Experimental measurement and finite element analysis of the deformation of a high-pressure sluice gate

655 Experimental measurement and finite element analysis of the deformation of a high-pressure sluice gate Chuen-Shii Chou and Shou-Chih Lou Abstrac...
Author: Elinor Fields
1 downloads 0 Views 1MB Size
655

Experimental measurement and finite element analysis of the deformation of a high-pressure sluice gate Chuen-Shii Chou and Shou-Chih Lou

Abstract: The deformation of a high-pressure sluice gate under an orthogonal water pressure load of 0.539 MPa (i.e., 55 m water height), acting upon the upstream side of a gate leaf, was studied numerically and experimentally. The sluice gate was installed at the end of a water-release tunnel in the Nan-Hwa Reservoir, Nan-Hwa, Taiwan, R.O.C. The numerical results obtained using the ANSYS 5.5.2 finite element program agreed reasonably well with the experimental data. The deformation of this high-pressure sluice gate under water pressure loads of 0.736 MPa (i.e., 75 m water height) and 0.931 MPa (i.e., 95 m water height) was predicted by ANSYS 5.5.2. The research reported here may provide a method for establishing a safety monitoring system for any high-pressure gate and provide engineers with useful information to evaluate the possibility of increasing the capacity of an existing reservoir. Key words: sluice gate leaf, finite element method (FEM), strain gauge, water pressure. Résumé : La déformation d’une vanne de pertuis à haute pression, sous une charge de pression d’eau orthogonale de 0,539 MPa (c. à d. 55 m de hauteur d’eau) agissant sur le côté amont d’une paroi de la vanne, a été étudiée numériquement et expérimentalement. La vanne de pertuis fut installée à la fin d’un tunnel d’évacuation d’eau au réservoir Nan-Hwa, Nan-Hwa, Taiwan, République de Chine. Les résultats numériques obtenus par l’utilisation du programme d’éléments finis ANSYS 5.5.2 concordent raisonnablement bien avec les données expérimentales. La déformation de la vanne de pertuis à haute pression sous des charges de pression d’eau de 0,736 MPa (75 m de hauteur d’eau) et 0,931 MPa (95 m de hauteur d’eau) a été prédite par ANSYS 5.5.2. La recherche rapportée ici peut fournir une méthode pour l’établissement d’un système d’observation de sécurité pour n’importe quelle vanne à haute pression, et fournir aux ingénieurs des données utiles pour évaluer la possibilité d’augmenter la capacité d’un réservoir existant. Mots clés : paroi de vanne de pertuis, modélisation par éléments finis (MEF), jauge de pression, pression d’eau. [Traduit par la Rédaction]

Chou and Lou

670

1. Introduction In 1997, the Taiwan Water Supply Company predicted that water demands for the southern area of Taiwan in the year 2001 would be 3 300 000 m3/d (TWC 1997). By comparing the predicted future water demands with the daily total amount of public water supplied to the southern area of Taiwan in December 1995 (2 460 000 m3/d), the shortage of public water in the year 2001 was estimated to be 840 000 m3/d. To provide for the future public demand for water in southern Taiwan, the Southern Water Resources Bureau of TPGWRD (Taiwan Provincial Government Water Resources Department) began constructing the Kou-Ping-Shee Transbasin project, which was completed in 1999. Recently, Received March 26, 1999. Revised manuscript accepted January 20, 2000. C.-S. Chou. Department of Mechanical Engineering, National Pingtung University of Science and Technology, Pingtung, Taiwan, Republic of China. S.-C. Lou. Southern Water Resources Bureau, Taiwan Provincial Government Water Resources Department, Pingtung, Taiwan, Republic of China. Written discussion of this article is welcomed and will be received by the Editor until December 31, 2000. Can. J. Civ. Eng. 27: 655–670 (2000)

the Southern Water Resources Bureau of TPGWRD also proposed a combination use of water resources, which integrates the water resources from the Nan-Hwa Reservoir and the Kou-Ping-Shee Transbasin project. The major advantage of this combination use of water resources is that the reservoir located upstream of the Kouping River can store water in the rainy season and then supply water to southern Taiwan in the dry season. Consequently, additional reservoir capacity located upstream of the Kouping River is needed. The Southern Water Resources Bureau of TPGWRD is currently evaluating the possibility of increasing the capacity of the existing Nan-Hwa Reservoir. In the first stage of evaluation, the optimum case involves increasing the crest elevation of the Nan-Hwa Dam from 187.5 to 207.5 m. Consequently, the reservoir capacity will be increased from 158 000 000 to 300 000 000 m3, and the expected environmental impacts will be acceptable. Whether the existing mechanical equipment within the water-release tunnel shown in Fig. 1 will be able to withstand the additional water load must be determined. The results obtained using analytical methods (Hydraulic Gate and Penstock Association 1991), which are usually used to design sluice gates, demonstrated that the stress due to a 95 m height of water is close to the allowable stress for the material in the sluice gate. On the other hand, Chou and Lou (1997, 1998) used ANSYS 5.0 to study the deformation of a © 2000 NRC Canada

656

Can. J. Civ. Eng. Vol. 27, 2000

Fig. 1. Mechanical equipment within a water-release tunnel in the Nan-Hwa Reservoir.

Fig. 2. Schematic drawing of a high-pressure sluice gate (side view).

resentative of a typical ship structural arrangement), which is similar to the structural arrangement of the gate leaf. The research reported here studied the deformation of a highpressure sluice gate leaf (see Fig. 2) installed at the end of the water-release tunnel of Nan-Hwa Reservoir using the finite element computer code, ANSYS 5.5.2, as well as experimental measurements. This high-pressure sluice gate is also called a control gate. By comparing the experimental data with the numerical and analytical results, the actual deformation behavior of a high-pressure sluice gate is understood completely. A feasible FEM model used to predict the deformation of the sluice gate leaf for increasing the height of the existing dam could be determined. In addition, a safety monitoring system (see Fig. 3) for any sluice gate installed at the end of the waterrelease tunnel of a reservoir, which constantly withstands huge water pressure, can be built based upon the experimental results and experience of this research. Consequently, the results of this research may provide a method for establishing a safety monitoring system for any high-pressure gate and provide engineers with useful information to evaluate the possibility of increasing the capacity of an existing reservoir by increasing the height of an existing dam. The research procedure is shown in Fig. 4.

2. Experimental apparatus and procedure

high-pressure sluice gate installed at the Mutan Reservoir, Mutan, Pingtung, Taiwan, R.O.C., and compared the numerical results obtained using FEM with the analytical results. It was found that the stresses obtained using the analytical method are greater than those obtained using FEM. Akhras et al. (1998) determined, numerically and experimentally, the ultimate strength of a box girder (i.e., the rep-

The dimensions of the half gate leaf shown in Fig. 5 are 2480 mm (length) × 600 mm (width) × 3185 mm (height) (Yamathita 1992). The gate leaf major components are a skin plate, five horizontal main beams, six vertical beams, and three bearing plates. They were made of structural steel SS 400 and were assembled by welding. The Young’s modulus and Poisson’s ratio used in this research were 207 GPa and 0.3, respectively. A strap, made of cast brass such as JIS BC3, was welded at the surface of the left, right, and top bearing plates in order to decrease the friction as well as to increase the water tightness of the sluice gate. The frame of the sluice gate (i.e., the supporting bonnet) was made of JIS SM490 steel. A schematic drawing of the contact situation between the supporting bonnet and the bearing plate of the gate leaf is shown in Fig. 6. Owing to the extensive water pressure acting on the sluice gate, a hydraulic system shown in Fig. 2 was used to close and open the sluice gate. To understand the actual deformation behavior of the high-pressure sluice gate installed at the end of the water© 2000 NRC Canada

Chou and Lou Fig. 3. Schematic drawing of a safety monitoring system.

release tunnel of the Nan-Hwa Reservoir, strain gauges were installed on the skin plate of the downstream control gate. A strain indicator was used to measure the strain on the gate. As water pressure load acted upon the upstream side of the gate leaf, strain gauges could only be mounted on the downstream side of the skin plate of the gate leaf. The layout of the strain gauges, mounted on the half gate leaf and included eight biaxial strain gauges and three uniaxial strain gauges, is shown in Fig. 7. To investigate the constraint effects on the deformation of the gate leaf, strain gauges A, H, and L were installed close to the boundaries. Reinforcement due to the horizontal and vertical beams may be validated by strain gauges B, C, D, E, G, J, and K. Finally, strain gauges F and F* provide important information about the deformation of the bottom of the gate leaf under nonconstraint conditions. The deformation of the centerline of the gate leaf may be determined by strain gauges A, B, C, D, E, F, and F*. In addition, strain values measured by strain gauges B, C, D, E, G, J, and K were compared with those determined by the analytical solution. The transverse sensitivity and gauge resistance of the biaxial temperature-compensated strain gauge (type KFG5120-D16-11L3M3S) were 0.4% and 120 ± 0.8 W, respectively. The transverse sensitivity and gauge resistance of the uniaxial temperature-compensated strain gauges (type KFG5-120-C1-11L3M3R) were 0.4% and 119.6 ± 0.4 W, respectively. The strain indicator (type SDB-410C) had the following specifications: measurement accuracy, ±0.2% × readout; applicable gauge, 60 ~ 1000 W; measurement range, 0 ~ ±19 999 × 10–6 strain. Prior to the installation of the strain gauges on the downstream side of the skin plate of the control gate, the water pressure load on the gate leaf of the control gate was removed by closing the upstream guard gate and opening the downstream control gate to drain the space between the two gates. The control gate was then closed and strain gauges

657 Fig. 4. The research procedure.

were installed on the downstream side of the skin plate of the control gate. The residual strain value measured by each strain gauge was recorded and listed in the second column of Table 1 (Kyowa Co. 1997). Water was readmitted to the space between the guard gate and the control gate by opening the water filling valve, and then the value of the strain measured by each strain gauge was recorded and listed in the third column of Table 1. To ensure that each strain gauge was functioning and to account for the cost of the experiment, the procedures for releasing water, adding water, and recording the strain values were repeated twice. The strain values measured by each strain gauge under water pressure loads of 0.539 MPa are shown in Table 1. The strain values measured under the loads of 0.539 MPa included the residual strain measured under the unloading. Consequently, the experimental net strain value for each strain gauge shown in Table 2 was obtained by (i) estimating the average of the strain values under the unloading, (ii) estimating the average of the strain values under the load, and (iii) subtracting the average value under the unloading from that under the load; this value was used to determine the stress.

3. Finite element model and boundary conditions An X–Y–Z Cartesian coordinate system was established at the bottom-left corner of the gate leaf. The coordinate X measures the parallel distances along the bottom of the gate © 2000 NRC Canada

658

Can. J. Civ. Eng. Vol. 27, 2000

Fig. 5. Geometry of a half gate leaf.

Fig. 6. Contact situation between the supporting bonnet and the bearing plate (top view).

leaf; Y measures the perpendicular distances above the bottom of the gate leaf; and Z points upstream. Two solid models were used to study the deformation of the sluice gate leaf. One solid model used a linear tetrahedron element, which has eight nodes with each node having three degrees of freedom (DOF). The other solid model used a linear tetrahedron element, which has eight nodes with each node having six DOF (ANSYS 1996a). A schematic drawing of the linear tetrahedron element is shown in Fig. 8.

For both models, the size of the element on the bearing plate was 4 cm and the size of the element on the other parts of the gate leaf was 6 cm. The Boolean operation was used to glue the individual volume together while establishing the geometric model. A free mesh was used to create the finite element solid model of the gate leaf shown in Fig. 9. Figure 10 indicates the load and constraints on the highpressure sluice gate leaf. No external load acted on the downstream side of the gate leaf. The water pressure load acting upon the upstream side of the gate leaf was between 0.508 and 0.539 MPa. A schematic drawing of the water pressure load acting upon the upstream side of the gate leaf is shown in Fig. 11. The bottom of the gate leaf was left free. The displacement in the Y direction for the points at the bottom of the gate leaf was equal to zero. Instead of the actual contact boundary condition between the bearing plate and the supporting bonnet, the three bearing plates were assumed to be simply supported when the sluice gate was closed (see Fig. 10). To decrease the discrepancy between the actual boundary condition of the bearing plate and the boundary condition used in this research, it was assumed that only some of the points at the three bearing plates had a zero displacement in the Y and Z directions and a zero angular displacement about the Z-axis. A schematic drawing showing the degree of constraint between the bearing plate and the frame of the sluice gate is shown in Fig. 12. In this research, it was found that © 2000 NRC Canada

Chou and Lou

659 Table 1. Field instrumentation data (55 m water height). Strain gauge AH AV BH BV CH CV DH DV EH EV FH FH* GH GV HH JH JV KH KV LH

Unloading I (×10–6) 503 690 382 355 140 598 318 468 352.5 124 –284 –535 161 475 –363.5 451 208 525 376 –711

1st load (×10–6) 501 624 421 332 227 548 430 397 465 45 –151 –408.5 250 426 –278.5 478 206 614 303 –647

Unloading II (×10–6) 503 688 381 357 139 598 318 470 350 122 –288 –541 154 458 –356 444 208 523 372 –711

2nd load (×10–6) 511 631 427 334 234 548 439.5 392 475 45 –142 –392 262 424 –251.5 493.5 206 622 306 –629

Unloading III (×10–6) 507 694 381 357 141 595 321 474 348 124 –285 –540 151 461 –350 445 209 524 370 –710

3rd load (×10–6) 517 646.5 423 334 234.5 547 444 397 477 48 –137 –392 265 421 –267 490 204 625 302 –631

Notes: Subscript H indicates the horizontal direction and subscript V indicates the vertical direction.

FEM results under a constraint of 35% of the width of the bearing plate (i.e., 7.875 cm) agreed reasonably well with the experimental results.

Fig. 7. Layout of strain gauges. (All dimensions are in millimetres.)

4. Calculation of stresses 4.1. Stress from measured strains The relationship between the strain measured by the strain gauge and the stress sxx is determined using [1]

æ e + ne ö sxx = ç H 2 V ÷E è 1 -n ø

where eH is the strain in the horizontal direction, eV is the strain in the vertical direction, n is Poisson’s ratio, and E is Young’s modulus (Dally and Riley 1978; Ross 1996). 4.2. Combined stresses The combined stresses, such as stress intensity sI and equivalent stress sE (ANSYS 1996b), are determined, respectively, using [2]

sI = max 冦兩s1 - s2兩, 兩s2 - s3兩, 兩s3 - s1兩冧

and [3]

ì1 ü sE = í 冤(s1 - s2 ) 2 + (s2 - s3) 2 + (s3 - s1) 2 冥 ý 2 î þ

1/ 2

where s1, s2 , and s3 are principal stresses, which are calculated from the stress components using the cubic equation [4]

sxx - l sxy sxz s yx s yy - l s yx = 0 s zx s zy s zz - l © 2000 NRC Canada

660

Can. J. Civ. Eng. Vol. 27, 2000 Table 2. Experimental net strain value obtained by subtracting the average value under the unloading from that under the load. Strain gauge A B C D E F G H J K L

Fig. 8. Schematic drawing of a linear tetrahedron element.

Strain (×10–6) eH

eV

3 43 92 119 22 143 104 91 40 96 75

–56 –23 –49 –76 –77 –41 –3 –69 Fig. 9. FEM solid model of a half gate leaf.

in which ls (three values) are eigenvalues (i.e., the principal stresses) of the stress tensor (Shames and Cozzarelli 1997). 4.3. Stress calculation by analytical method According to the technical standards edited by the Hydraulic Gate and Penstock Association (1991), the bending stresses of the horizontal and vertical beams, the shear stresses of the horizontal and vertical beams, as well as the bending stress and combined stresses in a bay on the skin plate were calculated. The bending stress sH of a main horizontal simply supported I-beam is determined using [5]

sH =

FH B 8Z H

where FH is the assigned load for a main horizontal beam, B is the span between the two side-seals of the gate leaf, and ZH is the elastic section modulus of a main horizontal beam. The shearing stress tH of a main horizontal beam is determined using [6]

tH =

FH 2AH

where AH is the section area of the web of a main horizontal beam. The bending stress sV and the shear stress tV of a vertical beam are determined, respectively, using [7]

sV =

ql 2 8Z V

[8]

tV =

ql 2AV

in which the average load q acting on a vertical beam is determined using [9]

q =

(D1 + D2 )PV 2

where PV is the water pressure acting upon that vertical beam, D1 (equal to 54 cm) is a distance, twice as long as the

distance between the vertical beam and the center line (see Fig. 3), D2 (equal to 48.5 cm) is the distance between two vertical beams, l is the span of the vertical beam, ZV is the elastic section modulus of the vertical beam, and AV is the section area of the web of that vertical beam. The bending stress sS generated in a bay on the skin plate from hydraulic pressure is determined using [10]

sS =

kPWa 2 100(t - eC ) 2

where PW is the water pressure acting on the bay, k is the shape coefficient determined by the effective width ratio of b © 2000 NRC Canada

Chou and Lou

661

Fig. 10. Loading and constraints on the high-pressure sluice gate leaf.

Fig. 11. Schematic drawing of the water pressure load acting on the upstream side of the gate leaf.

Fig. 12. Schematic drawing showing the degree of constraint between the bearing plate and the frame of the sluice gate.

Fig. 13. Stresses of a bay of the skin plate.

Table 3. k value. b/a

k1

k2

k3

k4

1.00 1.25 1.50 1.75 2.00 2.50 3.00 ¥

30.9 40.3 45.5 48.4 49.9 50.0 50.0 50.0

13.7 18.8 22.1 23.9 24.7 25.0 25.0 25.0

13.7 13.5 12.2 10.8 9.5 8.0 7.5 7.5

30.9 33.9 34.3 34.3 34.3 34.3 34.3 34.3

© 2000 NRC Canada

662

Can. J. Civ. Eng. Vol. 27, 2000

Fig. 14. Flow chart of the gate leaf design by the analytical method.

to a (see Table 3), b is the length of the major sideline of the bay, a is the length of the minor sideline of the bay, t is the nominal thickness of the skin plate, and eC is the corrosion allowance. The bending stresses sS1 and sS4 shown in Fig. 13 are determined by eq. [10] and the value of the shape coefficient k is obtained from Table 3. For example, if the ratio of b to a is 2 and k1 and k4 are 49.9 and 34.3, respectively, sS1 and sS4 are calculated by substituting k1 and k4, respectively, into eq. [10]. The combined stresses of point A located at the minor sideline of the bay (see Fig. 13) can be expressed as [11]

2 sA = s1A + (0.3sS1 + sV) 2 + s1A(0.3sS1 + sV)

in which s1A is determined using [12]

s1A = sH + sS1

The combined stresses of point B located at the major sideline of the bay (see Fig. 12) can be expressed as [13]

2 2 sB = s1B + sS4 + sS4

in which s1B is determined using [14]

s1B = sH + 0.3sS4

The analytical and traditional design procedures of the gate leaf are as follows: (i) estimating the water pressure acting on the gate leaf; (ii) assuming the number, dimensions, and material properties of the horizontal beam, vertical beam, and skin plate; (iii) calculating the bending and shearing stresses of the horizontal and vertical beams using eqs. [5]–[9] and the bending stress of the bay of the skin plate using eq. [10]; (iv) comparing these calculated bending and shearing stresses with the allowable stress for the material; (v) revising the original assumed design of the gate leaf © 2000 NRC Canada

Chou and Lou

663

Table 4. Comparison of the bending stress sxx (MPa) under a water pressure load of 0.539 MPa (i.e., 55 m water height). FEM result Strain gauge

Coordinates (X, Y, Z) (m)

Linear tetrahedron element with 6 DOF

Linear tetrahedron element with 3 DOF

A B C D E F G H J K L

(1.455, 3.15, 0) (1.455, 2.515, 0) (1.455, 1.915, 0) (1.455, 1.315, 0) (1.455, 0.715, 0) (1.455, 0.015, 0) (1.185, 0.3575, 0) (0.023, 0.015, 0) (1.185, 1.015, 0) (0.9425, 1.315, 0) (0.023, 1.315, 0)

–1.1 8.0 16.3 19.0 20.0 29.1 16.2 10.53 10.6 17.1 10.3

–0.73 5.6 15.6 19.5 21.2 25.0 16.3 5.7 16.3 17.3 5.3

Analytical solution

Experimental data

21.03 26.72 30.44 30.44 30.41

–3.14 8.21 17.6 21.8 22.5 32.8* 20.8 20.7* 89 17.1 17.0*

55.76 46.16

Notes: All strain gauges were bonded to the downstream side of the skin plate of the gate leaf. *Stress values sxx were determined using horizontal strain eH only.

Fig. 15. Upstream side of the gate leaf. The top-central panel of the gate leaf is reinforced with steel.

if any one of the calculated stresses exceeds the allowable stress for the material; (vi) calculating the combined stresses of the gate leaf using eqs. [11]–[14]; and (vii) revising the original assumed design of the gate leaf if any one of the calculated combined stresses exceeds the allowable stress for the material. The flow chart of the gate leaf design using the analytical method is shown in Fig. 14.

5. Results and discussion 5.1. Comparison of experimental and numerical results By substituting the data listed in Table 2 into eq. [1], only the stresses sxx for 0.539 MPa of water pressure load at the points where the strain gauges were located on the skin plate of the sluice gate were determined, which are listed in Table 4. The analytical method for the bending stress calculation (i.e., eq. [5]) was applied only to the points where the Y-

coordinate was equal to the height of one of the horizontal beams. The asterisk in Table 4 indicates that the stress values sxx were determined using horizontal strain eH only because strain gauges F, H, and L were uniaxial strain gauges and were close to the boundary. Since the strain gauge A was just below the first horizontal beam, the stress sxx was compressive. Because the panel (see Figs. 7 and 15) in which strain gauges A and B were located was reinforced with steel, the stresses obtained by both FEM solid models at points A (1.455, 3.15, 0) and B (1.455, 2.515, 0) were compressive and smaller than the measured values. At point B (1.455, 2.515, 0), the difference in the stress sxx between the results obtained using the FEM solid model with six degrees of freedom and the experimental measurement was 0.21 MPa, and the error was less than 2.6%. However, the difference in the stress sxx between the results obtained using the FEM © 2000 NRC Canada

664 Fig. 16. Bottom part of the vertical beam. The FEM model includes the wedge portion drawn by a dashed line.

solid model with three degrees of freedom and the experimental measurement was 2.61 MPa, and the error was 31.7%. At points C (1.455, 1.915, 0), D (1.455, 1.315, 0), and E (1.455, 0.715, 0), the difference in the stress sxx between the results obtained using the FEM solid model with six degrees of freedom and the experimental measurement was below 2.8 MPa, and the error was less than 12.9%. On the other hand, the difference in the stress sxx between the results obtained using the FEM solid model with three degrees of freedom and the experimental measurement was below 2.0 MPa, and the error was less than 11.4%. Because the bottom part of the vertical beam in both FEM solid models included the wedge portion, as shown by the dashed line in Fig. 16, the stress values obtained by both FEM solid models at points F (1.455, 0.015, 0), G (1.185, 0.3575, 0), and H (0.023, 0.015, 0) were smaller than those obtained by experiment. As the solid model with six degrees of freedom had three degrees of freedom more than the solid model with three degrees of freedom, for points close to the boundary, the results obtained by the solid model with six degrees of freedom were closer to experimental values than those obtained by the solid model with three degrees of freedom. Since the strain gauges at points F (1.455, 0.015, 0), H (0.023, 0.015, 0), and L (0.023, 1.315, 0) were uniaxial strain gauges, the experimental bending stresses sxx at these points were determined without the vertical strain eV, which had a negative value. Consequently, from eq. [1], it could be demonstrated that the experimental values are larger than the results obtained by both FEM solid models at these points. Finally, at point K (0.023, 1.315, 0), the difference in the stress sxx between the results obtained using both FEM solid models and the experimental measurement was below 0.2 MPa, and the error was less than 1.2%. In general, from Table 4, the bending stresses sxx obtained using analytical methods (Hydraulic Gate and Penstock Association 1991) were larger than those obtained by both the FEM analysis (ANSYS 1996a; 1996b) and experimental measurements. The numerical results agreed with the experimental data.

Can. J. Civ. Eng. Vol. 27, 2000 Fig. 17. Distribution of the bending stress sxx of a sluice gate leaf determined using the FEM solid element model with six degrees of freedom under a water pressure load of 0.539 MPa (i.e., 55 m water height).

Fig. 18. Distribution of the bending stress sxx of a sluice gate leaf determined using the FEM solid element model with three degrees of freedom under a water pressure load of 0.539 MPa (i.e., 55 m water height).

The distribution of bending stress sxx under a water pressure load of 0.539 MPa obtained using FEM solid models is shown in Figs. 17 and 18. A deformed half gate leaf under a water pressure load of 0.539 MPa obtained using FEM solid models is shown in Figs. 19 and 20. By comparing Figs. 17 and 18, the bending stresses sxx obtained by the FEM solid © 2000 NRC Canada

Chou and Lou

665

Table 5. Bending stress sxx (MPa) comparison between the analytical solution and the result by FEM linear tetrahedron element with six degrees of freedom for main horizontal beams. Analytical solution

I II III IV V

Horizontal beam

Element number

Tension side Compression Tension side Compression Tension side Compression Tension side Compression Tension side Compression

5159 2955 5148 3995 5138 7153 5128 6647 1352 434

side side side side side

75 m water height 29.11 –56.45 36.95 –104.66 41.94 –96.53 41.75 –88.49 41.55 –83.30

FEM result 95 m water height 38.91 –72.13 46.45 –130.73 53.41 –122.99 49.39 –113.78 52.63 –105.55

75 m water height 2.4 0.6 6.8 –13.0 21.3 –43.5 26 –59.2 29.5 –64

95 m water height 3.3 –10.7 8.37 –15.8 28.2 –59.2 34.3 –76.0 30.7 –82.5

Allowable stress 141.9 141.9 141.9 141.9 141.9

Table 6. Bending stress sxx (MPa) comparison between the analytical solution and the result by FEM linear tetrahedron element with three degrees of freedom for main horizontal beams.

I II III IV V

Horizontal beam

Element number

Tension side Compression Tension side Compression Tension side Compression Tension side Compression Tension side Compression

5154 2971 5144 4010 5134 7730 5124 6670 1348 431

side side side side side

Analytical solution

FEM result

75 m water height 29.10 –56.45 36.95 –104.46 41.94 –96.53 41.75 –88.49 41.55 –83.30

75 m water height 1.5 –0.25 5.94 –11.1 20.7 –44.4 26 –56.3 30.5 –60.9

Fig. 19. A deformed half sluice gate leaf determined using the FEM solid element model with six degrees of freedom under a water pressure load of 0.539 MPa (i.e., 55 m water height).

95 m water height 38.91 –72.13 46.45 –130.73 53.41 –122.99 49.39 –113.78 52.63 –105.55

95 m water height 3.51 –3.2 10.2 –13.7 25.4 –55.2 31.5 –69.7 35.9 –74.7

Allowable stress 141.9 141.9 141.9 141.9 141.9

Fig. 20. A deformed half gate leaf determined using the FEM solid model with three degrees of freedom under a water pressure load of 0.539 MPa (i.e., 55m water height).

© 2000 NRC Canada

666

Can. J. Civ. Eng. Vol. 27, 2000

Fig. 21. Distribution of the bending stress sxx of a sluice gate leaf determined using the FEM solid element model with six degrees of freedom under a water pressure load of 0.931 MPa (i.e., 95 m water height).

Fig. 22. Distribution of the bending stress sxx of a sluice gate leaf determined using the FEM solid element model with three degrees of freedom under a water pressure load of 0.931 MPa (i.e., 95 m water height).

model with six degrees of freedom are larger than those determined by the FEM solid model with three degrees of freedom because the node of the element with six degrees of freedom has three degrees of freedom greater than the node of the solid element with three degrees of freedom. From Fig. 19, the FEM solid model with six degrees of freedom predicted the wiggling movement of the centerline of the gate leaf. On the other hand, the FEM solid model with three degrees of freedom determined the smooth movement of the centerline of the gate leaf shown in Fig. 20.

5.2. Predicted deformation of the gate leaf for 0.735 and 0.931 MPa loadings From the comparisons of the experimental results to the FEM results, the solid models used in this research are the feasible models to predict the deformation of the sluice gate leaf for increasing the height of the dam of the Nan-Hwa Reservoir. A few values of the bending stress sxx comparison between the analytical solution and the FEM results obtained by both solid models for water pressure loads of 0.735 and 0.931 MPa are shown in Tables 5 and 6, respec© 2000 NRC Canada

Chou and Lou

667

Fig. 23. Distribution of the shearing stress t xz of a sluice gate leaf determined using the FEM solid element model with six degrees of freedom under a water pressure load of 0.931 MPa (i.e., 95 m water height).

Fig. 24. Distribution of the shearing stress t xz of a sluice gate leaf determined using the FEM solid element model with three degrees of freedom under a water pressure load of 0.931 MPa (i.e., 95 m water height).

tively. The distribution of the bending stress sxx determined using FEM solid models under a water pressure load of 0.931 MPa is shown in Figs. 21 and 22. The maximum bending stress sxx under a water pressure load of 0.931 MPa predicted by the analytical method is close to the allowable stress of the material. However, the maximum bending stress sxx under the same water pressure load predicted by the FEM analysis is well below the allowable stress of the material. Under 0.931 MPa of water pressure, the position of the maximum bending stress sxx predicted by the FEM solid

models was in the bearing plate. However, the stress in the center of beam II was as predicted by the analytical solution. The shearing stress txz comparison between the analytical solution using eq. [6] and the FEM results obtained using both solid models for water pressure loads of 0.735 and 0.931 MPa is shown in Tables 7 and 8, respectively. The distribution of the shearing stress txz determined using FEM solid models under a water pressure load of 0.931 MPa is shown in Figs. 23 and 24. The maximum shearing stresses txz under a water pressure load of 0.931 MPa, predicted by © 2000 NRC Canada

668

Can. J. Civ. Eng. Vol. 27, 2000 Table 7. Shearing stress t xz (MPa) comparison between the analytical solution and the result by FEM linear tetrahedron element with six degrees of freedom for main horizontal beams.

Horizontal beam

Element number

I II III IV V

2879 3431 4633 6908 1960

Analytical sololution

FEM result

75 m water height 8.62 16.76 22.93 22.93 24.01

75 m water height 2.59 10.1 15.8 19.2 26.8

95 m water height 10.98 21.07 29.2 29.2 30.38

95 m water height 4.1 9.3 16 20.3 28.5

Allowable stress (kgf/cm2) 89.6 89.6 89.6 89.6 89.6

Table 8. Shearing stress t xz (MPa) comparison between the analytical solution and the result by FEM linear tetrahedron element with three degrees of freedom for main horizontal beams.

Horizontal beam

Element number

I II III IV V

2907 3305 4629 6818 1906

Analytical solution

FEM result

75 m water height 8.62 16.76 22.93 22.93 24.01

75 m water height 3.11 7.99 12.8 16 22.3

95 m water height 10.98 21.07 29.2 29.2 30.38

95 m water height 3.8 10.3 15.9 19.8 22

Allowable stress 89.6 89.6 89.6 89.6 89.6

Table 9. Comparison of maximum stresses (MPa). Stress by FEM linear tetrahedron element with 6 DOF

55 m water height (existing loading)

sxx syy szz sxy syz sxz s1 s2 s3 sI sE

–66.5 –44.8 –93.9 –17.6 –19.7 –22.3 88.2 –63.7 –98.8 99.4 88.1

Combined stress by analytical method

75 m water height –92.4 54.3 –125 –23.3 –26.1 –30.3 120 –84.2 –131 134 118

96.53

the analytical method as well as by the FEM analysis, are well below the allowable shear stress of the material. 5.3. Principal stresses and combined stresses Since the strain gauges were installed on the downstreamside skin plate of the control gate, only stress sxx can be measured using field strain measuring method. Consequently, FEM solid models were used to calculate the principal stresses s1, s2 , and s3 through eq. [4], as well as the combined stresses sI and sE through eqs. [2] and [3]. On the other hand, the analytical method was used to calculate the

113.68

95 m water height

Allowable stress

Yield stress

–111 66 –164 –31.4 –34.7 –39.6 156 –98.4 –172 174 152

141.9 141.9 141.9 89.6 89.6 89.6 141.9 141.9 141.9 141.9 141.9

235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2

141.9

235.2

168.17

combined stresses through eqs. [5]–[14]. The maximum values of the bending stress, shearing stress, principal stress, and stress intensity obtained by both FEM solid models and the analytical method are listed in Tables 9 and 10. The results listed in Table 9 demonstrated that the stress intensity sI and the principal stress s3 predicted by the FEM solid model with six degrees of freedom and the analytical method, due to a water pressure load of 0.931 MPa (i.e., 95 m water height), are between the allowable stress and the material yield stress. However, from Table 10, the stress intensity sI predicted by the FEM solid model with three de© 2000 NRC Canada

Chou and Lou

669 Table 10. Comparison of maximum stresses (MPa). Stress by FEM linear tetrahedron element with 3 DOF

55 m water height (existing loading)

sxx syy szz sxy syz sxz s1 s2 s3 sI sE

–71.7 –43.8 –83.8 –13.5 –14.8 23.9 57.3 –65.6 –90.4 67.0 58.3

Combined stress by analytical method

75 m water height –72.42 –60.5 –119 –18.5 –22.9 –32.9 –78.9 –90.7 –125 92.4 80.5

96.53

grees of freedom under the same water pressure load is well below the allowable stress of the material.

6. Conclusions A finite element computer code, ANSYS 5.5.2, and a field method of strain measuring were used to study the deformation of a high-pressure sluice gate installed at the end of a water-release tunnel at the Nan-Hwa Reservoir, Nan-Hwa, Taiwan, R.O.C. By comparing the experimental data with the numerical results obtained using both FEM solid models and the analytical solution, the numerical results agreed in a general way with the experimental data. The deformation of this high-pressure sluice gate under water pressure loads of 0.735 MPa (equal to 75 m water height) and 0.931 MPa (equal to 95 m water height) was estimated using FEM solid models and analytical methods, respectively. The position of the maximum stress predicted by the FEM solid models was in the bearing plate. However, the stress in the center of the gate leaf was as predicted by the analytical solution. The sub-modeling and the actual contact boundary conditions may be worthy tasks to examine in further research. The research work reported here may provide a method for establishing a safety monitoring system for any high-pressure gate and provide engineers with important information to evaluate the possibility of increasing the capacity of an existing reservoir through raising the dam.

Acknowledgements This research was partially supported by the National Science Council, R.O.C., through a grant (NSC-86-2815-C020-001-E) and by the Southern Water Resources Bureau of TPGWRD.

References Akhras, G., Gibson, S., Yang, S., and Morchat, R. 1998. Ultimate strength of a box girder simulating the hull of a ship. Canadian Journal of Civil Engineering, 25: 829–843.

113.68

95 m water height

Allowable stress

Yield stress

–120 –72.7 –138 –22.6 –24.8 –39.3 87.5 –109 –149 111.2 96.9

141.9 141.9 141.9 89.6 89.6 89.6 141.9 141.9 141.9 141.9 141.9

235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2 235.2

141.9

235.2

168.17

ANSYS User’s Manual. 1996a. Expanded ANSYS workbook for revision 5.2. Swanson Analysis System, Inc., Canonsburg, Pa. ANSYS User’s Manual. 1996b. Structural strain and stress evaluations of theory manual of ANSYS 5.2. Swanson Analysis System, Inc., Canonsburg, Pa. Chou, C.S., and Lou, S.C. 1997. The structural analysis of high pressure sliding gate: finite element method. Journal of Taiwan Water Conservancy, 45(4): 73–81. Chou, C.S., and Lou, S.C. 1998. The effect of constraint on the deformation of sluice gate. Proceeding of the 4th International Conference on Numerical Methods and Application (NMA98), August 19–23, Sofia, Bulgaria, pp. 127–128. Chou, C.S., Lou, S.C., Lee, J.M., and Lai, W.S. 1998. Experimental measurement and FEM analysis of the structure of the penstock in the water release tunnel. Journal of Taiwan Water Conservancy, 46(4): 90–98. Dally, J.W., and Riley, W.F. 1978. Experimental stress analysis. 2nd ed. McGraw-Hill, Kogakusha, New York. Hydraulic Gate and Penstock Association. 1991. Technical standards for gates and penstocks. Tokyo, Japan. Kyowa Co. 1997. SDB-410C strain indicator operation manual. Osaka, Japan. Ross, C.T.F. 1996. Mechanics of solid. Prentice-Hall, London, U.K. Chap. 16. Shames, I.H., and Cozzarelli, F.A. 1997. Elastic and inelastic stress analysis. Revised printing. Taylor & Francis, Bristol, U.K., pp. 51–53. Chap. 2. TWC. 1997. The report of the project of public water coordination. Taiwan Water Supply Company, Taichung, Taiwan, R.O.C. Yamathita, T. 1992. Calculation sheets for 2500 mm × 3000 mm control gate and 2500 mm × 3000 mm guard gate. Kurimoto, Ltd., Osaka, Japan.

List of symbols a AH AV b B

length of the minor sideline of a bay section area of the web of a horizontal beam section area of the web of a vertical beam length of the major sideline of a bay span between two side-sealing of the gate leaf © 2000 NRC Canada

670

Can. J. Civ. Eng. Vol. 27, 2000 D1 distance twice as long as that between a vertical beam and a center line D2 distance between two vertical beams E Young’s modulus FH assigned load for a horizontal beam k shape coefficient l span of the vertical beam PW water pressure acting on the bay q average loading acting on a vertical beam t thickness of the skin plate ZH section modulus of a horizontal beam ZV section modulus of a vertical beam eC corrosion of allowance eH strain in the horizontal direction eV strain in the vertical direction l eigenvalues n Possion’s ratio sA combined stress of point A located at minor sideline of a bay

sB combined stress of point B located at major sideline of a bay sE equivalent stress sH bending stress of a main horizontal beam sI stress intensity sS bending stress generated in a bay of the skin plate sS1 bending stress of major sideline of a bay sS4 bending stress of minor sideline of a bay sV bending stress of a vertical beam sxx bending stress s1 principal stress (No. 1) s2 principal stress (No. 2) s3 principal stress (No. 3) t H shearing stress of a main horizontal beam tV shearing stress of a vertical beam t xz shear stress

© 2000 NRC Canada

Suggest Documents