Finite element seismic analysis of a guyed mast

1. 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

2. Synopsis • Introduction • Key features of guyed masts • Objectives • Modelling • Cable properties • Loading • Results • Modal analysis • Seismic response • Comparison with static wind analysis • Conclusions

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

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

10. 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

11. Shear force 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

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

13. Cable tensions

14. 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

15. 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