First European Conference on Earthquake Engineering and Seismology

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 n Introduction Key features of guyed masts ¨ Objectives ¨ n Modelling Cable properties ¨ Loading ¨ n Results Modal analysis ¨ Seismic response ¨ Comparison with static wind analysis ¨ n Conclusions

Key features of guyed masts n Support broadcasting equipment at 100 – 600 m above ground n Slender lattice structure supported by inclined, prestressed cables n Cable supports may be 400 m from base of mast n Mass of ancillaries is significant n Seismic loading normally assumed less onerous than wind

Objectives n Assess magnitude and distribution of forces developed under seismic loading n Compare forces due to seismic and design wind events n Identify trends and indicators for use in preliminary design n Evaluate effects of asynchronous ground motions n Assess significance of vertical seismic motions n Assess suitability of linear response spectrum analysis

Modelling n Four guyed masts with heights up to 314 m analysed using SAP 2000 n This paper focuses on the shortest mast – 99. 88 m n Mast data supplied by Flint and Neill Partnership, UK, masts designed according to BS 8100 n 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 n Wind loading – BS 8100 patch load method – wind speeds of 20, 23 and 28 m/s n Earthquake records scaled to PGA of 2. 5 – 4. 0 m/s 2 ¨ El Centro 1940 ¨ Parkfield 1966 ¨ Artificial accelerogram compatible with EC 8 type 1 spectrum, ground type C n 3 D motion used n Non-linear time history analysis using Newmark’s method

Linear mode shapes n Modes occur in orthogonal pairs n Numerous mast modes in period range of interest n Also numerous cable modes

Bending moment envelopes El Centro: Wind 23 m/s 4 m/s 2 3. 5 m/s 2 3 m/s 2 2. 5 m/s 2 Wind 20 m/s EC 8: Wind 23 m/s 4 m/s 2 3. 5 m/s 2 3 m/s 2 2. 5 m/s 2 Wind 20 m/s

Shear force envelopes El Centro: Wind 23 m/s 4 m/s 2 3. 5 m/s 2 3 m/s 2 2. 5 m/s 2 Wind 20 m/s EC 8: Wind 23 m/s 4 m/s 2 3. 5 m/s 2 3 m/s 2 2. 5 m/s 2 Wind 20 m/s

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

Cable tensions

Conclusions n Mass of mast ancillaries has a significant effect on dynamic response n In spite of the non-linearities present, mast behaviour under seismic loads shows broadly linear trends with PGA n With PGA of 4 m/s 2 mast bending response approaches and at some points exceeds that under design wind load of 23 m/s n Mast shear and cable tension remain below values due to design wind moment n Earthquake loading may be more onerous than wind in areas of high seismicity and/or low design wind speed

Other/ongoing work n Development of simple formulae giving preliminary estimates of natural period and key response parameters n Assessment of applicability of linear response spectrum analysis approach n Effect of asynchronous ground motions between mast and cable support points n Importance of vertical ground motion for overall seismic response