Finite element seismic analysis of a guyed mast First European Conference on Earthquake Engineering and Seismology Geneva, September 2006 Paper 1189 Finite element seismic analysis of a guyed mast Matthew Grey Martin Williams Tony Blakeborough Structural Dynamics Research Group Department of Engineering Science University of Oxford

Synopsis Introduction Modelling Results Conclusions 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 Cable catenary modelled by ~80 beam elements Prestress applied by iterative procedure of applying temperature loads

Cable properties 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 Modes occur in orthogonal pairs Numerous mast modes in period range of interest Also numerous cable modes

Bending moment envelopes El Centro: Wind 23 m/s 4 m/s2 3.5 m/s2 3 m/s2 2.5 m/s2 Wind 20 m/s EC8: Wind 23 m/s 4 m/s2 3.5 m/s2 3 m/s2 2.5 m/s2 Wind 20 m/s

Shear force envelopes El Centro: EC8: Wind 23 m/s 4 m/s2 3.5 m/s2

Base forces Mast base shear: Total base shear (mast plus cables): Mast base axial force:

Cable tensions

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