to cable connects the bottom socket to the foundation anchor. At the other end, the pin connects the top socket to a thick gusset plate welded onto the mast leg.

2.4 Structural Accessories

The structural accessories are generally supplied by the steel manufacturer of the mast and include:

the accessories for access to the mast, i.e. ladders with a cage or with a safety rail, the rest platforms and the work platforms.

the accessories which support feeders. the accessories for the electric insulation of the radiating masts: a

ceramic insulator is provided under the mast foot and an insulator for each guy rope. The insulators only withstand compression so that their connection to guy ropes under tension requires special equipment.

the accessories for the adjustment of the rope tensions which are placed between the bottom socket and the foundation anchor.

2.5 Equipment

The equipment is generally not supplied by the steel manufacturer of the mast and includes:

different antennae feeding cables beacon equipment lightning protection.

3. THE DESIGN OF GUYED MASTS

The design of guyed masts - as other structures - contains two main steps:

initial dimensioning final dimensioning and checking.

3.1 Initial Dimensioning

In this step, the engineer chooses a first set of sections for the bar elements which constitute the mast and for the different guy ropes in relation to the overall design requirements:

the height of the mast the dimensions of the area where anchoring of the guy ropes is

permissible.

and also in relation to the loads to be considered, i.e.

the self-weight of the mast and its equipment the initial tensions of the guy ropes the wind on the bare structure or on the structure covered with ice

(guyed structures are very sensitive to ice loads).

The difficulty of this step arises from the interdependence of the values of the actions and of the choice of the sections. The procedure can be as follows:

a. Choose the first set of sections for bar elements of the mast by considering the mast as a continuous beam on unmovable supports (at guy rope connection levels). This beam supports the actions of the self-weight and of the maximum wind. In this step, the dynamic factor on wind actions can be evaluated with a first vibration mode period (in seconds) equal to a hundredth of the height of the mast (in metres).

The engineer must provide the sections with a large margin in expectation of phenomena which have not been considered explicitly, i.e.

the compression in the mast due to the guy rope tensions.

the influence on the bending moment diagram of the misalignment of the supports in the real deformed structure.

the influence on the bending moment diagram of the eccentricity of the guy rope compression in the mast.

the effects of the non-linear behaviour of the structure. These effects are explained in Section 3.2.

the yielding of foundations in tension and compression.

It is not possible to state a definite percentage for the margin which should be provided because it depends on the overall design of each guyed mast.

b. Calculate the actions of the mast on its supports, according to the simplified procedure. Fi is the action of the mast on the support i, Tij is the unknown tension of the guy rope i.j when the maximum wind blows (j varies from 1 to 3 or from 1 to 4 following the number of ropes per support); i is the angle between rope and support i; i is at a horizontal plane.

c. In the case of a support i with three guy ropes, if the wind blows in the direction of the guy rope i.1, then:

Ti.2 = Ti.3

(Ti.1 - Ti.2) = Fi / cos i

The section of the ropes which constitute the support i is chosen so that:

Ti.1 - Ti.2 0,75

where

TR.i is the breaking force of the rope

s is the required safety factor.

d. In the case of a support i with four guy ropes , if the wind blows in the direction of the guy rope i.1, then:

(Ti.1 - Ti.3) = Fi / cos i

The section of the ropes which constitute the support i is chosen so that:

Ti.1 - Ti.3 0,75

e. After the choice of the guy rope sections, the engineer has to determine the values of initial tensions Ti.o (the same value for a given i and any j) which are necessary to keep the supports aligned when the maximum wind blows. The general slope of the mast for which initial tensions are calculated is chosen in relation to the supported equipment.

In this step, the following approximations are made:

the direct action of wind on the guy ropes is neglected

the effect of the temperature is neglected

the second order effects due to mast compression are neglected

the deformed shape of the rope i.j is considered as a parabola, the length of which is:

si.j = li.j +

where li.j is the chord length

fi.j = is the maximum cable deformation, measured perpendicularly to the chord.

pi is the weight per metre of the cable.

If i.j is the projection, on the vertical plane which contains the rope i.j, of the horizontal displacement i of the support i:

i.j =

i.j =

at the first order, where li is the initial value of the chord length. The above equation can be written in the form:

i.j = g (Ti.j) - g (Ti.o)

f. Where the support i has 3 ropes and when the wind blows in the direction of the rope i.1:

i.j = i = - 2 i.2 = - 2 i.3

The equations may be solved as follows: A graph of the function g (T i.1) is drawn, point by point for different values of Ti.1 together with a separate

graph of the function - 2 g (Ti.2) at the same scale on transparent paper. If the two graphs are superimposed in order to get simultaneously:

Ti.1 - Ti.2 = 0,75 (distance between the curves on the T scale)

g(Ti.1) + 2 g (Ti.2) = 2 i (distance between the curves on the g (T) scale)

then Ti.o is read at the intersection of the two curves, on the T scale.

g. Where the support i has 4 ropes, the same procedure is applied:

i.1 = i = - i.3

and the curves g (Ti.1) and - g (Ti.3) are drawn as above.

After the sections of the mast bar elements and the guy ropes, and the values of the initial tensions have been evaluated, the final dimensioning step can begin.

3.2 Final Dimensioning and Checking

The final values of forces and strains are calculated by computer.

It is necessary to use software which allows:

the calculation of the periods of the vibration modes of the structure (such software is commonly available).

account to be taken of the factors of the non-linear behaviour of a guyed mast (such software is less commonly available).

The first non-linear factor is that the stiffness of a guy rope is not constant. The stiffness varies with the tension. It is necessary therefore to have a cable element in the finite element library of the software. The stiffness matrix of the cable element contains terms which depend on the strain status of the element (geometric stiffness terms). A cable element is defined by the origin and extremity nodes, its length and its loading.

The second non-linear factor is that the displacements are generally not infinitely small so that the bar elements have to be described by a stiffness matrix, the terms of which depend on the displacement status (deformed stiffness terms).

It is not necessary to take into consideration the geometric stiffness terms of the bar elements if the calculation model contains a sufficient number of nodes (at least 5 nodes between two supports).

The calculation runs in which the above mentioned factors are taken into account are iterative ones and are executed independently for each loading combination. In the first step, the displacements are calculated with a cable stiffness corresponding to the initial tension and a bar element stiffness corresponding to nil displacements. The forces are calculated from the displacements.

In the second step, the stiffness matrix terms are modified in relation to the displacements and forces previously obtained. A new set of displacements and forces is calculated. The difference between the second step forces and the first step ones gives the equilibrium residuals. The forces and displacements due to the equilibrium residuals are calculated, using the second step stiffness matrix and added to those calculated at the first step.

The process continues until the residuals become negligible. The structure has then reached the deformed equilibrium status which corresponds to the considered loading combination.

The successive runs are generally:

equilibrium status research for the permanent loads and the initial tensions, which represents the final erection phase. The calculation gives the length of the cables to get the initial tensions for permanent loads.

To do that, a preliminary calculation model is used where the cable elements have the length of their chord in the unloaded status and where the anchoring node of each guy rope is free to displace along the chord. At the anchoring node of each cable, an external force equal to the initial tension is applied. The equilibrium length of a cable element is equal to the chord length plus the calculated displacement of the anchoring node.

research into the periods of vibration of the structure's modes around the equilibrium position for the permanent loads and the initial tensions. It is acceptable, for guyed masts, not to research the vibration mode periods around the deformed equilibrium position, loading case by loading case.

calculation of the wind loads, the dynamic part of which corresponds to the above calculated periods.

research of the deformed equilibrium status (displacements and forces) for each loading combination which is to be taken into consideration.

In the calculation model, the mast can be described in a detailed way (legs and truss bars) or in a global way (co-linear equivalent bars). In the global description, the influence of shear deformations is taken into account and also the eccentricity of the connections of the guy rope from the centre line of the mast.

4. SOME OTHER ASPECTS OF GUYED MASTS

4.1 In the Design Phase

The usual checks which norms and codes prescribe for steel structures have to be done from the results of the calculations mentioned in Section 3.2. They contain the following points in particular:

the displacements which have been calculated by non-linear runs have to be acceptable from the point of view of the performance of all supported equipment.

the design of a mast with a pinned foot must effectively permit the calculated rotations under loading.

the use of prestressed bolts is not absolutely necessary. In view of the difficulty of pre-stressing bolts (and of checking the prestress) at very high levels, bolts are often used without prestress. In such cases, the bolts have to be loaded in shear on their unthreaded part and placed in holes, the diameter of which is the bolt diameter plus 1mm (before protection).

in the calculation of the flanged connections, the prying effect should not be overlooked.

for masts of round hollow section, local studies are necessary of:

the mast foot

the reinforcement around apertures

the guy rope connection rings.

4.2 In the Manufacturing Phase

welding must be executed entirely by qualified welders. non-destructive tests must be executed on all tension welds. all the structure must be highly protected by galvanising or metal

spraying. the sockets of the guy ropes must be executed in workshop conditions

(not on site).

The current dimensions of the conical cavity of sockets to get a correct connection are:

diameter of the large part: 2,5 times the cable diameter

diameter of the narrow part: 1,15 times the cable diameter

height of the cavity: 5 times the cable diameter.

After the cable has been entered through the narrow part, it is bound for a distance of 5 diameters from the former. The wires are separated and bent over about 10 wire diameters in order to form a "flower" as regular as possible, the large diameter of which is about 2,5 times the cable diameter. The "flower" is entered in the socket. The socket is heated to about 200 C and then fulfilled with a molten alloy (electrolytic zinc or Pb - Zn - Sb alloy).

4.3 In the Erection Phase

The bottom part of the mast, e.g. four sections of about 6 metres each, is assembled at ground level and erected with a crane. This part is supported in its vertical position by temporary guy ropes, the tension of which has been calculated in the erection study.

An erection device is connected at the top of the erected part. It is used to lift the following section, either in one piece or face by face, or bar by bar, into position.

After the connection of the new mast section, the erection device is transferred to the 'new' top of the assembled part.

This operation is repeated section by section and the provisional guy ropes are placed as determined by the erection study.

When the level of the first permanent guy ropes is reached, they are mounted and their tension is adjusted to the calculated initial tension. The temporary guy ropes of the bottom part are removed.

After all the mast sections and permanent guy ropes have been assembled, the final adjustment of the tensions is made in order to ensure that:

the actual tensions correspond to the calculated ones the mast is in a vertical position.

The tension adjustment is made with a large diameter threaded bar which is placed between the bottom sock of the rope and the anchoring device through pins and flanges. The bar is aligned with the cables.

For the adjustment, the threaded bar is shunted by two parallel jacks.

The current tolerances for verticality are given by:

= cm for h 20m

5. CONCLUDING SUMMARY

Steel guyed masts may be designed specifically to meet the requirements of regional, national and international communications. Very high structures (up to 600 metres high) which are both light and stiff can be designed and built.

The component parts of a guyed mast are the foundations, the steel mast, the guy ropes, the structural accessories and the equipment.

The design of guyed masts contains two main steps, initial dimensioning and final dimensioning and checking. The final values for forces and strains are calculated by computers taking account of non-linear behaviour.

There are other detailed aspects in the design, manufacturing and erection phases of a guyed mast which require careful preparation and checking in order to achieve a mast which meets its performance requirements.

6. ADDITIONAL READING

1. Recommendations for Guyed Masts, International Association for Shell and Spacial Structures, IASS Madrid 1981.

2. Davenport, A. G. and Steels, G. N., "Dynamic Behaviour of Massive Guy Cables", ASCE Str. Div. July 1991.

3. BS 8100 Part 4, Code of Practice for Lattice Masts (in draft) 4. Davenport, A. G. and Sparling, B. F., "Dynamic Gust Response Factors

for Guyed Masts", J Wind Eng & Ind Aerodynamics 41-44, 1992. 5. ANSI/EIA Standard EIA-22-D Structural Standards for Steel Antenna

Towers, Electronic Industries Association, Washington DC, 1987.

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