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Towers, chimneys and masts

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Along-wind response - gust response factor. The gust response factors for base ... The gust response factors for b.m. and shear depend on the height of the load ... – PowerPoint PPT presentation

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Title: Towers, chimneys and masts


1
Towers, chimneys and masts
  • Wind loading and structural response
  • Lecture 21 Dr. J.D. Holmes

2
Towers, chimneys and masts
  • Slender structures (height/width is high)
  • Mode shape in first mode - non linear
  • Higher resonant modes may be significant
  • Cross-wind response significant for circular
    cross-sections

critical velocity for vortex shedding ?
5n1b for circular sections
10
n1b for square sections - more frequently
occurring wind speeds than for square sections
3
Towers, chimneys and masts
  • Drag coefficients for tower cross-sections

Cd 2.2
Cd 1.2
Cd 2.0
4
Towers, chimneys and masts
  • Drag coefficients for tower cross-sections

Cd 1.5
Cd 1.4
Cd ? 0.6 (smooth, high Re)
5
Towers, chimneys and masts
  • Drag coefficients for lattice tower sections

e.g. square cross section with flat-sided
members (wind normal to face)
ASCE 7-02 (Fig. 6.22) CD 4?2 5.9?
4.0
? solidity of one face area of members ?
total enclosed area
includes interference and shielding effects
between members
( will be covered in Lecture 23 )
6
Towers, chimneys and masts
  • Along-wind response - gust response factor

Shear force Qmax ?Q. Gq
Bending moment Mmax ?M. Gm
Deflection xmax ?x. Gx
The gust response factors for base b.m. and tip
deflection differ - because of non-linear mode
shape
The gust response factors for b.m. and shear
depend on the height of the load effect, z1 i.e.
Gq(z1) and Gm(z1) increase with z1
7
Towers, chimneys and masts
  • Along-wind response - effective static loads

Separate effective static load distributions for
mean, background and resonant components
(Lecture 13, Chapter 5)
8
Towers, chimneys and masts
  • Cross-wind response of slender towers

For lattice towers - only excitation mechanism is
lateral turbulence
For solid cross-sections, excitation by vortex
shedding is usually dominant (depends on wind
speed)
Two models i) Sinusoidal excitation
ii) Random excitation
Sinusoidal excitation has generally been applied
to steel chimneys where large amplitudes and
lock-in can occur - useful for diagnostic check
of peak amplitudes in codes and standards
Random excitation has generally been applied to
R.C. chimneys where amplitudes of vibration are
lower. Accurate values are required for design
purposes. Method needs experimental data at high
Reynolds Numbers.
9
Towers, chimneys and masts
  • Cross-wind response of slender towers

Sinusoidal excitation model
  • Assumptions
  • sinusoidal cross-wind force variation with
    time
  • full correlation of forces over the height
  • constant amplitude of fluctuating force
    coefficient

Deterministic model - not random
Sinusoidal excitation leads to sinusoidal
response (deflection)
10
Towers, chimneys and masts
  • Cross-wind response of slender towers

Sinusoidal excitation model
Equation of motion (jth mode)
?j(z) is mode shape
11
Towers, chimneys and masts
  • Sinusoidal excitation model

Representing the applied force Qj(t) as a
sinusoidal function of time, an expression for
the peak deflection at the top of the structure
can be derived
(see Section 11.5.1 in book)
Strouhal Number for vortex shedding ze
effective height (? 2h/3)
(Scruton Number or mass-damping parameter) m
average mass/unit height
12
Towers, chimneys and masts
  • Sinusoidal excitation model

This can be simplified to
The mode shape ?j(z) can be taken as (z/h)?
For uniform or near-uniform cantilevers, ? can be
taken as 1.5 then k 1.6
13
Towers, chimneys and masts
  • Random excitation model (Vickery/Basu)
    (Section 11.5.2)

Assumes excitation due to vortex shedding is a
random process
lock-in behaviour is reproduced by negative
aerodynamic damping
Peak response is inversely proportional to the
square root of the damping
In its simplest form, peak response can be
written as
A a non dimensional parameter constant for a
particular structure (forcing terms)
Kao a non dimensional parameter associated with
aerodynamic damping
yL limiting amplitude of vibration
14
Towers, chimneys and masts
  • Random excitation model (Vickery/Basu)

Three response regimes
Lock in region - response driven by aerodynamic
damping
15
Towers, chimneys and masts
  • Scruton Number

The Scruton Number (or mass-damping parameter)
appears in peak response calculated by both the
sinusoidal and random excitation models
Sometimes a mass-damping parameter is used Sc
/4? Ka
Clearly the lower the Sc, the higher the value of
ymax / b (either model)
Sc (or Ka) are often used to indicate the
propensity to vortex-induced vibration
16
Towers, chimneys and masts
  • Scruton Number and steel stacks

Sc (or Ka) is often used to indicate the
propensity to vortex-induced vibration
e.g. for a circular cylinder, Sc gt 10 (or Ka gt
0.8), usually indicates low amplitudes of
vibration induced by vortex shedding for circular
cylinders
American National Standard on Steel Stacks (ASME
STS-1-1992) provides criteria for checking for
vortex-induced vibrations, based on Ka
Mitigation methods are also discussed helical
strakes, shrouds, additional damping (mass
dampers, fabric pads, hanging chains)
A method based on the random excitation model is
also provided in ASME STS-1-1992 (Appendix 5.C)
for calculation of displacements for design
purposes.
17
Towers, chimneys and masts
  • Helical strakes

For mitigation of vortex-shedding induced
vibration
Eliminates cross-wind vibration, but increases
drag coefficient and along-wind vibration
18
Towers, chimneys and masts
  • Case study Macau Tower

Concrete tower 248 metres (814 feet) high Tapered
cylindrical section up to 200 m (656 feet)
16 m diameter (0 m) to 12 m diameter (200 m)
  • Pod with restaurant and observation decks
  • between 200 m and 238m
  • Steel communications tower 248 to 338 metres (814
    to 1109 feet)

19
Towers, chimneys and masts
  • Case study Macau Tower

aeroelastic model (1/150)
20
Towers, chimneys and masts
  • Case study Macau Tower
  • Combination of wind tunnel and theoretical
    modelling of tower response used
  • Effective static load distributions
  • distributions of mean, background and resonant
    wind loads derived (Lecture 13)
  • Wind-tunnel test results used to calibrate
    computer model

21
Towers, chimneys and masts
  • Case study Macau Tower

Wind tunnel model scaling
  • Length ratio Lr 1/150
  • Density ratio ?r 1
  • Velocity ratio Vr 1/3

22
Towers, chimneys and masts
  • Case study Macau Tower

Derived ratios to design model
  • Bending stiffness ratio EIr ?r Vr2 Lr4
  • Axial stiffness ratio EAr ?r Vr2 Lr2
  • Use stepped aluminium alloy spine to model
    stiffness of main shaft and legs

23
Towers, chimneys and masts
  • Case study Macau Tower

Mean velocity profile
24
Towers, chimneys and masts
  • Case study Macau Tower

Turbulence intensity profile

25
Towers, chimneys and masts
Case study Macau Tower Wind tunnel test
results - along-wind b.m. (MN.m) at 85.5 m (280
ft.)
26
Towers, chimneys and masts
Case study Macau Tower Wind tunnel test
results - cross-wind b.m.(MN.m) at 85.5 m (280
ft.)

27
Towers, chimneys and masts
Case study Macau Tower
  • Along-wind response was dominant
  • Cross-wind vortex shedding excitation not strong
    because of complex pod geometry near the top
  • Along- and cross-wind have similar fluctuating
    components about equal, but total along-wind
    response includes mean component

28
Towers, chimneys and masts
Case study Macau Tower
Along wind response
  • At each level on the structure define equivalent
    wind loads for
  • mean wind pressure
  • background (quasi-static) fluctuating wind
    pressure
  • resonant (inertial) loads
  • These components all have different distributions
  • Combine three components of load distributions
    for bending moments at various levels on tower
  • Computer model calibrated against wind-tunnel
    results

29
Towers, chimneys and masts
Case study Macau TowerDesign graphs
30
Case study Macau Tower Design graphs
Towers, chimneys and masts
31
End of Lecture 21John Holmes225-405-3789
JHolmes_at_lsu.edu
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