finite element seismic analysis of a guyed mast

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Finite element

seismic analysisof a guyed mast

Matthew Grey

Martin Williams

Tony Blakeborough

First European Conference on Earthquake Engineering and Seismology

Geneva, September 2006

Paper 1189

Structural Dynamics Research Group

Department of Engineering Science

University of Oxford



Synopsis

Introduction

Key features of guyed masts

Objectives

Modelling

Cable properties Loading

Results

Modal analysis

Seismic response Comparison with static wind analysis

Conclusions



Key features of guyed masts

Support broadcasting equipment

at 100 – 600 m above ground

Slender lattice structure

supported by inclined,

prestressed cables

Cable supports may be 400 m

from base of mast

Mass of ancillaries is significant

Seismic loading normally

assumed less onerous than wind



Objectives

Assess magnitude and distribution of forces developed

under seismic loading

Compare forces due to seismic and design wind events

Identify trends and indicators for use in preliminary design Evaluate effects of asynchronous ground motions

Assess significance of vertical seismic motions

Assess suitability of linear response spectrum analysis



Modelling

Four guyed masts with heights up to 314 m analysed using

SAP2000

This paper focuses on the shortest mast – 99.88 m

Mast data supplied by Flint and Neill Partnership, UK,masts designed according to BS8100

Analysed under:

indicative wind load using the equivalent static patch load

method non-linear time-history analysis under earthquakes of varying

magnitudes



Structural model of a mast

Mast lattice modelled by

equivalent beam elements

0 500

Mass distribution (kg/m)

Mast

Mast + ancillariesCable catenary modelled by

~80 beam elements

Prestress applied by iterative

procedure of applying

temperature loads



Cable properties

0

10

20

30

40

0 0.1 0.2 0.3

Displacement (m)

R e a c t i o n ( k N )

SAP2000

Goldberg

Davenport

Sparling

Zero SagEC8

Axial force-displacementcharacteristic of catenary cable

and comparison with theory

Lateral force-displacementcharacteristic of a stay cluster

Cables in this case are prestressed

to approx. 90% of max stiffness



Loading

Wind loading – BS8100 patch load method – wind speedsof 20, 23 and 28 m/s

Earthquake records scaled to PGA of 2.5 – 4.0 m/s2

El Centro 1940

Parkfield 1966

Artificial accelerogram compatible with EC8 type 1 spectrum,ground type C

3D motion used

Non-linear time history analysis using Newmark’s method



Linear mode shapes

1 2 3 4 5 6Mode:

0.60Period (s): 0.55 0.49 0.46 0.40 0.39

Modes occur in orthogonal pairs

Numerous mast modes in period range of interest

Also numerous cable modes



Bending moment envelopes

0

100

200

300

400

500

0 30 60 90

Height (m)

B e n d i n g m o m e n

t ( k N m )

3 m/s2

2.5 m/s2

3.5 m/s2

4 m/s2

Wind 23 m/s

Wind 20 m/s

0

100

200

300

400

500

0 30 60 90

Height (m)

B

e n d i n g m o m e n t ( k N m )

3 m/s2

2.5 m/s2

3.5 m/s2

4 m/s2

Wind 23 m/s

Wind 20 m/s

El Centro:

EC8:



0

50

100

0 30 60 90Height (m)

S h e a r F o r c e

( k N )

0

50

100

0 30 60 90Height (m)

S h e a r F o r c e ( k N )

Shear force envelopes

3 m/s2

2.5 m/s2

3.5 m/s2

4 m/s2

Wind 23 m/s

Wind 20 m/s

3 m/s2

2.5 m/s2

3.5 m/s2

4 m/s2

Wind 23 m/s

Wind 20 m/s

El Centro:

EC8:



Base forces

0

20

40

60

2 3 4

PGA (m/s2

)

M a s t B a s e S h e

a r ( k N )

100

200

300

2 3 4

PGA (m/s2

)

T o t a l B a s e S h e a r ( k N )

1000

1200

1400

2 3 4

PGA (m/s2)

B a s e A x i a l F o r c e ( k N )

Mast base

shear:

Total base shear

(mast plus cables):

Mast base

axial force:

El CentroEC8ParkfieldWind



Cable tensions

Cable Wind EC8-2.5 m/s EC8-4 m/s

23 m/s max min max min

A1 211.1 125.0 29.8 166.6 10.9

B1 351.7 168.3 37.5 252.7 21.5

C1 344.9 218.0 60.9 283.3 49.0

El Centro-2.5 m/s2

El Centro-4 m/s2

max min max min

A1 211.1 138.3 13.7 167.7 -2.8

B1 351.7 168.0 29.3 198.0 -1.3

C1 344.9 190.2 82.1 222.2 51.3

Parkfield-2.5 m/s2 Parkfield-4 m/s

2

max min max minA1 211.1 135.1 24.7 166.6 -5.3

B1 351.7 170.3 63.6 209.0 46.5

C1 344.9 176.3 100.6 199.7 79.2

Displacement

F o r c e



Conclusions

Mass of mast ancillaries has a significant effect on dynamic

response

In spite of the non-linearities present, mast behaviour under

seismic loads shows broadly linear trends with PGA

With PGA of 4 m/s2 mast bending response approaches and

at some points exceeds that under design wind load of 23 m/s

Mast shear and cable tension remain below values due to

design wind moment

Earthquake loading may be more onerous than wind in areas

of high seismicity and/or low design wind speed



Other/ongoing work

Development of simple formulae giving preliminary estimates

of natural period and key response parameters

Assessment of applicability of linear response spectrum

analysis approach

Effect of asynchronous ground motions between mast and

cable support points

Importance of vertical ground motion for overall seismic

response

finite element seismic analysis of a guyed mast

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