Abstract
This chapter deals with the studies on wind actions and effects on structures carried out between the late nineteenth and the mid-twentieth centuries. It starts speaking of the developments associated with the evolution and failure of suspension bridges, as well as with the new issue about the behaviour of towers and skyscrapers in the wind. It then passes to examine the renewed culture spanning the whole range of structures that came to maturity in this period; it gained ground through state of the arts and textbooks representing milestones of a discipline that is herein organised along four conceptually sequential topics: design wind speed, building aerodynamics, dynamic response to turbulent wind and aeroelastic phenomena. The presentation of the design wind speed addresses the mean and peak profiles, the time–space structure of turbulence and their probability of occurrence. Building aerodynamics is illustrated with special regard to the growing use and potential of wind tunnel facilities. The dynamic response to the turbulent wind is examined with reference to the transition from deterministic to random dynamics. Aeroelastic phenomena are discussed mainly with regard to vortex shedding, galloping and flutter.
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Notes
- 1.
Thanks to its single deck level, in Washington Bridge L/D = 350; previous bridges reached, at most, L/D = 84.
- 2.
Waiting for computers and finite elements methods, free vibration analyses were usually performed by the Rayleigh -Ritz method. Friedrich Bleich used the first two terms of the Fourier series. Steinman obtained simplified formulas of the characteristic frequencies and shapes.
- 3.
Oscillations were detected by means of theodolites through targets on lamps and sights on towers. Movie shootings were also performed. The wind speed was measured by an anemometer conceived for ventilation purposes, so they were little more than estimates. In this period, only vertical modes were activated.
- 4.
The diagram of the twisting motion coefficients in relationship with the angle of attack proved that the negative slope of the deck changed into positive slope for any examined measure. Since only vertical motions were observed, this result received scant attention.
- 5.
The persistent oscillation of this bridge led, in 1986, to the fitting of tuned mass dampers. In 2003, the truss beam was replaced with flow baffles.
- 6.
The study highlighted the importance of increasing the stiffness of the towers during the construction to balance the lack of the stabilising effect of the cables. This principle turned out to be fundamental in 1964, when the towers of the Forth Bridge exhibited large oscillations due to vortex shedding.
- 7.
The Severn Bridge, started in 1961 and finished in 1966, was built [50] transporting the floating deck quoins. Once they were positioned, they were hoisted by means of cables. Pioneering tests in 1:32 scale were carried out to evaluate wind actions and effects on the quoins during the hoisting stage. The results proved the dangerousness of this operation and identified the cable configuration that guaranteed the utmost stability.
- 8.
From 2520 BC, when the Pharaohs built the Great Pyramid, 146 m high, to 1884, the year the George Washington Monument, a 169-m-high stone stele designed by Robert Mills (1781–1855), was completed, mankind undertook a competition to build increasingly higher structures. Using stone and wood, over 4 millennia it improved by 23 m. With his steel tower, Eiffel made a 133-m jump upwards.
- 9.
Today, it is well known that this is the result of the composition of two harmonic motions with the same period in two orthogonal planes; it is also known that lattice towers give rise to alongwind and cross-wind displacements of comparable amplitude.
- 10.
The Palazzo Vecchio tower is 94 m high above the square floor and 45.3 m higher than the tip of the palace. Its sides vary from 6.34 to 8.69 m.
- 11.
The Campanile di San Marco, completed between 1156 and 1173, suddenly collapsed in 1902, after being repeatedly struck by lightning.
- 12.
After the Pulitzer Building (1892, 94 m) brought the record of the tallest building to New York, in that same city this record was broken by the St. Paul Building (1896, 95 m) by George Browne Post (1837–1913), by the Park Row Building (1898, 117.5 m) by Robert Henderson Robertson (1849–1919), by the Singer Tower (1907, 187 m) by Ernest Flagg (1857–1947), by the Metropolitan Life Insurance Company Tower (1909, 206 m) by Napoleon Eugene Charles Henry Le Brun (1821–1901) and Purdy , and by the Woolworth Building (1913, 242 m) by Cass Gilbert (1859–1934).
- 13.
The ASCE report remarked it was impossible to assess the contribution of secondary elements to stiffness and damping. It then proposed to express stiffness through the deflection index, namely the ratio between the top displacement of the load-bearing frame and its height. The building behaviour was satisfactory if the index was smaller than 1/500; in particular cases, indices as low as 1/250 or 1/200 were considered acceptable.
- 14.
The highest building record, established by the Woolworth Building in 1913 with 242 m, was broken, between 1930 and 1931, by three of the four New York giants: the Manhattan Tower, the Chrysler Building, the Empire State Building and the RCA Building. William van Alen (1883–1954) and Craig Severance (1879–1941) were tasked with the design of two skyscrapers on behalf of the Chrysler Corporation and of the Bank of Manhattan, respectively. They both decided to build the highest skyscraper in the world. Severance’s project overtopped the Woolworth Building by a few metres. Alen designed a 282-m-high Chrysler Building. Severance discovered this and modified the Manhattan Tower raising it to 283 m. Alen, informed of Severance’s variant, corrected his project during the construction, raising the Chrysler Building (1931) to 319 m: it was not only the highest building in the world, but also exceeded 300 m and 1000 (1046) ft. By just 3 m, it did not reach the Eiffel Tower that retained, for a few days, the absolute record, which was broken, in that same year (1931) by the Empire State Building. The latter, designed by William Frederick Lamb (1893–1952), 381 m high, surmounted by an antenna reaching 449 m, overwhelmed the Chrysler Building and the Eiffel Tower, bringing the height record to a stratospheric height. It also was the first building with more than 100 floors (102) and the first building holding the absolute record for the highest structure.
- 15.
The collapse of the spire was not the first catastrophic event that struck the Mole Antonelliana. In 1904, during a thunderstorm, a lightning knocked down the statue of the winged genius at its top. It was replaced by a five-pointed star, over 4 m in diameter, designed by Ernesto Ghiotti (1847–1938).
- 16.
According to Karman [114] “many excellent bridge builders were alarmed because our actual knowledge was not sufficient to predict aerodynamic instability without model tests. In the US Government Board of Inquiry about the Tacoma Narrows Bridge, a bridge builder told me: ‘You would not seriously think that, from now on, if we build a large suspension bridge we will have to test a model in a wind tunnel?’—‘This is exactly what I intend to propose’, I replied.”
- 17.
The fastest mile wind speed Vf is the mean speed associated with the passage of a mile of wind, i.e. the mean wind speed over a period Tf equal to the ratio between one mile and Vf.
- 18.
Despite an outstanding knowledge of probability and process theories, it is odd how Barstein attributed the normal distribution to the speed and its square.
- 19.
If there are multiple anemometers representative of the same zone at the gradient height, a′ and u′ can be obtained through weighting factors in relation to the number of the available years (objective criterion) and the quality of stations and measurements (subjective criterion).
- 20.
Actually, the pressure p should be replaced by p–p0, p0 being the environmental pressure of the undisturbed flow.
- 21.
The tests were not carried out in a wind tunnel. Large hangar models were used, simulating the application of the aerodynamic forces.
- 22.
Measurements were carried out on an experimental chimney built on the roof of a building at the National Bureau; it was 3 m in diameter and 9 m high; 24 pressure taps were arranged along a circumference. Taking advantage of the construction of a chimney at the power plant of the Bureau of Standards, other tests were carried out; the chimney was 3 m in diameter and soared 36 m above the roof; 24 pressure taps were installed along a circumference.
- 23.
According to Irminger and Nøkkentved, the copper roof of a Danish cathedral with many holes since ancient times was replaced by an airtight roof. During the first storm the roof was eradicated by wind, highlighting the role of holes, i.e. to counter the uplift taking advantage of the internal depression. Restoring the holes, the roof came through subsequent storms undamaged.
- 24.
Assuming that the quadratic term of the fluctuations is negligible, the power spectrum of the velocity pressure is proportional to the power spectrum of the turbulence. In the (high frequency) inertial regime, it then is proportional to n−2 (Sect. 6.7).
- 25.
Barstein developed a similar procedure to assess the response of a 2 DOF system subjected to a couple of independent fluctuating forces f1 and f2.
- 26.
In the light of current knowledge, Eqs. (9.43a) and (9.43b) should be rewritten as:
$$ \begin{aligned} S_{\text{D}} \left( {y,y^{\prime};n} \right) & = 4\overline{D}^{2} \left| {{\upphi}_{1} \left( n \right)} \right|^{2} \frac{{S_{v} \left( {y,y^{\prime};n} \right)}}{{\overline{V}^{2} }} + \left( {\frac{{d\overline{D}}}{{\text{d}{\upalpha} }} - \overline{L}} \right)^{2} \left| {{\upphi}_{6} \left( n \right)} \right|^{2} \frac{{S_{w} \left( {y,y^{\prime};n} \right)}}{{\overline{V}^{2} }} \\ & \quad + 4\overline{D}\left( {\frac{{\text{d}\overline{D}}}{{\text{d}{\upalpha} }} - \overline{L}} \right)\left| {{\upphi}_{2} \left( n \right){\upphi}_{3} \left( n \right)} \right|\frac{{S_{vw} \left( {y,y^{\prime};n} \right)}}{{\overline{V}^{2} }} \end{aligned}$$$$\begin{aligned} S_{\text{L}} \left( {y,y^{\prime};n} \right)& = 4\overline{L}^{2} \left| {{\upphi}_{2} \left( n \right)} \right|^{2} \frac{{S_{v} \left( {y,y^{\prime};n} \right)}}{{\overline{V}^{2} }} + \left( {\overline{D} + \frac{{\text{d}\overline{L}}}{{\text{d}{\upalpha} }}} \right)^{2} \left| {{\upphi}_{3} \left( n \right)} \right|^{2} \frac{{S_{w} \left( {y,y^{\prime};n} \right)}}{{\overline{V}^{2} }} \\ & \quad + 4\overline{L}\left( {\overline{D} + \frac{{\text{d}\overline{L}}}{{\text{d}{\upalpha} }}} \right)\left| {{\upphi}_{2} \left( n \right){\upphi}_{3} \left( n \right)} \right|\frac{{S_{vw} \left( {y,y^{\prime};n} \right)}}{{\overline{V}^{2} }} \end{aligned}$$where ϕ6 is an aerodynamic admittance.
- 27.
The study of vortex shedding at the NPL began in 1955 [46], when Scruton carried out wind tunnel tests on a sectional model of the Crystal Palace TV antenna. He simultaneously carried out full-scale measurements of the tower frequency and damping. Using a helicopter, he applied ex-military rockets at its top and periodically fired them to produce a resonant response. The experiments were suspended by the police.
- 28.
The measurements were carried out at the NPL on regular polygons with 6, 8 and 12 sides. Vortex shedding was always present, but its intensity varied in relationship with the number of sides; it was maximum for the square and minimum for the hexagon; in both cases, the worst situation took place with the wind perpendicular to a face. Other tests were carried out on L- and H-shaped cross-sections elements.
- 29.
Collapses due to vortex shedding from tubular elements of radar antenna frames were observed at the M.I.T. Lincoln Laboratory, where an element of a dish 8.5 m in diameter broke. Other collapses involved a reflector 25 m in diameter. An element of a similar structure widely vibrated in Boston, MA.
- 30.
Lanchester illustrated the aerial tourbillon, a clear case of autorotation, and then of galloping, like a game. It consisted of a bar with the semi-circular cross-section fitted on an axis perpendicular to the flat face orthogonal to the wind. When a rotatory motion was applied, it continued over time.
- 31.
In the rare cases in which the horizontal motion was comparable with the vertical one, the conductor moved along a clearly perceivable elliptical orbit.
- 32.
Corona discharge is a process by which a current flows from an electrode (cable) with high potential in a neutral fluid (air); the latter ionises the fluid and creates a plasma region around the source.
- 33.
In the expansion of cL and cD, the polynomial terms with even and odd exponents are missing since cL and cD are odd and even functions of α being the cylinder symmetrical with respect to the wind direction.
- 34.
- 35.
- 36.
Pinney provided modified expressions of \( \overline{L}_{h} \), \( \overline{L}_{\upalpha} \), \( \overline{M}_{h} \), \( \overline{M}_{\upalpha} \) to take account of the openings in the roadway, a widespread oscillation mitigation technique.
- 37.
Without tests on curved models, the effect of the angular velocity was previously studied through graphs of the static torsion obtained by rotating a non-curved model. Assuming α = β, the results should qualitatively coincide, since the dominant effect is the inclination near the leading edge. Quantitatively, the passage from the straight to the curved model made torsional stability worse.
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Solari, G. (2019). Wind Actions and Effects on Structures. In: Wind Science and Engineering. Springer Tracts in Civil Engineering . Springer, Cham. https://doi.org/10.1007/978-3-030-18815-3_9
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