ANALYSIS AND DESIGN OF THE PRINCIPAL AUXILARY …

Proceedings of the 6th International Conference on Mechanics and Materials in Design,

Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26

PAPER REF: 5682

ANALYSIS AND DESIGN OF THE PRINCIPAL AUXILARY TESTING

STRUCTURE OF A TOWER TESTING STATION IN PORTUGAL

PART II

Fábio Paiva1, Jorge Henriques

1, R

1Department of Civil Engineering (DE(*)Email: [email protected]

ABSTRACT

This work comes as Part II, of the work, that describes the analysis and design process of the

principal auxiliary testing structure of a tower testing station in Portugal (Trofa).

principal auxiliary structure, as a key element of the testing station, is in this part II,

conveniently characterized in terms of the numerical model used, types of analysis (elastic

linear and non-linear, buckling analysis) and design methodology acc

Eurocodes part 3 (steel structures).

during the design process of the principal auxiliary testing structure.

Keywords: Special Lattice Towers, Non

INTRODUCTION

As stated in Part I of this two part paper

tower to be tested, auxiliary testing structures are necessary (Paiva, 2013).

entirely in the principal auxiliary testing struct

The structure was modelled in Autodesk Robot Structural Analysis 2014.

Fig. 1 - Principal Auxiliary Testing

e)

f)

20 m

60 m


Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26-30 July 2015

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STRUCTURE OF A TOWER TESTING STATION IN PORTUGAL

, Rui C. Barros1(*)

(DEC), University of Porto, Porto, Portugal

his work comes as Part II, of the work, that describes the analysis and design process of the

principal auxiliary testing structure of a tower testing station in Portugal (Trofa).



linear, buckling analysis) and design methodology acc

Eurocodes part 3 (steel structures). This paper concludes with the difficulties experienced

during the design process of the principal auxiliary testing structure.

Lattice Towers, Non-Linear Analysis, Design, Eurocodes

two part paper (Paiva, 2015), to enable a horizontal loading on the

tower to be tested, auxiliary testing structures are necessary (Paiva, 2013).

entirely in the principal auxiliary testing structure. The numerical model is shown in Figure 1.

The structure was modelled in Autodesk Robot Structural Analysis 2014.

Principal Auxiliary Testing Structure Phase 1 (Left) and Phase 2 (Right) (letter a) to f) identifies

different types of elements)

a)

b)

c)

d)

100 m

40 m


STRUCTURE OF A TOWER TESTING STATION IN PORTUGAL -

his work comes as Part II, of the work, that describes the analysis and design process of the

principal auxiliary testing structure of a tower testing station in Portugal (Trofa). The



linear, buckling analysis) and design methodology according with the

This paper concludes with the difficulties experienced

Linear Analysis, Design, Eurocodes.

(Paiva, 2015), to enable a horizontal loading on the

tower to be tested, auxiliary testing structures are necessary (Paiva, 2013). This part II, focus

ure. The numerical model is shown in Figure 1.

Structure Phase 1 (Left) and Phase 2 (Right) (letter a) to f) identifies

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Analysis Design and Testing of Towers and Poles

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The structure was designed to satisfy two phases. The first phase (Figure 1), the structure has

60 m tall and 20 m width, in the final phase (phase 2) the structure achieves a total of 100 m

height and a width of 40 m.

The principal auxiliary testing tower can be described as structure formed by the association

of vertical trusses (2 in phase 1 and 4 in phase 2) in the principal loading direction (plane

ZX). In the perpendicular direction (plane ZY) a X bracing system between the center vertical

trusses provides sufficient stiffness and resistance for the structure (wind load direction).

Additionally, horizontal trusses (element type e)) with a constant space of 20m in height,

allows the connection of the structure at a horizontal level. All the cable loading is applied

through the lower chord (only at the nodes) of the horizontal truss mentioned. Each structural

member of the vertical truss is a built-up members composed of angle sections, except the

members that form the horizontal truss between the vertical trusses, these ones are formed

from hollow sections (square or rectangular). The structure is then conveniently anchored to

several reinforced concrete foundations, each to the base built-up member type a) and c). All

structural elements are in galvanised steel (type S355) and painted after the mounting.

A huge number of combinations for all the action were considered (self-weight, temperature,

wind, cable loads), according with the Eurocode 0 (EN 1990, 2002). In the next step, through

linear and non-linear static analysis the structure was calculated, the non-linear behaviour of

structure results of the bracing system (tension only elements).

For the design of the testing structure, many parts of Eurocode 3 were used, like part

Eurocode 3-1-1, 3-1-5, 3-1-8, 3-1-11 and 3-3-1 (EN 1993-1-1, 2005; EN 1993-1-5, 2006; EN

1993-1-8, 2006; EN 1993-1-11, 2006 and EN 1993-3-1, 2006).

NUMERICAL MODEL

The carrying structure, as mentioned, is made of a trussed framework, whose elements,

mainly based on single L angles (except hollow sections-profiles for the horizontal truss-

element type e)) are joined by bolted connections, constituting each a built-up beam-column.

The built-up members are realised by means of cross-section arrangements (Figure 2), type L

(for the main comer legs, diagonal and horizontal members), DL-arrangement (some bar in

the intersections between structural members, like a) and b) element types). Rod bar elements

(a total of 2 elements per level) in the OZY plane, provides adequate stiffness in that

direction, mainly because of wind loading. This means that the structure displays a non-linear

behaviour in the same direction. In the OZX plane, the direction where cable are applied, the

association of the different type of elements (a),b),c) and d)) constitute a global vertical truss,

which provided sufficient stiffness and resistance for the structure. It can also be said, that if

the cable loads are applied only through the plane ZX, the structure behave linearly (the rod

bar elements are for that situation nearly with no stress).

Fig. 2 - Different arrangements used for the built-up members



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In Figure 3 the main connections between the many built-up members are identified,

beginning in detail A and finishing in detail I. The details of each connections are shown in

Table 1 to Table 3, for an illustrative clarification. The connections in all the details results

basically from an overlapping of angle members in each intersection (by the built-up

members) which are then bolted at fixed pitch. Additionally steel plates are welded to some

bars in the connection, with the purpose of increasing node stiffness, reduce stress

concentration between elements and to provide greater stability to all adjoining bars.

Fig. 3 - Vertical truss (formed by built-up members) and details of the major connections

Table 1 - Details of connections A to C

Detail A Detail B Detail C

Detail A Detail B Detail C Detail D Detail E

Detail F

Detail G

Detail H

Detail I

Bar

overlapping

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Table 2 - Details of connections D to F

Detail D Detail E Detail F

Table 3 - Details of connections G to I

Detail G Detail H Detail I



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The structural analysis has been carried out by modelling the structure through a FEM model:

the complete scheme (final phase) required as much as 15639 structural joints, for a total of

93834 degree of freedom, using 9205 beam elements (for the corner legs and other passing

main connections), 16 truss elements and 80 shell elements.

For the simulations, the overall auxiliary testing structure can be considered as an assembly of

self-supporting four-legged steel lattice towers (with majority of angle members) – normally

built on ground. A general view of the model geometry is shown in Figure 1. The structure is

modelled as non-linear elastic, three-dimensional frame structures with frame elements for the

main legs, diagonal and horizontal members. The rod elements (type f) elements) are

responsible for the non-linear behaviour of the structure. The supports are assumed to be

pinned at the base.

TYPES OF ANALYSIS PERFORMED

Static analysis, linear and non-linear, of the structure has been carried out using the loads

prescribed by the Eurocodes as described in Part I of this paper. Stresses, deformations and

overall displacements have been assessed for all the combinations (only a few structural

deformed shapes are shown in this work). Three incident incoming wind directions have been

taken into consideration, in the next Figure 4 and Figure 5deformed shapes for wind load in x

and y direction are shown.

A non-linear analysis consists in the incremental applications of loads, the software used for

the structural analysis was Autodesk Robot Structural Analysis 2014 (Robot Structural

Analysis, 2014). During calculations, loads are not considered at a specific time, but they are

gradually increased and solutions to successive equilibrium states are performed. The non-

linear behaviour of a structure can be caused by a single structure element

(compression/tension elements, cable elements or non-linear constraints) or by non-linear

force deformation relation in the whole structure (geometric non-linearity). For the present

structure the non-linear behaviour results from the rod elements (elements type f)), and not

from the geometric non-linearities.

The method used to solve a system of non-linear equations was the incremental method. As

the present structure includes non-linear elements, the calculations are performed applying the

incremental method. With the incremental method, the right-hand load vector is divided into n

equal increments. A consecutive load increment is applied to the structure once the state of

equilibrium for the previous increment is achieved. The norm of unbalanced forces is

specified for each step, allowing for monitoring of the structure force-deformation relations.

The load increment is used when dividing a load into smaller segments, in this case 5 load

increments were used, with a maximum of 40 iteration per increment. The algorithm used to

solve the non-linear problem was the modified Newton-Raphson method, where exists only a

matrix update after each subdivision, and not after each iteration. The algorithm of the

Broyden-Fletcher-Goldforb-Shanno procedure modifies the stiffness matrix during

calculations. When the state of equilibrium is achieved, the iteration process stops, and the

convergence of the process is checked. The displacement increments dUn and the unbalanced

forces dFn are essentially zero, or sufficiently small in comparison with the tolerance

parameters for both values, for this case a value of 0,0001 was defined (Robot Structural

Analysis, 2014).

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Fig. 4 - Non-linear static analysis deformed shape for wind load in +x directions (3D and plan views)

Fig. 5 - Non-linear static analysis deformed shape for wind load in +y directions (3D and plan views)



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In Figure 6the deformed shapes for temperature load (+ and -) are shown.

Fig. 6 - Non-linear static analysis deformed shape for temperature load + (left) and – (right)

For the next deformed shapes, a few of the many load combinations, taking the cable load as

the leading variable load, are described. The load combinations are defined by Eurocode 0

(paper I). The wind load is drastically reduced during the test of the structures, because the

wind velocity was limited to a lower value.

Table 4 - Partial factors on actions for the ultimate limit states for persistent design situations, for the case where

the load cable 1a is the leading variable action

Leading load- Cable

load 1a

Permanent

actions Wind load Temperature load Cable load

Combination 25 1,10 0,03

Wind in y direction

0,84

Temperature+

2,0

Load applied at level 40m;

With an eccentricity 5.4m relative to

the center of the structure


Wind in y direction

0,84

Temperature+

2,0





Wind in y direction

0,84

Temperature+

2,0




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Fig. 7 - Linear static analysis deformed shape for a combination, with load cable 1a as the leading load,

combination 25 (left), 41 (center) and 73 (right)


the load cable 2-1 is the leading variable action

Leading load- Cable

load 2-1

Permanent



Wind in y direction

0,84

Temperature+

2,0

Loads applied at level 20-40m;

With spacing 3.6m between loads


Wind in y direction

0,84

Temperature+

2,0




Wind in y direction

0,84

Temperature+

2,0



Fig. 8 - Linear static analysis deformed shape for a combination, with load cable 2-1 as the leading load,




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the load cable 3b is the leading variable action

Leading load- Cable

load 3b

Permanent



Wind in y direction

0,84

Temperature+

2,0

Loads applied at level 40m;



Wind in y direction

0,84

Temperature+

2,0




Wind in y direction

0,84

Temperature+

2,0



Fig. 9 - Linear static analysis deformed shape for a combination, with load cable 3b as the leading load,


A buckling analysis has been performed to assess the safety degree of the structure towards

the instability phenomena, looking for a certain number of critical modes up to the instability

of one or more members in the structure. The classical linear stability analysis is based on the

imposition of the following condition:

where Ke, is the stiffness tangent matrix of the structure, while Kg is the geometric stiffness

matrix as a function of the stress state. From the above linear eigenvalue problem, the critical

load external factors and the corresponding critical modes are achieved. The method of block

subspace iteration is used to solve the generalized eigenproblem. The method of block

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subspace iteration consists in simultaneous iterations of a vector in subspace with a

determined dimension. Each vector for which the process of convergence has been performed

is removed from the working subspace and a new start vector is added in its place.

Orthogonality of the vectors is assured in each iterative step (Robot Structural Analysis,

2014).

The stability analysis has pointed out for the first critical mode, a critical mode related with

bars at node G at 40 m of height (local instability mode). For the critical mode 2 the bars at

node G also suffer local instability. Table 8 resume the critical parameters found for the

configurations with diagonal wind load, for the critical combination. These critical parameters

correspond to local instability of the bars generally at the major nodes identified in Figure 3.

The partial factors on actions for the critical combination, correspond to the values indicated

in Table 7.


the wind load is the leading variable action

Leading load- Wind load Permanent

actions Wind load Temperature load

Combination 10557 1,10

1,4

Wind at -45º direction

in XY Plan

0,84

Temperature+

Table 8 - Critical modes and critical loads factor of the buckling analysis

Nº critical mode Load factor

Combination 10557

1 2,85

2 3,02

3 3,05

4 3,16

5 3,36

DESIGN METHODOLOGY ACCORDING WITH EUROCODE 3

Structural members may be present as individual members or as part of the planar sub-

assemblage of a structure. Individual members are rarely encountered in practice. They

interact with the other members of the structure only in the case that they are loaded by them

or transfer their support reaction to them. Therefore, normally all members build part of the

overall structure, and a great number of them are beam– columns which are loaded by axial

forces and bending moments at the same time. The borderline cases are columns that are



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loaded by axial forces only and beams that are loaded by bending moments only (Lindner,

2000).

The ultimate states of the members were verified according with the Eurocode 3-1-1, 3-1-5

and 3-1-8. For that the following resistance were checked against the internal forces:

• resistance of cross-sections;

• resistance of members to instability assessed by member checks;

• resistance of joints;

A significant percentage of the angle bars of the built-up members were classified as section 3

and 4 class. Class 4 cross-section demands the calculation of the effective cross-sections

properties (area and section modulus), for that Eurocode 3-1-5 was required.

Particular attention was paid to the realization and to the criterions of verification of the

connections between the main structural elements (corner legs and diagonal elements). Many

structural connections were analyzed, in order to guarantee safety, reliability and durability,

by means of approaches defined Eurocode 3-1-8. These connections are designed under the

condition that they are able to transfer the maximum forces determined by the structural

analysis. Particular attention was also paid to the major nodes identified in Figure 3,

principally the connection between the steel panels and the bars. The overlapping bolted bars

that constitute the connection between built-up members, as shown in Table 1, were carefully

studied. Hollow section joints were also verified with part 7 of Eurocode 3-1-8, the horizontal

truss (member type e)) was built with rectangular and square hollow members. The static

design resistances of the joints in the horizontal truss, are expressed in terms of maximum

design axial and/or moment resistances for the brace members, and for the present work, these

are determined from uniplanar joints in lattice structure, with type of joints N, KT and T.

CONCLUSIONS

The part II of this work, completes the analysis and design process undertaken in part I.

Regarding part I of this work, the main difficulties felted, were due to the wind load

quantification, basically the complex surrounding topography of the structure and its

geometry generated situations that were not strictly within the scope of the code. Therefore

some simplification were needed for the assessment of the wind load.

Moreover the global stability analysis showed how the structural reliability is suitably assured

with regard to variable loads (wind, cable and temperature loads). Only local modes of

instability were detected in the first 100 buckling modes.

Probably, the major difficulty faced during the design, was the large amount of time taken to

verify the resistance of the numerous cross sections (cross-section class 3 and 4) and the

buckling resistance of each member as defined in Eurocode 3-1-1. Finally, specific attention

has been focused in joint design of the main elements. The connection of the corner legs has

been designed to guarantee the continuity of the cross-section. The others joints were verified

to comply with the requirements stated in Eurocode 3-1-8.

ACKNOWLEDGMENTS

This work was co-participated by funds from the project “VHSSPOLES-Very High Strength

Steel Poles” (Faculty of Engineering of the University of Porto, reference 21518) sponsored

by the European Fund for Regional Development (FEDER) through COMPETE (Operational

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Program Competitiveness Factors - POFC). The Authors acknowledge the financial support

and the opportunity to contribute to the development of the transmission towers testing site of

Metalogalva (Trofa, Portugal).

REFERENCES

[1]-Paiva F, Henriques J, Barros R.C. Analysis and design of the Principal Auxiliary testing

structure of a Tower Testing Station in Portugal - Part I. Recent Advances in Mechanics and

Materials in Design, Ponta Delgada/Azores, 26-30 July 2015.

[2]-Paiva F, Henriques J, Barros R.C. Review of Transmission Tower Testing Stations around

the World. Modern Building Materials, Structures and Techniques, 2013.

[3]-EN 1990: Eurocode 0: Basis of structural design, Brussel (Belgium): CEN Central

Secretaria, Rue de Stassart 36, B-1050, 2002.

[4]-EN 1993-1-1: Eurocode 3: Design of Steel Structures, Part 1-1: General Rules and Rules

for buildings. Brussel (Belgium): CEN Central Secretaria, Rue de Stassart 36, B-1050, 2005.

[5]-EN 1993-1-5: Eurocode 3: Design of Steel Structures, Part 1-5: Plated structural elements.

Brussel (Belgium): CEN Central Secretaria, Rue de Stassart 36, B-1050, 2006.

[6]-EN 1993-1-8: Eurocode 3: Design of Steel Structures, Part 1-8: Design of Joints. Brussel

(Belgium): CEN Central Secretaria, Rue de Stassart 36, B-1050, 2006.

[7]-EN 1993-1-11: Eurocode 3: Design of Steel Structures, Part 1-11: Design of structures

with tension components. Brussel (Belgium): CEN Central Secretaria, Rue de Stassart 36, B-

1050, 2006.

[8]-EN 1993-3-1: Eurocode 3: Design of Steel Structures, Part 3-1: Towers, masts and

chimneys-Tower and Masts. Brussel (Belgium): CEN Central Secretaria, Rue de Stassart 36,

B-1050, 2006.

[9]-Autodesk Robot Structural Analysis. Users Guide, 2014.

[10]-Lindner J. Stability of structural members General Report. Journal of Constructional

Steel Research 55, 29–44, 2000.

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ANALYSIS AND DESIGN OF THE PRINCIPAL AUXILARY …