Finite element seismic analysis of a guyed mast

Matthew GreyMartin 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)

Rea

ctio

n (k

N)

SAP2000

Goldberg

Davenport

Sparling

Zero SagEC8

Axial force-displacement characteristic of catenary cable and comparison with theory

Lateral force-displacement characteristic of a stay cluster

Cables in this case are prestressed to approx. 90% of max stiffness

Loading

Wind loading – BS8100 patch load method – wind speeds of 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 90Height (m)

Ben

ding

mom

ent

(kN

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 90Height (m)

Ben

ding

mom

ent

(kN

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)

She

ar F

orce

(kN

)

0

50

100

0 30 60 90Height (m)

She

ar F

orce

(kN

)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)

Mas

t B

ase

She

ar (

kN)

100

200

300

2 3 4

PGA (m/s2)

Tot

al B

ase

She

ar (

kN)

1000

1200

1400

2 3 4

PGA (m/s2)

Bas

e A

xial

For

ce (

kN)

Mast base shear:

Total base shear (mast plus cables):

Mast base axial force:

El CentroEC8ParkfieldWind

Cable tensions

Cable Wind EC8-2.5 m/s2 EC8-4 m/s2 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/s2 max min max min

A1 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

Fo

rce

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