# DESIGN CALCULATION OF SPILLWAY GATE 1 Design data Type Radial gate Max.Flood level 337 m High water level 336 m Low water level 336 m Crest El. 340 m Clear span 14 m

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25 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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DESIGN CALCULATION OF SPILLWAY GATE

1

Design data

Type

Max.Flood level

337

m

High water level

336

m

Low water level

336

m

Crest El.

340

m

Clear span

14

m

Height

11

m

-
H

11

m

Quantity

2

sets

All.stress
-
SS400

1200

kg/cm2

All.stress
-
SM490

1600

kg/cm2

Corr.all.

2

mm

2

R =

1.25 * H

=

1.25*11

=

13.75

m

sin β/2=

h/2

R

=

5.5

13.75

=

0.4

β/2 =

23.58

o

β =

47.16

o

< =

0.26

3

Arc length of gate

L =

=

3.14*13.75 *0.26

=

11.31

m

4

Spacing of horizontal girder

(a)

Number of girder
-
N, according to standard for H= 8.5 to 12

=

3

(b)

Water pressure, t/m2

spacing, m

kg/cm2

p0 =

0.000

0.000

a

2.245

b1 =

3.726

p1 =

4.491

4.491

b

6.134

b2 =

3.189

p2 =

7.778

7
.778

c

8.910

b3 =

2.644

9.559

p3 =

10.042

10.042

d

b4 =

1.441

10.521

p4 =

11.000

11.000

e

11.000

5

Vertical stiffeners

5.1

Bending moment on vertical stiffeners

M ab=

p1*b1^2/6

=

4.49*3.73^2/6

=

10.391

tm

=

1,039,086

kg
-
cm

M cb & bc =

(p1*b2^2/12)+(p2*b2^2/12)

=

(4.49*3.19^2/12)+(7.78*3.19^2/12)

=

10.40

tm

=

1,039,761

kg
-
cm

M cd & dc =

(p2*b3^2/12)+(p3*b3^2/12)

=

(7.78*2.64^2/12)+(10.04*2.64^2
/12)

=

10.38

tm

=

1,038,110

kg
-
cm

M de =

(p3*b4^2/2)+(p4*b4^2/3)

=

(10.04*1.44^2/2)+(11*1.44^2/3)

=

10.43

tm

=

1,042,558

kg
-
cm

Max. bending moment
-

Mb max.

Mb max. =

1,042,558

kg
-
cm

5.2

Number of

vertical stiffeners

Spacing, s =

0.60

m

N =

(B/s)+1

=

14/0.6+1

=

24

5.3

Bending stress

σcd =

Mmax

=

1042557.53

Zxl

815.90

=

1042557.53

815.90

=

1,277.80

tf/cm2

Ma
terial:

JIS G 3101

SS400

H

B

Tw

Tf

I

mm

450

200

9

14

Cor.all.

mm

1

I x1 =

18,195

cm4

Z x1=

816

cm3

Aw =

77.54

cm2

G =

60.87

kg/m

5.4

Weight of vertical stiffener

Gst =

N * L * G

=

24*11.31*60.87

=

16,75
3.18

kgs

6

Horizontal girder

6.1

The end frames shall be fixed at about 0.2 * B distance from each end.

Distance of end frame from each end of the gate, e

b =

0.2 * B

=

0.2 *14

=

2.8

m

=

280

cm

Distance between end frames

e =

B
-

( 2*b )

=

14
-
(2 *2.8)

=

8.4

m

=

840

cm

6.2

(1)

Beam B

wb = wb1 + wb2

wb1 =

(p0 + 2 * p1) * b1

6

=

(0 + 2 * 4.49) * 3.73

=

5.5
77

tf/m

6

wb2 =

(2 * p1 + p2) * b2

6

=

(2 * 4.49 + 7.78) * 3.19

=

8.908

tf/m

6

wb = 5.577 + 8.908

=

14.485

tf/m

=

144.85

kgf/cm

(2)

Beam C

wc = wc1 + wc2

wc1 =

(p1 + 2 * p2) * b2

=

6

(4.49 + 2 * 7.78)
* 3.19

=

63.930

6

6

=

10.66

tf/m

wc2 =

(2 * p2 + p3) * b3

=

6

=

(2 * 7.78 + 10.04) * 2.64

=

94.23

6

6

=

15.71

t/m

wc= 10.66 + 15.71

=

26.36

tf/m

=

263.60

tf/cm

(3)

Beam D

wd= wd1 + wd2

wd1 =

(p2 + 2 * p3) * b3

6

=

(7.78 + 2 * 10.04) * 2.64

=

12.278

tf/m

6

wd2 =

(2 * p3 + p4) * b4

6

(2 * 10.04 + 11) * 10.52

=

7.465

tf/m

6

wd = 12.278 + 7.465

=

19.743

tf/m

=

197.43

kg/cm

wmax =

=

263.60

kg/
cm

MBA =

wmax * b ^2

=

263.6 * 280 ^2

2

2

11,356,240.00

2

=

5,678,120.00

kg
-
cm

6.3

Bending stress

σBC =

MBC

=

5678120

Zxl

10454.64

=

11356240

10454.64

Upper girder

=

1,086.24

kgf/cm2

Material:

JIS

G 3101

SS400

H

B

Tw

Tf

I

mm

900

400

25

25

Cor.all.

mm

1

I x1 =

468,368

cm4

Z x1=

10,455

cm3

Aw =

379.50

cm2

G =

297.91

kg/m

6.4

Weight of horizontal girder

Gst =

N * B * G

=

3*14*297.91

=

166,828.20

kgs

7

Skin plate

From the practical safety consideration the thickness of skin plates is of not less than 10 mm.

An allowance of 2 mm thickness is made to allow for corrosion and rusting.

This allowance is included
in the minimum specified thickness of 10 mm.

So that the effective thickness of skin plate is only 8 mm.

7.1

Bending stress

σs =

K * a^2 * p

100 x t^2

7.2

Result of calculation

k =

50

a

b

b/a

p

t

(cm)

(c
m)

(kgf/cm2)

(cm)

σs

60

372.600

6.21

2.245

1.80

(kgf/cm2)

60

318.900

5.315

6.134

2.80

1247.4

60

264.400

4.407

8.910

3.80

1408.4

60

144.100

2.402

10.521

3.80

1110.6

allowable bending stress

SM
-
490

1311.5

Corrosion allowance

0.2

cm

Thickn
ess of skin plate

1

20

mm

2

30

mm

3

40

mm

4

40

mm

7.3

Weight of skin plate, G=W * H * t * g

Width
-
W

Height
-
H

Thickness
-
t

Weight
-
G

(dm)

(dm)

(dm)

(kg)

1

140

37.26

0.2

8,189.75

2

140

31.89

0.3

10,514.13

3

140

26.44

0.4

11,
623.02

4

140

14.41

0.4

6,334.64

5

Total

36,661.54

8

Total weight of moving parts exluding end frame

Weight of vertical stiffener

=

16,753.18

kgs

Weight horizontal girder

=

166,828.20

kgs

Weight of skin plate

=

36,661.54

kgs

Total

=

220,242.92

kgs

9

Friction force

9.1

Friction force on pin

Assume pin pin diameter
-
df

=

600

mm

=

0.3

m

Friction between bronze and steel
-

ff

=

0.25

(a)

Maximum horizontal thrust on pin, P=

P =

B * H^2

2 * n

where n = number of end frame = 2

=

14 *11^2

=

484

2 * 2

4

=

121

tf

(b)

Friction force on pin

Fp =

P * ff

=

121 * 0.25

=

30.3

tf

( c)

-

Tp

Tp * R = Fp * r

Tp =

Fp * r / R

=

30.25 *0.3 / 13.75

where

=

0.66

tf

R =

Fp =

Friction force on pin

R =

9.2

Friction force due to seal rubber

Assume width of seal bears water pressure
-

wr

=

50

mm

=

0.05

m

Pressure area of rubber
-

ar =

2*L*wr =

2*11.31*0.05

=

1.13

m2

Average water pressure
-

pw

=

5.578

t/m2

Friction coefisien between rubber and steel
-

fr

=

1.1

Load due to friction of rubber seal
-

Tr

Tr =

pw * ar * fr

=

5.58*1.1
3*1.1

=

6.94

tf

10

Center of gravity

DESCRIPTIONS

WEIGHT

DISTANCE

MOMENT

(kgs)

(mm)

(kgs.
-
mm)

1

gate leaf

220,243

11,311

2,491,162,385

2

end frame

24,575

6,875

168,953,560

3

total

244,818

2,660,115,945

4

center of g
ravity

10,866

from center of pin

11

Steel wire rope

11.1

Tension on Steel wire rope in normal condition

diameter, d

35

mm

breaking strength, T

kgf

unit weight, Wc

90

kg/m

Taking length of wire rope
-

Lc

=

12.31

m

Tension in wire rope due to its own weight

=

1.11

tf

Total tension in one side of wire rope in normal condition
-

Wc

Wc =

(Gg+Gf+Tr)/2

=

220.24+1.96+6.94/2

where

=

114.57

tf

Gg =

weight of gate leaf

=

220.24

tf

Df =

por
tion of end frame weight at wire rope position

(Dwg.3)

=

1.96

tf

11.2

Tension on wire rope in Emergeny condition

(a)

Related dimensions

span
-

B

=

14

m

-

R

=

13.75

m

tan A =B/R

=

13.75/14

=

0.98

angle < A

=

44.4
8

o

(i)

Nearest distance from pin to diagonal line of another pin to the edge of gate leaf
-

"X"

X/B=

SIN(A)

X=

sin(A)*B

=

9.81

m

angel < D =

=

45.49

o

(ii)

Distance from intersection of diagonal line and gate center line to pin centerline
-

"Y"

Y/X =

SIN(D)

y =

sin(D)*X

7.00

m

( iii)

C of G =

=

10.87

m

from center of pin

(iv)

Distance from intersection of diagonal line and gate center line to center of gravity
-

"Z"

Z =

10.87
-
7

=

3.87

m

(v)

Nearest distance from c.g to diagonal line of another pin to the edge of gate leaf
-

"p"

p =

sin(D)*X

=

2.758

m

(Dwg.4)

(b)

Moments

Taking moment about vertical plane passing through diagonal line

Gg*p = Rd*X

(i)

Reaction at point d, Rd

Rd =

Gg * p

X

=

110.12*2.76

=

303.68

9.81

9.81

=

30.94

tf

(downward)

(ii)

Taking moment about vertical plane passing through wire rope line P
-
Q

Rd*Cc
-

Gg*Dc = Ra*Bc

Ra

=

reaction at point A

Ra =

(Rd*Cc)
-

(Gg*Dc )

Bc

=

(30.94*0.6)
-

(110.12*6.4)

=

(686.21)

13.4

13.4

=

(51.21)

tf

(upward)

where

Cc =

nearest distance of wire rope from point D

0.6

m

Gg =

110.12

tf

Dc =

nearest distance of wire rope from point c.g

6.4

m

Bc =

nearest distance of wire rope from point A

13.4

m

(iii)

Tension in emergency

Taking moment about vertical plane passing through D, parallel to line
AK

X*(Ra+T')=Gg*(X+Cc)

(Ra*X)+(T'*X)=Gg*(X+Cc)

T'*X=Gg*(X+Cc)
-
(Ra*X)

T'*X=

Gg*(X+Cc)
-
(Ra*X)

T' =

110.12*(9.81+0.6)
-
(
-
51.21*9.81)

9.81

=

1,649.35

=

168.13

tf

9.81

=

175.07

tf

T=

12

End frame

12.1

Axial loads on end frame members

(a)

wb =

14.49

t/m

wc =

26.36

t/m

wd =

19.74

t/m

w max =

26.36

t/m

( b)

Maximum
-

F

F =

wmax * B /2

=

26.36 *14/2

=

621.52

tf

( c)

Inclined component along the line of end member
-

F'

-

R

=

13.75

m

Angle of end frame inclination
-

θ

=

11.51

o

Length of end frame
-

L = R /
cos (θ)

=

13.75/
-
0.87

=

15.80

m

F' =

F * L / R

=

621.52*15.8/13.75

=

713.98

tf

(d)

Profil for end frames

Upper girder

Material:

JIS G 3101

SS400

H

B

Tw

Tf

Double
-
I

mm

750

300

30

30

Cor.all.

mm

1

I x1 =

586,564

cm
4

Z x1=

15,726

cm3

Aw =

722.40

cm2

G =

567.08

kg/m

(e)

Bending moment
-

Bm

length of end frame, L' = L
-

(hf+hg)

=

14.45

m

where

L = incline distance of end frame

=

15.80

m

hf

= height of vertical stiffeners web

=

-

m

hg = height of horizontal girders web

=

-

m

Bm =

G * L'^2

8

=

567.08 *(14.45)^2

8

=

118,331

8

=

14,791.40

kgm

(f)

Bending stress
-

Sb

Sb
=

Bm*100

+

F'

z

A

=

14791.4*100

+

713.98*1000

15725.57

722.4

=

1,479,140.40

+

713975.11

15725.57

722.4

=

94.06

+

988.34

=

1,082.40

kg/cm2

(g)

Weight of one element of end frame

Gst =

L' * G

=

14.45*567.08

=

8,191.69

kgs

Total weight
-

Gef = N * Gst

=

24,575.06

kgs

N = number of arm

=

3