Design of the Low Head Slide Gate

Basic Parameters

Gate Width: 1.30 mGate Height: 1.30 m

0.00 m

C/C of Side Seal: 1.30 mC/C of Track: 1.31 mDesign head to Seal: 1.30 m

Allowable stresses

a) Structural Steel

Tension in bending: 0.4 YP = 100 MpaCompression in bending: 0.4 YP = 100 MpaShear Stress: 0.3 YP = 75 MpaCombined Stress: 0.5 YP = 125 MpaBearing Stress: 0.25 UTS = 102.5 Mpa

b) Bronze or Brass

Bearing Stress: 0.03 UTS

Material

Structural Steel conforming to IS-2062, for thickness less than or equal to 20 mm, YP = 250 MpaUTS = 410 MPa

Hydraulic Load on the Gate

Area of the Gate: 1.69 SqmWater pressure at top: 0.00 Kg/m2Water pressure at bottom: 1300.00 Kg/m3Total Hydraulic load: 1098.5 Kg

Placement of Girder

Horizontal Girders are to be located as per cl 6.1.2.1 of IS 5620Adoption of two girder design makes the system statically determinate, so, the selection of L1 equalling H/6 and L2 = H/3 gives equal loads on the two girder.

Distance of gorder 1 form bottom = H/6 0.22 mDistance of gorder 2 form bottom = H/6 + H/3 0.65 m

Maximum head difference in the opening:

Allowable stresses as specified for in Annexx "B" of IS-5620-1985 as applicable to wet and inaccessible conditions

1300.00Kg/m2 1083.33 Kg/m2 650 Kg/m2 0.00

Kg/m2

0.22 m 0.433 m 0.65 mR1 R2

1.30 m

Reaction / width at girder 1, R1 = 422.5 Kg/m

Reaction / width at girder 2, R2 = 422.5 Kg/m

Design of Skin PlateBoundary condition of the plate is all edges simply supported

where K= non-dimensional factor depending on values of a & b

0.0119 N/mm2a,b = bay width in mms = plate thickness, in mm = 6.5

III L3

II L2

I L1

PANEL I : Three edges fixed and one longer edge free

Maxim distance between vertical stiffeners, b = 0.43 mDistance to girder 1, a = 0.216667 m

Ratio, b/a = 1.98

Stress b/a ơ11x ơ11y ơ12x ơ12y ơ13x ơ13yValues of K 1.75 23 14 25.8 87 67.5 20.8Values of K 2 19.49 6.72 33.98 113.28 72.96 21.89Values of K 1.98 19.71 7.18 33.46 111.61 72.61 21.82

Bending Stress, ơ = 2.61 0.95 4.43 14.78 9.61 2.89

So, maximum stress is well below allowable.

PANEL II : All four edges fixed.

Bending Stress, ơ = K/100 X p X a2/s2

p = water pressure (relative to the plate center), in N/mm2 =

Maxim distance between vertical stiffeners, b = 0.430 mDistance between girder 1 & 2, a = 0.433 m

Ratio, b/a = 0.99

Stress b/a ơ2x ơ2y ơ3x ơ3y ơ4x ơ4yValues of K 1 13.7 13.7 40.3 12.09 10.17 33.9Values of K 1.25 18.8 13.5 30.9 9.27 9.27 30.9Values of K 0.99 13.54 13.71 40.77 12.23 10.21 34.03

Bending Stress, ơ = 1.79 1.82 5.4 1.62 1.35 4.51

So, maximum stress is well below allowable.

Design of Horizontal Girders

Loading on Horizontal GirdersGirder 1 Girder 2

Load on the girders: 422.5 Kg/m 422.5 Kg/mDistance between vert seals: 1.30 m 1.30 mDistance between supports: 1.31 m 1.31 mReaction from plate: 274.625 Kg 274.625 KgMaximum Bending Moment: 90.63 Kgm 90.63 KgmRequired section modulus: 9.063 cm3 9.063 cm3

Co-acting width of Skin plate for Horizontal Girders

Girder 1 Girder 2Spacing between horizontal girders, 2B: 0.65 m 0.433 mSpan length, L: 0.43 m 0.43 mL/B = 1.32 1.98Applicable factor, V1: 0.25 0.38Co-acting width, 2VB: 0.16 m 0.16 m

The coacting width is the least of the following value:i) Value calculated as above : 0.16 m 16 cmii) 40 X t: 32.00 cmiii) 0.11 X span(length of girder): 14.41 cm

Hence, co-acting width adopted : 14.41 cm

Selection of Horizontal Girder

W t Area Moment Ax hSkin Plate 14.41 0.65 9.37 0.33 3.04 3.455ISNT 80 8 12.25 90.63 71.2 78.65 2.64

21.62 71.53 81.69

Moment of Inertia of the built up section, Ixx: 268.72 cm4Moment of Inertia of the built up section, Iyy: 194.38 cm4

C G of built up Section: 3.78 cm from top 4.87 cm from bottom

Section modulus at top: 71.09 cm3

Ixx

Section modulus at bottom: 55.18 cm3 > Required section modulus, 9.063

Calculation of stress

Bending Stress, ơy : 16.4 N/mm2

Moment at Girder 1, M1 = 28.82 Kgm

Section modulus of skin plate: 4.58 cm3

Bending Stress, ơx : 62.93 N/mm2

VQ/I = 33.07 N/mm2 < 75 N/mm2

Combined Stress, ơv : 92.42 N/mm2 < 125

Hence OK.

Deflection

Formula for deflection: Deflection = A X B

where, A =

and B =

E = 2000000

q a I A B

Girder 1 4.225 65.5 268.72 0.01 5 0.50Girder 2 422.5 0.655 268.72 0.01 5 0.50

Allowable deflection: 1.64 mm > Actual deflectin Hence OK.

Design of Vertical Stiffeners

Bending moment distribution

Distance from top Due to variable load Total

0 0 00.65 45.77 0 45.771.08 211.90 -183.08 0 28.821.30 366.17 -274.63 -91.54 0

So, maximum B M: 45.77 KgmRequired section modulus: 4.577 cm3

Co-acting width of Skin plate for Vertical Stiffeners

Girder 1 Girder 2Spacing between Vertical Stiffeners, 2B: 0.43 m 0.430 mSpan length, L: 0.22 m 0.433 mL/B = 1.01 2.02Applicable factor, V2: 0.15 0.31

Shear Stress, Ƭxy:

√(ơx2 + ơy

2 -ơxơy + 3Ƭxy2) =

q x a4/(24 x I x E)

12 x b/a - 6 x b2/a2 - 1

2 x 106

Deflection (mm)

Due to R1 Due to R2

Co-acting width, 2VB: 0.06 m 0.13 m

The coacting width is the least of the following value:i) Value calculated as above : 0.06 m 6 cmii) 40 X t: 32.00 cmiii) 0.11 X span(length of girder): 14.3 cm

Hence, co-acting width adopted : 6.00 cm

Selection of Vertical Stiffeners

W t Area Moment Ax hSkin Plate 6.00 0.65 3.90 0.14 1.27 2.255Vertical Stiffeners 0.8 7 5.60 45.77 22.87 23.24 1.57

9.50 23.01 24.51

Moment of Inertia of the built up section, Ixx: 56.64 cm4Moment of Inertia of the built up section, Iyy: 44.00 cm4

C G of built up Section: 2.58 cm from top 5.07 cm from bottom

Section modulus at top: 21.95 cm3Section modulus at bottom: 11.17 cm3 > Required section modulus, 4.577

Hoist capacity

Hoisting force for operation comprises the following

i) Weight of the gateii) Bearing pad frictionii) Side seal friction

Weight of the GateL (m) B/D (m) T (cm) Unit Weight No Weight X (cm)

Skin plate 1.31 1.30 0.65 7800 1 86.34 0.325Horizontal Girder 1.31 9.6 2 25.15 6.42Vert Stiffeners 1.30 0.07 0.8 7800 4 22.71 4.15Top edge Stiffeners 1.31 0.07 0.8 7800 2 11.44 4.15Lifting plates 0.15 0.15 2.0 7800 2 7.02 1.325Side seal clamp plates 1.30 0.045 0.8 7800 2 7.30 1.60Bearing pad support 0.065 0.05 2.5 7800 6 3.80 1.25Bearing pad 0.05 0.04 1.6 7800 6 1.50 0.80Bottom seal support 1.31 0.016 0.8 7800 1 1.31 0.325Bottom seal clamp plate 1.31 0.08 0.8 7800 1 6.54 1.05Support angles 50 x 30 x 5 0.15 3.0 4 1.80 1.39Stem base 0.065 0.063 5.0 7800 1 1.60 3.15Stiffeners 0.05 0.025 0.6 7800 4 0.23 0.95

176.75 KgC G of Gate : 2.11 Cm

i) Structural weight of the gate: @ 195 329.55 Kg

ii) Rubber seal friction:

Ixx

Kg/m2 =

Say, water surcharge of gate: 0.00 cmCalculated Hudrostatic load: 1.0985 MTLength of Seal: 1.30 mWidth subjected to water pressure: 0.05 mWater Load/width: 845 Kg/mTotal Water Load: 42.25

Starting RunningCo-efficient of friction : 1.5 1.2Friction of force: 63.375 Kg 50.7 KgTotal Rubber Seal Friction: 126.75 Kg 101.4 Kg

iii)Bearing pad friction

Pad friction Material Starting Running

Co-eff of friction 0.5 0.3

Load on the pad (Kg) 274.625 137.31 82.39Total pad friction: 549.25 329.55iv) Seal Interference

Force due to interference: 50.00 Kg/mTotal Length: 2.6 mTotal force: 130 Kg

Starting RunningCo-efficient of friction : 1.5 1.2Friction of force: 195 Kg 156 Kg

Lifting force: i + ii + iii 1200.55 Kg

Adding for reserve capacity: 20% 240.11 Kg

Total force: 1440.66 Kg

Selected lifting force: 1.5 Ton

Selection of Stem Size

Designed capacity: 1.5 TonRequired unsupported length: 1.65 mThe safe adequate size of stem: 44 mm diawhose load capacity is 1972.9 Kg and unsupported length is 2.3125 m

Bronze on Steel

Adoption of two girder design makes the system statically determinate, so, the selection of L1 equalling H/6 and L2 = H/3 gives equal loads on the two girder.

ơ14x112

134.4132.96

17.6

A x h2111.8185.38

197.19

cm3

N/mm2

A x h219.8313.8033.63

cm3

WX

28.06161.48

94.2647.49

9.3011.68

4.751.200.436.872.505.030.22

373.27

Adoption of two girder design makes the system statically determinate, so, the selection of L1 equalling H/6 and L2 = H/3 gives equal loads on the two girder.

ơ14y ơ15x34.8 61

40.32 69.8839.97 69.32

5.29 9.18

c162.08

5.77 32.3194.38

Iyy

c0.325 11.70

3.5 32.3044.00

Iyy