ARIZONA DEPARTMENT OF TRANSPORTATION REPORT NUMBER: FHWAIAZ 851237 FIELD TESTING OF MONOTUBE SPAN-TYPE SIGN STRUCTURES Prepared by: Kipp A. Martin Moharnmad R. Ehsani Reidar Bjorhoude MARCH 1986 Prepared for: Arizona Department of Transportation 206 S. 17th Avenue Phoenix, Arizona 85007 in cooperation with U.S. Department of Transportation Federal Highway Administration I... ., . ... 2.- \ . "- , "- "The contents of this report reflect the views of the authors who are responsible for the facts and the accuracy of the data peresented herein. The contents do not necessarily reflect the official views or policies of the Aridona Department of Transportation or the Federal Highway Adnlnlstration. This report does not constitute a standard, specification, or regulation. Trade or manufacturers' names which may appear herein are cited only because they are considered essential to the objectives of the report. The U. S. Government and The State of Arizona do not endorse products or manufacturers." CHNICAL REPORT S T A N D A R D TITLE P A C 1. Rmpori No. 2. Govmrnmmnt Acca.s~on No. 3. R e c ~ p ~ m nCoto~op t'~ No. FHWA/AZ-86/237 4. Tltlm ond Subtltlm 5. Rmport Dotm September, 1985 FIELD TESTING OF MONOTUBE SIGN SUPPORT STRUCTURES 6. Pmrformrng Orgon~xot~on Coda 7. Au*or(r) ,a. Poriorm~ngGrgon~xot~on Rmport No. ATTI-85-5 K. A. Martin, M. R. Ehsani and Reidar Bjorhovde 7 - 9. P a k r m l n p O r g m l ~ o t l o nNomm ond Addrare 10. Work Unli No. Arizona Transportation and Traffic Institute College of Engineering and Mines UNIVERSITY OF ARIZONA Tucson, Arizona 85721 11. Contrast or Cront NO. HPR-1-25(237) 13. TIP* 12. )Consoring A p ~ c vNamm and Addr.8- FINAL July Arizona Transportation Research Center Arizona Department of Transportation ARIZONA STATE UNIVERSITY Tempe, Arizona 85281 2 of Report ond Parood Covmred 1984-September 1985 14. Sponeorinp Agency Coda 15. Supplrmmntory not*^ Prepared in cooperation with the U. S. Department of Transportation, Federal Highway Administration, from a study of monotube sign support structures. The opinions and conclusions are those of the authors, and not necessarily of the Federal . 1. n t r n t . r o n . +xtz+= The report presents the results of full-scale tests of actual monotube sign support structures in the field, along with detailed theoretical analyses of the structures and comparisons of the analytical and experimental results. Two structures were tested under actual service conditions: A 100-foot span structure in Phoenix, Arizona, and a 60-foot span structure in Tucson, Arizona, were instrumented with strain gages and an anemometer, to determine in-service strains due to winds of various speeds. Since the structures had been erected earlier, no measurements could be made of dead load strains. The same two structures were also analyzed by two- and threedimensional finite element modeling, using static as well as dynamic (due to vortex shedding) loads. It was found that the correlation between computed and measured strains was good, especially considering the complexity of the analyses. Maximum in-plane stresses occurred at the midspan of the beam for both structures, and the maximum out-of-plane stresses occurred at the column base. The maximum wind load stress was approximately 1 1 ksi (100 foot structure). This level did not vary a great deal with the wind speed. Resonance was not observed at any wind speed, due to the combined effects of structural damping and short duration of wind loads. This is in agreement with the results of an earlier study. It is also shown that the d2/400 dead load deflection requirement of AASHTOcannot be met. Recommendations for design criteria and further studies are made. Icrv wura Monotube ; sign support ' structures; single span; full-scale testing; theoretical evaluation; static; dynamic; stresses; design criteria "* 19. k d i y Cborrlf. (.I hie r-) UNCLASSIFIED Fern DOT F 1700.7 tr-as1 10. 18. ~ l ~ krudty Clmemr I. Lo4 this p e p ) UNCLASSIFIED ii ~ Stat-? l b u ~ ~ No restrictions. This document is available to the public through the National Technical Information Service, Springfield, VA 22161 11. (I. 160 mf P w a 22. Pdcm The investigation described in this report was funded by the Arizona Department of Transportation in cooperation with the Federal Highway Administration under Project No. HPR-1-25 (237). The authors are sincerely appreciative of the continuous support and helpful suggestions of the staff of the Arizona Transportation Research Center. In particular, the untirlng efforts of Mike Sarsam and Frank R. McCullagh were crucial to the success of this work. Much dssistance was provided by Richard D. Wingfield of the Arizona Department of Transportation and Charles Mele of the City of Tucson Department of Transportation during .the field testing in Phoenix and Tucson. The help of the Arizona DOT and the City of Tucson DOT was invaluable in securing access to the sign structures and the mounting of the gages. Dr. R. A . Jimenez, Director of the Arizona Transportation and Traffic Institute, provided assistance in the administration of the research project. Tom Demma, electronics technician of the Department of Civil Engineering at the University of Arizona, solved a great aany problems associated with the testing, installation and use of the multitude of electronic components. Computation assistance for the GIFTS program was given by Thomas R. Cram of the Computer-Aided Engineering Center of t.he University of Arizona. Sincere thanks are due Carole Goodman who did an excellent job in typing the report. METRIC CONVERSION TABLE This report utilizes U.S. customary units following may be used to convert to SI units. = 25.4 mm 0.305 m = 1.61 Km = = = 645 mari! 0.454 kg 4.45 N = 6.89 1 inch 1 foot 1 mile = 1 sq. i n . 1 Ib mass 1 lb force 1 psi kPa of measurement. The TABLE OP CONTENTS LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi ix ................................................... 1 1. INTRODUCTION 2. SCOPE 3. STRUCTURAL RESPONSE UNDER WIND LOADS 4. ANALYSIS OF MONOTUBE STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Modeled Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Computer Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Finite Element Model Development . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Static Loads on Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Dynamic Loads on Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Natural Frequencies of Vibration . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Static Load Results ..................................... 4.8 Dynamic Load Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Conclusions for Analytical Studies . . . . . . . . . . . . . . . . . . . . . . 17 17 25 26 32 35 38 46 56 65 5. FIELD TESTING OF FUI.L.SCA1.E STRUCTURES ......................... 5.1 Description of Equipment and Software . . . . . . . . . . . . . . . . . . . 5.2 Procedure f o r Gage Installation . . . . . . . . . . . . . . . . . . . . . . . . . 5 . 3 Theory of Strain Gage Operation . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Data Reduct.ion Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Statistical Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Calibration of Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 COMPARISON OF ANALYTICAL AND EXPERIMENTAL RESULTS . . . . . . . . . . . . . . 6.1 Tucson Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Phoenix Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 100 'SUMMARY. CONCLUSIONS AND RECOMMENDATlONS . . . . . . . . . . . . . . . . . . . . . . . 7.1 Summary and Conclusions ................................. 112 112 114 6. 7 . .......................................................... 6 ........................... 7 7.2 Recommendations for Further Studies REFERENCES ..................... .................................................... DATA COLLECTION SOFTWARE FOR HP-41CX CALCULATOR .... DATA REDUCTION SOFTWARE FOR HP SERIES 200 COMPUTER . SET-UP AND OPERATION OF FIELD TESTING EQUIPMENT .... DATA TRANSFER FROM CASSETTE DRIVE TO HP SERIES 200 COMPUTER ................................ APPENDIX E: DATA TRANSFER SOFTWARE FOR HP 41CX CALCULATOR ...... APPENDIX F: DATA TRANSFER SOFTWARE FOR HP SERIES 200 COMPUTER .. APPENDIX APPENDIX APPENDIX APPENDIX A: B: C: D: 72 77 78 85 86 95 104 116 118 123 133 136 139 140 LIST OF FIGURES & Fi~ure ...................... 3 ................... 3 1 Typical Truss Sign Support Structure 2 Typical Monotube Sign Support Structure 3 Long Span Monotube Sign Support Structure 4 Typical Monot-ube Structure Beam-to-Column Connection 5 Airfoil Illustrating Principle of Lift 6 Drag on Plate in an Air Stream 7 Vortices for Flow Around a Cylinder 8 Karman Vortex Sheet 9 Standing Vortices for Flow Around a Cylinder 10 ................. 4 ...... 4 .................... 10 ............................ 10 ....................... 12 ....................................... 12 .............. 14 Relationship between the Reynolds Number and the Strouhal Number ....................................... 14 ................................. 18 lla Tucson Monotube Structure llb Phoenix Monotube Structure 12 Dimensions of Tucson Monotube Structure 13 ................................ 18 ................... 19 Beam-to-Column Connection for Tucson Monotube Structure ................................. 21 ........... 22 .................. 23 14 Column Foundatian for Tucson Monotube Structure 15 Dimensions of Phoenix Monotube Structure 16 Beam-to-Column Connection for Phoenix Monotube Structure ................................ 24 17a Finite P.1ctment Model of Tucson Monotube Structure ......... 27 17b Finite Element Model of Phoenix Monotube Structure ........ 28 18 .?irst ....... 42 Natural 3D Mode for Tucson Monotube Structure LIST OF FIGURES (Continued) Figure Page 19 Second Natural 3 D Mode f o r Tucson Monotube S t r u c t u r e ...... 43 20 F i r s t Natural 3D Mode f o r Phoenix Monotube S t r u c t u r e ...... 44 21 Second Natural 3 D Mode f o r Phoenix Monotube S t r u c t u r e ..... 45 22a D e f l e c t e d Shape f o r Tucson Monotube S t r u c t u r e Subjected t o S t a t i c Loads ................................. D e f l e c t e d Shape f o r Phoenix Monotube S t r u c t u r e Subjected t o S t a t i c Loads ................................ S t a t i c S t r e s s e s a t Midspan of Tucson Monotube S t r u c t u r e ................................. S t a t i c S t r e s s e s a t Midspan of Phoenix Monotube S t r u c t u r e ................................ S t a t i c S t r e s s e s a t Column Base of Tucson Monotube S t r u c t u r e ................................. S t a t i c S t r e s s e s a t Column Base of Phoenix Monotube S t r u c t u r e ................................ S t a t i c S t r e s s e s a t J o i n t of Tucson Monotube S t r u c t u r e ........................................ S t a t i c S t r e s s e s a t J o i n t of Phoenix Monotube S t r u c t u r e ................................ T y p i c a l Histogram f o r Dynamic A n a l y s i s of Monotube S t r u c t u r e s ................................... P e r i o d i c H i s t o g r a n f o r Dynamic A n a l y s i s of Monotube S t r u c t u r e s .................................... T y p i c a l S t r a i n Gage ....................................... Anemometer Mounted on S t r u c t u r e Data A c q u i s i t i o n Equipment ........................... ................................ vii LIST OF FIGURES (Continued) Figure ........... 31 Locations of Strain Gages on Monotube Structure 32a Two-wire Quarter Bridge Circuit 32b Three-wire Quarter Bridge Circuit 33a Mounted Strain Gage with Cable Attached 33b Mounted Strain Gage with Protective Wax Coating 34 Typical Wheatstone Bridge 35 Dynamic Deflections in Monotube Structure at Various Times .................s........................ ........................... ......................... ................... ........... ................................. Stress Envelope for Midspan Stresses of Tucson Monotube Structure .................. P'""" Stress Envelope for Midspan Stresses of Phoenix Monotube Structure ................................ Stress Envelope for Column Base Stresses of Tucson Monotube Structure ................................. Stress Envelope for Column Base Streaaes of Phoenix Monotube Structure ................................ Apparent Strain in Strain Gage Due to Temperature ......... Correlation of Stresses for Tucson Monotube Structure Total Stresses for Tucson Monotube Structure .............. Correlation of Stresses for Phoenix Monotube Structure Total Stresses for Phoenix Monotube Structure viii ..... .... ............. LIST OF TABLES Table 1 Page Coefficient of Drag for Various Shapes ...................... 2a El enent ~iameters-'andThicknesses for Tucson Monotube Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2b Element Diameters and Thicknesses for Phoenix Monotube Structure .................................. 3a Drag Forces on Signs for Tucson Monotube Structure .......... 3b Drag Forces on Signs for Phoenix Monotube Structure 4 Average Diameters of Finite Element Subassemblies ......... ........... 5a Natural Frequencies of Tucson Structure (CPS) ............... 5b Natural Frequencies of Phoenix Structure (CPS) .............. 6a Midspan Deflections for Tucson Structure Due to Dead Load and Static Wind Forces (in.) ...................... 6b Midspan Deflections for Phoenix Structure Due to Dead Load and Static Wind Forces (in.) ...................... 7a Stresses at Critical Points for Dynamic Analysis of Tucson Monotube Structure (ksi) .......................... 7b Stresses at Critical Points for Dynamic Analysis of Phoenix Monotube Structure (ksi) ......................... 8 Wind Speeds (nph) for which Periodic Oscillation Occur in the Beam ........................................... 9a Stresses (ksi) for Tucson Structure for Dynamic Loading with Structural Mass ........................ 9b Stresses (ksi) for Phoenix Structure for Dynamic Loading with Structural Mass ........................ 10a Vertical Downwards Deflections at Midspan for Tucson Structure with Structural Mass ................... 9 LIST OF TABLES (Continued) Page Table lob Vertical Downwards Deflections at Midspan for Phoenix Structure with Structural Mass ................... 70 lla Results of Data Acquisition Unit Calibration Test - Day One .............................................. 99 Ilb Results of Data Acquisition Unit Calibration Test - Day Two .............................................. 99 12 13 Computed and Measured Stresses for 60-Foot Structure ........................................... 101 Computed and Measured Stresses for 100-Foot Structure .......................................... 108 Chapter 1 INTRODUCTION For almost as long as there have been roads, there has been a need for road signs to display information to travelers. As the width of the roads grew, so did the size o f the structures, until today spans in excess of 100 feet are not uncommon. To support signs over these large spans, truss type strnctures have traditionally been used. These typically consist of two coluans supporting a truss or tri-cord element. The traffic signs are arranged in the desired locations and bolted in place. Figure 1 shows a typical truss type structure The design of sign support structures is based on the American Association of State Highway and Transportation Officialst (AASHTO) 1975 "Standard Specifications for Structural Supports for Highway Signs, Lumir~ariesand Traffic Signals" ( I ) , which was revised in 1978 and and one of its predecessors, the AASHTO 1979, 1968 "Specifications for the Design and Construction of Structural Supports for Highway Signs". In the remainder of this report these will be referred to as the Specifications. The Specifications set minimum performance guidelines. Among these are criteria governing deflections. Essentially, the maximum load static dead deflection, in units of feet, is limited to the empirical value of d2/400, where d is the depth of the sign in feet. If the deflection of a sign-support structure is found to be excessive, the designer can satisfy the Specifications simply by specifying a deeper sign e . larger d). The rationale and consequences of this approach will be discussed in some 1 detail in An later chapters. extensive evaluation of the deflection requirement has been given by Ehsani and Bjorhovde (2). Over the yenrs, the performlance of the truss structures has generally been satisfactory. However, there are some drawbacks to their use. They are expensive to fabricate and in many cases the application of the deflection requirement produces a structure which is not as economical as some of the pre-engineered structures that are available. latter types that has seen One increased use is the nonotube sign support structure. In addition to being more economical, the monotube also has the advantage of of the being more structure attractive than most truss structures. As shown in Pig. 2, monotube structiires are constructed of tapering tubular eleaents that have a constant wall linearly thickness. They consist of two columns supporting a beam in a fashion similar to the truss type structures. The columns are one piece tapered members, with the largest diameter at the base. The beam normally consists of pieces that are joined with longer spans may consist of 3 two tapered the largest diameter at nidspan. piece^, with Beams of the middle one having a constant dianeter. Figure 3 shows one of these longer 3-piece spans. For both types, &he beam is connected to the column by shown in Fig. simple supports, as 4. Currently, the Specifications do not provide sufficiently detailed guidelines for the design of manufacturers of monotube structures. As a result, the these structures utilize individual design criteria that rake direct comparisons between different products very difficult. 2 In , II ,I .II - "-li 1 --- ~:~~~~~Wlm7v7Yx~rg7Jr 8' III! II! I .. ,~' i" 0/ -"..~ Figure 1. =9 ~ ;r ,.F -lI...r:. -''"''',~,-~, --~ Typical Truss !iF Sign ..~ .. ~ Support _ Structure . :89,. .. I .. ~ , Figure 2. Typical Monotube 3 [11 Sign Support Structure ~". Figure 3. " .#!!k. Long Span Monotube Sign Support REIKNABLE POLE TOP ::: () . I ~ Structure 1- 1/4" DIA. RIVET HEAD PIN WITH CUTTER PIN C( ).;; I ..... f BEAM TYP. %" X 7" CARR/AGE BOLTS ~- ,~" MIN. THREAD Figure 4.. Typical Monotube Structure Beam-to-Column Connection 4 -- [I] addition, the structures tend cross-sectional properties. authorities in the position to vary This widely has of having in material as well as placed the transportation to accept or reject different designs with no rational guidelines to follow. The absence of adequate design guidelines can partly be attributed to the sparsity of research and engineering data on the strength and behavior of monotube structures. The first major work in this area was a conducted by Ehsani and Bjorhovde (3) in 1984 at project the University of Arizona. This study modeled a monotube structure using the finite element method to determine its response to various static 2nd dynamic loads. It was found that the d2/400 monotube structures. deflection criterion was inappropriate for Dead load deflections in excess of the d2/400 limit were calculated, although the stresses associated with these deflections were well below the magnitudes of the allowable levels. The first aonotube study was purely analytical and the accuracy of the results obtained is a function of the assumptions that were made model to the structure. It is important to compare such theoretical results with actual performance data for a real structure. to verify as well as the responses that have obtained from testing, preferably using subjected to a variety of been the modeling found. The latter should be a full-scale structure being service conditions. With such teat data and correlations in hand. improved design guidelines can be developed. Chapter 2 SCOPE Before the validity of any analytical study can its resuits shauld be be fnlly accepted, compared tc the actuel behavior of the subject in question. While the study by Ehsani and Bjorhovde (3) provided detailed on the behavior of monotube structures, it lacked comparison with the data performance of an actual structure. The study presented here was conducted in three parts. two actual structures were modeled In the first, for computer analysis. These were analyzed for various static and dynamic loads to determine their response to different wind speeds. The data that were collected include dynamic histograms. deflections and stresses for a variety of wind speeds. Part two involved field testing of the same two structures. By testing the structures under service conditions, the true response was obtained. Strains at critical points on the structure were recorded, along with the wind speed corresponding to these strains. The final part of the study was aimed at comparing and evaluating the results obtained in the first two parts. would be Through this comparison, it possible to judge the validity of the computer nodel, as well as to reveal any problem conditions such as resonance. This study has been limited to nonotube structures as described in Chapter 1. Cantilever structures were not considered, and fatigue related problems have also been ignored due to time limitations. Chapter 3 STRUCTURAL RESPONSE UNDER WIND LOADS For most sign structures, the only loads acting on the structure are gravity and wind. The forces due to gravity are simply the self weight of the structure; their magnitude and effect on the structure are relatively easy to determine. In contrast to the gravity loads, which are dynamic. There are a static, wind loads are number of reasons for this dynamic nature. First, the magnitude of the wind is not constant. The wind tends to gust. The direction of the wind also changes. Finally. the cross-sectional shape of the structural elenents may cause dynamlc behavior. An object placed in an air stream will cause a disturbance in that air stream. This disturbance will create pressure on the object, the size and shape of which will determine the intensity and distribution of pressure. the As an illustration, it is this phenomenon that cre~testhe lift on an airplane wing. The wing is shaped such that as air flows around it, the pressure on the wing surface is larger on the bottom than on the top, as shown in Fig. 5. Thus, the airplane rises. In addition to lift, another force that is exerted on the object is drag. This has been experienced by anyone trying to pedal a bicycle into the wind. As long as the velocity of the airstream is constant, the drag force remains constant. Drag is therefore considered a static force. The magnitude of the drag force, shown in Pig. 6, can be computed as : 7 P where F PcD A V ~ ~ is the drag force, A perpendicular to the flow, of = the airstream, and p (1 is the projected area of the object is the density of the air, Vo is the velocity CD is the coefficient of drag for the object (4). Table 1 gives the coefficient of drag for some common shapes. If the object in the air stream has an irregular shape, the pressure distribution will also be irregular. Thus, for a certain range of wind speeds, the object may develop vibrations or direction of flow ( 5 ) . A oscillations normal to the common example of oscillation observed in telephone cables in a the phenomenon is the strong wind. Sometimes, these oscillations can result in excessive deformations or even collapse of a structure. This happens when the vibrations induced by have a the airflow frequency that is equal or close to one of the natural frequencies of the structure, and reflects the condition of structural resonance. The occurrence of resonance means that the structure will continue to oscillate with no additional energy or Probably the most played load applied to the structure. famous structural failure where resonance at least a part was the collapse of the Tacoma Narrows Bridge in the State of Washington. This bridge failed at a wind speed of 42 mph, although had it been designed to withstand winds up to 100 mph if no oscillations had occurred (6). However, the wind-induced vibrations were close to one of the natural frequencies of the bridge and this contributed to the collapse. The wind-induced vibrations are caused by vortex shedding. a phenomenon known as Fluid flowing around an object will develop vortices in 8 AS SPEED OF AIRFLOW INCREASES PRESSURE INCREASE Figure 5 . Airfoil Illustrating Principle of Lift Figure 6. Drag on Plate in Air Stream TABLE 1. Drag Coefficient for Various shape^ Form of Body L/D R Circular Disk Rectangular Plate ( L = length, D = width) Tandem Disks (L = Spacing) Cy i inder ( a x i s parallel to flow) 0 1 2 4 7 Cylinder ( a x i s perpendicular to flow) 1 105 5 0.74 0.90 20 1.20 4 5 Streamlined Foil 0.63 >5 x 105 0.35 the wake. These will alternate from one side of the object to the other, as illustrated in Fig. 7 for flow around a cylinder. study of these vortices was originated by von Karman (6), using a The double row of vortices in two-dimensional flow. He found stable equilibrium configuration that the only for the double row resulted when the vortices of one row were exactly opposite to points half-way between the vortices in the other row. Von Karman also found that for the rows to be stable, they would have to be spaced at 0.281 times the distance between two adjacent vortices of one row. Such an arrangement is known as a Karman vortex sheet and is illustrated in Fig. 8. Von Karaan hased this treatment of vortex shedding on the assumption of a perfect fluid. By definition, the only property possessed by a perfect fluid is density. Therefore, this treatment does not reflect the influence of fluid viscosity. Flow of a viscous fluid is accompanied by a pressure gradient that is proportional to fluid. the dynamic viscosity of the Since the density and viscosity for air are both relatively small, the viscosity can have as much effect on fluid flow as the density and must be taken into account. The Reynolds number, R, characterizes the relative importance of viscous action, with a highe~. number lesser importance ( 4 ) . indicating a Therefore, an infinite value of R corresponds to a flow in which viscous resistance plays no part. For flow past a cylinder, a number of changes occur as the Reynolds number and increases. For instance, for small values of R, the flow is smooth unseparated. vortices For higher values of R, two symmetrical standing form behind the cylinder, as shown in Pig. 9. As R increases, 11 Figure 7 . Vortices f o r Flow around Cylinder Figure 8. Karman Vortex Sheet these vortices stretch downstream. When vortices alternate in detaching from R is approximately 40, the the two sides of the cylinder and move downstream. This is the start of vortex shedding. For R values between 40 and 300, the shedding is very regular in both amplitude and frequency and can be approximated by a Karman sheet. As R increases past 300, the flow becomes irregular. The vortices are still shedding with a predominant frequency, but their amplitude is not easily determined, since it is more or less random. This irregular flow continues until R equals 3 x 105. At this point, the flow is so turbulent that the vortex sheet is no longer recognizable. For the range of Reynolds numbers where vortex the frequency with which shedding does occur, the vortices are shed can be expressed non-dimensionally by the Strouhal number, S. Since the vortex shedding frequency varies with R, S also varies with R, as shown in Pig. 10. For aonotube structures, the fluid is air and the structure can be considered a long cylinder. The Reynolds number is then defined as (6): R = 780.5.V-D (2) where V is the airspeed in riles per hour and D is the cylinder diameter in inches. It can be seen that except when dealing with very small cylinders and low wind speeds, R will be greater than 300. For values of R between 300 and 3x105, the shedding frequency is sinsoidual but with a random amplitude. For R larger than 3x105, both the frequency and the amplitude are random. For the range of 300 < R < 3x105, the vortex shedding forces rust be determined from the pressure distribution. 13 Figure 9. Figure 10. Standing Vortices for Flow around Cylinder Relationship between the Reynolds Number and the Strouhal Number The generally accepted expression for this force is ( 7 ) : where F(t) is the tine dependent vortex shedding f0rce.y is the density of air, V is the wind velocity, Ap is the projected area of the cylinder, C L is the coefficient of lift, R is the shedding frequency, and time. To account for the random t is the force amplitude, Weaver (8) experinelltally determined the root-mean-square (rms) values of CL, denoted as - CL. and using these, the expression for the vortex shedding forces becomes (4): A ~ sin C Q~t ~ ( t )= 1 / 2 ~ The determination equation. The R is of vortex shedding (4) critical in the use frequency is determined this of from the equation (2) Q = -sv 15 D where S is the Strouhal number, V is the air speed, and D is the cylinder diameter. As an example, the forcing function for a wind speed of 15 mph and a cylinder 14 in. in diameter will be determined. Prom Eq. loglO (780.5.15-14) number is S = = 5.21. From Pig. (2). loglO~ = 11, the corresponding Strouhal 1.48. Prom Eq. (5), using S in., the value of = 1.48,V = 15 nph = 264 in/sec. and D is found to be F(t) is now determined from Eq. (4). using CL = 1.0, as = 14 P(t) = 1/2 (0.002378) (22.0)~$(1.0) = 0.575 Ap sin (27.91t) sin (27.91t) where the wind speed is 22.0 ft/sec. From this expression. the forces on the structure can be deternined, given the corresponding values of Ap. For the ronotube structure, the vibrations caused shedding are more pronounced in by the vortex the beam, as it is a simply supported element. These vibrations are also more pronounced in longer spans. In the range of wind speeds where 300 < R < 3x105, the vibrations are usually of small amplitude, unless their frequency is close to the resonant frequency of the structure. In this case, the deflections may be excessive. As stated in Chapter 1, the quantity d2/400 is an empirically derived value. This criterion was originally developed primarily for use with truss type structures, where vortex shedding has a much smaller effect. This provision is very restrictive. Even structures with large signs feet deep) can deflect no more than 0.125 inches. Other codes ( a 7 (9.10) are not as restrictive in their deflection criterion. A deflection criterion should therefore be developed for the aonotllhe structures, independent of that used for trusses. Chapter 4 ANALYSIS OF MONOTUBE STRUCTURES To help in developing the design guidelines, as well as to provide data for a detailed compari8on with extensive the results structural analyses were performed. of of the models under static and testing, This evaluation was done by modeling the two tested structures using the finite response full-scale element dynamic method. loading was found, including the determination of the first ten natural frequencies and three-dimensional behavior. Detailed The stress for and two- deflection computations were also made. 4.1 Modeled Structures For this study, the Arizona shop drawings and site plans Department for two of Transportation sign structures. Both of these structures had been designed in accordance with the AASHTO (1). provided specifications The first structure has a span of 60 feet, and Is located across the north-bound lanes of Miracle Mile, just north of Glenn Avenue Arizona. This Arizona. of located across University Drive and University Hohokam Drive west Expressway in of Phoenix, are linearly given in Pig. 12. The tapering single tubes, with the largest diameter at the base. Due to the site topography, the west column is 21" shorter the column, east the This atructure is shown in Pig. l l b . The dimensions of the Tucson structure are columns Tucson, structure is shown in Fig. lla. The second atructure has a span of 100 feet, and is intersection in in order for than the bean to be level. The beam is also 17 .... II iii ."' III ' - .,' "..tZI -. 89 --'1'1' ~ .~ .", I -.g -Ell ~~-: r~, I Figure 11a. Tucson 11b. Phoenix Monotube Structure .,..-, ... --',-"- Figure 18 rI] Monotube Structure ul G 0 'PI ul c al .cBl PI constructed of linearly tapering elements. It is spliced with the largest diameter at midspan. The beam-to-column connection is shown in Fig. 13. It provides moment resistance to vertical loads and essentially free rotation under horizontal loads. This connection also offsets the center line of beam 18" from some the centerline of the the column, thus producing a true three-dimensional structure. The details of the column base and foundation are shown in Pig. 14. The column base can be reasonably assumed to be fully fixed in all directions. The location of the traffic signs can be seen in Pig. 12. The dinensions of the Phoenix structure are given columns are of 15. The similar construction to the Tucson structure. The beam, however, is made of between in Pig. three segments segments at approximately instead of two, the third with points. the splices The two outer segments have their largest diameter at the splices and taper linearly to the ends. The interior segment is of constant diameter. The beam is also cambered, so that the centroidal axis at midspan is 17" above the centroidal axis at the ends of the beam. The beam-to-column connection for the Phoenix structure is not the same as the Tucson structure. While the moment resistances are comparable, the connection is such that the axes of the columns and the beam all lie in the same plane. This connection is shown in Pig. 16. The column base is similar to that shown in Pig. 14 and can also be assumed to be fully fixed. The 1ocat.ions of the signs for this structure are shown in Pig. 15. 20 Figure 13. Beam-to-Column Connection for Tucson Monotube Structure Figure 14. Column Foundation for Tucson Monotube Structure Figure 16. Beam-to-Column Connection for Phoenix Monotube Structure 4.2 Computer Programs The structural analysis of the rnonotube structures was accomplished using a set of computer (Graphics-oriented System) (8). programs Interactive collectively Finite as GIFTS element analysis Time-sharing These programs constitute a post-processing and known finite clement pre- analysis package, which can be loaded and run on a variety of minicornputera and time-sharing systems. It can be used with standard alphanuaeric terminal or with a Department of Aerospace and a graphics terminal. For this study, the GIFTS package was run on a Data General Eclipse computer of Arf zona and the Mechanical Engineering at the University of . Each of the GIFTS programs (modules) is fully compatible with all of the other modules. A module ray perform a specific function, such as computing the natural frequencies of a structure, or a class of functions such as mesh definition and element generation. Many of the modules can be operated in either batch mode or interactively. In batch mode, the nodules obtain commands and data from a pre-existing steering file. In interactive mode, the user must input the commands and data through the keyboard. GIFTS can handle many different loads and load cases, and the stresses and deflections can be computed for each load case. Plots of deflected structure or also be provided. the the stress distribution on any cross-section can 4.3 Finite Element Model Development Using the guidelines of the GIPTS package model for each (11). a finite element structure was developed. These models are shown in Figs. 17a and 17b for the Tucson and Phoenix structures, respectively. The elements in both structures were modeled as beam one node at each end. was allowed displacements to have elements with In order to be as realistic as possible, each node three in the x-, translational degrees of y-, and z-directions), as well as three rotational degrees of freedom (rotations about the x-, y-, and The x-, y-, and (i,e,, freedom z-axes). z-axes for each model are shown in Pigs. 17a and 17b. These axes were considered to be the global axes for each model. The scale for this figure is shown on the lower left corner. For example, the length of the axes if Fig. 17a equals 60 inches. In GIPTS, a variety of cross-sectional shapes can be used beam for the elements, including the standard I-section and a hollow, circular section. Thus, the hollow circular sections were used for the beam and column elements while the I-shape was used for the elements connecting the (e.g., beam and the columns. GIFTS, however, cannot accept non-prismatic tapered) elements. To circumvent this limitation, each element was assumed to have a constant cross-section, with dimensions equal to the average of structure. be the two end cross-sections of the element in the actual In addition, a larger number of elements than would normally required were used in each model. The wall thickness of the circular elements was taken as the minimum specified on the shop drawings. of element diameters and thicknesses is given in Tables 2a and 2b. 26 A list Table 2a. Element No. 3 Element Diameters and Thicknesses for Tucson Structure. Dia. (in) Thicknesses (in.) 12.78 0.239 12.92 tI 11.02 I 12.04 I( 11.08 I 11.14 I, 10.22 I, 10.24 *I 12.96 13.72 14.48 15.12 15.18 15.68 16.12 16.58 14.92 14.20 13.42 12.90 Table 2b. Elenent Diameters and Thicknesses for Phoenix Structure. Element No. Dla. (in) Thicknesses (in.) The most difficult element to model was that representing the beam-to-column connection. The shear capacity of a connection is based on its cross-sectional area, while the flexural capacity depends on the moment of inertia. To ensure a realistic behavior for shear, the connection was modeled as a short I-section beam with the same area as the actual connection. The weak axis of the I-bear was oriented least bending resistance in the horizontal simple support condition for the beam under to give the direction, reflecting the the action of horizontal {perpendicular to the plane of the monotube structure) loads. The element was proportioned to give a moment capacity approximating that of in the vertical the real connection. The I- section was actually similar to a flat plate, as the flanges were only slightly wider web and direction than the ~ ) . The connection element for of negligible thickness ( 1 x 1 0 - ~in. the Tucson structure was 10" x 0.825" in section and 18" long. The connection element for the Phoenix structure was 7.1" x 1.25" and 7 . 8 " long. In selecting the nodal mesh for each structure, a node was placed at the actual attachment points of each traffic sign for signs wider than 4 feet, and at the center of the sign for signs 4 feet wide or Jess. In this manner, the mass of the signs would be applied at a node. A node was also placed at the midspan of the beam, to be able to determine deflections and stresses at this important point. The element lengths were maintained between 4 and 6 feet, and wherever it was possible, the elements were given the same length. This was difficult to accomplish for the Tucson structure, primarily due to the 31 sign locations. The Phoenix structure, however, was more easily modeled with elements of constant length. 4.4 Static Loads on Structure As explained in Chapter 3, air flowing past an object will drag force. However, for wind speeds less than about 23 mph the drag will be negligible, although the drag on the signs may be significant. mph create a wind speed is the upper The 23 limit for which the vortex shedding is deterministic. Using Eq. (1) and the tables for the coefficient of drag. CD, published by Rouse ( 4 ) , the drag force on the signs was computed for the wind speeds considered. These forces are shown in Tables 3a and 3b for the Tucson and Phoenix structures, respectively. A static analysis was then performed for the various wind signs and speeds, using the drag on the the self weight of the structure. The results of this analysis will be discussed in detail later in this chapter. The static analysis was performed by applying the drag force as a horizontal load. perpendicular to the axes of the beam and the columns. The loads were applied at the nodes corresponding to the attachment points of the signs. In addition, the weight of the signs was included as a lumped mass applied at these nodes. GIFTS can automatically calculate the mass nodes. of each element, and applies these massea in lumped form at the Table 3 a . Wind Speed Drag Forces on Signs of Tucson Structure (lbs.) (MPHL 7 ' x 13' S i g n Node 14 Node 16 7 ' x 10' Slgn Node 19 Node 20 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 23.2* *This is the maximum wind speed that was recorded f o r t h i s s t r u c t u r e . Table 3b. Drag F o r c e s on S i g n s o f Phoenix S t r u c t u r e (lbs.). A l l S i g n s are 4 ' x 5 ' Node 18 Node 20 Wind Speed (MPH) Node 15 2.5 0.353 0.353 5.0 1.411 1.411 7.5 3.175 3.175 10.0 5.644 5.644 12.5 8.819 8.819 15.0 12.699 12.699 17.5 17.285 17.285 20.0 22.576 22.576 22. I* 27.566 27.566 Node 22 *This is t h e maximum wind s p e e d t h a t was r e c o r d e d f o r t h i s s t r u c t u r e . 4.5 Dynamic Loads on Structure The equation for the vortex shedding frequency, Eq. ( 5 ) . is heavily dependent on the diameter of tapered cylinders of the cylinder. This means that for the the monotube structure, the shedding frequency will vary along the length of the member. This condition is difficult, if not impossible to model. Therefore, each structure was divided into three subassemblies, where the columns and the beam each was considered as one. An average diameter was determined for each subassembly, using the diameters of the elements in the subassembly. This average diameter was then used to compute the vortex shedding frequency and the corresponding forces for each node. The overage diameters of given in Table 4 . each substructure are The simplification will not result in any significant differences between the wind loads on the actual and the modeled structures. To perform a dynamic analysis of a structure using GIFTS, the loads on the structure at specific points in tire must be entered into the GIPTS modules. GIPTS assumes a linear load variation over any individual time interval. For this study, the loads were intervals for a total determined at 0.5 second time of 32 seconds. This gives a sum of 64 load increments. The time of 32 seconds was chosen on the basis of the earlier aonotube study ( 3 ) . which found that this would be a sufficient period to detect any form of excessive deformation (i.e., resonance). should be noted that apart from a wind However, it tunnel, the probability of a structure experiencing a constant wind speed for as long a period 35 as 32 Table 4. Average Diameters of Finite Element Subassemblies (in). Tucson Phoenix Column 1 11.50 13.81 Column 2 11.59 13.81 Beam 14.40 15.20 seconds will be extremely small. The wind generally blows in gusts, and while the variation in velocity may not be great, it is sufficient to keep the structure from vibrating at one frequency for any extended period of time. The probability of actual resonance occurring is therefore negligible (2,3). The loads were given as nodal loads. The magnitudes of these loads were determined using Eq. ( 4 ) . the average diameter of and the subaasemblies, the tributary projected area of each node. The loads were determined as acting normal to the axis of the subassembly and perpendicular to the direction of the wind. Dynamic analyses were performed for each structure for wind speeds ranging from 2.5 mph to 20 mph in steps of 2.5 mph. For the Tucson structure, additional analyses were performed for wind speeds of 22.5 and 23.2 mph. For the Phoenix structure, an additional analysis was performed for a wind speed of 22.1 mph. Above these maximum wind speeds, the vortex shedding forces are of random magnitude, and scope of this study. The 2.5 thus considered beyond the mph interval was chosen as a compromise between accuracy, data entry time, and computer cost. GIFTS allows the user to choose one of analysis. four approaches for dynamic These are Houbolt's Scheme, Newmark's Beta Method, Wilson's Theta Method, and the Trapezoidal Rule (8). Houbolt's Scheme was chosen for this study, since it is generally more accurate than the Trapezoidal Rule and does not need to use the arbitrary constants of Newmark's and Wilson's Methods. While recommended values for these constants exist. it is not known if they are applicable for monotube structures. 37 4.6 Natural Frequencies of Vibration The natural frequencies of a dynamic response of structure are representative of the structure in the absence of any external loads. They are the frequencies at which the structure will energy the vibrate when no is being provided to the structural system and can be determined by an iterative technique such as subspace iteration. The natural vibration characteristics of when a structure are important the structure is subjected to dynamic forces. The frequencies of the loads and those of the structure may combine in such a manner as to give a response that of a natural frequency. In the worst is a magnification case, the loading frequency equals a natural frequency. This causes the structure to develop ever-increasing deflections and thus constitutes resonances; the consequences of which were discussed in Chapter. 3. The structure can be modeled as a distributed or lumped mass system. The distributed mass system results in a structure with an infinite number of degrees of freedom. The lumped mass system results in a structure with the number of degrees of freedom given by: NDP where NP = = ( 61 (NP-NFP) - (NPP) the number of nodal points in structure, NFP degrees of freedom at each node, and suppressed degrees of freedom. (NPP), = the number of is the total number of The value of NDP therefore takes into account whether the structure has been modeled as a two- (2D) or three- dimensional (3D) system. GIFTS uses the subspace iteration technique, which is based on the lumped mass approach. In the computation of the natural 38 frequencies, the models that were used for the static and dynamic analyses also were utilized. The structural damping has been conservatively assumed to be zero. Tables 5a and 5b give the natural frequencies for the first 10 modes for both structures. These include 2D as well as 3D data. represents displacements in the x- The 2D data and y-directions, since the displacements in the out-of-plane direction (2-direction) havz beec suppressed. Prom Table 5a, it can be seen for the Tucson ( 6 0 foot) structure. the following 2D and 3D modes have the same frequencies: f l (2D) = f 2 (3D) = 2.834 cps f z (2D) = fg (3D) = 3.265 CPS f3 (2D) = fg (3D) - 12.290 cps f4 (20) = f~ (3D) = 27.301 cps f10 (3D) = 31.780 cps f5 (2D) Similarly, for the Phoenix (100 foot) structure, Table 5b gives f l (2D) (2D) = fl (3D) = 1.467 cps (3D) = 3.055 cps = f3 f3 (2D) = fg (3D) = 5.001 cps f4 (2D) = fg (3D) = 10.872 cps f5 (2D) = f10 (3D) Since the 2D nodes are all - 19.263 cps in-plane, this indicates that the above mentioned 3D nodes are dominated by in-plane behavior. Figures 18 and 19 show the first two 3D mode shape8 for the Tucson structure. Figures 20 and 21 show the first two 3D mode 39 shapes for the Table 5 a . Natural Frequencies of Tucaon Structure ( C P S ) . Phoenix structure. Similar to Fig. 17, the scales for the model and the deflections are given in the lower left and right corners of the figures, respectively. It should be understood that the deflected shapes shown do not indicate actual displacements, since the natural frequencies are not associated with any load. However, they do give an indication of the shapes that can be expected for a vabrating structure. 4.7 Static Load Results Both models were analyzed for a combination of static loads. These loads included the weight of the strucutral elements, the weight of the signs, and the drag on the signs. The drag forces for various wind speeds are shown in Table 3a for the Tucson (60 ft) structure and In Table 3b for the Phoenix (100 ft) structure. These forces were applied at the attachment points of the signs. For the wind speeds considered, the gravity loads due to the weight of the structure govern in all cases. structures can be seen in Pig. 22a and The deflected shape of the 22b. The vertical deflections due to gravity loads and static wind forces at the aidspan of the beam are given in Tables 6a and 6b. It can be seen that they are identical in every case. The out-of-plane deflections did vary with the wind speed as shown in Tables 6a and 6b. However, considerably smaller than the the out-of-plane deflections are in-plane deflections. This is especially noteworthy in the case of the Tucson structure which has two relatively large signs. Even with these large signs, drag was not a major factor. The stresses at midspan are also principally due to welght of the structure. The stress distributions for shear stress and normal stress at 46 Figure 22a. Deflected Shape for Tucson Monotube Structure Subjected to Static Gravity Loads (Elevation of Deflected structure) Table 6a. Midspan Deflections for Tucson Structure Due to Dead Load and Static Wind Forces (in.). Direction* Wind Speed 2.5 x 0.002 JL. 1.123 *For labeling of x - , y- and z-axes, see Pig. 17a. 0.008 Table 6b. Midspan Deflections for Phoenix Structure Due to Deed Load and Static Wind Forces (in.). Wind Speed 2.5 x 0.000 Direction* Y 5.513 *For labeling of x-, y- and z-axes, see Pig. 17a z 0.003 midspan of the Tucson structure are shown in Fig. 23a. Figure 23b shows a similar plot for the Phoenix structure. The magnitudes o f did not the stresses vary with the wind speed, but remained constant at the indicated values. For the Tucson structure, the aax.taum normal ksi, which stress was + 4.38 is about 13% of the yield stress of 34 ksi. The magnitude of the normal stress for the Phoenix structure was 8.86ksi, which is about 26% of the yield stress. The stresses at the column base for the Tucson structure became larger as the wind speed increased. The stress for the Phoenix structure, however, remained close to constant. This is probably due to the larger sign area for the Tucson structure, which results in higher drag forces. The drag on the Phoenix signs appears to be negligible. The maximum normal stress at the column base for the Tucson structure is and for the Phoenix structure + 2.51 ksi. Both are well below the yield stress of the steel. The stress distributions at shown in Figs. 24a and 1.34 ksi, 24b for the column base are the Tucson and Phoenix structures, respectively. At the connection between the column and the beam, shear stress is the governing factor. For both structures, the finite element model showed some normal stress, but this is largely due to the way was modeled rather than any actual stress. The shear stress at the joint was close to constant for both structures. The gravity govern. loads appear to For the Tucson structure the maximum shear stress is 2.64 ksi. For the Phoenix structure, it is 3.22 ksi. Both are well yield the joint stress of the steel, which 51 is 19.4 ksi. below the shear The shear stress distributions are shown in Pigs. 25a and 25b for the Tucson and Phoenix structures. As has been seen. the stresses at each the three critical locations on structure are significantly below the representative yield values for the steel. ft., and Por deflections, the Tucson structure has a sign depth of 7 the maximum allowable deflection according to the Specifications is: This compares to the actual value of inches. 1.123 For the Phoenix structure with 5-foot deep signs, the allowable deflection is: ' I and the 1 actual value is 5.613 inches. structure satisfies the d2/400 criterion, Phoenix structure with excess of the allowable. that if 5-foot It is seen that whereas the Tucson using 7-f oot deep signs, the signs exhibits a deflection very much in By the aame token, however, it is also clear the Tucson structure were to utilize 6-foot deep signs, it, too, would violate the AASHTO deflection criterion. 4.8 Dynamic Load Results The same models used for the static dynamic load tests. load tests were used for the The loads for these tests were determined using Eq. ( 4 The loads were calculated for the aame wind speeds as those used the static analysis. 56 in Initially, the loading included only those loads calculated from Eq. (4) and the drag forces on conducted over a tine period forcing function the signs. of input at 0 . 5 32 The transient analysis was seconds, with second the loads from intervals. the The weight of the structure was not included in these analyses. In order to determine the critical stress levels for each wind a hjstogram speed. for various points was constructed, using the GIFTS modules. Points considered included the midspan of the beaa for in-plane deflections, and the top of the left column for out-of-plane deflections. A typical histogram is shown in Fig. 2 6 . From the histogram, the times of determined, and the maximum the corresponding stresses are shown in Tables 7a and 7b. Prom Table 7a, it is apparent that the column base point deflections were for the Tucson structure. is the most critical However, Table 7b indicates that the critical point on the Phoenix structure is at the midspan of the beam. This shift in the critical location is probably due to the larger relative stiffness of the beam in the Tucson structure. The average moment of inertia, Iave for the bean of the Tucson structure is 206.6 in4, while for the Phoenix structures it is 2 6 1 . 5 in4. Iave/L, then the stiffness of The corresponding 261.5/(100*12) = values 0.22. for If the stiffness is defined as the Tucson sign is 206.6/(60*12) the Phoenix structure's = 0.29. beaa Is For a simply supported beaa, a larger stiffness will result in a lower stress level for a given load, thus the stresses at the midspan of the Tucson structure are relatively less critical than for the Phoenix structure. 59 Table 7a. Wind Speed Stressee at Critical Points for Dynamic Analysis of Tucson Structure ( k s i ) . Shear at Node 5 Normal at Node 1 Normal at Node 17 2.5 0.005 0.019 0.012 6.0 0.028 0.036 0.048 7.5 0.026 0.078 0.540 10.0 0.038 0.148 0.095 12.5 0.026 0.174 0.101 15.0 0.042 0.265 0.157 17.5 0.053 0.357 3.210 20.0 0.072 0.474 0.276 22.5 0.026 0.595 0.329 23.2 0.128 1.301 0.727 Table 7b. Stresses at Critical Points for Dynamic Analysis of Phoenix Structure (ksi). Wind Speed Shear at Node 5 Normal at Node 1 Normal at l o d e 16 2.5 0.005 0.009 0.017 6.0 0.017 0.020 0.038 7.6 0.025 0.029 0.071 10.0 0.051 0.068 0.125 12.5 0.163 0.196 0.314 15.0 0.186 0.252 0.483 17.5 0.159 0.206 0.330 20.0 0.246 0.270 0.525 22.1 0.252 0.330 0.674 Another factor may be the size of the signs. The signs on the Tucson structure are significantly larger than on the Phoenix structure. The moment induced at the base by the drag on the signs will than the moment be much larger induced at midpsan. This will cause a greater stress at the column base. An interesting development. occurs between the wind speeds of 22.5 mph and 23.2 mph for the Tucson structure. The stresses more than double for the small increase in wind speed. This does not occur at any other wind speed. The deflections also show a disproportionate increase in their magnitude. This increase is due to the beam approaching one of its natural frequencies. Prior studies (2.3) indicated member diameter ( ~ 1 4 " )would that a structure with this have a natural frequency at a wind speed of approximate1y 23 mph . Because the beam is simply supported, it can be consjdered to act by itself. For the wind speed of 23.2 mph, the beam vibrates at a frequency of 5.94 cps. The second 3D natural frequency of the beam is 6.44 cps. The deflections and stresses increase as the structural frequency approaches a natural frequency. Another interesting phenomenon occurs for both the Tucson and Phoenix structures. For various wind speeds, the histogram for the node at the midspan of the beam shows a periodic vertical deflection. This is shown in Pig. 27. The frequency of these oscillations is very low (between 0.082 to 0.165 cpe). These are well below any of the natural frequencies, nor do they cause excessive stresses or deflections, as would natural frequency. be expected of a These oscillations appear to have been caused by the 63 0.5 sec. time step chosen in the transient analysis. oscillations are real, additional However, if these studies are needed to determine their effect on the fatigue strength of the structure. The wind speeds for which these periodic oscillations occur are shown in Table 8. The results discussed so far are somewhat misleading. For the dynamic analysis, the mass of the structure was not considered. However, the mass of the structure will This may increase the inertia of the vibrating structure. increase the deflections and stresses experienced by the structure. Therefore, additional computer analyses were run to include the mass of the structure. The maxiaua stresses for each wind speed are given in Tables 9a and 9b for the three critical points on each structure. It is interesting to note that for both structures the magnitudes of the maxinum stresses equal superimposed stresses from the static analysis and the the first dynamic analysis. This can render the dynamic analysis simpler by removing the structural mass from the calculations. A simple static analysis will take care of that. The deflections can also be superimposed. The deflections caused by the self weight (= dead load) dominate. The maximum deflections for the various wind speeds are given in Tables 10a and lob. 4.9 Conclusions for Analytical Studies Prom this, it can be seen that the monotube structures as modeled are safe for the wind speeds considered. The maximum stresses were lese than 40% of the yield stress in all cases. The possibility of fatigue failure warrants further study, especially where the periodic oscillations occur. 65 Table 8 . Wind Speeds (mph) f o r which Periodic Oscillation Occur in the Beam. Tucson ( 6 0 ' ) 10.0 17.5 20.0 Phoenix (100' ) 7.5 Table 9a. S t r e s s e s (ksi) f o r Tucson Structure f o r Dynamic Loading with Structure Mass. Wind Speed (mph) Shear a t Beam End Normal a t Column Base Normal a t Beam Mldspan Table 9b. Stresses ( k s i ) for Phoenix Structure for Dynamic Loadlng with Structure Mass. Wind Speed (mph) Shear at Beam End Normal at Column Base Normal at Beam Midspan Table 10a. Vertical Downwards Deflections a t Midspan for Tucson Structure w i t h Structure Mass. Wind -- Speed (mph) Bflection ( i n . ) 2.5 1.12 5.0 1.13 7.5 1.13 10.0 1.14 12.5 1.13 15.0 1.14 17.5 1.14 20 .o 1.15 22.5 1.16 23.2 1.18 Table l o b . Vertical Downwards Deflections at Mfdspan for Phoenix Structure with Structure Mass. Wind Speed (nph) Deflection (in.) 2.5 5.52 5.0 5.53 7.5 5.55 10.0 5.55 12.5 5.63 15.0 5.75 17.5 5.65 20.0 5.74 22.1 5.86 Neither of the structures nodeled meets the d2/400 deflection limitation. Since the stress levels were low, even for the large deflections computed, this indicates that the d2/400 limitation may be unnecessarily restrictive when applied to monotube structures. As stated previously, these parametric studies are only as accurate as the data used to model the structures and forces. The results presented in this chapter must be compared with the results of the full-scale field testing discussed in Chapter 5 . Chapter 5 FIELD TESTING OF PULL-SCALE STRUCTURES The second phase of the research study consisted of actual sign the testing of support structures under service conditions. This was accomplished by instrumenting two strain gages, as well structures with electrical resistance as an anemometer to determine wind velocity and direction. The data were used to determine the st-ressesand strains at a number of important locations in the structures, and subsequently to evaluate the correlation between theoretical and actual structural performance. 5.1 Description of Equipment and Software The equipment used for the field testing can be categorized into two main groups: The first was the portable equipment used for the data collection, and included all sensors, electrical hardware and software used in obtaining data directly from the structures. The second group consisted of the equipment that was used for data reduction. This included all the electrical hardware and software that was utilized analyze the collected data. to manipulate and The data collection group can be further subdivided into six sections; namely, sensors, data acquisition, control, mass storage, communications, and support. The sensors are the strain gages and the anemometer. The gages were of the bonded electrical resistance foil type, with a resistance of 0.3 120 t R , a gage length of 10 mm, and a gage factor of 2.12. A typical gage is shown in Fig. 28. The anemometer was a Weathertronics Combination Wind 72 Sensor, Model 2132, consisting of 3 standard anemometer cups connected to an AC generator, and a weather vane connected to a DC potentiometer. This unit can be seen in Pig. 29. The data acquisition equipment was success of the field work. To read of crucial importance to the the strain gages as well as the anemometer, a Hewlett Packard (HP) Data Acquisition and Cont-rolUnit, Model 3421A. was used. This can measure AC and DC voltages, resistances, and amperages, and can also be used to control other devices. It also has a built-in power output that may be utilized to run peripheral devices. unit The can accept input from twenty different sources or channels. For the field measurements of this project, 16 channels were used by the strain gages, 1 by the wind speed sensor, and 1 by the wind direction sensor, for a total of 18. The control unit of the data collection group was an HP-41CX calculator. This is a user programmable calculator whose software had been designed to control the data collection activities and a number arithmetic functions. The calculator has a built-in clock and calendar, making it possible to record the data and gages. The data were of time of initially stored each reading of the in the calculator's memory and subsequently transferred to the mass storage unit. The software used Geotechnical by the BP-41CX was originally written by Engineering and Mining Services, Inc. of Littleton. Colorado. However, it was found necessary to modify portions of the code to better perform the required tasks. A comp1et.e listing of this software is given in Appendix A. L C O P P E R - ~ ~ A T ETERMiNt.Ls D Figure 28. Figure 29. Typical Strain Gage Anemometer Mounted on Structure 74 After the strain gages were read, the readines were stored in the calculator's memory. When this memory was full, the readings were transferred to the mass storage unit, an HP Model 82161A cassette drive. This tape drive uses micro-cassettes to record the data, and each cassette can store about 128 Kb of data, or slightly over 16,000 numbers. The HP-3421A, -41CX, and tape drive were arranged to communicate by means of a HP Interface Loop (HP-11,). This is a serial loop that is controlled by the HP-IL module which is connected to the HP-41CX. Through this loop, directions and data are sent from one device to another. this is a serial As loop. any device that is shut off or disconnected will interrupt data flow in the loop. The support equipment consisted of a multi-channel nC power supply, a Wheatstone Bridge circuit board, a 5 HP, 2000 Watt portable generator, and a radial blower. The power supply was used to provide a voltage to the gages and the wind direction potentiometer. The Wheatstone Bridge circuits were connected to the strain gages to form quarter bridges. This will discussed be in detail later in this chapter. The portable generator was needed to provide power at the remote testing sites. and the blower was necessory to keep the power supply from overheating. Figure 30 shows the 3421A, 41CX, tape drive, power supply, Wheatstone Bridge board, and blower. The data reduction equipment group comprised of the following items: an HP Model 9836 (Series 200) desk top computer, an HP Model 82169A HP-TL/HP-IB interface, an HP 82905B dot-matrix printer, and an HP Model 7470A two-pen plotter. DC Power Supply 1 Fan HP-3421 Data Acquisition unit/ Figure 30. ' Cassette Drive Data Acquisition Equipment The HP-9836 computer was equipped with two 270 Kb double-sided disk drives, and peripheral 640 K b of random access memory. It connunicated with devices through the Hewlett-Packard Interface Bus (HP-IB). The computer was used for all the coaputational work of the project, with the exception of running the GIFTS program. The dot-matrix printer and the plotter are HP-IB peripheral devices and were used to obtain hard copy output of the information ~enerated by the HP-9836. The HP-IL/HP-IB interface allows an HP-IL device to communicate with an HP-IB device. It can be operated with a controller on the HP-IL side, the HP-IB side, or in "mailbox" mode, where controllers exist on both sides. The latter approach was chosen for this project. Thus, the interface was used to allow data that were stored on the micro-cassette to be transferred to the HP-9836 for storage on 5-1/4" floppy disks. The controller consisted of the HP-41CX calculator on the HP-IL side and the HP 9836 on the HP-I0 side. The data transfer required siaultaneously on the HP-41CX and the JfP-9836. that programs be run These are listed in Appendix B. 5.2 Procedure for Gage Installation A total of 16 gages were attached to each structure. They were mounted in groups of four at the following locations: midspan of the beam, end of the beam, top of the column, and base of the column. The gages were arranged around the perimeter of the tube at 90° intervals such that one pair of gages measured in-plane strains and the other pair measured out-of-plane strains. The locations of the gages are indicated in Fig. 31. The gages were installed in accordance with normal procedures ( l o ) , with the exception that Elmer's "Dura-Bond" contact cement was used instead of the suggested adhesive. This was done to facilitate gage installation in the field. Otherwise, the installation followed common procedures for cleaning of the steel, aligning and bonding of the gages, and so on. Once the gages were installed, cables were soldered to the gage leads to connect them to the data acquisition unit. On the Tucson structure, a quarter bridge using two wires, as shown in Pig. 32a, was utilized. On the Phoenix structure, a quarter bridge was again used, but this time with a three-wire circuit, as shown in Fig. 32b. The three-wire arrangement helps eliminate the effect of lead wire resistance on After the cables had the gage readings. been attached, the gages were further protected by applying a covering of paraffin wax. Figure 33a shows a gage with cables attached, and the Pig. 33b shows the same gage after the wax has been applied . 5.3 Theory of Strain Gage Operation The operational function of an electrical strain gage is based on Ohm's Law (15). which states that V where V ohms. = IR (6) is voltage, I is current in amperes, and R is the resistance in For a constant I , a change in the resistance will cause a proportional change in the voltage. The electrical strain gage functions 7 POWER SUPPLY W ~ i ~01 R E s i s T o . PI F i g u r e 328. Two-Wire Quarter Bridge C i r c u i t ACTIVE GAGE P+ I C (- @ SUPPLY F'igure 32b. \ sp = LI O2 ~ ~ U Y RESISTOR Y Y Three-Wire Quarter Bridge C i r c u i t b Figure 33a. Figure 33b. Mounted Strain Gage with Cable Attached Mounted Strain Gage with Protective Wax Coating as a resistor, and as the gage increases; as the gage corresponding change in is strained in tension, the resistance is compressed, t.he resistance decreases. The voltage is measured to determjne the strain. However, In order to keep the magnitude of t.he current constant, it must be supplied at a constant voltage. in the If the strain gage were the only element circuit, this would be impossible. Fortunately, by adding other elements to the gage circuit, it. becomes possible to supply the current the circuit at a constant value. to One arrangement for the gage circuit is the Wheatstone Bridge, as shown in Fig. 34. The Wheatstone Bridge consists of four resistors arranged closed circuit. to form a The voltage (and current) is supplied at a constant value across nodes A and C, and the change in voltage is measured across nodes 3 and D. The drop in voltage from A to B is ( 1 3 ) : here R1 voltage. and R2 are the resistances of the resistors, and V is the applied Similarly, the voltage drop from A to D is: The output voltage. E , from the bridge is equivalent to: or (9) The bridge is considered balanced when E bridge = 0 or RIR3 = R2R4. When the is balanced, any change in the resistance will cause a voltage differential AE to develop across BD. If AR1, A R 2 . W 3 , and AR4 are the Figure 3 4 . Typical Wheatstone Bridge changes in resistance of R1 , R2, R 3 , and Rq, respectively, then A E has a value equal to: Simplifying Eq. (10)and neglecting second-order terms gives: For quarter bridge circuits, such as those used for the sign structures, the strain gage is the only resistor that will show a change in resistance. Therefore, W2 where r = R1 = 4R3+ hRq = 0 and Eq. (11) becomes: . The quantity AR/Rrepresents a change in resistance and is related to the strain as here Sg is a proportionality constant know41 as the gage factor,andsis the strain. The gage factor allows the manufacturer to calibrate his gages to give the proper v a l u e s . For this study, R1 = R2, and r becomes 1.0. Substituting into Eq. (12) gives: Rearranging and solving for the strain then yields: This equation was used to determine the strains from the voltages recorded by the data acquisition unit. 5.4 Data Reduction Procedure Data reduction is the process by which the strain gage voltage readings are manipulated to determine the corresponding values of and strain. The only unknown in Eq. (15) is AE. stress If it were possible to balance each Wheatstone Bridge before each gage reading, the gage reading (voltage) would have been AE, since it was recording zero before the strain occurred. However, due to the dynamic nature of loading, such balancing is normally not possible. the structural It was, therefore, necessary to determine an initial value, or offset, of the gage voltage. After the data had been transferred to a file on a floppy disk, the HP-9836 was used to search through the data file for gage readings that were made at wind speeds of less than 0.1 mph. This value was selected as the basic "zero" wind speed, after experimentation on calm days showed that strains induced by a wind of that magnitude were negligible. An average value of all such readings was computed for each gage, and these were then defined as the gage offsets and stored on a floppy disk in a data file. The offsets were recomputed for each day of data collection. This was necessary to do, as disconnecting the data acquisition unit from cables caused the offsets to change from day to day. data acquisition unit had to be disconnected from day, as the gage (It is noted that the the gage cables every it was not possible to monitor the unit 24 hours a day, and no provision could be made to secure the unit from weather and vandals). Once the offsets had been determined, the strains were computed. The true value of AE was determined from Eq. (16): where Vi is the voltage reading for a strain gaga, and Vo is the offset for that gage. If Vi is less than Vo, a negative value of AE is obtained. This indicates compression. A positive value of A E indicates tension. With the value of AE computed, the strain was determined using Eq. (14). The value of the corresponding stress was then calculated using Hooke's Law (17) a where U = EE (17) is the stress and E is the modulus of elasticity of steel, taken as 29x103 ksi. The stress and strain data were all stored, along with the corresponding normal wind component. This made them available for further data reduction and evaluations of the results, such as determining statistical characteristics of the stresses. 5.5 Statistical Analysis of Results The data collection equipment was capable of reading the anemometer and strain gages approximately every 34 seconds. The data acquisition unit would first read and store the wind speed and direction in the calculator's 86 memory, which calculator would perpendicular memory. took to approximately then compute seconds. 5 the magnitude Using of these values, the the wind component of the structure and store this value in its the plane This process consumed about 2 seconds. All strain gages were scanned, one after the other, which required about 3 seconds. now The remaining 24 seconds was needed to transfer the gage readings from the data acquisition unit to the calculator's memory. Due to the vibrating nature of the structures, the strain gage readings were not necessarily always made at the maximum, as Pig. 35. As can be seen from this figure, the deflection at time tl will be different from that at time t 2 . any indicated by The readings might have been taken at point in the cycle, and it was therefore determined that a statistical evaluation of the data was the only way in which logical explanations of the results could be provided. The analysis was increments of 1 mph. either side of conducted for each gage for all wind speeds, using Each nominal wind speed covered a range of 0.5 nph on the nominal value. Therefore, actual wind speed values exactly halfway between two nominal wind speed increments were rounded up to the higher value. For Por the Phoenix structure, 1133 readings were taken per gage. each the Tucson structure, a total of 1244 readings were made by each nominal wind positive For speed, the maximum positive and negative stresses were found, and the average stress and standard deviation average gage. and negative stresses, along were with deviations were then determined. The standard deviations 87 computed. The their respective were calculated using : where o is the standard deviation, n is the number of data certain nominal wind speed, and X I , X2, X3, The two ... points for a Xn are the data points. locations of primary interest for each structure are at the midspan of the beam and at the base of the column. A stress envelope was determined for each of these by plotting the average stresses, along with points identifying values of plus and minus 3 standard deviations to either side of the average. This envelope includes 99.5% of all possible stress levels ( I d ) , assuming that the readings are normally distributed. The envelopes for the midspan of the Tucson and Phoenix structures are shown in Pigs. 36a and 36b. respectively. It can be seen that the maximum values of the stress envelope are well within the safe range. For the Phoenix (100' span) structure, the maximum value given by the envelope is 18 ksi, which stress of 34 ksi. For is only 53% of the yield the Tucson (60'span) structure, the margin of safety is even larger. The maximum value given by the envelope is 8.2 ksi, or 24% of the yield stress. values tend to be extremes. confidence to Furthermore, it is emphasized that these The large number of tests that were made lend the statistical evaluations; further data are not likely to alter the averages nor the 2 3 standard deviations to a significant degree. It is therefore clear that the low level of service load stress that was predicted by the analytical study has been substantiated. 89 It is interesting to note that both structures exhibit local maxima in the nph. envelopes at wind speeds of approximately 2 mph, and again at 14 to 16 The frequency of oscillations at 2 mph frequency mph, for both both structures. structures are is well below any natural However, between wind speeds of 15 and 16 near a natural frequency. For the Tucson structure, the frequency corresponds to the third 3D mode of 3.26 cps. the Phoenix structure, the mode is also the third 3D node, at of It cps. 3.06 is believed that the a For frequency maxima observed in the stress envelopes at this wind speed indicates that the structure is tending toward resonance at these points. However, due to the inherent structural damping and the gusting of the wind, the resonance condition is the actual structure. not achieved for It is noted that in the theoretical evaluations of the structures, damping was set equal to zero, and the wind was assumed to blow at constant (sustained) speeds. The stresses counterparts. structures at The the column bases are not as large as their midspan envelopes for the out-of-plane are shown in Pigs. 37a and b. stresses for The maximum value for the Tucson structure is 7.7 ksi, and for the Phoenix structure it is 17.0 ksi. demonstrates that the span structure were This length has a greater Influence on the column base stresses than does the sign size. Tucson both about twice It is noted that the signs as large as on the those on the Phoenix structure, but the latter has a span that is 67% longer. The column base stresses also exhibit local the same wind speeds as was found for tha beam. is vibrating at close to a natural 92 frequency, maxima at approximately Here, again, the structure but is prevented from t a + + * A r Y I # 20 - - * + Wind Speed -20 . (mph) # W E . STRESS +3 STD. DEV. -3 STD. DEV. *For wind speeds greater than 16 mph, the statistical population is too small for accurate analysis Figure 37a Stress Envelope for Column Base Stresses of Tucson Monotube Structure The maximum stresses discussed so f a r were n o t t h e a c t u a l maximum s t r e s s e s r e c o r d e d , b u t t h e maximum v a l u e s t h a t a r e l i k e l y t o the s t a t i s t i c a l d i s t r i b u t i o n of t h e d a t a . than t h o s e p r e s e n t e d . stress envelope is occur, The recorded stresses were l e s s For example, a t 16 mph, t h e wind speed f o r which t h e the widest for the Tucson s t r u c t u r e , t h e maximum recorded stress was 7 . 3 k s i , a s compared t o 1 2 . 2 k s i of t h e is therefore clear given that the use envelope. It of a s t a t i s t i c a l approach h a s made it p o s s i b l e t o i n c l u d e e s s e n t i a l l y a l l of t h e p o s s i b l e s t r e s s levels in the T h i s a l s o r e f l e c t s t h e c y c l i c n a t u r e of t h e s t r u c t u r a l behavior, analysis. as well as t h e i n f l u e n c e of t h e time l a p s e involved i n t h e r e a d i n g of the gages. C a l i b r a t i o n of Equipment 5.6 Due to the h i g h ambient temperatures d u r i n g t h e times when t h e d a t a f o r t h e Phoenix s t r u c t u r e were c o l l e c t e d , it was n e c e s s a r y t o c a l i b r a t e t h e equipment and the gages to reflect the higher than normal o p e r a t i n g temperatures. The d a t a were c o l l e c t e d d u r i n g t h e months of June and with temperatures ambient ranging between 10W and 115OP. July, Data f o r t h e Tuceon s t r u c t u r e were a l s o c o l l e c t e d on one day d u r i n g t h i s p e r i o d , with an ambient temperature of 1020P. It was not found necessary t o apply c a l i b r a t i o n c o n s t a n t s t o t h e o t h e r Tucson d a t a which were c o l l e c t e d during t h e month of March when t h e temperature was i n t h e mid 8 0 ' s . The first correction was made t o account f o r t h e a p p a r e n t and t r u e s t r a i n s caused by thermal c o n d i t i o n s . calibrated to read The gages t h a t were used had been z e r o s t r a i n a t 7SOP. However, auch of t h e time t h e s e 95 gages were surface used when temperature temperature the ambient of the temperature structure was that this can cause an error of -50 nicro k ~ i compressive 1.5 greater than strain, which atreas. To corresponds compensate of the structure. other 16 gages were. other gages. to for this, a separate gage was bonded to a piece of steel of the same thjckness wall The 140°F. curve of the gage that is shown in Fig. 38 indicates response approxinately was over 100oF, and the the as The gage was covered and protected exactly as the It was then placed in the sun and read along with the When the gage readings were reduced, the voltage difference of the separate gage was subtracted from the voltage difference of the other gages, thereby canceling the elevated temperature effects. A more significant correction was needed to compensate influence of higher operating temperatures on the Data for the Acquisition Unit. The service manual (17) states that the optimum operating temperature is in the range of 62O to 780P. In the field, the unit would temperatures as high and to work in as 13PF, resulting in some impairment of accuracy. Since the unit had been routinely run in the sun at 120° have temperatures between 1 3 0 9 , a test was conducted to see if the error was systematic, and how It could be accounted for. The unit was set in the sun on a warm day. Wheatstone temperature. was connected Bridge, across which a known voltage was applied. of approximately one Acquisition It Unit, hour, the bridge voltage was read to a At intervals by the Data as well as by a voltmeter that was kept at its optimum The voltages and the tine and temperature were recorded a period of two days. 96 over Micro- strain Temperature ( Figure 38 OF ) Apparent S t r a i n i n S t r a i n Gage Due t o Temperaturz The results of the experiment are shown in Tables lla and I l b . For temperatures above 10SOP, it is seen that the voltages read Acquieition Unit were 43% greater then difference appeara to be independent of 1050P. by the Data the actual voltages. the level of This temperature above During the data reduction, the voltage differences were reduced by this amount to correct for the temperature effects on the equipment. All stress and strain values that are given in these correction factors. this chapter reflect Table lla. Time Results of Data Acquisition Unit Calibration Test Temperature (OF) Voltage Read Actual Voltnge % - Day One Brror Average % Error = 43.1% Table llb. Time Results of Data Acquisition Unit Calibration Test - Day Two Temperatare (*PI Voltage Read Actual V o l t a g e Average X Error t Error = 43.0% Chapter 6 COMPARISON OF ANALYTICAL AND EXPERIMENTAL RESULTS The full-scale test results that have been obtained in the present research project represent a new contribution to the pool of information that previously provided only theoretical data on the response of monotube sign support structures. In the following discussion, a detailed evaluation of the data will be given, affording comparisons between actual in-service behavior of the structurea and have been made. In addition the theoretical studies that to giving unique comparisons between analytical and ex~erimentalresearch, the results will also be used to examine and verify the design recommendations that were made earlier (3). 6.1 Tucson Structure The 60-foot Tucson structure is the lower limit of what is considered a normal span for monotube experimental structures. The analytical and results both showed that the point of maximum in-plane stress was at the aidspan of the bear; these are detailed in columns 2 and Table 12. It should for wind speeds greater than 20 mph. recorded. readings were The stresses that are given for the full-scale tests are the absolute values of that were the maximum stresses In most cases, the absolute values of the positive and negative stresses were almost identical, as would be expected type of 3 of be noted that the measured stresses for the 20 rph wind speed represents only two individual readi~~ps, and no obtained the for the cross section that is used in the structures. It is also noted Table 12. Computed and Measured Stresses for 60-Foot Structure In-plane at mldapan. ksi Ont-of-plane at colbase, k s f .................... Wind Speed. mph Campated lIessured .................... Campmated --------------- * + No data collected for this wind speed. Only two readings obtained at this wind speed. Heasured that the stress levels do not vary a great deal over the range of wind speeds that were measured. The data in Table 12 illustrate the good obtained between the analytical and the experimental results. This is further emphasized when the complexities of of actual structures, and correlation that was full-scale testing, modeling so on, are considered. dimensional, non-prismatic nature of the structure makes Thus, the threeit particularly difficult to model, especially when dynamic wind loads must be accounted for. The strain gages were not conditions, and climate. installed under ideal laboratory the field neasureaents had to be made in a very demanding In spite of these obstacles, the results of the analytical and experimental investigations are in good agreement. The largest deviation between the measured occurs at a wind speed of 5 mph, although it is noted value of the difference is still small. and computed stresses that the numerical Also, the magnitudes of the stresses are well below the yield stress. The reasons for the differences and their magnitudes can be explained in part by examining the statistical characteristics of the measurement results. As shown in Chapter 5, the maximum stress that is likely to appear at a wind speed of 5 mph is 7.32 ksi, which equals the mean stress of 0.63 ksi plus 3 standard deviations. The maximum recorded stress of 5.69 ksi is greater than 95% (mean plus 2 standard deviations) of the stresses that can be expected to develop at this wind speed. It is also interesting to note that at the higher wind speeds, the analytical model consistently predicts a higher level of stress than was 102 measured. This nay be partly due to the lower number of readings that were taken at the higher wind speeds, as compared to at the speeds. However, it is clear that the major influence is provided by the modeling of the structure. For example, the use of results In a smaller section at midspan compared to the real structure. This by higher lower wind stresses at the aidspan beam-to-column connection also is restraint of same will lead prismatic elements of the analytical model, as itself will location. lead to somewhat The modeling of the important in the sense that a to higher low stresses in the beam. This difference between the results is not as consistent at the lower wind speeds, because random electrical disturbances that nay have occurred during the data collection process would tend to cancel the modeling effects. The sensitivity of the equipment is also a factor in this case. The experimental and theoretical results agree that the point of rnaxiaum out-of-plane stress is at the column base. given in columns 4 and 5 of Table 12. These stresses are The correlation between the computed and measured stresses is good, although maybe not as satisfactory as for the midspan location. However, it is emphasized that the column base stresses are very low. At these levels, a 0 . 5 ksi difference appears large. It is observed that the full-scale test results are consistently higher than those of the analytical study. This is most likely due to the element chosen to model the beam-to-column connection. The in-plane % bending stiffness underestimates that of the actual connection and, therefore, leas of As the moment in the beam is transferred to the column. a consequence, the stresses at the column base in the model are lower. Perhaps the best way to comprehend how well the two studies correlate is to view the data graphically. Figure 39 displays the results for the measured and computed column base and beam midspan stresses. When drawn to scale, it is readily apparent how well the findings support each other. The figure shows the stresses due to the dynamic effects of the wind, which is the primary live load the monotube structures will experience. However, the structural designer must know the total stress from both live and dead loads. measurements Therefore, the computed dead load stressses (no could be taken for dead loads) were added to those due to the wind load, and the sums for the in-plane and the out-of-plane directions are shown in Pig. 40. It is clear that the stress levels are still well below the yield stress of the steel. In fact, the margin of safety indicates that the Tucson structure appears to have been designed quite conservatively. 6.2 Phoenix Structure The 100-foot Phoenix structure is close to the upper limit of normal spans for nonotube structures. Longer spans ~ s yprove to be uneconoaical. As for the Tucson structure, the computations and testing both the the determined that the point of maximum in-plane stress was at the midspan of the bean. Columns 2 and 3 of Table 13 give the maximum stress at each wind speed as determined by computations and measurements. It should 5e noted that for the wind speed of 17.5 mph 104 only one reading -- - -- - -- - F Computed In-Pl ane S t r e s s e s --- Measured In-Pl ane S t r e s s e s -- Computed g u t - o f - P l a n e -.- Measured Out-of-Pl + - - 3-4- k s- -i -- - -- - -- - Y - =- Szresses ane S t r e s s e s - - - *--4 .- -_ -- *---* J' -. y -+--2-- a - ., \ - - - 4 - - - \ \ c - 1 I Wind S p e e d Figure 39 I I (rnph) Correlation of S t r e s s e s for Tucson Monotube Structure - ---- -*----- --- -.- I L i v e Load Stresses In-Plane - - - a - F y.-----= 34 ksi In-PI ane Tot a1 S t r e s s e s Out-of-Pl a n e L i v e L o a d S t r e s s e s Out-of-PI a n t T o t a i S t r .--T. S P S - - a C---C--&--4---a---*---C---------v - - b - - - /' " P - -----t A : A - - - d - - d - ~ - ~ I I I I 5 10 15 20 Wind S p e e d Figure 4 0 - (mph) Total Stresses for Tucson Monotube Structure 25 was obtained, and none could be had for wind speeds of 20.0 mph or greater. It is seen that the correlation between the theoretical and actual stresses is good. The stresses are greater than at point the corresponding in the Tucson structure, as would be expected due to the longer span. The analytical study also predicts stresses that are consistently higher than the measured ones. The reasons for this were detailed in the description of the Tucson test results. In the out-of-plane direction, both studies agree that the point of maximum stress is at the base of the column, and these data are given in columns 4 and 5 of Table 13. The stresses are low, and hence the numerical values of the differences between the measured and the computed data appear more significant than they are. Similar to the Tucson results, the column base stresses predicted by the analytical study are consistently lower than those that were measured. This is attributable to the modeling of the beam-to-column connection element, as discussed earlier. The stresses are presented graphically in Pig. 41. As in Fig. 39, this demonstrates how well the two studies correlate. Figure 42 gives the total live plus dead comparison with the load stresses (computed values), providing a level of the yield stress. It is apparent that the 100-foot monotube structure represents a more realistic design than the 60-foot one, since the margin of safety is closer to the values that are considered desirable in practice. The average total stress for all wind Table 13. Computed and Measured Stress for 100-Foot Structure In-plane at midspan, ksi Wind Speed, mph .................... .................... Caplted w t e d Measured --------------+ * Oot-of-plane at colmm base. ksi Only one reading taken at this wind speed. No data collected for this wind speed lleasm-ed - = 34 k s i FY---------------- --------- -- I n - P I ane S t r e s s e s Computed ---- - -.- M e a s u r e d In-Pl ane Stresses Computed Out-of-PI ane Stresses Measured Out-of-Pl ane Stresses - a - .. *--a---a---* - -- -&-- '7 \ \ \ \ \ - \ P-./. ' 4 /. + - r,i, 4 - +--- \b t I Wind S p e e d Figure 4 1 1 4 (mph) Correlation of Stresses for Phoenix Monotube Structure -- - -- - -- - F k -s-i-Y-= 3- -4- - Live I n - P l ane - - - . In-Pl ane -- Out-of-Pl - -.- Load Stresses Total ane _ -- - ----- Stresses L i v e Load S t r e s s e s Out-of-Fl a n e T o t a l S t r e s s e s *---& I i a-------*------t t - - - - a *.-.-* I *_-----4-d----.-* 1 I Wind S p e e d Figure 4 2 1 1 (mph) Total Stresses for Phoenix Monotube Structure speeds is approximately first yield of 1.8. 19 ksi; this gives a factor of safety ageinst Chapter 7 SUMMARY, CONCLUSIONS AND RECOMMENDATlONS The purposes of this study were to gather data on the performance of monotube sign support structures under service conditions. and to evaluate possible methods of structural analysis. Through the use of field testing and computer modeling, such data were collected, reduced and analyzed to determine the service load the ~0n0tube response characteristics of structures. 7.1 Summary and Conclusions On the basis of the two full-scale structures that have been tested and analyzed, the following conclusions can be made: 1. The service load stresses can be accurately predicted by of finite element modeling. the use The computer models in this study correlate very well with the field measurements, as well as with the similar models studied by Ehsani and Bjorhovde (3). 2. Due to the correlation between past and recommendations that were made by well-founded and should recoinmendations include be present results, the Ehsani and considered for Bjorhovde are adoption. These suggested methods of analysis, new performance criteria, and topics in need of further study. 3. The two full-scale structures did not meet the d2/400 dead load deflection requirement of the AASHTO Specifications. 4. The stress levels associated with the actual deflections are below the magnitudes we11 of the allowable stresses, even though the struct.nres do not meet the d2/400 deflection criterion. 5. As was found in the earlier stndy ( 3 ) , the stress level at any point can be found by superimposing the stresses due to static loads and those due to dynamic loads. 6. The maximum in-plane stresses occur at. midspan of the beam. 7. The maximum out-of-plane stresses occur at the column base. 8. Resonance did not occur in the field shedding took place at testing, even frequencies equal frequencies of the structures. when vortex the natural to It is believed that this can be attributed to the inherent damping of the structure, as well as to the gusting nature of the wind. 9. A monotube struct.are of moderate or greater span ( > 60') cannot meet the d2/400 dead load deflection requirement of most AASHTO. In cases, It would prove to be very uneconomical to design such a structure to meet this requirement. A new deflection criterion was proposed in the original monotube study ( 3 ) , thus: where This A is the dead load deflection, and Q is the span length. criterion is based on stiffness requirements, as the strength (i-e., stress level) is not likely to govern. In the original study on monotube structures ( 3 ) , a number of other recommendations also were made in regard to the analysis and design of these structures. Two of the recommendations are of particular interest in relation to the findings of the current project. The first recommendation is to consider the analysis of the monotube structure for out-of-plane behavior independent of the in-plane behavior. The current project hat? shown that this is a rational approach. It makes the analysis much simpler, and does not introduce any appreciable error. The second recommendation was structure to help ellainate to camber the beam of the rnonotuhe the undesirable visual effects of larger deflections. This is especially worthwhile if a maximum deflection-to-span ratio of 1/150 is adopted. The 100' span of the Phoenix structure that was tested in the current study had such a cambered beam. Although the dead load deflections were large, the camber kept the midpsan above the end points. Thus, the visual effect was that of a low-pitched arch, which is much more appealing than if the beam was deflected downward. Therefore, cambering the beam is a viable option in the design of aonotube structures. 7.2 Recommendations for Further Studies This study has significantly increased the pool of existing knowledge on the behavior of monotube structures. It has been shown that the design guidelines for truss-type structures cannot monotube structures. Therefore. been recommended; studies of the nonotube structure under high wind conditions are needed, as well as a examination: rationally applied to New design guidelines have however, certain additional characteristics. be better understanding of other the following subjects are in need of 1. wind Wind Tunnel Testing_- The performance of rnonotube structures at speeds up to at least 80 mph needs to be determined. This is best accomplished by using scale models in a wind tunnel. The effects of sign placement and size should also be studied. 2. Beam-to-Column Connection Behavior and study has indicated that Strenpth - The current. the connection can play a major role in deter- mining the stresses in the structure. More precise methods are needed to model the actual behavior of typical connections. 3. Evaluations of Fatigue Characteristics this study did not - Due to time constraints. investigate fatigue phenomena in the members or the connections of the structures. However, due to the dynamic nature of wind the load, cyclic stress variations are common. Although the stress levels are low as compared to the yield fastening details of stress, the stress ranges and the beam-to-column connections may make the them susceptible to fatigue cracking. It is recommended that connection and base details should be tested statically and dynamically in the laboratory to determine strength and fatigue life characteristics. 4. Behavior of Cantilever Structures - addre~sed the behavior structures are of span-type also in widespread The current study only structures. use. Cantilever It is expected that the deflections will be greater than for the span-type structures, as will the stresses at the column base. sign be Further, the dynamic response of cantilever structures is likely to be considerably more complicated, since the torsional mode of behavior may play a major role. Fatigue also would appear to be more serious. REFERENCES American Association of State Highway and Transportation Officials (AASHTO), "Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals," AASHTO, Washington. D.C., 1976 (revised 1978 and 1979). Ehsani, Mohammad R. and Reidar Bjorhovde, "Deflection Criteria for Sign Support Structures," paper submitted to the Journal of Structural Division, ASCE, February 1985. Ehsani, Mohammad R., S. K. Chakrabarti, and Reldar Bjorhovde, "Static and Dynamic Behavior of Monotube Span-Type Sign Structures," Report I and 11, Arizona Department of No. FHWA/AZ/194. Vols. Transportation. Phoenix, Arizona, June 1985. Rouse, Hunter, "Elementary Mechanics of Fluids", Dover Publications, New York, NY, 1978. Hoerner. Sighard P . , "Fluid Dynamic Drag", Published by Author, 1965. Pung, Y. C., "An Introduction to Aeroelasticity", John Wiley Sons, Inc., New York, NY, 1955. and Lamb, H. "Hydrodynamics", 6th Edition, Cambridge, London, 1932. Weaver, W., "Wind-Induced Vibrations in Antenna Members," "Journal of the Engineering Mechanics Division", ASCE. Vol. 87, No. EMl, 1961, pp. 141-165. American Institute of Steel Construction (AISC), "Specification for the Design, Fabrication and Erection of Structural Steel for Buildings", AISC, Chicago, Illinois, November 1978. American Concrete Institute (ACI). "Building Code Requirements for Reinforced Concrete (ACI 318-83)," ACI, Detroit, Michigan, 1971. Kamel, H. A . and R. R. Nagulpally, "GIFTS Primer: A First Introduction to the GIFTS-5 System," AME Department, University of Arizona, Tucson. Arizona, Rev. December 1985. Micro Measurements, "Student Manual for Strain Gage Technology," Bulletin 309, Measurements Group Inc., Raleigh, North Carolina, 1983. Dally, J. W. and W. F. Riley, "Experimental Stress Analysis", 2nd Edition, McGraw-Hill, New York, 1978. 14. Hoel. P. G . and R. J. Jessen, "Basic Statistics for Business Econoaics", John Wiley & Sons, Inc., New York, NY, 1983. and F. and E. B. Kurtz, "Electricel Eneineering Fundamentals", John Wiley and Sons, Inc., New York. NY. 1976. 15. Corcoran, G . 16. Popov, E. P . , "Mechanics of Materials", 2nd Englewood Cliffs, New Jersey, 1976. 17. Hewlett-Packard, "Model Edition, Prentice-Hall, 3421A Data Acquisition/Control Unit: Operating. Programming and Configuration Manual," Hewlett-Packard Company, Loveland, Colorado, 1082. APPENDIX A DATA COLLECTION SOFTWARE FOR HP-41CX CALCULATOR REGISTER INPUT DATA: The following registers must contain specific data, as given in the tabulation below. in order for the programs to execute properly Register No. Value 03 Wind conversion factor 05 Current storage pointer; must be 20 at the beginning of the data collection 06 = 9.2593 mph/VAC Wind direction conversion factor; equal to 41.7633 "/VDC 12 Number of values to store before writing to tape 01LBL "GO" 02 F I X 9 03 " R E G . = ? " 0 4 PROMPT 05 " F I L E = ? " 06 PROMPT 07 XED " S E E K H " 0 8 XEG! " L O G " (:I 9 R T N 1 0 END S t a r t s program. Prompts f o r t a p e F i l e and beginning r e g i s t e r . OlLBL "SETS" Reads s t r a i n g a g e s and s t o r e s v a l u e s 02 " O P N " in calculator. 03 OUTA 04 "LS3-17" 0 5 OUTA 06 " F I R A 0 7 0 N 5 F ? - l : T 3 " 07 OUTA 08 1 09 S T 0 0 1 lOLBL O l 1 1 16 1 2 RCL 0 1 1 3 X=Y? 1 4 GTO 0 2 15 I N D 1 6 XEB " P U T S " 17 1 18 S T + 01 1 9 GTO 0 1 2 0 L B L 02 21 "DPN" 22 OUTh 23 R T N 24 END 01LBL "LOG" 02 XEQ "INI3421" 03LBL 10 04 DATE 05 XEQ "PUT5" 06 TIME 07 XEQ "PUT5" 08 "OPN" 09 OUTA 10 XEQ "WNDSPD" 11 XEQ "PUT5" 12 RCL 00 13 RCL 04 14 X(=Y? 15 GTO 20 16 3 17 ST- 05 18 GTO 10 19LBL 20 20 CF 01 21 XEQ "WNDIR" 22 XEQ IIPUT5" 23 XEQ "HDCLC" 24 XEQ "PUT5" 25 RCL 02 26 RCL 08 27 X(=Y? 28 GTO 30 29 5 30 ST- 05 31 GTO 10 32LBL 30 33 XEQ IISET3" 34 RCL 05 35 RCL 12 36 X(=Y? 37 XEQ IIWCASS" 38 GTO 10 39 RTN 40 END Main program. 120 fIJJ Directs program flow. OILEL "INI3421" 02 A U T O 1 0 03 CF 17 0 4 Selects Data Acquisition Unit as the primary device in the IL loop. "HP3421AU 05 F I N D I D 06 SELECT 07 R T N 08 END O l L F L "WNDSPD" 0 2 "RC)#:)ZO" 03 O U T A 0 4 "OPN" 0 5 OUT4 06 " C L S O O " 07 OUTCI 08 " F Z N 4 R i : T 2 " 09 O U T A 10 IND 1 1 '"OFSN" 1 2 OUTCI 1 3 RCL 03 14 t 1 5 S f 0 00 16 R T N 17 END Reads wind speed. OlLBL "WNDIR" 02 "RAOZO" 03 O U T A 04 "OPN" 05 O U T A 06 " C L S 0 1 " 07 O U T A 08 " F l R A O N 3 R l : T 2 " 09 O U T A 10 I N D 11 "OPN" 12 O U T A 13 R C L 06 14 15 S T 0 0 1 16 R T N 17 END Reads wind direction. * 0 1L E L "HDCLC" 0 2 RCL 0 1 03 C D S 0 4 ABS 05 R C L 00 06 Computes the wind velocity perpendicular to the sign. t 07 S T 0 0 2 08 R T N 09 E N D O l L B L "PUTS" 0 2 S T 0 IND 05 Stores values in calculator's memory in sequential order. 03 1 0 4 S T + 05 05 R T N 06 E N D OILEL " W C A S S " 02 020.119 03 WRTRX 0 4 20 0 5 S T 0 05 06 R C L 12 07 1 9 08 09 S T + 13 1 0 RTN 1 1 END Writes data to cassette tape. APPENDIX R DATA REDUCTION SOFTWARE FOR HP SERIES 200 COMPUTER Ii j 20 36 43 50 bc! 71' 80 90 t i 111:1 12C !14 149 150 151 150 110 PROGRAI REDUCE !THIS PRDGRPM REDUCES T I E DdTA COLI.ECTED KIFP VclHTlti FOR HIS 'THESIS PROJECT. I T COIIF'UTES THE STRESSES AliE STRAINS FOR THE 'vAR!OUS WIN11 SPEEDS, THIS PKOGRAH HPiS BEEH NQlTTEN T O & ' USEFUL 'FOR BOTH S1514S TESTED WITIIOUT flODIFlCliTION OTHER TP&ti RESIZIHC; THE 'DIMEHSlONSTATt~ENTSATTHEPEGltiflllJG ! FIHKNl; l o t i ECCH ARRAY AI.GNG THE FDLLilWIHi; L I WES: ! 1, OS(Nl!HbER OF G M S I ! 2 . D E I I E OF DATA F I L E ) 3 . EP!S;!E OF DCITA FILE/tH!lflBER ?F GIIFES+S)tfJUflPEFi ?F GPGES! ! 4 . SlG!SlZE Of DATA FILEI(NUHBER OF GkGES+S)tMUntiER OF GkGESi ! 5, GEI.V(SIIE OF DATA FILE/IPJUHPEit OF GA~P~+FI)?HUHBEROF GRGES) ' b . kJSIS!lE OF DATA FIIE!NUMBER OF GAGES! ! 7 . F l ! r?iNl!t!, GbGES!tli% lS11E OF DRTA FILE! IHUM. G6GES+5!!! ! OPTION RASE t IBO D I M 0 5 i 15) ,D145011! ,Ep(45O?),Siq145i]0! ,Delvl4500!, Wsi?5il) !F I b 9 7 5 ) 181 RANUOH! 1E 37490660 199 OUTPUT 2: " K " ; !CLEAk SCREEN ?bO C4LL O f f s e t l t l g , D s l l i i I INPUT GAGE OFFSETS 210 CALL Check1 ItJg,051#!) 'CHECK F?R CORRECT OFFSETS ' I " L:~I C N L Gages iBbI Gf i 'IIIF'UT BRIDGE VSltTclGE AND GAGE FACTCIH -iJu , ' CALI. O a t a i n t N n $ , F s l D I 1 i ) !REAP DATA FILE !NTO ARRAY D 240 CALL U i n d ! F s , D f t ) ! W s ! t ) , N q ~ '2E4D WIND SPEEDS INTO bRRAY US 250 CALL Dele(Nq,Fs,L,?s!f) , C [ t ),De1v ( 1 ) ) ICOflPUTE DELTA E!YOtTAGE! ?b!~ C h t l ? t r a i n ~ l J q , B v , G f , L , F s , D e l v l t i ,Epf t ) 'COMP!ITE STRAIHS ?70 CALL S!resstL,Eplt),Siq(t)) 'COMPUTE STRESSES 230 ! 291) OIjTPUT 2; IO? INPUT "DG I?!l 9 k t U STRESSES BHD STRAIt+S SAVED TC A F I L E ( Y / f i ) " , A n $ 1 I F Bs$='Yu THEN CALL S a v e i t li.,Fs,Nq, W s ! t )!Ep I t ),Sig(?) , F ( t l ! 'STORE STRESSES AND STR4:WS I N 1 . 1 FILE :31] ELSE 340 ENC I F 350 ! 560 CRLL Out(Fs,Hq,W5(i),EpiC),Siq(i)I !PRINT STRESSES AND STRAINS "'I; 7 r . 370 PRINTEF I S 1 ,380 END 190 ' !RETURN PRINTER TO SCREEN 4 00 418 4?(1 4!ii 440 ! Lttttttitttt~t~t$ttttt~ttttttt~t~tt.itt~tt 't 1 !t SUBR?UTINES t t !lr !lt$ltt4t3ttl%tltt9Jttt~tttt$t~titttt%~1.l 461:) 471) 480 490 500 510 520 ! ~ltttiilttt~t~t?~tttttit1$1t1t1:t~t¶ttt~tt !1 OFFSET t !tlltttltttt?tttfltt?tttttt~tIttt~tt1itt~ ! SUR O f f s e t ( t i g , O s [ t I ) 53? ! 530 First: 550 5b0 570 586 540 A!)(! blil b20 5 brli! b50 5 b70 ,580 b9[! 700 710 7?0 730 :,\g 750 7Cil 710 780 :/'a) b0;i P.18 IIIPUT "EtlTEP t4UIIBER OF S T R A I N GAGES",OLq 'CHECK F n F PROPER !dUnPEP OF STHGIN 69GES DUTPUT 2; " k ' C L E M SCREEN PRlHT USING "15/, 20X!"NUUlER OF STRAIH GAGES: " ' , 2 0 \ N g INPUT "RRE CORRECTIONS NEEDED I N NliHEER OF GAGES IY /!Fieturn:) I F AnQ="Yu THEH G?TO First 'I; ",An% 1 G!SP "INSERT OFF SET DFlTA DISK INTO h T . DRIVE Al1D PRESS Continue" F'kLISE CAT " N M E OF DFlTn OFF SET DATPi F!LE",th$ ASSIGN @ P a t l ~ i TO l Na$ FOR I = l T O Ng OUTFLIT ?;"1.'"; ENTER tPa!h?, I;Os(I) NEIT I ASSIGN @ P a t h ? 'I@ t SUEEND i/lP!I-I I '$tltf$ttttf$tttttltItt?ttt$t1~ttttt8I1t~ !t CHECK1 t !lt6tltttt!rrtlttttit$ftt11tttt1tt1:iI$~1t ' SUB Check1 (liq,Os(l)) ' 'PRINT OFFSETS 820 CALL P r i n t o s ( N g , O s l t ) ) TI! SCREEN $!(I 1 840 'CHECk FOR CORRECT OFFSET ENTRY 850 ! 950 INPUT "ARE CORREClIFNS NEEDED FOR ANY OFFSET'(Y!(Retuin:) 970 I F dnC='Yb THEN ChLL C o r r e c t l N g , O s l t ! ) 8@0 890 SUBEND 90? ! 910 ! 120 ! t t ! t t t t t J t ? O t t i t t t t t t t t $ t ? t t t ? t 1 t t % 1 ; 1 t I ~ 9;d !1 PRINTLlS ? 940 950 960 !ttittlttt?tlltttlttt1tittttttf?ttitt~ft~ ! SUB P r i n t o s l N q , @ s l t ) ) ! OUTPUT 2 : " K " : s?0 980 'CLEAR SCREEN 990 ' !On(! 'F'RIII: OFFSETS T@ SCREEN It4 HENUE FORM I010 1020 PFiItlT USlt46 "31X, ""AGE Er"",5X, ""OFFSE!5""" !030 FOR 1.1 70 Cg 1040 PRlllT USIllG ":13%,2D,7X,D.5D";1,05!1) 10511 NEXT I 1Obl:I ' 1070 SUPEND 1090 ! 1090 1140 ' I t $ t t t t t t l t t t ~ $ t t ! t t t i t t f t t t t t t t t t t t t t ~ t 11\10 I t CORRECT t 1120 ftttt?tlttl?t$ttttftItltLttttttIttttttt$t 1131 ' 114? S!l9 C o r r e c t lNq,Os(t;) 115f:) ' l1bO Tnrr: CALL C o r r e c t 2 f N q , O s l t i ! 1170 ! 1la() IC H E C ~ :FOR MORE CORRECT IONS 115'0 ! 1290 CALL P r i n t o s ( t i q , O s ( t ) ) 1210 ' 1220 INF'UT "lihlY MORE CORRECTIONS!Y!!Return'.i", Rn) 1230 IF Rn+="YVTHEN GOTO C o r r ',4nb 1?4C 1 2 5 0 SUBEPJD 12.j(! 1 1270 ' 1280 118$titttttti$tftl$r$tfl~it$tltttktt~ttit 12911 I t GAGES t !309 ! t t t t t t t l l l l t t ! l t t l t I 1 t t t d t t t t I I t ~ t t t t t i i lSi(1 ' l5?1! SUB Gaqes rBv,C;f) 1330 ! 1340 OUTFLIT 2;"K": 1351) 1361? Pridijer.: CALL Bl-idqe(Bv,Ff 1370 1 1 3 8 0 ICHECK FOR CORRECT DATA EHTPY i37Ci ! 1 4 0 0 OUTPUT 2; "k "; 1410 ! 1 4 2 0 PfiItIT USING "151',3?Y,"L FPIDGF: VOI.T(IGE: "",[l.DD,/!,?.i!Y~nn22 GAGE FhCTOfi: "',D.4DX; bv,Gf 143 ! 1 4 4 0 lI4F'LIJ "AM CCfiRECTIONS NEEDEB?iY/(Rpturn)! ", Flni 1 3 5 0 I F A r 4 = " Y n THEN 60TO bridges 1460 I 1 4 7 0 SI!BENQ 1490 ' 14QO ' 1500 l t t l J f l t $ ~ t O L l ? t t l l f t t t t t t ? ? I i ? l t t ? t t t ~ t ~ 1510 I t DATAIN k 152I:i ! t t l t t l ? t $ $ t l f $ $ t l $ t f ? ? t t t $ 1 t I 1 t t t t ~ . t t l t $ !51b ! 1540 SUB D a t a ~ r i \ N a S , F s , l l i l l !551] ' 'CLEAR SCREEY l:bc OUTPUT 2: " f H : 157!1 I 1 5 8 0 DlSP "F'LdCE O l S K M I T N DACR F1i.E I N RIGhT D k I V F 4HD PRESS CORTIIJUE" 1590 PCUSL: 1600 ! Ib!O Torr.3: CALL Corrert3(lin%,Fs) lt2(! ' I.~;I)OlJTpYT 2; " K " ; 154c1 ' 20?4 2[ql ' 20:0 'tlttt4litttttttlttt1tttittt4!$1tt?tttIIt :II:IC 1t DELF: t 2110 ! l l t l l t t t l t t l t l l l i r t I t t t t t t t ~ l d S I % t 1 t t O % ~ 212? 1 2130 SiJB DelelNq,Fs,LIDs!O~,Dit)l@~I~r'~l)~ 2140 2150 2160 ?I?O 21ao ! 'COMPUTE VOLTRGE CHANGE ' 'TOTA1. READINGS PER SPAY !NUMBER OF GAGE READItiGS I!-Rg+5 L.: I!=I 22cfl ' 2210 FOR J = 1 TO 219(1 F5 STEP I? k=K.t: 2230 FOR J = l TO Ng 2240 D e l v ( L ) = D I K ) - . @ s f I ) ?250 K=Ktl ?;?ij ! DELTR C=SEADING - OFFSET 27bD l-=Lti 2270 ??91) 2210 ?3(10 2310 2320 IJE'LT I NEXT J !.=L-! 'CORRECT FOR LAST TIHE THSOUGH LOOP SUEEND ! 233) 1 2340 !tttltttttttttttrtttttttttttt~tttt~tttxt~ 2350 ! 1 STRAIN t ?361:] ! t t f $ t t t l ? t t t l t l t t t ~ t t t t t I I t t I t t t t t t t 1 t l t 237(r 2380 SUB Strain(Nq,Bv,Ff,t,Fs,Delv(t),Ep(t!~ 2;9fi ' 2460 lSTRAIN=IDE!TR V) /(GAGE FhCTORtERIDGE VOLTAGE) i!410 ! 1420 L = F s l ( N q t 5 ) lttg 24311 FOR 1.1 TD L :.14o E p f ~ ) = a e l v ( l ) ! r s ~ t s ~ ~ 2441 I F bBSIEp ( 1 1 ) >.000b07655 T H E N 2449 I F Ep(l!c!l THEN Ep(l)=-ll!liHD?lrj!!21000.0 ?445 I F E p ( l l :(ITHEN E p ( l ) = (814DtlO) 1290QO.O 2444 ELSE 244: END I F 2451:1 NEXT I 24t.9 2470 2480 2430 'I=" LJ~![! 1 SIJBEND ! ! !tttitlt$t$S~!tttlttttttt5~ttttt$i$tIitt$ 2510 11 STFESS C 253) ' I : l l t t l t t : l l t t f t t $ t t t I t t 1 i t t t t t t I t t t l $ t t 25311 1 2540 SUE S t r e s 5 ! L , E p ! t ) , 5 i g ( t ) ) ?(I: ' 2560 ISTRESS = STBAIWIE 2570 ' 3811 FOR 1.1 TO L 2590 S i g ( I)=Ep! I)t 2 ? 0 0 0 2600 NEk! 1 2610 ! ?52D SUBEtlD 25.0 ! 2640 1 ?55? ~ l t t l t t 1 t t t t l t t J t f t t t t t t t ~ 1 t t t t t t t t t t t t S ~ 2660 ' t SAVEIT t 2670 l t t t t t t i t t t t t t t : $ f t : t t t ~ i # t t t ~ t t t ~ t t ~ t t t ? ?b%O ! 2690 SUP Save~t!L,Fs,Ng,Wsit!,Ep!t),Sigti!,F~tr! 27(1(1 ' ? ? I 0 'SAVE WIND SPEED ,STRRINS, AND STbESSES ???(I 1 2730 INPUT "KAHE DF NEU DATk FIlEI',t4m$ 2?J(l ' 27511 H i - F s / I H q t 5 ) ! S I Z E DF NEW F I L E 2769 Sl;e=?IHglMl+!ll ?77!! ' ICkEAT F I L E U I T H SIZE RECORDS AT 8 PITSIRECORD 2731) CREATE kDAT tInb,Siz?, B ?7?0 ! 23X) 'OPEN 110 PATH TO NEW F I L E 2810 2920 ASSIGN BP3th2 TO Fin3 7330 ! :540 ?!JTPbT ? ; ' ' K H ; 245ri!F'FtlNT !ISlN[i "l!rl,iOX,""STDRIHG DATh I N F I L E u",lOA";Nml 28CO 2970 'STORE DIITA I N FI1.E ?Bp,() 1 2990 N=F5/ lNg+S) 2900 E.1 2910 N = l 2920 FUR J = 1 TO H 2'750 F ( N ) = W 5 ( J ) 2940 N-N+I 2950 FOR 1.1 TO Ng 2?b? FIN)=Ep(Y! 2970 F l N + l ) = S i g ( K I 2980 N=Nt? 2990 K=Ktl 3000 N E I T 1 :OJO NEXT -1 302? 3031:l !CLOSE Ii0 PATH TO FILE 3040 1041 OUTPUT @ P a t b ? ; F l t ) 3050 hSSIGN @Path? T D t :!)A0 3!!70 S\IEEN[I 3000 ' I.09i) 3106 Tll? 5120 1171) 3!40 315? 31bC 3170 'ttltttt?~tf~lltttlt%tCtt~1I?tIftt?~t$t1t '1 GUT t !lllttftttStlit3?lttttf1tttt$~~tttt~ttIt~ r SUE O u t r F s , P l q , b l s ( t ) , E p ( ? ) ! S i g ~ t ) ! ! INPUT "DO VoLl WhNT RESULTS PRINTED OH P S I N T E R ? ( Y / ( R ~ ~ U ~ ~ ) ) ~ , B ~ S I F An$='Yn THEN PPIHTER I S 701 181) 1 3170 Hr=Fs/lNq+5) 3200 ' 3?10 FOE d = l T O Nr-1 STEP 2 322!1 ! > , . > l - l !=[.J-l! Ib 3240 D=IIiTIC) 3250 I F D=C THEN PRItiT CHR6(1?) 3250 ! ITDTAL NUEBEfi OF SCOHS 7-7 '0tiLY PRINT b DATA SETS PER PfiFE 3270 I:JfNq-(tiq-l) 3290 K=L+Ng-I !29!! PRlt.IT USIIiG "!/,I2)r,""UIV? SF'EED: '",?D.2Dl23X,""bilND SPEED: " : ' ! ? D , Z D 1 ; ; # ~ ( . ! i,Ws(Jtl, 1 3 0 0 PRINT USItjI; "!,?12k',""[;AC.E N0,"~',2X,""STPA]l~(in/~n~"",~~,""~~PE';~f~~~!"~!:~ 1" - 1 3 1 0 N=L 7 .d:? FDR (=L TD I 3330 PRINT USItiG " 5 X , ? 0 , 9 Y , D ~ 5 D , ! 1 , 5 O O ~ D , 9 ~ D , B X , D , : D , 7 ~ , 5 ~ ~ , 2 D u ; N , E p ~, l5~i g ! l ) N,Epll+Ng),Sig(l+Ng) 3340 ti-tl+l 3350 R U T 1 3360 tlEIT J 337f) ' !3YC SUBEND ?:q!:l 34110 3410 3420 3450 3440 3550 1460 3470 3420 1190 3500 3510 3520 3530 1 1 lttt~ttttt:~ttttt;~itr~t~ttt~t~ttt$tttttt '1 CORRECT2 t !ttttlttltttittfjltt$#ttttttitt:tttttttt$ ' SUB C o r r e c t 2 i t 4 q , O s l t ) ) ' CnLL P r i n t o s l ! l q , O5!?)) INF'UT "!JUMBER OF GAGE T O C@RRECTM,H INPUT "NEW DFFSETn,D51Y) ' SllEEt4D ' 5540 ! 3550 !tttttttttttttltdtltttt1tt$ttttt1tt$ttt1i 355(1 ! t PFt I3GE 1 3570 ' L t t l % t t ~ t t l t t l l t l l t t t I t t I I t t t t 1 $ I t t $ t t 1 ~ 3581) 3590 SUP F r i dqe lPv,F4) 7500 ! 3610 IMPVT VWHT I S THE BRIDGE VI)LTPIGE?",Pv 3b2C INPUT '#H6T I S THE STR41N 6A6E FRCTDR?",Ef 363ir ' ?A40 SUEEtID !b50 , $.:$j 3670 'tlttttttt?$$ttttfttd$?t1tttttttt11tttttt 35SI:I ! t CCIRftECTS t 3690 ! t t t t t l t ~ t ? t t t t t ? t t t t t t t $ t t d ~ t t 1 t t t t t t I t ? :70(1 1 3710 3720 3730 3740 3750 3760 3770 3780 3790 3800 SUP Correct.I(Nsl,Fs! ! OUTPUT ?;*Kg; CAT ' ' CLLAR SCREEN 'DISK DIRECTORY IHF'UT "YAME ?F DATb F I L E TO LISE?" ,th$ INPUT " S I Z E OF DbTA F I L E USEDINUHPEE DF RECORDS)1",Fs ! SUREND APPENDIX C SET UP AND OPERATION OF PIELD TESTING EQUIPMENT These procedures should be followed when Acquisition Unit to collect strain gage data. using the HP3421 Data List of needed equipment: HP3421A - Data Acquisition Unit HP-4lCX - Calculator C. HP-IL - Module D. HP83161A - Cassette Drive E. DC Power Supply P. Wheatatone Bridge A. B. Steps 1-5 must be completed in the laboratory. 1. Make sure charged. that all battery packs in all devices are fully 2. It is necessary to initialize and create a file on a tape before data can be stored on it. It is recommended to make the file big enough to fill the entire tape. Detailed instructions can be found in the HP-IL module's owner's manual. 3. For strain gage measurements, it is necessary to use a Wheatstone Bridge. The Wheatstone Bridge requires an external DC power supply. There are many different ways to configure the Wheatstone Bridge. The user should refer to the strain gage manual for these variations. Figure A 1 shows a two-wire circuit. 4. Once a Weatstone Bridge configuration has been selected, connect the appropriate wires from the bridge to the terminal block. Make sure to connect the wire8 to the correct channel slots. Each slot haa a high terminal and a low terminal. These are clearly marked on the terminal block. Take care not to connect any wires in the unnumbered slots between slots 1 and 2, or the unit will not function properly. It does not latter which wire goes in the "hi" slot or the "low" slot as long as they remain the same for the entire study. 5. If it will be necessary to disconnect and reconnect the gage cables to the bridge, it is recommended to use some sort of quick disconnect device, such as the spade connectors shown in Figure A2. Steps 6.-20 are to be completed in the field 6. Make sure all devices are turned O x . 7. Connect the terminal blocks to the option slots on the back of the HP3421A. The block for channels 0-9 goes in slot 0, the block for channels 10-19 goes in slot 1 . Connect the strain gage cables to the Wheatstone Bridge, following the manner of the bridge configuration selected. Use the quick disconnect devices, if available. Plug the HP-IL module into an expansion port on the calculator. If the calculator has memory modules installed, the IL module must be in a higher-numbered port than a memory module. Plug the lead from the IL module with the nale end into the HP-IL receptacle marked "IN" on the back of the HP3421A. Only one of the leads will fit, ao there is no possibility of a mixup. Using the short IL cable supplied with the cassette drive, plug the female end into the receptacle marked "OUT" on the rear panel of the HP3421A. Plug the other end of the cable into the receptacle marked "IN" on the rear of the cassette drive. Plug the other lead from the IL module into the receptacle marked "OUT" on the cassette drive. The HP3421A calculator and cassette drive should form a continuous, uninterrupted loop. If they do not, repeat Steps 6-12. Connect the power supply to the Wheatstone Bridges. Turn on all devices and check for proper operation. Adjuet the voltage across the Wheatstone Bridge to the desired value. Place prepared data cassette in drive. my. I t will only fit Set tape to proper file and data register. Refer to owner's manual for details. in one IL module Set any parameters required by calculator software and begin data collection. Check equipment frequently to insure proper operation. 20. When disconnecting devices, make sure "OFF" before beginning to disconnect. all devices are turned Quick disconnect points Data acquisition uni.t HP-342 1 A Power Figure A l . Two-wire Wheatstone Bridge C ire _f tf- Spade connector /--Bolt Wire to Wheatstone Bridge Spade connectors Wire to gage Figure A2. Spade Connector and How to Use APPENDIX D: DATA TRANSFER FROM CASSETTE DRIVE TO SERIES 200 COMPUTER These procedures should be followed to transfer data from a tape in the cassette drive to the Series 200 computer for storage on a floppy disk. List of needed equipment: A. HP Series 200 Computer B. HP-41CX Calculator C. HP-IL Module D. HP82161A Cassette Drive E. HP82169A HP-IL/HP-I6 Interface F. Floppy Disk for Storage 1 Floppy disk must be initialized before it may be used. Refer computer manual for details. to 2. To facilitate data transfer, two programs have been written. TRANS runs on the HP-41CX and TRANSFER runs on the Series 200 computer. Listings of these programs are given in Appendices E and F. TRANS first prompts the user to enter the beginning and ending registers of the desired data, as well as the data file where the data are located. It then reads a portion of the data into the calculator's memory. One register at a time, it recalls the data into the alpha register of the calculator, selects the I L / I B interface as the primary device and outputs the alpha register to the interface. TRANSFER also prompta the user for the beginning and ending tape registers plus the name of file where the data are to be stored. It creates this file, reads the data from the interface, and stores it. 3. TRANS and TRANSFER continue until all transferred and stored. the data have been 4. To use these programs, follow Steps 5-29. The user may wish write his own program(8). 5. Make sure all devices are turned O B . to Plug t h e HP-IL nodule i n t o a n expansion p o r t on t h e c a l c u l a t o r . Make s u r e t h a t no memory modules a r e plugged i n t o a h i g h e r numbered p o r t than t h e IL module. Plug t h e l e a d of t h e I L module w i t h t h e male end i n t o t h e r e c e p t a c l e marked " I N " on t h e IL/IB i n t e r f a c e . Using t h e s h o r t I L c a b l e s u p p l i e d with t h e c a s s e t t e d r i v e , plug t h e f e n a l e end i n t o t h e r e c e p t a c l e marked "OUT" on t h e IL/IB i n t e r f a c e and t h e o t h e r end i n t o t h e r e c e p t a c l e marked "IN" on the cassette drive. Plug t h e remaining lead from t h e IL module i n t o t h e r e c e p t a c l e marked "OUT" on t h e I L / I B i n t e r f a c e and t h e o t h e r end i n t o t h e r e c e p t a c l e marked " I N " on t h e c a s s e t t e d r i v e . The c a l c u l a t o r , c a s s e t t e d r i v e , and IL/IB i n t e r f a c e should form a continuous loop. I f t h e y do n o t , r e p e a t s t e p s 5-9. Plug a n HP-IB c a b l e from t h e computer i n t o t h e I t w i l l o n l y f i t on one way. Plug t h e power c o r d devices . into the IL/IB IL/IB interface. interface. Turn on all Boot o p e r a t i n g system on computer. Make s u r e IL/IB i n t e r f a c e Owner's Manual f o r d e t a i l s . i8 s e t t o "Mailbox" mode. See IL/IB P l a c e proper c a s s e t t e i n d r i v e . Execute "TRANS" on t h e c a l c u l a t o r . To "START REG?" prompt, e n t e r t h e s t a r t i n g r e g i s t e r of t h e t a p e and p r e s s R/S. To "END REG?" prompt, e n t e r t h e ending r e g i s t e r of t h e t a p e and p r e s s R/S. To "PILE?" prompt, e n t e r t h e t a p e d a t a f i l e name and p r e s s R/S. When "URT DATA" a p p e a r s i n c a l c u l a t o r d i s p l a y , load program 200 computer. W NOT touch t h e "TRANSFER" into Series calculator. Re-dimension t h e a r r a y s used i n "TRANSFER", u s i n g t h e g u i d e l i n e s found a t t h e beginning of t h e program. 22. Place the floppy disk to contain the data in the logged-in drive. 23. RUN program "TRANSFERn. 24. The program will prompt the user to enter the data file name and the beginning and ending tape registers. Press the ENTER Key after each item. 25. After a short pause, the Series 200 will display "Ready to read data, press CONTINUE". When this happens, press the R/S Key on the calculator and watch the red "BUSY" light on the tape drive. 26. VERY IMPORTANT: When the "BUSY" light on the tape drive goes off (after approximately 6 seconds) IMMEDIATELY press the "CONTINUE" Key on the Series 200 computer. 27. Check the first number on the Series 200 screen to see if correct. it 28. Wait until finished. Calculator will display "END OF DATA". 29. Turn all devices OFF before disconnecting. is APPENDIX E DATA TRANSFER SOFTWARE TO HP-41CX CALCULATOR HP-41CX program to transfer data from cassette tape to an 200 computer via the HP-IL/HP-IB interface. O l L R L "TRANS" 0 2 XEQ " C I U T O I O " 03 F I X 9 04 "STaRT REG?" 05 PROMPT 06 S T 0 00 07 "END. R E G ? " 08 P R O M P T 09 S T 0 0 1 1 0 R C L 00 1 1 "FILE?" 1 2 PROMPT 13 S E E K R 1 4 R C L 00 15 1 16 17 S T D 0 2 18 S T 0 0 4 19 MAN10 2 0 "WRT D h T A " 2 1 AVIEW 2 2 STOP 23LPL 0 1 24 2 25 SELECT 26 10.219 27 RECIDRX 2 8 10 2 9 S T 0 03 30 XEQ 0 2 '31 210 ST+ 02 RCL 0 2 R C L 01 X<=Y? G T O 03 37 G T D 0 1 38LBL 0 2 39 1 32 33 34 35 36 40 S E L E C T 4 1 LISTEN 4 2 L R L 04 43 C L A 4 4 A R C L I N D 03 4 5 OUT6 46 1 4 7 S T + 03 4 8 ST+ 0 4 49 RCL 0 4 50 RCL 0 3 51 X = Y ? 52 GTO 0 3 5 3 R C L 03 5 4 220 55 X-Y? 56 RTN 57 G T O 0 4 5 8 L B L 03 5 9 "END O F D A T h m 60 & V I E W 61 AUTOID 62 .END. HP Series APPENDIX P DATA TRANSFER SOFTWARE FOR HP SERIES 200 COMPUTER 10 @In 1 j f 2 1 ) ,A(?O,l!!r 20 Start: OUTPUT 2; Y V " ; 36 40 C' d l 60 'CLEAR SCREEN 1 INPUT STAFiTItiS REGISTER, ENDING ! 'ALL Data..in(Er ,Er ,HmBI REGISTER, !(I 80 90 !Oil 110 S = - 0 !C?lrPUTE S I Z E OF [lBTfi F I L E ! 'CREATE Dk7RFILE ! IRECEIVC DATR FROM HPILtHPIF INTERFACE I ' F P l V T DATA \ SUP Data-in!br.Er,!hZ) OU7PlJT 2; V):".; Wmf."" I ! ItlPUT DkTA F I L E NkHE I CAT lHPUT 'NAME OF DATh FILE 70 CHEATE?\th% 1 'lE!PUT STAFtTTIII; AHlr ENCIllG REGISTERS INPUT "STkRTI!iG REGISTEV i)F TAPE?", Br INPUT "ENDIHG REGISTER OF TAPE?", Er SUEEN? SUE Mail (Si;e,Nr$,Glt!) I IFSSlGH I/U PATHS 79 DATA F I L E AMD IPITEPFACE kHL1 D4TA FILE l 4 Y E ASSIGN B P a t h l T O l.h$ ASSIGN e l b i l TO ??J I " OUTPL1T 2; ; D I S P "heady t o read da!a. PAUSE K" Press CONTINL~E !o procede." I @!SF "READING DATA AND WRI!lNG DATA Ti1 ? I S k F I L E " I N= 1 FOR I = l T ? S i z e STEP ?1 FDF J = 1 T? 21 ENTER Plbil:D~J) 'USE ONLY 4PLO!UTE D(J)=ABS(DIJI I VflLUES I !PRINT VALUES TO SCREEN F'RIHT UE;lNG '51,4D,4C. IOD";N,D!J) 'STORE DATR IN FILE I #=It.!-1 OUTPI(1 FPath1,K;DI.J) I ! C?NT INUE LOOP 1 N=H+ I NEXT J NEXT 1 SUPEtJD SU6 D a t a - g i 1 t i N 1 1 9 , ~ ~ t ) ) 'PRINTER IS 701 F'RIIiT CHRQ I!?) SUBEND