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Development of Analytical Formulation for the Intelligent Diagnosis of

Navigation Steel Structures Subjected to Hydraulic Torsional Loading

Ángel J. Alicea1, Guillermo Riveros2, Ingrid Padilla1

1University of Puerto Rico, Mayagüez 2U.S. ARMY Corps of Engineers, Engineering Research and Development Center

Abstract

Nowadays great interest on the study of navigation steel

structures has been arising. This may be the effect of

catastrophic disasters that has occurred in the past due to the

limited information available concerning these types of structures

and the loads to which they are subjected to. This research

focuses entirely in the study of miter gates structures subjected to

the effects of torsional loading. A structural analysis creating a

finite element model was executed to The Dalles Dam Miter Gate

in Oregon after its failure. By means of this analysis a forensic

study of the dam was realized for determining the causes of

some major cracks and fractures in the bottom girders of the

quoin block side. The deterioration in the extreme ends of the

structure is a major issue changing its boundary conditions and

causing a redistribution of forces whose components were

directed to members for which that kind of loading was not

considered in the design process. In order to perform an

intelligent diagnosis of these types of structures an analytical

formulation was developed that determines torsion and shear

stresses in hydraulic steel structures from field experiments. It

provides a reliable tool for real-time monitoring of the structure

and anticipates any abnormal structural behavior that may occur

during its functional life with actual results that will avoid failure or

collapse of the structure resulting in longer functional life and

economical solutions for repairs and designs.

Problem Description

Case Study: The Dalles Miter Gate

The Dalles Dam Location:

► 192 miles upstream from the mouth of the Columbia River and two miles

east of the city of The Dalles, Oregon

Concept

► Navigation lock, spillway, powerhouse, and fish passage facilities

Main Purpose

► Provide safe navigation between The Dalles and Celilo falls in the

Columbia River

Significant issues in Miter Gate

Quoin block deterioration

► 30 – 40 ft without contact

Miter block deterioration

► 1.5 in. gap at bottom

Cracking

► Rib 35 (pintle region)

► End diaphragm

Shock loading

► Mitered and during operation

3D Finite Element Analysis

Base Case

► Force Boundary Conditions

• Gravity, hydrostatic

► Displacement Boundary Conditions

• Gudgeon pin Ux=Uy = 0

• Pintle Base Ux=Uy=Uz = 0

► Perfect design conditions

• Facilitate calibration of quoin and miter blocks degradation

Need for Intelligent Diagnosis

There is a tremendous need for the constant monitoring of this

type of structures because they are subjected to hydraulic

torsional loadings, fatigue, and deterioration. That combination of

adverse conditions produces a considerable decay of the

structure resulting in unpredictable structural behavior and abrupt

cracks that may propagate and end in a functional failure of the

structure of collapse. Tools must be developed in order to avoid

catastrophic events and economical losses. They are a valuable

resource for real-time monitoring and future forensic studies.

Objectives

Create a formulation in which from experimental warping

normal stresses we can obtain:

► Torsion

► Shear Stresses

Formulation must be oriented to provide real-time

experimental results that will be used in the monitoring and

assessment of hydraulic steel structures.

Methodology

1. Establish boundary conditions and load type:

► Constant Torsional moment:

2. Selection of cases to formulate and obtain its solution for Θ::

a) Fixed ends:

• Concentrated torques at ends of member

• Concentrated torque at intermediate section of

member

b) Pinned ends

• Concentrated torque at intermediate section of

member

c) Fixed – Free ends

• Concentrated torque at any point on member

3. Derivate each solution to obtain Θ’, Θ’’, Θ’’’ as a function of z

(element length) and which contains the torsional term T.

4. Obtain the Normal Warping Stresses from field experiments

and calculate the experimental Θ’’.

Methodology (cont.)

Conclusions

Acknowledgements

•Location of the strain gages in typical structural elements:

6. With the experimental value of Θ’’ obtain the experimental

value of T from the respective formulated equations.

7. Use the value of T to obtain the values of Θ’ and Θ’’ if is

desired to obtain the experimental torsional components:

8. To obtain the experimental shear stresses decompose the

torsional moment obtained into an equivalent force couple:

9. Analyze each flange as a beam subjected to the force:

10. With the resultant value of Vf it is possible to obtain the actual

shear stresses that act on the structure:

Hydraulic steel structures are subjected to different types of

loadings with variations in magnitude and diverse environments.

A great majority of those structures are old, some dating back to

the 1950’s and 1960’s, and many of them have suffered

deterioration, which in many cases have led to structural

fractures and collapses. In addition, many of those old structures

were designed with obsolete design codes that didn’t considered

many of the loading aspects that are known today and doesn’t

account for possibilities of a failure of the structural system. The

collapse of a hydraulic structure can be devastating producing an

adverse economic impact, significant infrastructure damage, and

life losses. It is for that reason that scientists and engineers are

searching for tools and techniques that may help to significantly

anticipate any unexpected structural behavior and drastically

reduce the risks for damage or collapse.

Typical issues encountered in miter gates:

Significant number of lockage & repeated loadings

Unsatisfactory performance► Fatigue cracking caused by welded connections

► Poor welding quality

► Unanticipated structural behavior or loading

► Failures of diagonals on miter gates.

• These appear to be fatigue-induced failures driven by the connection details

• Current design guidance results in a much larger prestress than may be requiredGirder 35, Quoin Side

-25

-20

-15

-10

-5

0

5

10

15

20

25

13:19 13:26 13:33 13:40 13:48 13:55 14:02 14:09 14:16 14:24 14:31 14:38

Time (minutes)

Str

ess (

Ksi) S-G35-Q1

S-G35-Q2

FEM-DS

FEM-US

Numerical simulation

► Both sides carry 47% more stresses than

experiments

► Less than 10% difference when

compared with design calculations

Indicates additional degradation of

quoin and miter blocks

Lack of proper contact in miter end

Girder

Web

U.S.

Skin

PlateD.S.

Flange

S-A

S-B

S-C

S-D

Miter

End

Plan View

S1 S2 S3

Upstream

Section

DownstreamQuoin

End

References

Excellent tool for the monitoring and assessment of hydraulic

steel structures

Possible to obtain actual torsion forces and its induced shear

stresses

Help in the failure prevention of critical fracture members

Experimental results can be compared with numerical

analysis in order to calibrate 3D models of structures.

• Alicea, A. . Analytical Formulation for the Determination of Torsional

Forces and Shear Stresses in Hydraulic Steel Structures from Field

Experiments. Engineer Research and Development Center, Information

Technology Laboratory, Vicksburg, MS. September 2010

• Seaburg, Paul A. . Torsional Analysis of Structural Steel Members.

Steel Design Guide. American Institute of Steel Construction. Oct 2003

This work was supported in part by Gordon-CenSSIS,

The Bernard M. Gordon Center for Subsurface

Sensing and Imaging Systems, under the Engineering

Research Centers Program of the National Science

Foundation (Award Number EEC-9986821).