instruction report itl-93-0 october 1993 us ad-a273 398 li ...loads. the development of...
TRANSCRIPT
Instruction Report ITL-93-0
October 1993
US Army Corps AD-A273 398of Engineers N lIWaterways ExperimentStation
Computer-Aided StructuralEngineering (CASE) Project
Load and Resistance FactorDesign for Steel Miter Gates
by Bruce R. El/ingwoodJohns Hopkins University
DTICN.-•: '•OV 19
Approved For Public Release; Distribution Is Unlimited
93-29270
93 1 1 29 1 4 4 Q61111111111Prepared for Headquarters, U.S. Army Corps of Engineers
The contents of this report are not to be used for advertising.publication, or promotional purposes. Citation of trade namesdoes not constitute an official endorsement or approval of the useof such commercial products.
O P FJR1H ON RI•YCLmID PAIM
Computer -Aided Structural Instruction Report ITL-93-4Engineering (CASE) Project October 1993
Load and Resistance FactorDesign for Steel Miter Gates
by Bruce R. Ellingwood DTIC QUALMIY IN8IECTED 5
Department of Civil EngineeringJohns Hopkins University Accesion ForBaltimore, MD 21218 NTIS CRA&I
OTIC TABUnannounced IJustification
Distributiori I
Availabiiity Cc ýes
Avail a1d I orDist Special
Final report
Approved for public release; distribution is unlimited
Prepared for U.S. Army Corps of Engineers
Washington, DC 20314-1000
Under Work Unit 32484
Monitored by Information Technology LaboratoryU.S. Army Engineer Waterways Experiment Station3909 Halls Ferry Road, Vicksburg, MS 39180-6199
USo Army Corpn
SWOWN
Waeray Expinermetstao Caaoig.n lcto Data"
Elingwood, Bruce.Load and resistance factor design for steel miter gates / by Bruce R. Ellingwoodl ; pre-
pared for U.S. Army Corps of Engineers ; monitored by Information Technology Laboratory,U.S. Army Engineer Waterways Expeuiment Station.
63 p. :1il. ; 28 cm. -- (Insructilon report ; ITL-93-4)Includes bibliographical references.1. H-ydrauli gae - Design and construction. 2. Load factor design. 3. Strains and
stresses. 4. Structural design. I. United States. Army. Corps of Engineers. II. U.S. Army•Engineer Waterways Experiment Station. Ill. Information Technology Laboratory (USArmy Corps of Engineers, Waterways Experimnent Station) NV. Computer-aided StructuralEngineering Project. V. Title. VI. Series: instruction report (U.S. Army Engineer Water-ways Experiment Station) ; ITL-93-4.TA7 W34 no.ITL-93-4
Contents
Preface ................................................. v
Conversion Factors, Non-SI to SI Units of Measurement ............. vii
1- Background ........................................... I
2-Objectives and Scope .................................... 5
3-Reliability Bases for LRFD ................................ 6
Basic Methods of Reliability Analysis ......................... 6Stochastic Modeling of Load Events ......................... 11
4-Load and Resistance Data for Lock Structures .................. 15
Basic Description of Structural Loads ........................ 15Structural Resistance of Steel Shapes and Plates ................. 35
5-Development of Probability-Based Design Requirements ........... 38
Reliability Associated with ASD ........................... 38Probability-Based Load Criteria ............................ 40
6-Recommendations ...................................... 46
7- References ........................................... 48
SF 298
List of Figures
Figure 1. Stochastic responses to environmental events ............. 3
Figure 2. Pulse process models of loads ....................... 12
Figure 3. Idealization of loads developed during lockage ........... 17
Figure 4. Temporal characteristics of loads during lockage .......... 18
Figure 5. Typical miter gate vertical section .................... 19
Figure 6. Typical seismic hazard curves ....................... 32
IWi
Ngure 7. Reliability indices for fiexuni members designed by
ASD and by LRFD .............................. 40
Ust of Tables
Table 1. Lockages in 1986 in Locks with High Damage Rates ....... 16
Table 2. Statistics for Hydwstatic Loads ...................... 21
Table 3. Accident Incidence Statistics by River System ............ 25
Table 4. Accident Incidence Statistics for High-Risk Locks ......... 26
Table 5. Barge Impact Test Results ......................... 29
Table 6. Load Statistics .................................. 34Table 7. Statistics of Tensile Properties of Steel Plate and Shapes .... 36
Table 8. Resistance Statistics for Steel Members and Components .... 37
Iv
Preface
The work described in thi report was sponsored by Headquarters,US Army Corps of Engineers (HQUSACE), as part of the Civil Works Guid-ance Update Program (CWGUP). The work was performed under theCWGUP Work Unit S031, "Design of Hydraulic Steel Structures," for whichMr. Cameron P. Chasten, Information Technology Laboratory (ITL), US ArmyEngineer Waterways Experiment Station (WES), was Principal Investigator.Mr. Donald R. Dressler (CECW-ED) was the CWGUP Technical Monitor forthis project, and Mr. Thomas J. Mudd, lTL, WES, is the CWGUP ProgramManager. Funding for acquisition of miter gate load data and the publicationof this report was provided by the Computer-Aided Structural Engineering(CASE) Project sponsored by the Directorate, HQUSACE. The CASE Projectis managed by the Scientific and Engineering Applications Center (S&EAC),Computer-Aided Engineering Division (CAED), ITL, WES.
The work was performed at the Department of Civil Engineering, JohnsHopkins University, by Dr. Bruce R. Eliingwood, under US Army Corps ofEngineers (USACE) Contract No. DACW39-92-M-1280. The report wasprepared by Dr. Ellingwood, under the general supervision of Mr. Chasten,Mr. H. Wayne Jones, Chief, S&EAC, CAED, and Dr. N. Radhakrishnan,Director, ITL. Some of the results of this work are included in Engineer Man-ual 1110-2-2105, "Design of Hydraulic Steel Structures."
Acknowledgement is expressed to the Load and Resistance Factor DesignField Review Group (LRFDFRG), assembled to monitor this project, for pro-viding assistance in this work. Members of the LRFDFRG and theiraffiliations are: Mr. Joseph P. Hartman, HQUSACE; Dr. John J. Jaeger,US Army Engineer District, Jacksonville; Dr. Nathan Kathir, US ArmyEngineer District, St Paul; Mr. Chasten, ITL, WES; Mr. Robert J. Smith, CivilEngineering Consultant; Mr. W. Scott Gleason, Civil Engineering Consultant;Dr. Ellingwood, Department of Civil Engineering, Johns Hopkins University;,Dr. Theodore V. Galambos, Department of Civil and Mineral Engineering,University of Minnesota; and Dr. Wei-Wen Yu, Department of Civil Engi-neering, University of Missouri - Rolla. The data on hydrostatic and hydro-namic loads and tow impact required to utilize the response combinationmodels were obtained with the assistance of staff members at WES.
V
At the time of publication of this report. Director of WES wasDr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN.
vi
Conversion Factors,Non-SI to SI Units ofMeasurement
Non-SI units of measurement used in this report can be converted to SI unitsas foil ws:
mum* By To Obimin
eet 0.3048 mews
inches 0.0254 mwetas
kips 4.448 klonewtons
tons 907.185 klograms
mile e hour 0.447 meoers per second
kips per squar inch (ksi) 6894.57 kmlopascels
Vii
1 Background
Miter gates and other hydraulic steel stuctures (HSS) must be designed towithstand loads due to the weight of the structure and pennanent attachments,operating equipment, barge impact, hydrostatic and hydrodynamic effects, andenvironmental effects. The maximum structural response to approprate com-binatiom of operating and environmental effects is compared to the designstrength of the structure to ensure acceptable performance.
The design of miter gates in the past has been based on allowable stressdesign (ASD) principles (Heauarters, Department of the Army 1972), thetraditional approach to steel design embodied in the American Institute of SteelConstruction (AISC) specification (AISC 1978). In ASD, the design safetycheck is of the form
A(EQ) < Fan - Fu IFS (1)
where
ftEQi) = the elastically computed stress arising from the combined nominalloads, EQ
Fay = allowable stress
Fu = limiting stress (for yielding, rupture, buckling)
FS = overall factor of safety
The FS represents the traditional way of addressing the problem of designuncertainty and does so in a purely subjective way.
There are a number of shortcomings in ASD (Galambos et al. 1982) whichare remedied in the new 'load and Resistance Factor Design Specification forStructural Steel Buildings" (AISC 1986). In contrast to ASD, Load and Resis-tance Factor Design (LRFD) is a limit states design method which is muchbetter keyed to the behavior of steel structures at design conditions. Designuncertainties are taken into account using modem structural reliability analysis
ChopW1 Bagmu1
techniques to suAtem t professional Judgment. In LtFD, the basic safetycheck is of the foam
Required stren,:;, < Design strength (2a)
Eyj nj <#R4(2b)
where
R= nominal strength
* - resistance factor that reflects uncertaunty in sutengt
- load factors to account for unertainty in the loads
Note that the factors # and yj serve the s-me purpose as the overall FS inEquation 1. However, they are reflective of the variability in the individualparameters to which they are assigned.
The LRFD Specification (AISC 1986) provides a comprehensive treatmentof design strength for the limit states of yielding, inelastic deformation, frac-ture. and instability for steel members and cmnectios. Studies have shownthat cost savings often can be achieved in design by using LRFD rather thanASD. Efforts are now underway to adapt the LRFD Specification to thedesign of miter gates and other hydraulic steel structures (Headquarters,Department of the Army 1991 and 1993).
The required strength in Equation 2b is defined for ordinary buildings andother structures by the load requirements in Section 2.4 of American Societyof Ovil Engineers (ASCE) Standard 7-88 (formerly American National Stan-dard (ANSI) Standard A58.1-1982) on minimum design loads (ASCE 1990).Environmental effects (wind speed, for example) are specified as N-year meanrecurrence interval (MRI) values, i.e. those values with a probability of I/N ofbeing exceeded in a given year. Generally, however, two or moretime-varying effects must be considered in combination. As illustrated by thetypical load sample functions in Figures la though c, the extreme values ofthe individual effects rarely occur simultaneously, and simply combining theN-year MRI values is unduly conservative. Probabilistic load combinationanalysis methods (Ellingwood et al. 1982; Galambos et al. 1982) were used todevelop the load factors and load combinations used to compute the requiredstrength in Equation 2b for building structures (ASCE 1990). Statistical dataare required to define the cumulative probability distribution functions for theenvironmental loads and to set these loads and load combinations.
2 ChaPW I Bakgrund
t
a. Pemanent static response
Z (t) \ 0A
tI L-- L ,2 V
b. Intermittent static response
X 3(t)
T 3 T I 3 -1
c. Intermittent dynamic response
Figure 1. Stochastic responses to environmental events
The application of the load factors in ASCE Standard 7-88 (ASCE 1990) tothe loads considered in design of miter gates is questionable, because the loadcombination analysis alluded only to above utilized data on common structuralloads for buildings. One might expect that the load requirements for design ofmiter gates would have a similar format but that the load factors would bedifferent. Moreover, the load factors in Equation 2b were determined througha calibration process in which common strucftura members designed by ASDwere evaluated using structural reliability techniques. The new loadrequirements for LRFD were based on the target reliabilities determinedthrough this assessment of existing designs. This calibration process makes
Chip~r I -a~w
sawse for ordinary construction, where design criteria are supported by years ofexperience. There is less experience for miter gates. A review of the patcriteria for hydraulic suctus (Headquarters, Department of the Army 1972)does not reveal any rational basis for some of the design requirements, e.g.that the AISC-specified allowable stresses be multiplied by a factor of 5/6 inpl ortioning members for combinations of normal operating or hydrostaticloads.
The development of probability-based load requirements for use in LRFDrequires the following steps:
a. Identification of structures to be covered.
b. Identification of limit states for structural components and systems.
c. Identification of significant loads and load combinations, and the devel-opment of a statistical database to suppon probabilistic load combina-tion analysis.
d. Collection of statistics to describe the structural capacity.
e. Analysis of reliabilities associated with current design procedures(Headquarters, Department of the Army 1972), and selection of targetreliability levels.
f Development of LRFD load requirements, including load combinationsand load factors.
g. Comparative design studies to determine cost savings or penalties asso-ciated with the proposed criteria.
This report focuses on steps c, e, and f.
4 Chqr 1 Ba omund
2 Objectives and Scope
This repw describes an improved basis for determining load requirementsfor design of hydraulic steel structures using modem structural reliability anal-ysis and probabilistic load combination techniques. This methodology willfacilitate the development of design loads and their combinations for use inLRFD.
The methodology is demonstrated for miter gates by considering load com-binations involving dead load, hydrostatic load, hydrodynamic load during gateoperation, temporal hydraulic head, and barge impact load.
Chapmr 2 Objs•cvm d Soap 5
3 Reliability Bases for LRFD
Basic methods of Reliability Analysis
This section presents some of the basic tools for the development ofreliability-based load combinations for hydraulic structures such as miter gates.
First-order reliability methods
A limit state represents a condition in which the structural system or one ofits componens fails to perform its intended functions. For HSS, strength orsafety-related limit states include yielding, rupture, instability, or loss of over-all equilibrium. Serviceability limit states include excessive deformation orvibration. A limit state is described by a behavioral equation or failure func-tion developed from principles of structural mechanics
.3D =0 (3)
where
X. =xx2,.,x.)
= random variables describing loads, material strengths, and dimensions.
Failure is taken, by convention, as the state in which G(.) < 0.
The limit state probability or probability of failure provides a quantitativemeasure of reliability and performance. If the joint distribution of the Xi isknown, this probability is
6 ChaptW 3 RMObiW Baes for LRFD
where
fla) - Joint probability density function of X and the integration is per-formed over diat portion of the domain of a in which G(j) < 0
The joint density in Equation 4 is rarely available and the integration isdifficult to perform. Moreover, Pf is very sensitive to the behavior of theextremes of ff), which awe diffilcut to define with the limited data that typi-cally are available in structural reliability analysis. First-order (F0) reliabilitymethods have been developed to address these problems. In FO reliabilityanalysis, Pf as a measure of reliability is replaced by a "reliability index." P,defined as the minimum distance from the mean of I to the failure surface,measured (when the random variables are statistically independent) in standarddeviation units (Melchers 1987). The coordinates of the point of minimumdistance on the failure surface (sometimes termed the checking or design point)can be defined as
X i - mi * ki Oi,. i - l,2,..., n (5)
where
Mi, Ii = mean and standard deviation in Xi
ai = sensitivity coefficient describing the relative importance of variableX in the reliability analysis
The plus or minus sign on oý depends on whether Xi is a load or strength vari-able, respectively. If all variables are described by a normal distribution andfunction G(.x) is linear in x, P and P/are related by
Pf 0-P (6)
where
0 = standard normal probability integral
In this case, FO reliability analysis is a tool for approximately integratingEquation 4. Clearly, estimates of means and standard deviations in loads areessential in developing probability-based design requirements.
7chwimr 3 RuI~y Bags b LRFD
Eammadon of mesures of uncertinty
Let X denote a basic resistance or load variable. The true statistical charac-tr.cs of X shoud be emploe when evaluating P or P and when derivingapp op ate factors of safty for design. However, ie random characteristicsof X seldom are known precisely in suuctful enineerti owing to insuMcientdata and imperfect information. Ths is especially tire for miter gates, where aconsistent database on opeating events does not exist. Estimates of the mean,mx, and the standard deviation, ax, and coefficient of variation, Vx, thatdescribe inherent variability, are obtained from small samples of data or areinfenul on the basis of expert opinon Additional ucertainties arise ftom thesmall sampie sizes, differences between the laboratory conditions under whichsome data are gatmed Nd field conditions, and structural modeling errors.As a result of these additional uncertainties, the mean and coefficient of varia-tion used in structunl reliability analysis should be determined as
mx B mx (7)
VX [VX2. VD] (8)
where
mx and Vx = data based
B =bias in prediction
V3 = modeling uncertainty, assumed to be vested in the uncertaintyin predicting the mean, mx.
When data are available, mx and Vx can be estimated from data samples.Frequently, little data are available to supplement engineering judgement.Occasionally, the engineer may be able to estimate from past experience therang over which the data should lie. In this case, the mean and coefficient ofvariation can be estimated from the range if some assumption is made aboutthe general shape of the probability distribution. If, for example, it is assumedthat X has a bell-shaped frequency distribution and that roughly 95 percent ofall values lie between x1 and x2, the implied mean amc! coefficient of variationin X are
mx - (xI + X2)/2 (9)
8 3ha S Rsby Bms for LRFD
vX - 0-5(X2 - XI)% + xI) (10)
Because of the scarcity of data, it will be necessary to estimate statistics forseveral of the loads using similar techniques in the sequeL
The Delphi as a basis for uncwtnty analysis
A slgniflcut amount of load survey and modeling data were available todevelop the load combinations in ASCE 7-88 (ASCE 1990) for building struc-tares and in the AISC LRFD specification. The loads used in miter gatedesign are defined in EM-I 110-2-2703 (Headquarters, Department of the Army1984). These loads apparently are based on experience rather than on in situload measurements, and their quantitative basis, if any, cannot be determined.Statistical data of the sort available for buildings are not available for loads onmiter gates and other hydraulic structures, and it is not feasible to perform thenecessary load surveys.
A Delphi, or consensus estimation survey, was conducted to remedy thissituation and to provide statistical data on loads necessary to develop proba-bility-based load combinations. A Delphi is an organized method for elicitingexpert opinion or intelligent judgement from a group and is used to quantify aphenomenon when empirical data are limited or do not exist. Delphi's havebeen used in a number of structural engineering applications: in revising thelive load tables in ASCE 7-88 (Corotis, Fox, and Harris 1981) and, morerecently, in seismic hazard analysis at nuclear plant sites in the Eastern UnitedStates where there is little or no historical seismicity (Bermreuter et al. 1989).Of course, the accuracy of the results depends on the knowledge, biases, andjudgement of the participants and the extent to which they utilize any availableempirical data. In a typical application, a load questionnaire initiaily is circu-lated to the group and each participant is asked to provide a best estimate of aparameter and an estimate of its variation. The results of the questionnaire arecompiled and recirculated for revisions. Although in the ideal situation theremay be several iterations of the questionnaire, constraints prevented this in theCurrent project.
The questionnaire was developed and distributed to each U.S. Army Corpsof Engineers (USACE) District and to the locl-ý'-aster of each lock and damthat is operated and maintained by the Corps (Ciasten 1992b). Each lockoperator was asked to c~mplete the survey on the basis of his own experience.A total of 108 responses were received, representing most of the major riversystems in the eastern United States.
A typical survey question asked for a best estimate of a parameter, X (say,hydrodynamic head), and a plus-or-minus variation, AX. This information isused to estimate the mean and standard devirtion (or c~efficient of variation)in variable X. The variation given was interptit, As corresponding to * 2
clpeW 3 RdIt, y for b' LRFD9
standard deviations (representing approximately the 95 percent confidencebomnd for normal random variables).
Suppose thnt di. two estimates provided by die 0 participant are xk and£.Xk. k a 12,...N. The mean value of X is estimated from
E~ k mk -MX
Assuming that the participants am equally experienced, X is an unbiased esti-mate of the mean.
The actual value of X can be expressed as
X - mx + U + V (12)
where
mX= true mean of X
U = zero-mean random variable describing deviation of mean values esti-mated by participants
V zemr-mean random variable denoting the deviation in the variationestimated by each participant.
Assuming that U and V are statistically independen the variance in X is esti-mated by
2 2 +(13)
where
a 2 (14)U i kk
10Chapla 3 PAbIWty Buns.tar LRFD
E E (xk)2(15)
The coefficient of variation in X is estimated as Vy - GvoX
The results of the Delphi are summarized later in this report
Stochastic Modeling of Load Events
Load events occur randomly in time, and the magnitude during any eventalso is random. If the effect of the load on the structure is static, it can beassumed that the load magnitude remains essentially constant during an eventwith mean duration, c. (If the load varies slowly in the interval, the loadmagnitude can be set equal to the maximum value within the interval). Withthese assumptions, each load can be modeled as a sequence of random pulses(a so-called pulse process), as illustrated by the sample functions in Figure 2.Permanent loads, such as dead and permanent equipment loads, are essentiallyconstant in time. Sustained loads may change their magnitude in a stepwisefashion from time to time but in between these changes remain relatively con-stant. Hydrostatic loads fall into this category. Such loads may be intermittentin nature, i.e., there are substantial periods when the load is not acting.Finally, transient loads occur infrequently and usually last for a very shortduration; the durations of such loads often are so short in comparison to thoseof sustained loads that they can be modeled as impulses. Earthquake loadsand barge impact loads are examples of short-duration transient loads. Theprobability densities for these load processes sampled at an arbitrary point intime are illustrated at the left-hand side of each sarwple function in Figure 2.The discrete probability mass ax zero magnitude represents the probability thatthe load is absent (not acting) at the time of load sampling.
The load processes in Figure 2 must be described statistically to performthe load combination analysis. The probability distributions of thepoint-in-time loads, Q, and the maximum loads to occur during an interval oftime (0,t), Q.. are required for load and load combination analysis (Turkstraand Madsen 1980; Ellingwood et aL 1982). It often is assumed that theoccurrence in time of load events is described by a Poisson process. With thePoisson model, the probability of observing n events in interval (04) is
P[N(t) - n] - ('tR e-Xt; n - 0,1,2 .... (16)n!
where
X = mean rate of occurrence of events
chWs 3 eW Bý for• UW11
a. Pemavent loads
2
b. Sustained loads
1[3
maim
N
c. Tramsent loads of short duration
d. Total load
Figure 2. Pulse process models of loads
12 Chaplr 3 ReabMW Bases fS o LRFD
The probability distribution of the maximum load to occur during (0,t) can beobtained from the theorem of total probability
Fq.w (,X) " o•Q_ < XW IN n] PIN(.) - n] (17)
If the Individual loads in the sequence are assumed to be identically distributedand statistically independent random variables, the cumulative distributionfunction of the maximum load in (04) is obtained from Equations 16 and 17 as
F(IU(x) - exp [- Xt(l - F N))] (18)
This distribution of the maximum load demonstrates the importance ofobtaining daft on the rate at which accidental events occur (parameter X) andon their magnitude (described by FQ (x)).
The distribution of the maximum of a combination of time-dependent stoch-asic variables generally cannot be determined exactly, and approximationsmust be sought. Several methods for evaluating combinations of stochasticvariables are available (Larrabee and Cornell 1981; Pearce and Wen 1984;TurkstM and Madsen 1980). All of them require infonnation on the mean rateof Occurnce, ,, of each load event, the duration, c, of the event (see Fig-ure 2), and the probability distribution, FQ (x), of each load magnitude.
Suppose that a combination of loads is defined as
U(t) - X(t) + X2(0) ÷. . (19)
Um = maxU(); o: t 5T (20)
where
X4t) = stochastic load event
An upper bound for the probability that Umax exceeds the value, x, during per-iod (O,T) is given by
Chqmr 3 Reidy Bamfo LRFD 13
Gu.(x) < vv(x)T (21)
where
VV(x) = mean rate at which the combined process U(t) crosses x with apositive slope
The function vJ(x) can be pprximamd by (Peare and Wen 1984)
VgXX) M EV1 GUU() + EEvij Gui.v,(x) +.. (22)
where
Gua and v1 - conditiona probability of U, exceeding x and meanoccurrence rate of U, alone
GUi+Uj and v.- = conditional pwobability of U,+U. exceeding x and meanoccunvnce rate of U,+UO occurring simultaneously
If the individual loads are modeled as Poisson pulse processes, the mearate of occurrence and duration are sufficient to describe the temporal charac-teristics of the load. The probability, p, that the load is nonzero at any timeequals v1i. If the load is always nonzero, p = .0 if the load is inemittent.pi will be less than 1.0. If two intermittent processes combine, the mean rateof occurrence and duration of a coincidence of the two loads i and j are givenby (Pearce and Wen 1984)
vii -vi v ( el +*j) (23)
' ,=j .. 2+ (24)
As can be seen from Equations 21 and 22, events (or combinations of events)with very small vi (or v.) contribute very little to the probability of exceedingx. Load combinations involving loads with very low probability of coinci-dence do little to enhance structural reliability. This ot-vervation will be usedsubsequently to screen certain load combinations from Aurther consideration.
14 chsP3 R3labi•t Ba•s. for LRFD
4 Load and Resistance Datafor Lock Structures
Basic Description of Structural Loads
Structural actions on miter gates due to hydrostatic pressure (H.), temporalhead (Ht), hydrodynamic load (He), equipment loads (Q), and impact (I,) arisefrom the normal operation of the locks. Thus, the statistical analysis of struc-tural loads requires knowledge of the operating characteristics of the lockgaes, which depends on the usage of the locks. General operating character-istics of locks on heavily traveled rivers may be quite different from those onsecondary rivers, and it might be expected that the design requirements woulddepend on river use. For this study, the emphasis is on high-use riversbecause of the economic impact of lock design and operation.
The "Ohio River Standard" (110 by 600 ft or 34 by 183 m) lock is com-mon on rivers in the North Central Division, USACE. There are 21 of theselocks on the Mississippi and 7 on the Illinois River (Reuter 1990). The tow-boat or tug and the collection of unpowered barges are referred to collectivelyas the "tow." On the Upper Mississippi River, tows are limited to a maximumof 15 barges which typically are 35 ft wide by 195 ft long (11 m by 59 in).When locking through an Ohio Standard Lock, such tows must be recon-figured. The first lockage would involve nine barges, and the second lockagewould involve six, plus the towboat.
The starting point for load event analysis is the rate of occurrence of lock-ages. The "Lock Accident Study," TR-REMR-HY-7 (Martin and Lipinski1990), Appendix B, provides data on number of lockages and total tonnageobtained from seven USACE District Offices, comprising up to 11 years ofdata at 80 locks on 10 rivers. A review of these data revealed that on theMississipp. River, lockages occurred nearly uniformly during the period Aprilthrough December of each year, while during the January through Marchquarter, lockages were approximately 70 to 80 percent of those in the otherthree quarters. On the Ohio River, on the other hand, lockages were essen-tially uniform throughout the year. This lack of a strong seasonal effectimplies that lockages may be assumed to occur uniformly during the entireyear for load combination analysis purposes. A summary of 1986 lockage data
hMrw 4 L.ad ,dW R*Wsta af l r Lo* Smeun 15
for six locks showing the highest average annual damages to miter gates ispmsented in Table 1.
Table 1Lockag-- In 1986 In Locks with High Damage Rates
Tomme&Wr LAW* Ldmm SarOM (OmWAd) Raw (me,)
blsksp 17 4.236 25.616 27.125 35321 4,385 25,726 26.088 36522 4.443 26.446 26.8N6 37024 4,581 28,064 28,161 38325 4.718 28,101 28.15
Ohio GWX& 1 5.972 34.617 34.282 496
Some of the data prsented in Appendix B of REMR-HY-7 (Martin andLipinski 1990) are for 9, 10, or 11 months; all data in Table I have been nor-malized to a 12-month period. No differentiation was made between upstreamand downstream lockages in the TR REMR-HY-7 database. Although some ofthe lockages might have been associated with pleasure craft, the database is notspecific on this point
An idealization of lock operation for purposes of idealizing the temporalcharacteristics of loads Hr, Hd, Hr and Q is shown in Figures 3 and 4. Fig-ure 3 shows a downstream lockage and the loads developed. Figure 4 illus-ttes the temporal characteristics of the resulting loads from two successivelockages, the firat from a vessel traveling downstream and the second from avessel traveling upstream. The upper gate is assumed to be open at the begin-ning of the cycle. Several distinct stages that are repeated in sequence foreach lockage are identified in order to relate temporal characteristics to avail-able data. Appendix D of TR REMR-HY-7 (Martin and Lipinski 1990) indi-cates that at Mississippi River Locks 24 and 25, the "processing time" isapproximately 80 min. In the context of Figures 3 and 4. the processing timeis interpreted as the time from when the tow begins maneuvering to enter thelock to the time it exits, including gate operation time. The "chambering" time(time tV dewater the lock and open the lower gates) for these two locksaverages about 35 min. The time required to open or close the gates isapproximately 2 min. (Green, Murphy, and Brown 1964), and the dewatering(watering) period is approximately 30 min. At a typical tow entry velocity of2 mph (0.90 m/s) (Rteuter 1990), the entry or exit period is about 5 to 7 min.Finally, operator experience suggests that tows typically spend 20 to 30 min inthe holding area in the handling/maneuvering phase. These times aresummarized:
16 ChqpW 4 Load and Rmstais Data for Lock Struaws
-iii
]a If
Figure 3. Idealization of loads developed during lockage
C,6 4 Lood WAf Rtwm Deft for Loj c w 17
z
I - • -1 m- -It, *-
a "U
Figure 4. Temporal characteristics of loads during lockage
Handling and maneuvering 20 to 30 minTow enters upper lock 5 to 7 min
lose upper gate 2 to 3 minDewater lock 20 to 30 minOpen lower gate 2 to 3 minTow exits 5 to 7 min
Total 54 to 80 min
Operating Loads
The hydrostatic load, H., on the miter gate in the closed position is deter-mined by the upper and lower pool elevations. These pool elevations aresite-dependent. Their variation is dependent on weather conditions upstream,primarily rainfall/nInoff. Figure 5 shows a vertical section through a typicalmiter gate, illustrating the resultant hydrostatic pressures and the overall forcedeveloped.
18 Chapir 4 Load and Rrestan Data for Lack Stucms
Lip-r PoolI EL. 95.- C.L. Top Girder-i. EL. 99.5
76I
3
p--- _ _.._ __-----ga.,
VERTICAL SECTION C-a Ftower Pool EL. 64.0
A)
H -\/ --- :
C.L. Bot. 1 Gir 0EL. 47.0,
Figure 5. Typical miter gate vertical cross section
The resultant force per linear unit width acting on the miter gate is
F=w(2p _ 2)/2 (25)
where
yw = density of water
Hp= depth of upper pool
HP = depth of lower pool
Since the differential elevation is A = HP - Ht.
19chqsrw 4 Load and Resitsios Datafor L~ock Sbnctms
F- WARH P H,)I (26)
The maximum animal rensuam force occurs when A is at Its annual maximumvalue or when H is at its animal maximum value. The pressure at any dis-tance, z, below tre top of the gate is given as
0; Z:H8 -Hm
p([ - - (HS - HpA] Hg - Hp <Z < HS ,(7
YW(Hp - H,) = YWA, HS - H, < z
where
Hs height of the gate
The load per unit length on a horizontal girder at z is
H, M s p(z) (28)
where
s = vertical spacing of the girders
The mean and standard deviation of F or H. can be developed from Equa-tions 26 or 28, as appropriate.
Stage duration curves at Lock and Dans (LD) 24, 25, and 27 on the UpperMississippi River and at Cheatham LD on the Cumberland River were ana-lyzed to determined statistics of annual extreme pool and tailwater elevationsand annual maximum differentials in elevation. The elevations are measuredupstream and downstream from the LD's. Statistics on pool elevation anddifferential are summarized in Table 2. While there is natural variation in poolelevations from year to year, the variability in elevation and in differential issmaller than one might expect because the river level is controlled by damsupstream and downstream for flood control.
The characteristics of river flow are different from lock to lock, and theannual maximum differential does not necessarily coincide with the maximumpool. At LD's 24 and 25, for example, the annual maximum differential oftenoccurs at the same time as the maximum pool, whereas at LD 27, they rarely
20 ChpWr 4 Load and Rwsrsm Dat for Lo ck Siruces
Table 2StatM c for Hydrosta Loads
LD Yews MSm 8D COV Mni 8D WOV
24 48 451 2.6 0.01 13.8 0.94 0.07
25 48 437 2.9 0.01 14.3 1.25 0.00
27 37 417 7.5 0.02 15.7 2.6 0.17
Chefan 15 389 4.0 0.01 rNSI"
occur together. The mean values of pool elevation and mean differentialsshown in Table 2 are dependent on the site of the LD. They are of less inter-est for the probabilistic load modeling herein than the standard deviations (SD)or coefficients of variation (COV), which measure the relative control on waterlevel provided by upstream and downstream dams and directly impact the vari-ability in the load that must be taken into account in the load combination
The randomness in F ad Hs can be inferred from the statistics presented inTable 2. At LD 27, where the maximum overall force is associated with maxi-mum pool, the COV in F from Equation 26 is about 0.30, while the variabilityin H. from Equation 28 is 0.17. At LD's 24 and 25, where maximum forceand pressure both tend to be associated with the maximum differential, theCOV's in F and H. are on the order of 0.20 and 0.10, respectively. Theseobservations are based on an examination of data at only three sites. Pendingacquisition of additional data, the COV in Hf, and F is set equal to 0.25; thisvalue contains an allowance for load modeling uncertainty.
The hydrodynamic load Hd and equipment load Q arise during operation ofthe miter gates from fluid-structure interaction. Miter gates are never operatedunder static head, and thus loads Hd and Q are mutually exclusive of HrWater level on each side of the gate is equalized before the movement of thegate is initiated. Hd and Q include effects of friction, wind loads, surges, andhydraulic drag. Friction and wind effects normally are very small in compar-ison with the hydrodynamic effects due to fluid-structure interaction (Green,Murphy, and Brown 1964). Under normal operating conditions, the effects ofHd and Q represent a statically equilibrated force system. These loads are notuniform in time. Uncertainty in Hd and Q may arise from variations in poolelevans, which affect the depth of submergence, from surge effects causedby movement of the gates or overtravel of water in the culvert system duringfilling and from variations in the angular velocity of the gate.
Green, Murphy, and Brown (1964), in Technical Report (TR) 2-651, sum-marize the results of tests conducted on 1:20-scale models of miter gates.Three different types of operating machinery linkage were considered: modi-fied Ohio River, Panama, and Ohio River. To consider a variety of operating
COlwlpr 4 L•od an R"sw Dab for Lai* ftudwn 21
cmnidltoni6 depth of sumrecoperating time, chamber length, bottomclearance under gate, and presece of barges in the chamber were varied inde-pefdenty. These model itudles indicate that the hydrodynamic effects dependwimarily an the angular velocity of the gate leaf and the depth of submer-Sence, and that the maximum effects usually occur as the gate leaf reaches themitered position upon closure. Plots of maximum torque versus operating timeand depth of sbmergece (e.g. Plate 47 of TR 2-65 1) show that the loads arerelatively predictable and depend primarily on the velocity of the gate leaf andthe depth of submergence, both of which are likely to be known. The Appen-dix to TR 2-651 summarizes the results of scaled model (I".5) tests conductedin 1942 for the Third Locks of the Panama CanaL Figures 7 and 8 of thatAppendix show the torques measured during opening and closing operations atvarious times with baseline conditions. The maximum deviation from averagein four tests was 8.1 percent during the opening operation and 3.8 percent dur-ing the closing operation. Using these data with Equation 10, the impliedcoefficient of variation in Q would be about 0.05.
This variability in Q is associated with the basic hydrodynamic effect, sincethe tests were conducted under baseline conditions. Additional variabilitywould arise from variations in the pool elevations (submergence) and angularvelocity of the gate leat, these additional uncertainties would increase theoverall variability in HR and Q.
The Delphi partcipants were requested to provide information on the differ-ential in water level as the gate moves through the water. The current designvalue is 6 in. (154 mm). On the basis of the Delphi and using Equations 11through 15, the mean differential is 4.4 in. (112 mm) and the COV is 0.53.This value represents a substantially higher uncertainty in Hd than that indi-cated from the model tests discussed above.
If there is a submerged obstruction, the bottom of the gate leaf may bindduring operation while the operating load is applied at the top of the leaf,causing the gate leaf to twist. In this case, Hd and Q do not form a force cou-ple. The maximum twist in the leaf depends on the maximum operatingequipment load, Q. Operating machinery often includes a safety device thatlimits the maximum force and acts as a structural fuse. Common devicesinclude shear pins that are attached to the operating strut and fail at a certainforce, hydraulic relief valves limiting the cylinder pressure supplied to theoperating strut, and overload torque devices on electric motors. The maximumoperating strut force is s•pplied to the structural designer by the mechanicalengineer.
Many Delphi respondents (59 of 108) indicated that the load-limiting deviceon their gates had been activated at some time. The frequency of activationvaried, but most values cited ranged from I in 1,000 lockages to I in100 lockages. Reasons cited included debris or ice caught in the gate bays,high water or opening against a head, and human error. Shear pins usuallywere reported as mild steel 0.5 to 0.75 in. (13 to 19 mm) in diameter. Thebehavior of such pins is relatively predictable; the mean and coefficient of
22 Char 4 Load and Resitn=e Data for Lock Swuc•me
varlaion In ultimate shear strength a about 125 times the nominal R. =FvAbalt and 0.10 (Galambos et aL 1982). Hydraulic opering systems withrelief valves apparntly are most common. Th behavior of such systems is atleast as predictable as the behavior of shear pins. Sources of variability arisefrom possible malfunctions of the safety relief valve on the cylinder. Few datawere reported on torque limits for electric motwo.
Temporal hydraulic loads, H. occur due to temporary variation in waterlevel and wave action caused by tow movement in the lock or overfilling orunderfifling the lock chamber. These loads can occur while the gate is in themitered or open position. Delphi participnts were asked to provide inform-ation on both cases. The curremnt design value for any cause of H, is S in.(381 mm).
In the mitered position, H, can occur due to overfill or underfill of the lockchamber. The momentum of the flowing water determines whether the cham-ber is filled or emptied to the appropriate level. Using Equations 11 through15, the mean and coefficient of variation for overfill were 5.4 inches (137 mm)and 0.94; for underfill, 3.8 in. (97 mm) and 1.03. Waves also may be pro-duced by the towboat and barge as the lock is exited. The mean and coeffi-cient of variation were 12.0 in. (305 mm) and 0.76; the latter mean H, is thelargest value of all those repoted.
In the open position, H, may occur from water entrapment as the gate ismoved into the lock wall recess. The difference in water elevation behind thegate and in the chamber has a mean value of 3.0 In. (76 mm) and a coefficientof variation of 0.87. Waves also may be pushed outward toward an open andrecessed gate as the tow ent or exits the lock. The mean and coefficient ofvariation for this event are 6.4 in. (163 mm) and 0.88.
The means for temporal head, H,, for gates in the open position are sub-stantially less than for gates in the mitered position. This suggests that H,should be treated differently in load combinations intended to be applied toopen and mitered gates; in particular, H,, (mitered) and H,, (open) should bespecified in separate load combinations addressing these conditions.
Ice and mud (denoted C and M) may accumulate on a miter gate and act asa gravity load that adds to the weight of the gate. This accumulation causestwist about the shear center of the gate when the gate is not in the miteredposition. A significant number of the Delphi respondents believed that iceaccumulation is a significant problem, both on upstream and downstream facesof the gate. Most accumulations reported ranged from 6 to 36 in. (152 to914 mm); using Equations 9 and 10, the mean and coefficient of variationwould be 21 in. (533 mm) and 0.35. Mud and silt do not appear to be assignificant a consideration; accumulations reported ranged from 2 to 12 in.(51 to 305 mm), suggesting a mean of 7 in. (178 mm) and a coefficient ofvariation of 0.36.
Chqf. 4 Loe ud Reik-ne Deb for Lock Sbuchm 23
In addition to the accumulation of ice and mud on the gate, accumulationof ice sheets in the water on either side of the gate may result in lateral forceson the gate due to latral expansion of the ice. Many Delphi respondents(59 out of 108) indicated that this is a potential problem. An analysis of theirresponses suggests that the mean ice thickness is 10.1 in. (257 mm) and tiecoefficient of variation is 0.77.
Inpac loads
Impact loads, Ira, arise from accidents in which vessels collide with lockstructures. Such accidents may be caused by misalignment during entry ordeparture, failure of steering or towing accessories, wind and current, turbu-lence, excessive entry velocity, or pilot error. Each lockage presents an impacthazard. These accidents can result in extensive repairs to both the lock and/orthe vessel and in long costly delays. Vessel entry is the most critical part of alockage. Proper entry velocity is 2-1/2 mph (1.1 m/s) or less. The primarycauses of accidents include excessive speed or inability to stop; misalignmentof the tow'. faulty communications between the lockmaster and tow operator,equipment failure; pilot error, surges in the lock chamber due to filling system;river stage and discharge; current patterns; and visibility (Martin and Lipinski1990; Reuter 1990). The Delphi reported 71 instances of collision over anunspecified period of time. Most of these collisions involved damage to thegirders or the skinplate of the gates.
The incidence of significant impacts, the duration of the impact hazard, andthe intensity of the impact are required for event combination and reliabilityanalysis. The basis for the data on impact occurrence is the records kept byeach USACE District office on accidents involving damage to U.S. Govern-ment property of collisions at locks and dams within the individual jurisdic-tions. These data are summarized in "Lock accident study," a technical reportby Martin and Lipinski (1990). Accident data reflecting the severity and fre-quency of vessel collision to USACE lock facilities, specifically to miter gates,were collected.
Data on accidents involving lock structures and, in particular, miter gatesare summarized for several heavily used rivers in Table 3. These data presenta rough overall picture of the incidence of accident loads and, in particular,those affecting miter gates. The Mississippi, Illinois, Ohio, and Tennesseerivers are considered "high-use" rivers, while the Cumberland River (CheathamLock) is considered a "low/moderate use" river. The average rate of accidentsinvolving miter gates at locks on the Mississippi, Illinois, and Ohio rivers isapproximately 0.06/month. A majority of these accidents involve bargeimpact. Not all accidents result in significant lock downtime, however.
It has been suggested that downstream tows carry a higher impact hazardan upstream tows. Data obtained independently on operation of the
Demopolis Lock, USACE District, Mobile, over the 11 -year period 1979through 1989 (private communication), indicate that the annual number of
24 ChapWr 4 Load and Resistance Dat eor Lock Sbucwums
Accident Incidence Statistics by River System
PAeddnea
SAU Acciden MM isW
Lo-l .ee.mOI -Look-
INO No. MOID•tl Num~ber Rate (me')"1 Mm• Rmi(neO"
Molt kmin 12 1.248 124 0.099 76 0.061
& Louis 4 352 97 0.276 s5 0.165
s& Paw 12 1.500 173 0.129 134 0.069
ToWI 28 3.100 394 0.127 266 0.096
a 632 21 0.025 9 0.011
Ohio
Hunrflon 6 738 64 0.114 55 0.075
Lousvb 6 a08 52 0.064 25 0.031
PtItbugh 6 540 32 0.059 na na
TOWi 20 2.066 168 0.081 s0 0.052
TOen .6 576 }32 J 0.056 6 0.010
i mnod I72 1 10.014 0o -
upstram and downstream tows is roughly equal. However, !he annual down-stream tonnage exceeded upstream tonnage by factors ranging from 2:1 tomore than 10:1 over the I l-year period. Miter gates are not symmetric - theupstream face is smooth while the stiffeners are fabricated on the downstreamface. It is assumed that for data analysis and design purposes it is not neces-sary to distinguish between upstream and downstream tows. Since the down-stream and upstream tows occur more or less uniformly over the year, thedifference in tonnage downstream and upstream simply would contribute to thevariability in the impact load, given that an impact occurs.
Some locks are more hazardous and prone to accidents because of theirposition with respect to the channel, turns in the river, current outdrafts, windand turbulence, and other factors noted previously (Reuter 1990). Additionalinformation is provided by considering accident statistics at specific locks.Table 4 presents the same information as Table 3 for the six locks with thehighest average annual damages to miter gates (Table 8 (Martin and Lipinski1990)). The five Mississippi River locks are all single-chamber locks, whilethe Gallipolis Lock has an auxiliary chamber. These locks also appear in listsof the locks with the most number of accidents, highest average cost per acci-dent, or highest average annual damages, and with the most damages (Martin
ChWI 4 t.o and PwW R"s IDat for Loca Stuctu 25
Table 4Accident Incidence Statistics for High-Risk Locks
AM Aesidmnt M1W Goes CadMWG
FWLeok. Raft Ras RO AteRive Lee uM, N (I,") No. (,e-) N. (meo)
MAs. 17 104 10 0M8 5 0.077 4 0.038
21 104 6 0.077 5 0.048 4 0.038
22 104 25 0.240 1i 0.173 5 0.048
24 as 26 0.296 15 0.206 3 0.034
25 as 29 0.329 15 0.170 1 0.011
"Qapo s 2 0.42 3A 3 0.268 7 0.057
and Lipinski 1990). The "All accidents" column refers to total accidentsinvolving lock Structures; "Miter" refers to accidents involving miter gates; and"Cat/MG" refers to those accidents having damages greater than $50,000 inwhich the miter gate was struck. Approximately 25 percent of the accidentsinvolving miter gates fall in the "CaIMG" category. Assuming that these per-cenages apply to locks in general, the mean rate of occurrence of structurallysignificant accidents to miter gates is approximately 0.016/month, or about 1every 5 years. Accidents over $50,000 accounted for 77 percent of total dam-ages, and over 72 percent of such accidents involve miter gates.
The force due to tow impact depends on the mass of the tow and itsvelocity at impending collision. Because of the limited data available todescribe these parameters, several questions on the Delphi were designed toelicit this informiaon. Included were queries on the number of barges perlockage, fractions of barges that were full, partially full, or empty of cargo,weight of a fully loaded barge, and initial and terminal velocity of the tow inthe lock chamber. A large amount of data were generated in response to thesequeries, and it was not possible to analyze these data completely in the courseof this study. It is clear, however, that impact should be treated as a concen-trated force in design rather than as a uniformly distributed load, as is currentpractice.
The total mass (weight) of a tow in the lock is modeled as
26 ChaptWr 4 Load and Resistanm Data for Lock Statures
Nb (29)WT E W(i
i-l
where
WbI = weight of an individual barge
Nb = mmtbr of barges comprising the tow
Both Wbe and Nb am random variables. The mean and variance of WT are(Benjamin and Cornell 1970)
WT - Nb WbN (30)
4T = ]'a W b ' b"CN b (31)
in Which k. W~b are mean values and,0bad 4 aevrace2fN nWbir Note that randomness in both Wb1 and Nb contibute to the overall uncer-tainty in WT.
A standard barge measures 35 by 195 ft (10.7 by 59.4 m) and, when fullyloaded, draws 9 ft (2.74 m); when empty, the barge draws 1.5 ft (0.46 m).Thus, the cargo capacity of a fully loaded barge is approximately 1,500 tons;the empty barge displaces about 290 tons. The randomness in the weight ofan individual barge arises from its overall capacity, density of cargo, and thepercentage of barge capacity taken up by cargo. The mean and variance in Wbwere obtained from the lock operator responses to questions concerning therelative percentage of fully or partially loaded barges passing through the lockand the type of barge. Taking into account the fact that some barges are fullyloaded while others are not, the overall mean and standard deviation in indi-vidual barge weight for all locks reporting such weights in the Delphi were870 tons (7.89 x 10" kg) and 303 tons, respectively; the COV is 0.35. Exami-nation of subsets of the data led to similar values. For example, in subset (I),10 locks measuring 110 by 600 ft on the Mississippi River, SL Paul District,were considered. For this subset, the mean and standard deviation in Wb were911 and 120 tons, respectively. In subset (2), 10 locks measuring 110 by600 ft on the Mississippi River, Rock Island District, were considered. Forthis subset, the mean and standard deviation in Wb were 986 and 298 tons,respectively. Both subsets correspond to high-use rivers.
chopu 4 Load md Rsdslto - Deb M Lock Skums 27
A brief examination of data reported for other river and districts did notindicate my significant variations in t statistics of individual barge unitweights. These barge weights am consistent with dxe summarized inTable 4.1 (Martin and Upiskli 1990); at LD 25, for example, the unit bargeweight reported in 1986 was 1.002 Utare. Additional data on barge masswere obtained from an hInependent survey by USACE personnel (QCuten1992a) of 48 lockages at locks on the Ohio, Kanawha, and Tombigbee Rivenwith chumber lengths ranging from 360 ft (110 m) to 1,200 ft (366 m). 7Thmean aid standard deviation of barge weight for downstream lockages was1,361 tbarge and 623 tbare. respectively. For upstream ckaeps, the meanand sMt•d deviation were 659 Vbarge and 703 tibarge, respectively, the highstandard deviation is due to the fact that many of the barges were empty. Tlioverall tonmage in each lockage dearly was dependent on the length of thelock; thus, it would be reasonable to assume that the total mass at impact islinearly proportional to the damber length for chambers of the same width.
The number of barges in a lockage, Nb, clearly depended on the dimensionsof the chamber, and the mean and variance in N•1 are similarly depent.Chamber sizes in the Delphi varied from 56 by 360 ft (17.1 by 109.7 m) to110 by 1,200 ft (33.5 by 365.8 m). The lockinasters participating in the Del-phi provided estimates on the frequency of the number of barges per lockage.These data can be used to determineNb a a2 Nb; WT aid 02 wT follow
directly from Equations 30 and 31. However, the number of barges per lock-age reported in the Delphi frequently ranged from I to 15 in 110- by 6O0-ftlocks that cannot admit more than 9 barges per lockage. in such cases, thedata were enonmalized by apportioning the barges to two successive lockages:the first consisting of nine barges and the second consisting of the the remain-ing barges (plus the towboat). For data subset (1) above, WT = 6,031 tons andOwT = 2,343 tons; the coefficient of variation is 0.39. For data subset (2)above, WT = 6,863 tons and a = 2,242 tons; the coefficient of variation is0.33. To this, of course, must le added the weight of the empty barges incomputing the total mass involved in the impact. These values are higher thanthose implied from the data in Table 1; at 1D 25, e.g., WT averages5,968 t/lockage. Additional data was provided for the Demopolis Lock during1979-89. The lock chamber at Demopolis measures 110 by 600 ft, admitting amaximum of nine barges/ockage. The mean and standard deviation of esti-mated monage/ow downstream was 6,615 and 595 tons, respectively. Datareported from the same lock (Chasten 1992a) on 12 downstream lockagesshowed that the mean and standard deviation were 7,117 and 3,143 tons,respectively. Clearly, more work is required to evaluate statistics of mass atimpact.
The lock operators were asked to provide information on the entry andapproach velocity of tows in the lock. The entry velocity averaged 2.9 fA/s(0.88 m/s), with a COV of 0.56. The approach velocity averaged 2.2 ft/s(0.66m/s), with a COV of 0.62. The kinetic energy of the tow is proportionalto the square of its velocity, and thus the coefficient of variation in kineticenergy at impending impact may be over 100 percent if these estimates are tobe believed. Additional confirmation of these values was obtained from an
28 ChapW 4 Liod and &Retshu Dama for Look Sftuws
independent survey of barge tow velocity measurements (Chasten 1992a). Themean entry velocity ranged from 1.8 to 3.4 ft/s (1.2 to 2.3 mph). wrisistentwith prudent navigtion. The terminal (approach) velocity is defined as thetow velocty in the last t 100 ft(15 to 30m) of the locL The weightedmean and COV in terminal velocity are 1.26 ft/s and 0.42, respectively.
Ift y, neither the entry nor the terminal velocity depended on the lengthof the lock.
A set of barge impact tests were conducted recently at LD 26 on theMississippi River. The miter gates at LD 26 are vertically framed. Table 5smnarizes the loads measured from a fully loaded nine-barge tow of approxi-mately 15,000 tons (Chasten and Ruf 1991).
Table 5
Barge Impact Test Results
Veod•,y (Ml) Imped Foe (kips)
0.36 4420.50 4430.73 4880.94 60
These tests were conducted at very low velocities to avoid permanent damageto the miter gates. Unfortunately, the relation between impact force and veloc-ity in Table 5 is not linear, making it difficult to determine forces due to theterminal velocities reported in the Delphi by extrapolation.
Dead load
The dead load consists of the weight of the miter gate. In contrast to thedead load in building structures, where nonstructural attachments are the mainsource of variability in dead load, miter gates are well defined as structuresand their dead loads are quite predictable. Accordingly, the dead load isassumed to be described by a normal distribution, with a mean value equal to1.0 Dn, where D. is the nominal dead load and a coefficient of variation takenas equal to 0.05.
Uve loads
Live loads are due to the weight of moveable equipment and attachmentsand individuals and their possessions. Live loads are not significant in designof miter gates, and thus need not appear in the load combinations. For appur-tenant structures, the load combination for live loads appearing in ASCE 7-88(ASCE 1990) is recommended.
cOm.m 4 L.OW adW R c De Lock ftr' O " 29
loads
Ehquae effects on building structures usually are determined using anequivalet utatic-for-dynamic analysis in which a base shear is computed fromdie slsmnic hazard mid general structural characteristics, and from it a distrbu-don of lateral foces Is determined in a manner consistent with the fundamentalmode shape of the structure. In the new NEHRP provisions (Federal Emer-gency bMuigement Agency (FEMA) 1992), this base shear is determined as
V - CS W (32)
where
Cs = seismic design coefficient
W = total dead load and portions of other loads
Coefficient C. is defined as
C, W 1.2 A, S/RT" < 2.5 A./R (33)
whene
A. and A, = effective peak acceleration and velocity-related accelerationsdetermined from seismic ground acceleration maps or site-specific seismic hazard analysis
S = coefficient for soil profile characteristics
R = structural response modification factor
T - fundamental period of the structure
The coefficient, C,, is tantamount to an inelastic yield spectrum for an oscilla-tor with 5 percent damping. For hydraulic structures, the seismic hazard anal-ysis is used to determine a value of acceleration; inertial hydrodynamic forceson the gate resulting from the design ground motion are determined fromWestergaard's equation (Westergaard 1933; Chiarito and Morgan 1991)
(34)p(y) - 0.875 Ty A, rHW
30 CWpr 4 I.od and R ustomo Data for Lock Sucturcs
Whem
-- density of water
A, = velocity-raed effective peak ground acceleration (expmssed in unitsof gravitational acceleration, g)
H - pool depth
y - depth below pool surface
It is apparent that the basic seismic hazard analysis is a key ingredient inthe analysis of earthquake force, regardless of which of these two approachesis taken. Research in earthquake-resistant design during the past 15 yeats hasenabled seismic hazard analysis and design ground motions at a particular siteto be placed on a probabilistic basis (Algennissen et al. 1982). Earthquakehazards in the western United States generally can be associated with a seriesof capable faults. Such faults are not apparent in the eastern United States,and the seismic hazard analysis there begins with an identification of postu-lated seismic source zones. Seismicity is determined within these zones ofpotential future earthquake occurrence, and mean rates of occurrence of earth-quakes of various magnitudes (or intensities) are identified. Attenuation func-tions relating peak ground acceleration to magnitude and epicentral distanceare used to relate the arthquake ground motion at the building site to themagnitude or intensity at the source. Finally, a probability distribution ofeffective peak ground acceleration at the site is detenrined by summing (inte-grating) over all possible earthquake sources and magnitudes consistent witheach underlying source hypothesis. The result is usually presented as a com-plementary cumulative distribution function, GA(a), or seismic hazard curve,showing the annual probability of exceeding a specified ground acceleration.
Typical seismic hazard curves for building sites in the western UnitedStates and the eastern United States are compared in Figure 6. For moderateaccelerations a seismic hazard curve can be described by a Type II distributionof largest values (Cornell 1968).
GA (a) = 1 - FA (a) 1 - e1p[-(a/u-] (35)
where
FA(a) = cumulative distribution function of effective peak groundacceleration
a = ground acceleration u and a are parameters of the distribution,as described below
Chopqr 4 Load aid Retmios Date for Lock Sucwss 31
Parameter a detemnnines the slope of the hazard curve. The curve in tieeastern United States is much ftier (smaller a) dan that in the westernUnited States (see Figure 6); this is because of the relatively larger uncertaintyassociated with eastern seismicity due to the absence of larg historical eventsduring tie pedriod of modern I.tnumentatkn. The western U. S. hazard curvesaturates at acceleration levels on the orde of 1.2 to 1.8 times the designeartquake; in the east&e United States, the saturation level is unknown but isbelieved to be on the order of 2.0 to 3.0 times ft design earthquake.
0 a)
a a
Ninetern us Western us
%€,C,
1/475
A Ground acceleration, amap
Figure 6. Typical seismic hazard curves
Parameter a is related to the coefficient of variation in annual maximumeffective peak acceleration. The seismic hazard analyses (Algermissen et al.1982) on which the NEHRP Recommended Provisions for Seismic Regulations(FEMA 1992) are based indicate that a tends to be larger for sites in the west-ern United States, decreasing from about 5.5 (COV = 0.28) at San Francisco,CA, to approximately 2.3 (COV = 1.38) at Boston, MA, and Memphis, TN.The latter coefficient of variation is substantially larger than coefficients ofvariation in other loads considered in the load combinations.
32 ChOPW 4 Load and RAsstncs Date - La& SbkuMs
The NEHRP R, ecmmended Provisions are being adopted, with minor var-ants, by ASCE Standard Committee 7 for its revision to the Standard onStnrctural Loads and by the Model Codes. 71le design earthquake envisionedfor buildings. as rfflected in the design Wgound motion contour maps, is basedon a specified probability of 0.10 or less of being exceeded in 50 years; thiscorresponds to a mean recurrence interval of about 475 years. This probabilityis much less than the probabilities of exceeding the design snow or wind loadsin ASCE 7-88 (ASCE 1990), which are 0.01 to 0.02 on an annual basis.Earthqakes with magnitudes less than ML = 4.0 or Mercallintensifies lesstham V were not considered in evaluating seismicity for this map, because itwas believed that their capability for causing structural damage was negligible.The uncertainty in the earthquake effect is vested in this conservative speciff-cation of the structural action, E, due to the earthquale. As a result, the loadfactor on E in the NEHRP Recommended Provisions is set equal to 1.0 ratherthan a greater value.
The design earthquake proposed for USACE hydraulic structures reportedlyis based on a probability of 50 percent of being exceeded in 100 years, corre-sponding to a mean recurrence interval of about 145 yearn. Under the assump-tion that the seismic hazard is described by a Type H distribution of largestvalues, two mean recurrence intervals N1 and N2 and corresponding effectivepeak ground accelerations a, and a2 can be related by
N21NI - (a2/al)u (36)
For example, if a = 2.3, the NEHRP and USACE design-basis ground motionswould be related by
I (37)aNEHjtP - aUSACE (475/145)"a = 1.68 aU&4CE
If at = 5.5, the NEHRP and USACE design-basis ground motions would berelated by
aNFJRp - aUSACE (475/145)"a = 1.24 aUSACE (38)
In the eastern United States, the selection of a design earthquake groundmotion has a more substantial impact on the economics of design because theseismic hazard curve is so flat.
There has been substantial research in earthquake-resistant design since theSan Fernando earthquake of 1971 began accelerating developments in this
Chqr 4 Load wd RPsistm Data for Lack Skuckns 33
area. most of tis research has shown that the earquake hazard unds to beunderestimated. The eurnee intervals betwem larg events In the easternUnited State e Im becamse the hazard curves are laL, amd as a result mosteasternrs have little or no experience with eartihuakes. Nonetheless, thedamae potetial is ther; the coneq --ces- economic and otherwise, of lockand dam filume should be considerd carefully in etuing the design criteria.
0te mnvironmeental loadl
Loads due to sow, wind, temperature, and self-training actions generallyare not significant in the design of miter gates. For appurtenant structures, ftload combination for these loads appearing in ASCE 7-88 (ASCE 1990) isrommended.
Summary
Table 6 summarizes the mean occurrence rates, durations and statistics ofH,, Rd and Q, Rd and 4, based on the data summarized. Figure 4 shows theidealizations for the load pulse idealizations used in the subsequent structuralreliability analysis. The hydrostatic load, H,, has been idealized in time by auniform rather dum a trapezoidal pulse for simplicity. Note that the meanoccurrence rate of H, is the number of lockages per year divided by 2 (assum-ing upstream and downstream lockages alternate), while the mean occurrencerate of Hd and Q is the total number of lockages (each gate must be operatedfor each lockage).
Table 6Load Statistics
Nab (mO-i) Ouadmef MGM COY pt.L
D 50 Yr 1.0 Dn 0.06 NormalHe 200 90 min 0.9 Ha 0.25 Type IHeCOequi) 400 2 min 0.7 Hdn O03 Type Io (obet.) 0.4 1 mi 1.25 On 0.10 Type IH,, 400 2mm 0.6 Hin 0.76 TypeIH a 400 2 min 0.43 Hi 0.68 Type Im 0.016 15 sc 1.0 tIr e Type I
The nominal values, denoted with subscript "n", are assumed to be thosedefined in EM 1110-2-2703 (Headquarters, Department of the Army 1984). Ifthese were to change at some future time, the mean values in Table 6 alsowould change. It is assumed that a best estimate of impact force would beused for design.
The statistical data summarized in Table 6 on mean rate and duration ofsignificant load events can be used to screen certain event combinations from
SChqpar 4 Load aW Raisom Deaa for Look S•u•ws
subsequet -- ldeain For examIe, comsider the ccmbuntion of Card)-quake with ate operation loads H nr Rd nd 0). The mean durati of theseevents is .rinoxmately 2 min (3.803 x I0" yr) and they occur at a rute of4,800/yr. If te mean rant of occurrece and duration of a significant (gmreatrthan ML - 4) eardlpake is assumed to be O.l1/yr mad 30 sc (9.506 xI0"? yr). Equation 23 cm be used to show that the mean rate of a coincidenceof earthquake with gate operation is
v,£E - (4,800XO.IX3.8 x 10-6 + 9.51 x 10-7 )
- 2.29 x 1O'3/yr
Similarly, significant impacts occur at 0.O16/mo or 0.19/yr and have a durationof 15 sec (4.75 x 107 /yr) or less. The mean rate of coincidence of earthquakeand impact is
ViE - (0.19X0.1)(4.75 + 9.51) x 10-7(40)
- 2.71 x 104tyr
The mean rates of occurrence of combined loads due to these effects are verysmall in comparison to those loads associated with normal gate operation,which typically occur on the order of 4,000 to 5,000 times/yr. On the otherhand, the mean rate of occurrence and duration of Hs are 2.400/yr and 90 min(1.711 x 10"4yr). Accordingly, the mean coincidence rate of H, and Ebecomes
vHJE - 2,400(0.1OXI.171 x 104 + 9.506 x 10-7) - 0.0413/yr (41)
This mean rate is sufficiently high that H. and E should be considered incombination.
Structural Resistance of Steel Shapes and Plates
Properties of structural steel required for structural reliability analysisinclude the yield strength and modulus of elasticity. The existing literature onthis subject for common grades of structural steel was reviewed in depth aspart of the effort to develop load and resistance factor design for steelstructures (Galambos and Ravindra 1978). These data are summarized in
Ohmbr 4 Load wid R"islm Daf for Lock Swum 35
Table 7. Probability disbuions of mec a properie of gae typicanyMare Cew-positve, and t'he lognonnal distribution has been a satsactory model
in previous Smudlme
TOMas 7
Str ttics7 of Tensile PMperties of Strel PlM and Shapes
puimemIr••ma ftpt ,.m Co.,
Pkps. wtW in bda •.aF 10o 0.10
P--ms.-I - 9 1.10F 0.11T,_ T_ 0.64 F 0.10Tensio coupon. s cbun 0.06Tenin, coaqwpmsuon coupon PoisGson' 0.3 0.03
Strength properties depend on the rate of load. For mill test conditions, theyield strength is somewhat higher than is obtained under so-called stMc loadconditions. All dMa Presented in Table 7 have been corrected to a satic rateof load.
Additional daM was located on strength of SASl6/Grade 60 carbon steelplate used as a liner in nuclear power plant n For l/4-in.-thick
plate- the mean, standard deviation and coefficient of variation in yield strengthwere 48.5 ksi, 3.3 ksi, and 0.07, respectively (122 samples). For l/2-in.-thickplate, the mean, standard deviation and coefficient of variation in yield strengthwere 42.1 ksi, 2.6 ks/, aid 0.06, respectively (48 samples). The specified yield,Fy, for tWs material is 32 ksi. The lognormal distribution provided the best fitto the data of several common distributions teged statistically.
Structural resistance used in LRFD is defined in terms of the structuralaction or limit state. For example, the resistmce for the limit states of tension,flexure, shear, and compression are summarzed in the foliowing.
Tension:Inelastic deformation: R = F ANet section fracture: R W Ae
Flexure:Formation of plastic hingein compact beam: R= FyZ
Compression:Instability: R =Fcr AInelastic deformation: R = Fy A
Shear:Yielding: R = Fv Av
Other limit states are expressed similarly. Statistics to describe strengths ofstructural shapes and plates for various limit states can be developed from thestatistics prented in Table 7. The resistance statistics in Table 8 are typical
36 Ohqimr 4 I,.oa tond Raul~ ieno Daa for Lock Swu•mc
TawleSi mie im P, Staesilo for SteW Msembwe and Components
Mamobw e= TC.O.V.Ydh& member
YIeld 1.05 FA ________1_
CMpegf em 1.1 FuZ 0.13
Cutinusu 1.11 F, Z 0.13
C~nompol 1.04 Liu 0.14
Laerel-ksiane buck 1.06 Fv 8 0.14
8*e In howe 1.10 F, Aw 0.15
hftm ONelm
Ylelin 1.06SFy S 0.14
-Laftrul4ateWrd buck 1.20 FerS 0.17
Shea 1.0S F, A 0.17
Celmu 1.0SFor A 0.15
Wei"e ohned mese 0.86SF, A 0.18
Boiled Cosmeedee, skw0.60 Fu A 0.10
for h-oftrold steel and welded-plate girder stnjctural members. In this table,the strengths F F5 , F1,, and Fc and section properties A, S. and Z are thosenominally spciled by AISC for design.
Chqier 4 Lied MWd Rseielu Data for Lock Skuuchir3s
5 Development ofProbability-Based DesignRequirements
Reliability Associated with ASD
Reliability indices 0 associated with existing design criteria provide bench-marks for the development of new probability-based load combinations. Expe-rience with ordinary building structures has revealed that the P's for existingcriteria vary over a considerable range, reflecting the fact that past codes andstandards have not dealt with uncertainty in a consistent fashion (Galambos etal. 1982). One simple illustration of this point is the treatment of dead load incombination with other loads in ASD. It might be observed from Equation Ithat the same factor of safety is applied to dead load and to other variableloads in the combination. However, dead loads are relatively predictable,whereas operating and environmental loads can be highly unpredictable (uncer-tain). Consequently, the likelihxod of failure in structures in which overallstress is dead load dominated is much less than in structures where the majorportion of the stress arises from operational loads that may vary in time.
To illustrate the calibration process, we consider a compact flexural mem-ber in a gate, for which the limit state is the formation of the first plastichinge. It is assumed in this illustration that the combination of hydrostatic andtemporal head governs the design. This component is designed by ASD usingthe current requirements in EM 1110-1-2101 and EM 1110-2-2703 (Head-quarters, Department of the Army 1972 and 1984, respectively)
5/6 Fb Sx k Hsa + Hm (42)
where
Fb and S. = allowable stress and elastic section modulus from the AISCSpecification
38 Chapar 5 DeveIopmyo of Probablty-Based Desgn Requa.ments
H and Has - force resultants in the flexural member from nominal(code-specified) hydrostatic and temporal head
(The subscript "a" has been appended to the forces to emphasize that these arenominal forces rather than random variables.) The factor 5/6 is required byEM 1110-1-2101; although the basis for this factor is uncertain, it is believedto reflect the severity of the operating environment for lock structures and thepossibility of material deterioration over time. A flexural element that satisfiesthe code requirements is obtained from Equation 42 as
Sx > (Ha,, + HM)A56"Fb) (43)
The limit state for this member is given by (cf Equation 3)
G( ) •y zx - H., - R, < 0 (44)
where
FY = yield strength
Zx = plastic section modulus
H. and H, - random forces from hydrostatic and temporal head
Observing that Zx typically is about 1.12 Sx for W-shapes, the limit-state equa-tion for a flexural member designed according to code is defined by substi-tuting Sx from Equation 43 into Equation 44
1.344 (H.= + Ht) F/Fb - Hs - H, - 0 (45)
The reliability index associated with the current code requirement (Equa-tion 43) now can be determined by first-order methods (page 6), using the loadand resistance statistics summarized in Tables 6 and 8.
Consider a design situation in which the structural effect of Hsn rangesfrom I to 25 times H,,. The latter situation might exist for the submergedlower girders on the miter gate. The results of the FO reliability analysis arepresented in Figure 7 as the curve labeled ASD. In the limiting case in whichthe structural action arises almost entirely from H., P = 3.1. The P's amlower for low H,,/H,, because H,, is relatively more important in the loadcombination and its coefficient of variation is substantially larger than thecoefficient of variation in Hs. When H,, - Hsn, relevant for girders in thepartially submerged upper portions of a gate, P = 2.7.
ChWW 5 DevsepM of Probabft-BasWd Deagn Reqremnts 39
4
Aim
3 .
,~~ 1r, .4
2 -. 2
1
I i
5 10 15 20 25
as/t
Figure 7. Realabkty Indices for flexural memners designed by ASD and by LRFD
To estabfish a frame of reference for thes reliability indices, an FO relia-bility analysis of simply supported compact stee beams designed by ASD forthe combination of dead plus live load leads to O's that decrease from about3.0 to about 2.2 (50-year basis) as La/In increases from about 0.5 to 4(Galambos et al. 1982). On a comparable 1-year basis, these P's would beapproximately 4.1 to 3.4, assuming the loads to be statistically independentevents.
Probability.Based Load Criteria
The basis for the load combination analysis is the probability distribution ofthe maximum, U,. of a sum of time-dependent structural loads. Difficultiesin determining the distribution of Umax exactly have led to the approximation(Turkstra and Madsen 1980)
40 Cho@. 5 Dismvlpnent of Pmba-Bas9d Design R wquirwsmen
UOU - max [ max Xi WQ + E X (0t (46)i 0<t<T
which truusftms the load combination analysis into a problem of randomvariables rather than random procesm . Research i probabilistic load combi-natio analysis has shown tih failures usually occur when one of thetime-varying lokus attains its maximum value (Equatio 46, term max X1(t),termed the "pricipal action") while the other loads equal their point-in-timevalues (terms Yxt) In Equation 46, the companion actions). Since it is oftennot known which of the actions is at its maximum value when the maximumcombined effect occurs, each time-vayg load must be positioned, in turn, asthe principal action to determine the maximum combined effect
The required strength, Us in Equation 2b is determined as an appropriateconservative fractile of U.., i.e., Ud has an acceptably small probability ofbeing exceeded. QOmistent with the principal action/companion action formatin Equation 46, the required strenm is expressed as the set of equations
Ud - ,D)+ *yQQ + E yQ1 (47)
The factord load, QQ is denoted the principal acton, while the terms -aQiare the companion actions. In principle, if them are n time-varying loads,Equation 47 consists of n equations in practice; however, it seldom is neces-say to consider all n equations in designing a particular member, since experi-ence rapidly indicates those that control design. Equations 46 and 47 are thebasis for the principal action-companion action format used in LRFD and mostmodern limit state codes (ASCE 7-88; Eurocode No. I (ASCE 1990)).
The focus in the following is on the load factors needed to define therequired strength, Ud in Equation 47. The first objective in the load combin-ation development process is to minimize the variation in reliability as theloads in a combination vary in proportion to one another. A second objectiveis to balance the design risk associated with the different load combinations. Itis desirable that these two objectives be met so that the load combinations areapplicable to the relatively broad scope of structures and components withinthe purview of the code.
Load factors for designing miter gates are determined using methods similarto those used to develop probability-based limit-state design criteria for build-ing structures (Ellingwood, et al. 1982), utilizing the load and resistance data-p--sented in Section 4 and the results of the calibration studies in Section 5.Noting from Equation 5 that the factored load for a prescribed reliability indexis equivalent to the load at the checking point, we have that
chsprs 5 D•wlam of RIIbksMd Moon Reimn" 41
where
"* = load fahcor
Xu = nominal or characteristic load value speciffed by the standard
V5 a coeflicient of vaito in Xi
Solving for yi, we obtain
.Y - (M,,) (10 + i Vi) (49)
Experiece has shown that although the product 0 vules in reliability-baseddesign accordin to the reliability level and the relative imponrtace of load X,In the combination, a typical value is approximately 2 when X., is consideredas the principal varia=le load in the combination and when p 3-3.5. Thus, inapproximation
S- (m/Xg ) (1 2 V,) (50)
The ratio (m/X, ) reflects the bias in the specified nominal load with respect toits mean value. In curmt design puaice, where the nominal loads tend to beestimated conservatively, this ratio often is less than 1.0. The coefficient ofvariation Vi is a dimensionless way of representing uncerainty arising frominherent randomness and modeln
The relIability requirement can be expressed by one equation (Equation 4),while there are many load factors in the design requirements. Thus, the selec-tion of load factors is a trial-and-eror process (Eliingwood et al. 1982). Equa-tio 50 provides an initial estimate of the load factor for each load. Forexample, for the load Hs, we have that
y,. - (0.9) (1 + 2 x 0.25) = 1.35 (51)
Subsequent adjustments to the individual load factors and load combinations
are made from FO reliability analyses.
42 Chopr 5 DwFlop •t-at obft-ased Design Reqrmemt
It was determined frm the discussion of See operati d e inSection 4 mad Equation 23 and 24, dt the following coincidences of loadshad u•fflclunly mail pmbability that they could be neglected in the load
I need not be combined with H., Q. mad H,;
1m need not be combined with E;
HR Q, and H, need not be combined with E; ard
H, need noA be eombined with HR, Q
The load combinations Preommended below correspond to specific loadscenarios: (1) gates in the mitered position; (2) gates operating, and(3) emnnmimental effects. Permaum loads appear in all combinations.Time-varying loads appear as principal or companion actions, as appwopriate.Postulated loads are assigned a load factor of 1.0, since it is assumed that thec mservatalm necessary for design is taken into account in the associated haz-ard scenario rid specification of the nominal load. The load specification ismade as general as possible; note, however, that the maximum stnuctura actionmay occur when one (or more) of the loads in a combination is equal to zero.This advisory also is contained in ASCE 7-88 (ASCE 1990) and in the AISCLRFD Specifcation (AISC 1986). The subscript "n" on load, denotingnominal value, has been omitted in the following for simplicity.
The following loads are considered, individually and in combination:
D = deadloadC = ice loadM = mud loadH, - hydrostatic headH, = teLporal hydraulic load (1io: gates open; H,,: gates mitered)Q = operating equipment loadI, = impact loadE = earthquake load
The hydrodynamic force, H& is not considered since it does not govern instrength design. Hd should be considered in fatigue analysis of the gate; how-ever, fatigue behavior is outside the scope of this study.
Gate In the miterd posMton
(1) 1 .4 H, + 1.0 Ham
(2) 1.0oIm + 1.I H,
Ch r 6 Dsbwpmu PofRbsIHt-Ba"ed D@si Rsesment 43
Combia~n (1)is applicable to the ubmerged portion of the pae. Combina-tion (2) is applicable to the girders above the wMatedine. Ice and mud kmads arenoM included in these load combinatdos becate their effects are not sipgifi-ct They are included in the operating load combinations where their effectsmay control. Lateral forces due to ice have less of an effect than does theimpact force in combination (2). The probablity of a coincidence of impactand latal Ice is negligible. Ths this effect is not considered. It is assumedthat there is a potential for impact any tme from the bepging of handlingand maneuvering in the holding area to the time when the tow completes itsexit from the lock.
GateM opwUng
(3) 1.2D + 1.6 (C+M) + 1.0 H,
(4) 1.2D + 1.2Q + 1.6(C+M)
During normal gate operation, there are no differential hydrostatic loads. Thetemporal hydraulic load acts on the submerged portion of the gate as it movesthrough the water and is staticaly equlbrted by the fore on the opematingsawL This may cause twist of the gate leaf the effects of which are checkedby combination (3). However, if there is a submerged obstruction, the gatemay bind during operation, causing a force on the operating stmt not staticallyequilibraed by the hydrodynamic effects; combinaton (4) addresses this sium-ton. Mxload factor 1.6 on (C + M) is consistent with a mean od of0.95 times the nominal specified load and a Coefficient of variation of 0.35.
Envdronmmtal efct
(5) 1.2D + 1.0E + 1.2 Hs
The presumption in combination (5) is that the gate is in the mitered position.The probability of a coincidence of earthquake forces with forces from gateoperation or impact is negligible (cf Equation 23 and related discussion inSection 4). The earthquake force, E, on a structural component is determinedfrom p(y) defined in Equation 34. The load factor of 1.0 on E is based on theassumption of a NEHRP-magnitude design earthquake. For an earthquakewith an MRI of 145 rather than 475 years, this load factor should be increasedto 1.4.
The design equation is (cf Eqn 2b)
aRt # R >Ud (52)
44cha s 5 Developmenw of Prababft-ty Wd Degp Reqxemme•
A reliability factor, a, has been introduced to the design equation to accountfor the severity of the operating environment for hydraulic structures and thedifficulties in their inspection and maintenance. Factor a normally is 0.9; ifthe strcture cannot be inspected regularly or if it is in brackish water or sea-water, a = 0.85. Each adjustment increases the reliability index by about 0.5.No adjustments are made for the nominal resistance, R.. or resistance factors,*. defined in the current LRFD Specification (AISC 1986).
The results of reliability analyses of flexural components designed by theproposed LRFD load combinations are presented in Figure 7 where they arecompared to similar analyses for flexural components designed by ASD.Three curves are presented, correspondirg to load factors on H. (in combi-nation 1) of 1.2, 1.4, and 1.6. The load factor 1.4 leads to designs that aresomewhat less conservative than those obtained using ASD and EMl 110-2-2101 (Headquarters, Department of the Army 1972). However, the decrease inP is comparable, in an average sense, to the decrease that occurred in thechangeover from ASD to LRFD for steel buildings. Moreover, the reliabilityof the gate leaf as a structural system is substantially higher than indicated inFigure 7 due to its highly redundi.t nature.
Chqsr 5 Dev.Japy" of Prmhft-BaW. Desigo Roqswir 45
6 Recommendations
The development of load combinations for designing miter gates was handi-capped by the lack of statistical data on which to base the reliability analysesand load factors. A Delphi was designed to provide the necessary data on aninterim basis. A large amount of data was developed by the Delphi, and itwas not possible to analy'e these data completely within the scope of thiswork. Additional analyses of these data should be performed, focusing inparticular on the data needed to specify barge impact load Im. Attempts alsoshould be made to design a data acquisition program to improve the databaseon operating loads.
The current specification for loads due to temporal head, Hr also should berevised. The Delphi indicated that the characteristiks of temporal head forgates in the mitered and open positions were substantially different. Under thecircumstances, consideration should be givern to specifying two different valuesto Ht rather than one value, such as the 15 in. (381 mm) found in EM 1110-2-2703 (Headquarters, Department of the Army 1984). Suggested values mightbe H,,, = 15 in. (382 mm) and Hto = 9 in. (229 mm); however, additionalmeasurements should be taken at selected locks to confirm and possiblymodify the s.atistics reported in the Delphi.
The previous REMR study and the Delphi in this study provided informa-tion on the incidence of barge impact, tonnage, and velocity at the time ofimpending impact There appear to be inconsistencies in the data reported inthese two studies. Additional work is needed to develop improved bargeimpact loads to be used in design. This research should take into account thesignificant nonlinearities in material and structural behavior that are likely tooccur during significant impacts. Reportedly, a test program is in progressaimed at shedding light on miter gate behavior during impact. It makes senseto consider design procedures that are based on the concept of energy dis-sipation rather than withstanding the force by traditional elastic design meth-ods, since the latter are likely to lead to prohibitive weight requirements. Inthe load combinations, a load factor of 1.0 was assigned to impact; it is cus-tomary to deal with rare events in this way, and the load combinations will notneed to be redone when additional data on impact forces becomes available.In any event, impact should be treated as a concentrated force, not as a uni-formly distributed load.
46 Chapter 6 Recommendtons
TMc LRFD seismic icquirmnet should be made as consistent as possiblewith the new NEHRP provisions nearing mpinmentadon (NEHRP 1992).NoeMwtMt curnet practice, the possibility of eafthquake damage to lockand dmn structues and the economic impacts of such damage shdd beconiduef
A set of tulative designs of miter iae componet should be performedusing ft proposed design requiements xad a compariso should be made withgates desined by ASD and EM 1110-1-2101 (Headquartes, Department ofthe Army 1972) before the LRFD criteria supphant ASD.
Ch~pW 6 Pbm dmw nb 47
References
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American Institute of Steel Cotnrsnction. (1978). "Specification for thedesign, fabrication and erection of snrctumrl seel for buildings," Chicago, IL.
- (1986). "Load and resistance factor design specification for stnac-tural steel buildigs" Chicago, IL.
American Society of Civil Engineers. (1990). "Minimum design loads forbuilings and other stnuctums (ASCE 748)," New York
Benjamin, J. R., and CormeiL C. A. (1970). "Probability, stadstics and deci-sion in civil engineering." McGraw-Hill, New York.
Bemreuter, D. L. et al. (1989). "Seismic hazard charaterization of 69 nuclearpower plants east of the Rocky Mountains," Report NUREG/CR-5250,U.S. Nuclear Regulatory Commission, Washington, DC.
Chasten, C. P., and Ruf, T. (1991). "Miter gate barge impact testing, Lockand Dam 26, Mississippi River." Corps of Engineers Structural EngineeringConference, 8-12 July 1991, St. Johns County, Florida. U.S. Army EngineerWaterways Experiment Station, Vicksburg, MS.
Chasten, C. (1992a). "Barge tow velocity measurements," Letter Report,U.S. Army Corps of Engineers, Washington, DC.
Chasten, C. (1992b). "Load combinations and a survey for miter gate loads,"Letter Report, U.S. Army Corps of Engineers, Washington, DC.
Chiarito, V. P., and Morgan, J. R. (1991). "Seismic analysis of a lock anddam system." Proceedings of Structures Congress '91. American Society ofCivil Engineers, New York, 809-812.
Cooper, P. B., Galambos, T. V., and Ravindra, M. KL (1978). "LRFD criteria
for plate girders." Journal of the Structural Division, ASCE 104(9), 1389-1407.
48 Rinelws
Cornl, C. A. (1968) "Engineering seismic risk analysis." BulletinSeismological Society of America 58(5), 1583-1606.
ComUts, R. B., Fox, R., and Harris, J. C. (1981). "Delphi methods: theoryand design load application," Journal of the Structural Division ASCE 107(6),1095-1105.
Ellingwood, B., MacGregor, J. G., Galambos, T. V., and Comell, C. A.(1982). "Probability based load criteria: load factors and load combinations."Journal of the Suctural Division, ASCE 108(5), 978-997.
Federal Emergency Management Agency. (1992). "NEHRP rcommendedprovisions for the development of seismic regulations for new buildings(2 Vol.)," FEMA Report 223, Washington, DC
Galambos, T. V. and Ravindra, M. K (1978). "Properties of steel for use inLRFD," Journal of the Structural Division, ASCE 104(9), 1459-1468.
Galambos, T. V., et al. (1982). "Probability based load criteria: assessmentof current design practice." Journal of the Structural Division, ASCE 108(5),959-977.
Green, J. L., Murphy, T. S., and Brown, F. B. (1964). "Operating forces onmiter-type lock gates," Technical Report No. 2-651, US Army Engineer Water-ways Experimen Station, Vicksburg, MS.
Headquarters, Department of the Army. (1972). "Working stresses for struc-tural Design," Engineer Manual-I 110-1-2101, Washington, DC.
. (1984). "Engineering and design: lock gates and operating equip-men," EM 1110-2-2703, Washington, DC.
_ (1991). "Load and resistance factor design for miter gates," ETL-1110-2-004, Washington, DC.
• (1992). "Reliability assessment of navigation structures," ETL-1110-2-532, Washington, DC.
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Larmbee, R. and Comell, C. A. (1981). "Combinations of various load pro-cesses," Journal of the Snructural Division, ASCE 107 (STI), 223-239.
Martin, S. K., and Lipinski, M. E. (1990). "Lock accident study," TechnicalReport REMR-HY-7, U.S. Army Engineers Waterways Experiment Station,Vicksburg, MS.
note0 49
M es PR. E (1937). Stcwal reiablity.: a*ysL and praedon. EllisHarwood PdU . LUd., 7-'s-, UK.
PeNce T. IL, and Win, Y. KL (1984). "Sochudtc combinatomn of loadehcts," Jornal qfStrUcaul Eqlneerig, ASCE 110 (7), 1613-1629.
Reuter, CE. (1990). "Navlgion lock commentary," pablisied report,U.S. Amy Crps of Engeme Wu*tc DC.
Toussi, S., Mlakar, P. F., mad Kao, A. K. (1989). "Reliability of miter pte"Proceedins International Coqference on Sucnoul Sufesy and Reliability, Vol.III. American Society of Civil Engier New York, 2055-2058.
Tudkatra C J., Nd Madsen, H. (1980). "Load combinatons in codifiedstrucural desin" Jowna of the S ctral Division, ASCE 106 (SF12),2527-2543.
Weftergad, H. M. (1933). "Water praum on dams during earthquakes."Troawactons American Society of Civil Engineers. New York, 98:418-471.
Yura, J. A., Galmnbos, T. V., and Ravindm, K. K. (1978). "mc bendingreMistMce of steel beams," Jornal of the Strctwal Division, ASCE 104(9),1355-1370.
50
REPORT DOCUMENTATION PAGE jwN.07)I11ide Pii. bins = tf WaliWesuiawfu. leftim. OleoaeIdamt ,puii "OU 1*"A'-,, U JoffeOftis
OW2.ai to Oie Office of UwMawKeme &W @~ge. Pon ewooI hutioxa pies 4070aw4 IS) *mwgLs oc 2g103
.am Ma (LOOM v L4 "IN D. REPORT TYPE AND DATES COVERED
4. AD SUTIMS. FUNDING NUMBERS
LoAf and Resistnew Factor Design for Steel Mite Gates
C AUHOIC)Work Unit 32484
Bruce R. Eliingwood
7. PWORFMING ORGANIZATION NAME(S) AND ADORESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER
Departime of CAiv Eniern Instuction ReportJohn' Hopkins University rIL-93-4Baltimome MD 21218
S. SPOSORING/MONITORING AGENCY NAMEDS) AND ADDRESS(ES) 10. SPONSORINGI/MONITORINGAGENCY REPORT NUMBER
U. S- Army Corps of Engineers Washington DC. 203 14-IM00U. S. Army Engineer Waftewas Experiment StationInforma111tion Technology Laboratory3909 Halls Fely Road, Vickurg MS 39180-199
11. SUPPLEMENTARY NOTES
Available from National Technica Information Service, 5285 Port Royal Road, Springfield, VA 22161
128. DISTRIBUTION/IAVAR.AUILI STATEMENT [12b. DISTRIBUTION CODE
Approved for public release; distribution is unlmite.
13. ABSTRACT (M~aximum 200 woahk)
The design of hydraulic stel structures (HSS) in the pust has been based on allowable stres design (ASD)principles that address design uncertainty in a subjective amane. This technical report describes the methodologyfor -n improved basis for determining load requirements for the design of HSS using modern structural reliabilityanalysis and probabilistic load combination techniques. This methodology will facilitate the development of designloads and their combinations for use in load and resistance factor design (LRM). This report demonstrates themethodology for miter gate by considering load combuiations involving dead load, hydrostatic load, hydrodynamicload during gat Operation, temporal hydiaulic load, earthquake load, and barge impact load.
This report describes the reliability bases for LRFD, load and resistance data for lock structures, and develop-nient of probability based design requirements. Significaint loads and load combinations for miter gates areidentified, a statistial O.nabase to support probabilistic load combination analysis is developed, and analysis ofreliabilities associated with current ASD procedures and selection of target reliability levels is presented. Based onthese studies, LRFD load requirements for miter gate including load combinations and load factors are developed.
14. SUBJECT TERMS 15. NUMBER Of PAGES63
See reverse. 16. PRICE CODE
17. SECURITY CLASSIFICATION 10. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT
UNCL-ASSITFIED UNCLASSIFID I_______I__NSN 7540-O1.ZWS0SO0 Standard Form 298 (Rev. 2-89)
Pffflntied byv ANSI Std. Z39-i8
2W6-142
14. Subject Tunis
AUOable OWN "~P
LAmi and ruimmcc facui d"igLoot cembiusion
NliW gity
Reliailty
Suasimics
WATERWAYS EXPERIMENT STATION REPORTSPUBLISHED UNDER THE COMPUTER-AIDED
STRUCTURAL ENGINEERING (CASE) PROJECT
Title Date
Technical Report K-78-1 List of Computer Programs for Computer-Aided Structural Engineering Feb 1978
Instruction Report 0-79-2 Use's Guide: Computer PomWram with Interatve Graphics lor Mar 1979Analysis of Plae Frame Structures (CFRAME)
Technical Report K-40-1 Survey of Brkie-Orlented Design Software Jan 1960
Technical Report K-M0-2 Evaluation of Computer Programs for the Deslgn/Analysis of Jan 1980Highway and Railway Bridges
Instruction Report K-S0-i User's Guide: Computer Program for DesigRevlew of Curvi- Feb 1960liner Conduits/Culverts (CURCON)
Instruction Report K-SO-3 A Thro.;Dimsion' Finite Element Data Edit Program Mar 1960
Instruction Report K-80-4 A Three-Dimensional Stability AnalslsiDesM gn Program (3DSAD)Report 1: General Geometry Module Jun 1960Report 3: General Analysis Module (CGAM) Jun 1982Report 4: Special-Purpose Modules for Dams (COAMS) Aug 1983
Instructim n Report K-0-6 Basic Users Guide: Computer Program for Design and Analysis Dec 1980of Inverted-T Retaining Wags &d Floodwas (TWDA)
Instruction Report K-W0-7 Users Reerence Manual: Computer Program for Design and Dec 1960Analysis of Inverted-T Retaining Wals and Floodwals (MWDA)
Technical Report K-60-4 Documentation of Finite Element AnalysesReport 1: Longview Outlet Works Conduit Dec 1960Report 2: Anchored Wall Monolith. Bay Springs Lock Dec 1960
Technical Report K-80-6 Basic Pile Group Behavior Dec 1960
Instructin Report K-81-2 User's Guide: Computer Program for Design and Analysis of SheetPile Walls by Classical Methods (CSHTWAL)
Report 1: Computational Processes Feb 1961Report 2: Interactive Graphics Options Mar 1981
Instruction Report K-81-3 Validation Report Computer Program for Design and Analysis of Feb 1981Inverted-T PReining Wale and Floodwall (IWDA)
Instruction Report K-41-4 User's Guide: Computer Program for Design and Analysis of Mar 1981Cast-In-Place Tunnel Linings (NEW1rUN)
Instruction Report K-81-6 User's Guide: Computer Program for Optimum Nonlinear Dynamic Mar 1981Design of Reinforced Concrete Slabs Under Blast Loading(COARCS)
Instruction Report K-81 -7 User's Guide: Computer Program for Design or Investigation of Mar 1981Orthogonal Culverts (CORTCUL)
Instruction Report K-81-9 User's Guide: Computer Program for Three-Dimensional Analysis Aug 1981of Buliding Systems (CTABSSO)
Technical RPW K-81-2 Theoretical Bis for CTABSS0: A Computer Program lor Sep 1981Three-Dimensional Analysis of Building Systems
Instruction Report K-82-6 User's Guide: Computer Program for Analysis of Beam-Column Jun 1982Structures with Nonlinear Supports (CBEAMC)
(Continued)
WATERWAYS EXPERIMENT STATION REPORTSPUBLISHED UNDER THE COMPUTER-AIDED
STRUCTURAL ENGINEERING (CASE) PROJECT
(CntkiruedTite Date
instuction Report K-82-7 Users Guide: Computer Progwra for Bowing Capacity Analysis Jun 1Io2of Shelby Foundations (C8EAR)
instruction Report K4-1S- U..' Guide: Computer Program with interactive Graphics for Jan 1985Analysis of Plans Frame Structures, (CFRAME)
instruction Report K-83.2 U..?.s Guide: Computer Program for Generation of Engineering Jun 1963-401m (SKETCH)instruction Report K-854 Uses Guide: Computer Program to Calculate Shear, Moment, Jul 1983
and Thrust (CSMT) from Sorew Results of a Two-DimensionalFinite Element Analysis
Technical Report K-83-i Bauic Pile Group Behavior Sep 1983Technical Report K-OS" Reference Manual: Computer Graphics Program for Generastion df Sep 198
Engineering Geometry (SKETCH)Technical Report K-83.4 Cos Study of Six Majo General-Purpose Finite Element Program Oct 19USirstruction Report K-04-2 U... Guide: Computer Program for Optimum Dynamic Design Jan 1964
of Nonlnea MeOa Plates Under Blest Lmain (OSDOOR)instruction Report K414-7 Liser's, Guide: Computer Program for Determining inuced Aug 1984
Stresa.. and Consolidation Sattiements (CSETY)instruction Report K-111O Seepage Analysis of Confined Flow Problems; by the Method of Sep 1984
Fragments (CIFRAG)
instruction Report K-84-1 1 user's Guide for Computer Program COFAG, Concrete General Sep 1984Flexure Analysis with Graphics
Technical Report K-84-3 Computer-Aided Draftin and Design for Corps Structural Oct 1984Engineers
Technical Report ATC-86- Decision Logic T"bl Formulation of ACI 318-77, Buldidng Code Jun 1986Requirements for Reinforced Concrete for Automated Con-strahn Processing, Volumes I and H
Technical Report fTL-87-2 A Case Committee Study of Finite Element Analysis of Concrete Jan 1987Flat Slabs
instruction Report ITL-87-1 User's Guide: Computer Program for TWO-Dmensional Analysis Apr 1987of U-Frame Structures (CUFRAM)
instruction Report rTL-87-2 U.ser's Guide: For Concrete Strength investigation and Design May 1987(CASTh) in Accordance with ACt 318-M
Technical Report ITL-87-6 Finite-Element Method Packaige for Solving Steady-State Seepage May 1987Problems,
instruction Report fTL-87-3 thefts Guide: A Three Dimensional Stability AnaiyulsDesign Jun 1987Program (SOSAD) Module
Report 1: Revision 1: General Geometry Jun 1967Report 2: General Loads Module Sep 1989Report 6: Free-Body Module Sep 1989
WATERWAYS EXPERIMENT STATION REPORTSPUBLISHED UNDER THE COMPUTER-AIDED
STRUCTURAL ENGINEERING (CASE) PROJECT
Tiles Date
Instruction RPort ITL-7-4 User' Guide: 2-1) Frame Analysis Lrink Program (UNK2) Jun 1987
Technical Report ITL7-874 Finite Element Stuides of a Horizontally Framned Miter Gate Aug 1987Relport 1: Iitial and R'efined Finite Element Models (Phasesi
A. B. and C% Volumes I asidNReportt2 Simpiled Frames Model (Phms D)Report 3: Alternate Configuration Miter Gate Finite Element
Studleso-pen SectionReport 4: Alternate Configuration Miter Gate Finite Element
Rport 5: Alternate Configuration IA~r Gate Finite ElemnentStudise-Additional Cboee6 Sections
Report 6: Elastic Buckling of Girders in Horizontally FramedMk~ Gate
Report 7: Application and Summary
instruction Report GL-87-1 Users Guide: UTEXAS2 Siope-Stabliky Package; Volume i, Aug 1967User's Manuel
Instruction Rport1 ITL-87- Sliding Stability of Concrete Structures (CSUIDE) Oct 1967Instruction Report rTL-87-4 Criteria Specifications for and Validatlon of a Computer Program Doec 1967
for the Deeig or hwestlgatlon of Horizontully, Framed MiterGates (C MITER)
Technical RPort ITL-87-8 Procedure for Static, Analysis of Gravity Dam. using the Finite Jan 1986Element Method - Phase isa
Instruction Report ITL4W8- User' Guide: Computer Program for Analysis of Planar Grid Feb 1968Structures (CGam)
Technical Report ITL418-1 Development of Design Formulas for Ribbed Mat Foundations Apr 19688on Expensive Sobe
Technical Report ITL-882 User's Guide: Pile Group, Grephics Display (CPGG) Post- Apr 1988processor to CPGA Program
Instruction Report ITL-88-2 Users Guide for Design and Investigation of Horizontaly Framed Jun 1988Miter Gates (CMIfTER)
Instruction RPort ITt-88-4 User's Guide for Revised Computer Program bo Caiculate Shear, Sep 1988M=men and Thrust (CSMTi)
Instruction Reoport GL-87-1 User's Guide: UTEXAS2 Siope-Stablity Package; Volume 11, Feb 1989Theory
Technical Report ITL419-3 User's Guide: Pile Group Analysis (CPGA) Computer Group Jul 1969
Technical Report ITL-894 CSASIN-Structural Design of Saint Anthony Falls Stillng Basins Aug 1989According to Corps of Engineers Criteria for HydraulicStructures; Computer Progiam X0098
(ConthieM
WATERWAYS EXPERIMENT STATION REPORTSPU3USIED UNDER THE COPUTER-AIDED
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Title Dafte
Technical Repot ITL-89-5 CC*IAN-Structural Design of Rectangular Channels According Aug 1989to Corps of Enginees Criteria for HydraullcStructures; Computer Program X0097
Technical Report rrL-894 The RuSPoe-Sn04pectr .Dyramic Anal sofGravity Dams Using Aug 1989the Finite Element Method; Phase II
Contract Report lTL491 State of the Art on Expert Systemns Applications in Design, Sep 1989Co -tuton- and Maintenance of Structures
Instruction Report ITL-90-1 Us1e's Guide: Computer Program for Design and Analysis Feb 1990of Sheet Pil Waft by Classical Methods (CWALSHT)
Technical Report ITL-90-3 Investigation and Design of UI-Frame Structures Using May 19900Program CUFRBC;
Volume A: Program Crit&i and DocumentationVolume B: User's Guide for BasinsVolume C: User's Guide for Channels
Instruction RPort ITL-90-6 Useis Guide: Computer Program for Two-Dimensional Analysis Sep 1990of U-Frame or W-Frame Structures (CWFRAM)
Instruction Report ITL-90-2 Use?. Guide: Pls Group-Concrete Pile Analysis Program Jun 1990(CPGC) Preprocessor to CPGA Prograrn
Technical Report ITL-91-4 Application of Fnirde Element. Grid Genertio, and Scientific Sep 1990Visualization Techniques to 2-D and 3-D Seepage and
GrondwterModelinglinstruction Report ITL-91 -1 Useers Guide: Comrputer Program for Design and Analysis Oct 1991
of Sheet-Pile Wale by Classical Methods (CWALSHT)Including Rowe's Moment Reduction
intrction Report rnTL-87-2 User'. Guide for Concrete Strength Investigation and Design Mar1992(Revhised) (CASIR) in Accordance with ACI 31-869Technical Report ITL-92-2 Finite Element Modeling of Welded Thick Plates for Bonnevill May 1992
Navigation LockTechnical Report rFTL-92-4 Introduction to the Computation of Response Spectrum for Jun 1992
Earfthuake LoadingInstruction Report ITL-92-3 Concept Design Example, Computer Aided Structural
Moeln (CASM)Report 1: Scheme A Jun 1992Report 2: Scheme B Jun 1992Report 3: Scheme C Jun 1992
Instruction Report MT-92-4 User's Guide: Computer-Aided Structural Modeling Apr 1902(CASM) - Version 3.00
Instruction Report ITL-92-6 Tutorial Guide: Computer-Aided Structural Modeling Apr 1992(CASM) - Version 3.00
(Contiued)
WATERWAY8 EXPERIMENT STATION REPORTSPUBLISHED UNDER THE COMPUTER-AIDED
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(ConcLKde)"Title Date
Contract Report ITL-92-1 Optimization of Steel Pilo Foundations Using Optimality Criteria Jun 1992
Technical Report ITL-92-7 Refined Strees Analysis of Melvin Price Locks and Dan Sep 1992
Contract Report ITL-92-2 Knowledge-Based Expert System for Selection and Design Sep 1992of Retaining Structures
Contract Report ITL-92-3 Evaluation of Thermal and Incremental Construction Effects Sep 1992for Monoliths AL-3 and AL-5 of the Melvin Price Locksand Dam
Instruction Report GL-87-1 Users Guide: UTEXAS3 Slcpe-Stability Package; Volume IV, Nov 1992Users Manual
Technical Report ITL-92-11 The Seismic Design of Waterfront Retaining Structures Nov 1992
Technical Report ITL-92-12 Computer-Aided. Field-Verifded Structural EvaluationReport 1: Development of Computer Modeling Techniques Nov 1992
for Miter Lock GatesReport 2: Field Test and Analysis Correliation at John Hollis Dec 1992
Bankhead Lock and DamInstruction Report GL-87-1 User's Guide: UTEXAS3 Slope-Stability Package; Volume III. Dec 1992
Example Problems
Technica Report TL-931 Theoretical Manual or Analysis o4 Arch Dans Ju 1993
Technical Report ITL-93-2 Steel Structures for Civil Works, General Considerations Aug 1993for Deig and Rehabilitation
Technical Report ITL-93-3 Soil-Structure Interaction Study of Red River Lock and Dam Sep 1993No. 1 Subjected to Sediment Loading
Instruction Report 111-93-4 Load and Resistance Factor Design for Steel Miter Gates Oct 1993
Desmoy this report when no longer necdd. Do not return it to the originator