Author: Design of masts
Design of masts
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 crosssection. 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.
In this first 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.
- 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).
In the secound step, the difficulty arises from the interdependence of the values of the actions and of the choice of the sections.
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.
Masts can be designed according to Eurocode 3
Eurocode - resources - http://www.eurocode-resources.com/