Fatigue Design - · PDF fileStructural Welding Code 01.1-Steel. Fatigue de ... Section 11:...
Transcript of Fatigue Design - · PDF fileStructural Welding Code 01.1-Steel. Fatigue de ... Section 11:...
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Section 11:
Fatigue Design
Constant-amplitude tatiguethresholeJ-also known as constant-amplitude fatigue limit (CAFL) or endurance limit, a stress range below which a fatigue life appears to be infinite.
SPECIFICATIONS
11.1 SCOPE
1his section contains provisions for the fatigue design of cantilevered steel and aluminumstructural supports for highway signs, luminaires,and traffic signals.
COMMENTARY
This section focuses on fatigue, which is defined herein as the damage that may result infracture after a sufficient number of stress fluctuations. It is based on NCH RP Report 412, FatigueResistant Design of Cantilevered Signal, Sign andLight Supports (Kaczillski et al. 1998). The studyfocused on critical support structures that show
A
Fatigue-c-damage resulting in fracture caused by stress fluctuations.
In-plane bending-bending in-plane for the main member (column). At the connection of an arm or arm'sbuilt-up box to a vertical column, the in-plane bending stress range in the column is a result of galloping ortruck-induced gust loads on the arm and/or arm's attachments.
Limit state wind load effect-a specifically defined load criteria.
Load bearing attachment-attachment to main member where there is a transverse load range in the attachment itself in addition to any primary stress range in the main member.
Non-load bearing attachment-attachment to main member where the only significant stress range is theprimary stress in the main member.
Out-ot-plane bending-bending out-of-plane for the main member (column). At the connection of an arm'or arm's built-up box to a vertical column, the out-of-plane bending stress range in the column is a result ofnatural wind gust loads on the arm and the arm's attachments.
Pressure range-c-magnitude of force, in terms of pressure, of a limit state wind load effect.
Stress range-c-magnitude of stress fluctuations.
Yearly mean wind velocity-long-term average of the wind speed for a given area.
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Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
SPECIFICATIONS
11.3 NOTATIONS
COMMENTARY
bCddDEtntn1(F)n9H
Ilavg
Itop
Ibottom
Ii:
LLLLPGPNWPTG
PvsrRSnSRttbtctpVcVmean
Wwpa.a.t!..cr
= flat-to-flat width of a multisided section (m, ft)= appropriate drag coefficient from Section 3, "Loads," for given attachment or member= diameter of a circular section (m, ft)= inside diameter of exposed end of female section for slip-joint splice (mm, in)= modulus of elasticity (MPa, ksi)
first natural frequency of the structure (cps)= first modal frequency (cps)= fatigue strength (CAFL) (MPa, ksi)= acceleration of gravity (9810 mm/s2, 386 in/s2)
= effective weld throat (mm, in)= moment of inertia (mm4, in4)
average moment of inertia for a tapered pole (mm4, in4)= moment of inertia at top of tapered pole (mm4, in4)= moment of inertia at bottom of tapered pole (mm4, in4)= importance factors applied to limit state wind load effects to adjust for the desired level of
structural reliabilitylength of the pole (Article 11.7.2) (mm, in)slip-splice overlap length (example 1 of Figure 11-1) (mm, in)length of reinforcement at handhole (example 13 of Figure 11-1) (mm, in)
= length of longitudinal attachment (examples 12, 14 and 15 of Figure 11-1) (mm, in)= galloping-induced vertical shear pressure range (Pa, psf)
,= natural wind gust pre~sur,e rClnge(Pa, psf)= triJck-il1duc'ed gust, pressure range (Pa, psf) , _~~i"
~" .,~. - •••• ~ ~ "<. _ T' •
" = ' ~,vortex ·snedding-induced'pressure range (Pa, psf)= .racji(,Jsof c~ordor column (mm,~in),=·-tra~sit~onraqiu§9fIOl")gitudinal attaqhment (mm,in): ".' .. -:," .- .Strouhaln-umber '. ",= .. nomina:! stre'ss range o(the !)iainmember or branching member (MPa;'ksi)= thickness (mm,in)= wall thickness of branching member (mm, in)= wall thickness of main member (column) (mm, in)= plate thickness of attachment (mm, in)= critical wind velocity for vortex shedding (mis, fUs)= yearly mean wind velocity for a given area (mis, mph)= weight of the luminaire (N, k)= weight of the pole per unit length (N/mm, k/in)= damping ratio= angle of transition taper of longitudinal attachment (example 14 of Figure 11-1) (deg)
ovalizing parameter for bending in the main member (note b of Table 11-2)indication of stress range in member resulting from applicable axial loadings or moments
/. -t ..
11.4 APPLICABLE STRUCTURE TYPES
Design for fatigue shall be required for thefollowing cantilevered-type structures:
a:) overhead cantilevered sign structures,
b) overhead cantilevered traffic signalstructures, and
c) high-level lighting structures.
The fatigue design procedures outlined in thissection may be applicable to steel and aluminumcantilevered structures in general. However, onlyspecific types of cantilevered structures are identified for fatigue design in this article. Commonlighting poles and roadside signs are not includedsince they are smaller structures and normallyhave not exhibited fatigue problems. An exceptionwould be square lighting poles, as they have ex-
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Section 11: Fatigue Design
SPECIFICATIONS
11.5 DESIGN CRITERIA
Cantilevered support structures shall be designed for fatigue to resist each of the applicableequivalent static wind load effects specified inArticle 11.7, and modified by the appropriate importance faCtors given in Article 11.6. Stressesdue to these loads on all components, mechanical fasteners, and weld details shall be designedto satisfy the requirements of their respectivedetail categories within the constant-amplitudefatigue thresholds provided in Table 11-3. Asummary of typical fatigue-sensitive cantileveredsupport structure connection details is presentedin Table 11-2 and illustrated in Figure 11-1.
COMMENTARY
hibited poor fatigue performance. Square crosssections have been much more prone to fatigueproblems than round cross-sections. Cautionshould be exercised regarding the use of squarelighting poles even when a fatigue design is performed. The provisions of this section are not applicable for the design of span wire (strain) poles.
In general, overhead cantilevered sign andtraffic signal structures should be designed for fatigue due to individual loadings from galloping,natural wind' gusts, and truck-induced wind gusts.High-level lighting structures should be designedfor fatigue for loadings from natural wind gusts.Vortex shedding should be considered for singlemember cantilevered members that have tapersless than 0.0117 m/m (0.14 in/ft) , such as lightingstructures or mast arms without attachments.
NCH RP Report 412, Fatigue Resistant Designof Cantilevered Signal, Sign and Light Supports(Kaczinski et al. 1998) is the basis for the fatiguedesign provisions for cantilevered structures. Otherstructures, including overhead bridge support
","strlJctur(3s for signs and signals, are, also suscepti~'\:',ble tt)"',fati~j'ue'dariiage: SOmehofthe design pro\ii~~'
sionsof this section can also be applicable to non-, ",_cafl,ti!E?V~J~q,,~tr~:~tur,e.s.;'.A' r'e.searc,t"1project isc:ur~ j;._.L .. ,:
" ' rentJy underWay to deverop"compret€r'tatigu~de~"-:';;'-""~' ,"pign proyi~iolJs" J9r ,I,.or)ca,ntil,E;)y.ereq,$"'upporj"sJrlJc~ ..
tiJres.'
Accurate load spectra and life prediction techniques for defining fatigue loadings are generallynot available. The assessment of stress fluctuations and the corresponding number of cycles forall wind-induced events (lifetime loading histogram)is practically impossible. With this uncertainty, thedesign of cantilevered sign, luminaire, and trafficsignal supports for a finite fatigue life becomes impractical. Therefore, an infinite life fatigue designapproach is recommended and considered soundpractice. It is generally based on the constantamplitude fatigue limit (CAFL). The CAFL valuesprovided in Table 11-3 are approximately thesame as those given in Table 1O.3.1.A of the Standard Specifications for Highway Bridges (AASHTO1996).
An infinite-life fatigue approach was developed in an experimental study that consideredseveral critical welded details (Fisher et al. 1993).
11-3
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Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
SPECIFICATIONS COMMENTARY
The infinite-life fatigue approach can be used whenthe number of wind load cycles expected duringthe lifetime of the structures is greater than thenumber of cycles at the CAFL. This is particularlythe case for structural supports where the windload cycles in 25 years or greater lifetimes are expected to exceed 100 million cycles, whereas· typical weld details reach the CAFL at 10 to 20 millioncycles.
Fatigue critical details should be designedwith nominal stress ranges that are below the appropriate CAFL. To assist designers, a categorization of typical cantilevered support structure detailsto the existing AASHTO and American WeldingSociety (AWS) fatigue design categories is provided in Table 11-2 and Figure 11-1. Based on areview of state departments of transportation standard drawings and manufacturers' literature, theabove referenced list of typical cantilevered support structure connection details was produced.This list should not be considered as a completeset of all possible connection details, but rather it isintended to remove the uncertainty associated withapplying the provisions of the Standard Specifica-
tions for Highway Bridges to. the fatigue design ofcantilevered support structures .
. This detailed categorization of fatigUe~sensitive connection 9E!tails..can be us~d ..by de-
. 'signersand fabricators to produce more fatigueresistant cantilevered support structures. Properdetailing will improve the fatigue resistance ofthese structures, and it can eliminate or reduceincreases in member size required for less fatigueresistant details.
The notes for Table 11-2 specify the use ofStress Category K2- This stress category corresponds to the category for cyclic punching shearstress in tubular members specified by the AWSStructural Welding Code 01.1-Steel. Fatigue design for the column's wall under this condition mayrequire sizes of the built-up box connection or column wall thicknesses that are excessive for practical use. For this occurrence, an adequate fatigueresistant connection other than the built-up boxshown in Figure 11-1 should be considered.
Regarding full-penetration groove-weldedtube-to-transverse plate connections, NCHRP Report 412 did not fully investigate the effects fromthe possible use of additional reinforcing filletwelds. Additional research and testing of thesetypes of detail configurations are needed to support future updates of this section.
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Section 11: Fatigue Design
SPECIFICATIONS
11.6 FATIGUE IMPORTANCE FACTORS
An importance factor, IF, that accounts forthe degree of hazard to traffic and damage toproperty shall be applied to the limit state windload effects specified in Article 11.7. Importancefactors for cantilevered traffic signal, sign, andluminaire support structures exposed to the fourwind load effects are presented in Table 11-1.
COMMENTARY
Importance factors are introduced into theSpecifications to adjust the level of structural reliability of cantilevered support structures. Importance factors should be determined by the owner.For combined structures, such as traffic signal andluminaire combined structures, use of the more conservative importance factor is recommended.
Three categories of cantilevered supportstructures are presented in Table 11-1. Structuresclassified as category I present a high hazard inthe event of failure and should be designed to resist rarely occurring wind loading and vibrationphenomena. It is intended that only the most critical cantilevered support structures be classified ascategory I. Some examples of structures thatshould be considered for category I classificationinclude the following: large sign structures (including variable message signs [VMS]), traffic signalstructures with long mast arms, and high-levellighting poles in excess of 30 m (98 ft) that are installed on highways where the vehicle speed issuch that the consequences of excessive deflec
.•tiol}9r'a cpllisiol1 with a f!3-lIenstnJcture .is intolerable. Category II and III structures are not lesslikely to expe[i~ncethe full limit state wind loadsassociated 'with' category I. If category II or IIIcantilevered support structures· experience the limitstatel6ads ()Ver. a' peti6doftime: they woilldbeexpected to experience fatigue damage. Soundengineering judgment shall be used in the classification process.
Table 11-1. Fatigue Importance Factors, IFFatigue Category
Importance Factor, IF
GallooinqVortex SheddinqNatural Wind GustsTruck-Induced Gusts
ISign 1.0X 1.0 1.0
Traffic Signal1.0X 1.0 1.0
Liqhtinqx1.0 1.0 x
IISign 0.65X0.750.89
Traffic Signal0.65X0.800.84
Lightingx0.65 0.72x
IIISign 0.31X0.490.77
Traffic Signal0.30X0.590.68
Liqhtinqx0.30 0.44x
Note:x-Structure is not susceptible to this type of loading.Category Descriptions:I -Critical cantilevered support structures installed on major highways.II-Other cantilevered support structures installed on major highways and all cantilevered supportstructures installed on secondary highways.III-Cantilevered suooort structures installed at all other locations.
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Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
SPECIFICATIONS
11.7 FATIGUE DESIGN LOADS
To avoid large-amplitude vibrations and topreclude the development of fatigue cracks invarious connection details and at other critical
locations, cantilevered support structures shall bedesigned to resist each of the following applicablelimit'state equivalent static wind loads actingseparately. These loads shall be used to calculate, nominal stress ranges at fatigue-sensitiveconnection details," as described in Article 11.5.The calculated nominal stress range shall notexceed the CAFL values given in Table 11-3 foraparticular connection detail.
In lieu of using the equivalent static pressures provided in this specification, a dynamicanalysis of the structure may be performed usingappropriate dynamic load functions derived fromreliable data. '
, ;, ~
11.7.1 Galloping
, Overhead cantilevered sign and traffic signalsupport structures shall be designed for galloping-induced cyclic loads by applying an equivalent static shear pressure vertically to the surfacearea, as viewed in normal elevation of all sign
COMMENTARY
Cantilevered support structures are exposedto several wind phenomena that can produce cyclicloads. Vibrations associated with these cyclicforces can become significant. NCHRP Report 412has identified galloping, vortex shedding, naturalwind gusts, and truck-induced gusts as windloading mechanisms that can induce large amplitude vibrations and/or fatigue damage in cantilevered traffic signal, sign, and light support structures. The amplitude of vibration and resultingstress ranges are increased by the low levels ofstiffness and damping possessed by many of thesestructures. In some cases, the vibration is only aserviceability problem because motorists cannotclearly see the mast arm attachments or are concerned about passing under the structures. In othercases, where deflections mayor may not be considered excessive, the magnitudes of stressran-gas induced in these structures have resulted inthe development of fatigue cracks at various connection details including the anchor bolts.
", _The wind-loading phenomena specified in thissection possess the greatest potential for creatinglarge .amplitude vibrations in cantilevered support
pstructures.ln partiqJlar, galloping and vortex shed-'ding are aeroelastic instabilities that will typicallyinduc!3vibratibns at the, natural frequency of the "structure (Le., resonance). These conditions canlead to fatigue failures in a relatively short period oftime.
Design pressures for each of the four possiblefatigue wind-loading mechanisms are presented asan equivalent static wind pressure range, or ashear stress range in the case of galloping. Thesepressure (or shear stress) ranges should be applied to the structure as prescribed by this sectionin a simple static analysis to determine stressranges at fatigue-sensitive details. In lieu of designing for galloping or vortex-shedding limit statefatigue wind load effects, mitigation devices maybe used as approved by the owner. Mitigation devices are discussed in NCHRP Report 412.
Galloping, or Den Hartog instability, results inlarge' amplitude, resonant oscillations in a planenormal to the direction of wind flow. It is usuallylimited to structures with nonsymmetrical crosssections, such as sign and traffic signal structures
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Section 11: Fatigue Design
SPECIFICATIONS COMMENTARY
panels and/or traffic signal heads and backplatesrigidly mounted to the cantilevered horizontalsupport. The magnitude of this vertical shearpressure range shall be equal to the following:
In lieu of designing to resist periodic galloping .forces, cantilevered sign and traffic signalstructures may be erected with approved vibration mitigation devices. Vibration mitigation devices should be approved by the owner, and theyshould be based on historical or research verifi- .cation onts vibration damping characteristics.
(Pa)
(psf)
Eq.11-1
with attachments to the horizontal cantileveredarm. Structures without attachments to the cantile
vered horizontal support are not susceptible togalloping induced wind load effects.
The results of wind tunnel (Kaczinski et al.1998) and water tank (McDonald et al. 1995) testing, as well as the oscillations observed on cantilevered support structures in the field, are consistentwith the characteristics of the galloping phenom"ena. These characteristics include the sudden on
set of large-amplitude, across-wind vibrations thatincrease with increases in wind velocity. It is important to note, however, that galloping is typicallynot caused by support structure members, butrather by the attachments to the horizontal cantilevered arm, such as signs and traffic signals.
Alternatively, for traffic signal structures,the owner may choose to install approved vibration mitigation devices if structures display a galloping problem. The mitigation devices must beinstalled as quickly as possible after the gallopingproblem appears.
........... Th~,ovynE3r may. choose to .exclude gal~. loping' loads for the fatigue design of overhead
..J.._ __._._._.~.~_t:1!i!e.Y§!r(3~.~Jg~.suPP9J:t,._~~~~t~i~.~\'Jj~h,gl,lc:i_~ri~__. ,~ ". chord (Le:;four-chbrd) h'orizontal trusses ...
The geometry and orientation of these attachments, as well as the wind direction, directlyinfluence the susceptibility of cantilevered supportstructures to galloping. Traffic signals are moresusceptible to galloping when configured with abackplate. In particular, traffic signal attachmentsconfigur'ed with or without a backplate are moresusceptible. to galloping' when subject to flow from
'the Tear: .Galloping of sign attachments is lnde-_.,-pen,dent-of-:aspeet ratio~nd is r;nore,8f,ev~le.n!'y.'ith-
wind flows from the front of the'structure. - . ,__•. *_ .....••.. ; ., r.••• · ._." , .•..._ .•.••. _ •...
By conducting wind tunnel tests and analYticalcalibrations to field data and wind tunnel test re
sults, an equivalent static vertical shear of 1000 Pa(21 psf) was determined for the galloping phenomena. This vertical shear range should be applied tothe entire frontal area of each of the sign and trafficsignal attachments in a static analysis to determinestress ranges at critical connection details. For example, if a 2.5 m by 3.0 m (8 ft by 10ft) sign panelis mounted to a horizontal mast arm, a static forceof 7500 x IF, N (1680 X IF, Ib) should be appliedvertically to the structure at the center of gravity ofthe sign panel.
A pole with multiple horizontal cantileveredarms may be designed for galloping loads appliedseparately to each individual arm, and need notconsider galloping simultaneously occurring onmultiple arms.
Overhead cantilevered sign support structures with quadri-chord horizontal trusses do notappear to be susceptible to galloping because oftheir inherent high degree of three-dimensionalstiffness.
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Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
SPECIFICATIONS COMMENTARY
Two possible means exist to mitigate galloping-induced oscillations in cantilevered supportstructures. The dynamic properties of the structureor the aerodynamic properties of the attachmentscan be adequately altered to mitigate galloping.The installation of a device providing positive aerodynamic damping can be used to alter the structure's response from the aerodynamic effects onthe attachments.
A method of providing positive aerodynamicdamping to a traffic signal structure involves installing a sign blank mounted horizontally and directly above the traffic signal attachment closest tothe tip of the mast arm. This method has beenshown to be effective in mitigating gallopinginduced vibrations on traffic signal support structures with horizontally-mounted traffic signal attachments (McDonald et al. 1995). For verticallymounted traffic signal attachments, a sign blankmounted horizontally near the tip of the mast armhas mitigated large amplitude galloping vibrationsoccurring in traffic signal support structures. Thi~sign blank is placed adjacent to a traffic signal attachment,' and a separatiOn __~xistsbetween thesign,blank an~ the, top of the mast arm. In bothcases, ,the sign blanks are required, to provide a
_,u sufficient -surface-·area' for rnitigationto occur.'U However,. the installation of sign blanks may influ'; enqe Jhe, designoLstructures for truck-induced
wind gusts by increasing the projected area on ahorizontal plane. NCHRP Report 412 provides additional discussion on this possible mitigation device, and on galloping susceptibility and mitigation.
(
11.7.2 .Vortex Shedding
Nontapered lighting structures shall be designed to resist vortex shedding-induced loads forcritical wind velocities less than approximately 20m/s (65 fps; 45 mph).
The critical wind velocity, Vc (mis, ft/s), atwhich vortex shedding lock-in can occur may becalculated as follows:
The shedding of vortices on alternate sides ofa member may result in resonant oscillations in aplane normal to the direction of wind flow. Typicalnatural frequencies and member dimensions preclude the possibility of most cantilevered sign andtraffic signal support structures from being susceptible to vortex shedding-induced vibrations.
where fn is the first natural frequency of thestructure (cps); d and b are the diameter and flat-
Vc = fnd (for circular sections)Sn
Vc = fnb (for multisided sections)Sn
Eq. 11-2
Eq. 11-3
Cantilevered mast arms and lighting structures that have tapers less than 0.0117 m/m (0.14in/ft) may be required by the owner or designer toresist vortex shedding-induced loads.
Structural elements exposed to steady, uniform wind flows will shed vortices in the wake behind the element in a pattern commonly referred toas a von Karmen vortex street. When the frequency of vortex shedding approaches one of the
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Section 11: Fatigue Design
SPECIFICATIONS COMMENTARY
(\
to-flat width of the horizontal mast arm or poleshaft for circular and multi-sided sections (m, ft),respectively; and Sn is the Strouhal number. TheStrouhal number shall be taken as 0.18 for circular sections, 0.15 for multisided sections, and0.11 for square or rectangular sections. For a tapered pole, d and b are the average diameterand width.
natural frequencies of the structure, usually the firstmode, significant amplitudes of vibration can becaused by a condition termed lock-in. The criticalvelocity at which lock-in will occur is defined by theStrouhal relationship:
Eq. C 11-1
The equivalent static pressure range to beused for the design of vortex shedding-inducedloads shall be:
In lieu of designing to' resist periodic 'vortex .shedding forces, approved vibration mitigationdevices may be used.
where Vc is expressed in m/s (ft/s); Cd is the dragcoefficient specified in Section 3, "Loads;" and {3
is' the damping ratio, which is conservatively es-timated. as 0.005: .-
Eq.11-4(Pa)
A lower bound wind speed can be establishedfor traffic signal and sign structures. Although vortices are shed at low wind velocities for wind
speeds less than 5 mls (16 fps, 11 mph), the vorticesdo not impart sufficient energy to excite moststructures. Typical natural frequencies and mem-ber diameters for sign and traffic signal supportstructures result in critical wind velocities well be-low the 5 mls (16 fps, 11 mph) threshold for the occurrence of vortex shedding. Because of extremelylow levels of damping inherent in many nontaperedsupport structures, vortex shedding may exciteresonant vibration. At wind speeds greater thanabout 20 m/s (65 fps, 45 mph) enough natural turbulence is generated to disturb the formation of vortices. -.:..._.
The <equivalent static pressure range' Pvs Aithough possible; recent'tests (Kaczinskietshall be applied transversely to poles (Le.,.hori- al. 1998; McDonald et al. 1995) have indicated that
- .. - -. - 'zontal'-direction) and horizontal" mast:" arms--:(Le.,>:.' ·theoccurrenceof· '{ortexshedding: froQ:1-attach-- - - .. ' verticalcHrection).· ..... u.'· merits to cahtilevered sfgnand traffic sr~Ynalsup- .~..
......PQetstructuresJs.l1otcriJical., Ih fact, Jh·es!'Lattach~._:,...ments are' more susceptible to galloping-induced .vibrations. Finally, support structures composed oftapered members do not appear susceptible tovortex-induced vibrations when tapered at least0.0117 m/m (0.14 in/ft). The dimensions of mosttapered members result in critical wind velocitiesbelow the threshold velocity; and, furthermore, anyvortices that may form are correlated over a shortlength of the member, and they consequently generate insignificant vortex-shedding forces.
Calculation of the first modal frequency forsimple pole structures (Le., without mast arms) canbe accomplished using the following equations:
fn1 = 1.75 J Eig1& wL4
(without luminaire mass)
Eq. C 11-2
f 1 = 1.732 I Eign 21& V We + 0.236we(with luminaire mass)
Eq. C 11-3
where W is the weight of the luminaire (N, k), w isthe weight of the pole per unit length (N/mm, klin),
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Standard Specifications for Structural Supports for Highway Signs, Luminaires and TrafficSignals
SPECIFICATIONS COMMENTARY
9 is the acceleration of gravity, L is the length ofthe pole (mm, in), and I is the moment of inertia ofthe pole (mm4, in\ For tapered poles, lavg is substituted for I, where:
Itop + Ibottom
lavg = 2 Eq. C 11-4
where Cd is the appropriate drag coefficientspecified in Section 3, "Loads," for the consideredelement to which the pressure range is to be applied. The natural wind gust pressure range shallbe applied in the horizontal direction to the exposed area of all support structure members,signs, traffic signals, and/or miscellaneous attachments. Designs for natural wind gusts shallconsider the application of wind gusts for any direction of wind.
Cantileve'r~d overhead sign, overhead traffic .. ". Be.cause of the inhere~t v,arii3.9ility in the ye~: .,~":_h'""signal; a[1d .high;le"vel; lighting 'supports 'shall be'" hlo"cifY- ~uid 'direCtion"of air. fiow', natural wind gusts
designed to resist an equivalent static natural are the most basic wind phenomena that may in-wind gust pressure range of: duce vibrations in wind-loaded structures. The
equivalent static natural wind gust pressure rangespecified for design was developed with data obtained from an analytical study of the response ofcantilevered support structures subject to randomgust loads (Kaczinski et al. 1998). This parametricstudy was based on the 0.01 percent exceedancefor a yearly mean wind velocity of 5 m/s (11.2mph), which is a reasonable upper-bound of yearlymean wind velocities for most locations in thecountry. There are locations, however, where theyearly mean wind velocity is larger than 5 m/s(11.2 mph). For installation sites with more detailedinformation regarding yearly mean wind speeds(particularly sites with higher wind speeds), thefollowing equivalent static natural wind gust pressure range shall be used for design:
11.7.3' Natural Wind Gust·.... -- '. ' .... - ._- ---- -- ..- ..-.- --.-.-"-"
(Pa) Eq.11-5
Itop is the moment of inertia at the tip of the poleand Ibottom is the moment of inertia at the bottom ofthe pole.
Determining the first modal frequency forpoles with mast arms, however, is best accomplished by a finite element based modal analysis.The mass of the luminaire/mast arm attachmentsshall be included in the analysis to determine thefirst mode of vibration transverse to the wind direction. Poles that may not have the attachments installed immediately shall be designed for thisworst-case condition. Because the natural frequency of a structure without an attached mass istypically higher than those with an attachment, theresultil19 critical wind speed and vortex sheddingpressure range will also be higher.' .
('.
The design natural wind gust pressure rangeis based on a yearly mean wind speed of 5 m/s(11.2 mph). For locations with more detailed windrecords, particularly sites with higher windspeeds, the natural wind gust pressure may bemodified at the discretion of the owner.
P.= 250C (V;ean )NW d 25 F
P. = 5.2C (V;ean )NW d 125 F
11-10
(Pa)
(psf)
Eq. C 11-5
Section 11: Fatigue Design
SPECIFICATIONS
11.7.4 Truck-Induced Gust
COMMENTARY
The largest natural wind gust loading for anarm or pole with a single arm is from a wind gustdirection perpendicular to the arm. For a pole withmultiple arms, such as two perpendicular arms, thecritical direction for the natural wind gust will usually not be normal to either arm. The design naturalwind gust pressure range shall be applied to theexposed surface areas seen in an elevation vieworientated perpendicular to the assumed wind gustdirection.
Overhead sign and traffic signal supportstructures shall be designed to resist an equivalent static truck gust pressure range of:
where Cd is the appropriate drag coefficient fromSection 3, "Loads," for the considered element to ,which theu pressure range is to beapPlied>Thepressure range shall be applied in the vertical
direction to the cantilevered horizontal support. as___welL as the_area of alLsigns, attachments,walk" .
ways, and/or. fighting fixfures projected on' ahOri-______ ._z:QD!i3t R!c:lllE!~Tb!s..P[~§gJre Gln9.~Lsb_aIJJ:~~_~ppJi€Zd_:_.
along the· lull: length- of any sign panels/enclosures or the outer 3.7 m (12 ft), whichever is greater~ The equivalent static truck pressure range lTlay be reduced for locations wherevehicle speeds are less than 30 m/s (65 mph),
{" The truck-induced gust loading may be ex-+ 1 eluded for the fatigue design of overhead cantile-
l vered traffic signal support structures, as allowedby the owner...•.
(Pa)
(psf)
Eq. 11-6
The passage of trucks beneath cantileveredsupport structures may induce gust loads on theattachments mounted to the horizontal support ofthese structures. Although loads are applied inboth the horizontal and vertical direction, horizontalsupport vibrations caused by forces in the verticaldirection are most critical. Therefore, truck gustpressures are applied only to the exposed horizontal surface of the attachment and horizontalsupport.
A pole "'lith multiple horizontal cantilever ar.msmay be designed for truck gust loads applied separatelyto each.individucil arm and need not consider
. trLJ9kgw3tloads· applied. simultaneouslY to multiplearms.
-Recent vibration problems on sign structures'
with large projected areas in the horizontal plane,such as VMS enclosures, have focused attentionon vertical gust pressures created by the passageof trucks beneath the sign. To improve fuel economy, many trucks are outfitted with deflectors todivert the wind flow upward and minimize the dragcreated by the trailer. It has been proposed to represent this gust pressure as that imposed by a 30m/s (65 mph) wind to approximately coincide withexisting vehicle speed limits (DeSantis and Haig1996).
The equivalent static truck gust pressure isdetermined by utilizing the wind pressure formulain Section 3, "Loads," where the velocity is 30 m/s(65 mph) and the height factor is 1.0. To accountfor an increase in the relative truck speed causedby head winds, a factor of 1.3 is also included. Asthe truck passes under the structure, a pressure isapplied upward, and then suction pressure is applied downward. Therefore, the load is doubledbased on the assumption that on the first cycle thedownward and upward forces are equal. Forstructures installed at locations where the posted
11-11
Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
SPECIFICATIONS COMMENTARY
speed limit is much less than 30 mts (65 mph), thedesign pressure may be recalculated based on thislower wind velocity. The following equation may beused: '
,( V )2Pm = 1760Cd ' / IF (Pa)30 m s
Pm = 36.6Cd ( V r IF (psf)65 mph
Eq. C 11-6
, ,. ".o-'-.~··''''·.-...~.•.......
where V is the truck speed in m/s (mph).
Utilizing appropriate drag coefficients (Cd), thetruck gust pressure range can then be applied toall horizontally projected areas, which include boththe horizontal support and any attachments. Forstructures with large sign panels, pressures shallbe applied along the entire length of the horizontalareas to recognize the possibility of passage of twotrucks side-by-side. For structures without largesign panels, the equivalent static truck gust pressure,sh?II ..be ?ppJied. to the. outer 3.7_m (12.ft).
-length Of the horizqriJaLsupport and to any attach-ments located within this length, '
A drag coefficient yalu$.of ~,.20was,u~ed :,'bYUeSantis'arid Hai£f' (1996) to determine an'u equivalent. static.-tr~uck 'gust pres.sure range :on
VMS .. ' ,
The magnitude of applied pressure resultingfrom a truck-induced gust will vary depending onthe elevation of the horizontal support and the elevation of the attachments above the truck. Eq. 116 neglects any decreases in design pressure resulting from increasing elevations above the trucks.Fatigue Related Wind Loads on Highway SupportStructures (Dexter and Johns 1998) includes arecommendation for the variation of truck-induceddesign pressures for a range of elevations abovethe road surface.
The given truck-induced gust loading may beexcluded for the fatigue design of overhead cantilevered traffic signal structures, as allowed by theowner. Many traffic signal structures are installedon roadways with negligible truck traffic. In addition, the typical response of cantilevered traffic signal structures from truck-induced gusts can be significantly overestimated by the design pressuresprescribed in this article. However, some cantilevertraffic signal structures have experienced largeamplitude vibrations from truck-induced gusts applied under the right conditions.
11-12
Section II: Fatigue Design
SPECIFICATIONS
11.8 DEFLECTION
Galloping and truck-gust induced verticaldeflections of cantilevered single-arm sign supports and traffic signal arms should not be excessive so as to result in a serviceability problem,because motorists cannot clearly see the arm'sattachments or are concerned about passing under the structures.
---_ .. ,.~.... _._._._-'. _._- --- ..--.-.--
COMMENTARY
Because of the low levels of stiffness and
damping inherent in cantilevered single mast armsign and traffic signal support structures, evenstructures that are adequately designed to resistfatigue damage may experience excessive vertical deflections at the free end of the horizontalmast arm. The primary objective of this provisionis to minimize the number of motorist complaints.
NCHRP Report 412 recommended that thetotal deflection at the free end of single-arm signsupports and all traffic signal arms be limited to200 mm (8 in) vertically, when the equivalentstatic design wind effect from galloping and truckinduced gusts are applied to the structure. Double-member or truss-type cantilevered horizontalsign supports were not required to have verticaldeflections checked because of their inherentstiffness. There were no provisions for a displacement limitation in the horizontal direction.
11-13
Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
Table 11-2. Fatigue Details of Cantilevered Support Structures
Construction
Plain Members
MechanicallyFastenedConnections
1.
2.
3.
Detail
With rolled or cleaned surfaces. Flame-cut
edges with ANSI/AASHTO/AWS D5.1 (Article 3.2.2) smoothness of 1,000 micro-in.or less.
Slip-joint splice where L is greater than orequal to 1.5 diameters.Net section of fully-tightened, high-strength(ASTM A325, A490) bolted connections.
Stress
Cat~A
B
B
Application.
High-level lightingpoles.
Bolted joints.
Example
2
4. Net section of other mechanically fastenedconnections:
Steel:Aluminum:
5. Anchor bolts or other fasteners in tension;stress range based on the tensile stressarea. Misalignments of less than 1:40 withfirm contact existing between anchor boltnuts, washers, and base plate.
6. Connection of members or attachment of
miscellaneous signs, traffic signals, etc.with clam s or U-bolts.
Holes and Cutouts 7. Net section of holes and cutouts.
~.r~~~~:~k~et~·_·~1~;~~·~~-~~~~I~~~ig~~~:I~~I~~;~I:~~~I~hedi-. - rection of Hie applied stress.9. Full-penetration groove-welded splices with
...... "cL·. '. welds ground tdprbvideasriibothfransi~-
_ _--'- _1~_:.tiC>fl~e~~en ..me.rT1~~.rsj'Nith()r 'lVit~()u.!-.--------:.r bacKing ring removed).10. Full-penetration groove-welded splices with
weld reinforcement not removed (with orwithout backing ring removed).
11. Full-penetration groove-welded tube-totransverse plate connections with thebacking ring attached to the plate with afull-penetration weld.
12. Full-penetration groove-welded tube-totransverse plate connections.
E I Column or mast arm
butt-splices.
E I Column-to-base-plateconnections.
Mast-arm-to-flangerl plate connections.E' Column-to-base-plateconnections.
Mast-arm-to-flangerl plate connections.E Column or mast armrl lap splices.E Angle-to-gusset con-nections with weldsterminated short of
plate edge.Slotted tube-to-gusset
connections withrl coped holes.E' Angle-to-gusset con-nections.
Slotted tube-to-gussetconnections without
coped holes.
8
3
4
5
5
5
3
2,6
2, 6
··6- ...
Anchor bolts.Bolted mast-arm-to
column connections.
Wire outlet holes.
Drainage holes.Unreinforced hand-
holes.
Longitudinal seam ~.: ..welds~ -
Column or mast.armbutt-splices:'
DED
D
D-
D
B'
14. Members with axial and bending loads withfillet-welded end connections withoutnotches perpendicular to the appliedstress. Welds distributed around the axis ofthe member so as to balance weldsstresses.
13. Fillet-welded lap splices.
15., Members with axial and bending loads withfillet welded end connections with notchesperperidicular to the applied stress. Weldsdistributed around the axis of the memberso as to balance weld stresses.
Fillet-WeldedConnections
11-14
Section 11: Fatigue Design
Table 11-2. Fatigue Details of Cantilevered Support Structures (continued)
Application I Example( ConstructionI Detail
Fillet-Welded
16.Fillet-welded tube-to-transverse plateConnections
connections.(continued)
117.Fillet-welded connections with one-
l--psided welds normal to the direction of
the applied stress.18.
Fillet-welded mast-arm-to-column l--Ppass-through connections. 19.
Fillet welded T-, Yo, and K-tube-to-
I
Seetube, angle-to-tube, or plate-to-tube
notesconnections.
a and b
Attachments 20. Non-load bearing longitudinal attachments with partial- or full-penetrationgroove welds, or fillet welds, in whichthe main member is subjected to longitudinalloading:
L < 51 mm (2 in):
- 51mrn(2 in) 5, L5,12t and102mm(4 in):
C
D
Column-to-base-plate or I 7, 8mast-arm-to-flangeplate socket connections
Built-up box mast-arm- I 8to-column connections.
Mast-arm-to-column pass- I 9through connections.
Chord-to-vertical or I 8, 10, 11chord-to-diagonal trussconnections (see note a).
Mast-arm directly weldedto column (see note b).
Built-up box connection(see note b).
Weld terminations at I 12, 13ends of longitudinalstiffeners.
Reinforcement at handholes.
,. ' .. , ~... "- -
L> 12tor 102 mm(4 in) when t 5, 25 mm(1 in):
____ 21; Non-I()Cld_bearingJongitudinalgttach~~-",I- ments with-:L > 102-mm (4 in) and-full--,
. pe'netration groove welds. The main-_____n.-:,;: - -:-- _:'-'u ------ --:_-'--- ---;::':"1':::""': :::-membe rig-subJeCted tolongitudfnal ~::---
- -- loading and weld tem;ination embodiesa transition radius or taper with the weldtermination ground smooth:
E
, Welds terminatioosat-ends of longitudinal -_~stiffeners_, _
14
. -.---- ..
R2:152mm(6in)or a:S; 15°: I C
152mm(6in) > R> 51 mm (2 in) or 15°< a 5, 60°: I D
R5,51mm(2in)ora>500: I E
22. Non-load bearing longitudinal attachments with L> 102 mm (4 in) and filletor partial-penetration groove welds. Themain member is subjected to longitudinalloading and the weld terminationembodies a transition radius or taperwith the weld termination ground smooth:
Weld terminations at
ends of longitudinalstiffeners.
14
R> 51 mm (2 in) or 15° < a :s;60°:
R :s;51 mm (2 in) or a > 60°:
23. Transverse load-bearing fillet-weldedattachments where t:s; 13 mm (0.5 in)and the main member is subjected tominimal axial and/or flexural loads.[When t> 13 mm (0.5 in), see note d].
11-15
D
E
C Longitudinal stiffenerswelded to base plates.
12,14
-------------~---'---'-~-'~=--'----------------------
Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
Table 11-2. Fatigue Details of Cantilevered Support Structures (continued)
Construction DetailStressApplicationExampleCategoryAttachments
24. Transverse load-bearing longitudinalGusset -p late- to-cho rd15(continued)
attachments with partial- or full- attachments.penetration groove welds or fillet welds, in which the nontubular main member issubjected to longitudinal loading andthe weld termination embodies a transi-tion radius that is ground smooth:
R> 51 mm(2in)or 15° < a ~ 60°:
D
R ~ 51 mm(2in) or a> 60°;
ESee note c
Notes:
a) Stress category ET with respect to stress in branching member provided that !..- J 24 for the chord member. Whent
0.7
!..- > 24 ,then the fatigue strength equals: (F) = (.1F)Er X(y;24Jt n n r
t
Stress category E with respect to stress in chord.
b) Stress category ET with respect to stress in branching member.
( ET,where .1F ) n is the CAFL for category ET.
.. " ... ,,', ' " ,- --"-, -. - - r
Stress category K2 withrespect to stress in main m.ember (column) Rfc:>yidedthat ~ ~24. for the main member.
, .,.---------"."~::::.,-.-"-.--, ..:~-- ..• -- .. '. - .,.,," : tc ,',' "._ ., ' " 0.7
~~en'~:2~~,t~i;L:;~~~s~~~-(~)~(:;"f{xJ ,whem(.d~istheCAFl fo, categoryK,--:.:~---tc""---:-:, --, -- ,•.... , ,,' ,--." --,n ., n - r tc - .. ---, - n '
The nominal stress range in the main member equals: (5R ) main member = (5R ) branching member ( ~: )a,Where tb is the wall thickness of the branching member, tc is the wall thickness of the main member (column), and
ex is the ovalizing parameter for the main member equal to 0.67 for in-plane bending, and equal to 1.5 for out-of
plane bending in the main member. (5R ) branching member is the calculated nominal stress range in the branching
member induced by fatigue design loads. (See commentary of Article 11.5.)
The main member shall also be designed for stress category E using the section modulus of the main member andmoment just belo"w the connection of the branching member.
c) First check with respect to the longitudinal stress range in the main member per the requirements for non-loadbearing longitudinal attachments. The attachment must then be separately checked with respect to the transversestress range in the attachment per the requirements for transverse load-bearing longitudinal attachments.
d) When t > 13 mm (0.5 in), the fatigue strength shall be the lesser of category C or the following:
where (.1Ft is the CAFL for category C, H is the effective weld throat (mm, in), and tp is the attachment platen
thickness (mm, in). ,
11-16
i\
i\
Section 11: Fatigue Design
Table 11-3. Constant-Amplitude Fatigue Thresholds
Detail
SteelAluminumCategory
ThresholdThreshold
MPa
ksiMPaksi
A
165247010.2
B
11016416.0
B'
8312324.6
C
6910284.0
D
487172.5
E
314.5131.9
E'
182.671.0
ET
81.230.44
K2
71.02.70.38
_____ .. . . "'"'"'~_;._.' __....:....d_. ._._.~_.-.;.. ..__._." -,."_0 __ .-
--_._~--_.,--- . ___ '__ " • ": .. __ •••• _. •__ .~ • •• • ._ •• _. 0_" .••u •__ .__·._~+ .._·~'_
11-17
'I'I : ! !
~;::
§-i3..
~""C')
'Si2:::1-.c;::""
~..,Vl::;;::C')..•.;::
i:!-Vl{;'15ca.~..,
::x::
~'"~Vl
~'~""
t'-<;::~S'!:I::;.'"""
!:I;::~~§,';:J)C')
VlaQ';::!:I1;;'
Fillet Weld(Detail 13)
ShmdnnJ IIlIlt
(Delull 4)
Backing Ring
+ 60
"-~M
Fillet· Welded Lap-Splice
Example 3
~6a
Example 5
l'iIIct Weld·(UclnilI4)
lIi!:h Strenglh lJolls(Detail 3)
Gruuve-Welded Tube-Iu-Trunsverse 1>loleConnection
, t.
Hole amI/or Culuut(Detail7)
,.
. ,
Duubhi.AlIgle-l·russ Gusset
Examille 2
·Weld slopped.sbu~t of gusset edge•
i
,i
Backing Rllig
Grouve Wetd(Del'alllO) ,
,.,
Gusset
Fillet W Cld
(DclaIl15)
; 60
~M
Grouve-Welded Dutt-Slllice
Example 4
~
fl. = 1.5x ()----I._
~ 60
; 60
Groove Weld(DelDll 9)
Slip-Joint Splice
Example 1
~Slip Splice(Delall 2)
"to's=..•(p....•....•I....•-!»
~Iy
2"UI-..•!»-<t(pm><!»3'tICDUI
<..~ ..~-•...,
'"
C/'.)'"<">
:::toc;:::
..........",
~~";::'"t1'"""
aQ';:::
Gussel
Coped Hole
Fillet Weld
(Detail 14)
Example 6
Section A-A
SluUed Tube-tu-Gusset Connection
l<'illetWeld
(Detail 16)
Fillet Weld
(DetoilIS)
Gusset
Seum Weld
(Detail 8)
,
: Example 6: .. ' !
:.• 't 11~
'1":
, !Section A·A ,to ;
'Fillet Weld.(DetaiI16)
~. ,
'I.
I:!
'I . ! "
Sh)~tcd 'l't,be-to-Gusset Cunnectiun
FilM Weld
Seam Weld
(Detail 8)
l.A
Example 6
~ 110
SluUed Tube-to-Gusset Connection
.....110
i:III..•...•DI..•.<"CD
m)(DI
3"tJCDIII
"cQ'e..•.CD
-"-"I-"-
C"":"'"
....•.
....•.I
....•.
<D
;Ih
Fi1~et-W~lded Socket Connection:,
:!,,~
: :Expmptc 7".
i'
t"<
;::;:s
5'~::j'~'"~;::~~§,';::R
C")
CI)~.;::~~
CI)
~;::
!}~~~
C")
'SiC")
~:::t,c;::'"
~.,CI)~;::C")•..•;::~...•CI)
.§'1:3ca.
~.,::t:
~';::..~~CI)
~';::~'"
~D.a
Fillet Weld(DelaIl19)
Fillel Weill
(Delaill'J)
Fillel Weill
(Uelail 17)
"--
~lIcr
~cr
Example II
Sec!iull/l·/l
Fillet· Welded Angle-to-Tube Connection
Exalllple 11
JIt:t;!P
~D.cr
Fillet Weld(OcIIlIl19)
Fillet- Welded Mil.~I-l\rJIl-tu-Cohllllll COlllledioll
(Built-Up Hux)
Fillet Weld\Uel:1i116J
Ui~1I Slrell!:11I Hult
(\)e(all SJ
i,
EXllluule 10'. .
;--;
, ., ,
1
Tl~i,I '.. 1\
.,
~.
lIa.: :
lrillct- WcldcdTubc-tu-Tubc Couucc Iiun, ...
Fillet Weld(Deta\l18)
Fillet Weld(Detll\l18)
Fillet Weld(Detail I?)
I'illel Weld
(Oelulll 'J)
Fillet. Welded Must-I\rm-tu-Columll Connectioll
(Buill·Up Uox)
Example 8
.,
~D.cr
t tJ.a
Fillet Weld(DclaIl16)
t1\
Fillet-Welded Tube-to-Tube Colullln
.Pass-Through Connection
EX8l1ll)le9
"TI
10'e:...•. (1)....•....•I....•
~I
~
e:
III-...•DI-<'(1)m><DI3"0(j)III
,. '
~<-~"--.
if
: ! .....
Non-Loud llearingLollgiludinal Attachmenl.' ,I :. ; 'l .
E~ample 12 '',. ", i
VJ<1:>
""
~"c;:::
....•
....•",
~~,
!:::'"
I;::,'"'"aQ'
;:::
FilM Weld(Detail 23)
Fillet Weld
(Delail 2U)
Section A-A
o, ~ Fillet Weld' (Delail 20)
ickness = tReinforcement,ih
,,.!
11.
i +" '
t, .Acr ;:" ", '
. ' .. ,' ,.. " ,
i" '6. ~ ,i 'i ;"; ."1' •
:\'I; ,
,;1
, 11...
Handhole : i
"j>:
Reillrorcem~'nti
i;
--,A
"T110'"I:..,(I)....•.....•.I....•.
~,-"-" I:
+ 6CJ
~I1/1
..•...,III..•.<'(I)m><III3
f-
"C
CD
A
1/1
Reinforced Handhole
Example 13
i'",,'
!
Reinforced Halldhole
Exumple 13
iIIi!,
fI,
'1'"
q't-!
Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals
'""'- c...• "-:: ..,.- •.....•
/I.,-
,-
i\.
Figure 11-1 (e). Illustrative Examples
11-22
/\.
Section 11: Fatigue Design
11.9 REFERENCES
/ American Association of State Highway and Transportation Officials. AASHTO Standard Specifications forHighway Bridges. Washington, D.C.: AASHTO, 1996.
·./Cook, R. A, D. Bloomquist, A M. Agosta, and K. F. Taylor. Wind Load Data for Variable Message Signs.Report no. FUDOT/RMC/0728-9488. City, Fla.: University of Florida, Florida Department of Transportation, 1996 .
./ Creamer, B. M., K. G. Frank, and R. E. Klingner. Fatigue Loading of Cantilever Sign Structures from TruckWind Gusts. Report no. FHWA/TX-79/10+209-1F. Austin, Texas: Center for Highway Research,Texas State Department of Highways and Public Transportation, 1979 .
./ DeSantis, P. V. and P. Haig. "Unanticipated Loading Causes Highway Sign Failure." Proceedings ofANSYS Convention, 1996.
Dexter, R. J. and K. W. Johns. Fatigue-Related Wind Loads on Highway Support Structures. AdvancedTechnology for Large Structural Systems, report no. 98-03. Bethlehem, Pa.: Lehigh University,1998.
<> Fisher, J. W., A Nussbaumer, P. B. Keating, and B. T. Yen. NCHRP Report 354: Resistance of WeldedDetails Under Variable Amplitude Long-Life Fatigue Loading. TRB, National Research Council,Washington, D.C., 1993.
v'Kaczinski, M. R.; R. J. Dexter, and J. P. Van Dien. NCHRP Report 412: Fatigue Resistant Design of Canti
levered Signal, Sign and Light s.upports. T~B~ ,N(3.tional R~~earc~ 9ounc)I,. Was_hing!qn, D ..~.,1998'.. n'
McDonald, J. R.; et al. Wind toad Effects on Signals, Luminaires and Traffic Signal Structures. Report no.
.... - -~~~,.~.30~-.~.~~~~~~ock,.·T~~~~;~~!n.~,E~9~n.e.er.inQRes~rq.h y~.!1ter!..I~.X9-~.T-~~h.d~l/tliy.~~~Jty;1.~~!?-,".d.:: , .._'_' . _--.--- ." .--- . ----," .
11-23