WR401 01 Design of Syphon

 Hydraulic Structures  –  Structural Design of Syphon

Design of Syphon Barrels Design barrels of the canal syphon as reinforced concrete box. The data is given below: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Number of barrels Size of barrel Bank level Drain H.F.L Uplift at base of barrel Unit weight of dry earth Unit weight of saturated earth Weight of submerged earth Angle of internal friction in all conditions

=2 =3 m ×2.5 m =254 m =253.25 m 2 =4.5 t/m 3 =1.6 t/m 3 =2.0 t/m =1.0 t/m3 =30º

Design Assume the thickness of the frame 30 cm all through so that the effective length of horizontal and vertical members are 3.3 m and 2.8 m.

1

 Hydraulic Structures  –  Structural Design of Syphon

1. Distribution factors

At joint A  A B For  AB



For A B ,

2.8 2.8  3.3

For A D ,

 0.46

Therefore, distribution factors:

 A D For  AD



3.3 2.8 2.8  3.3

 0.54

For

At joint D For  D A=0.54  D C =0.46 =0.46

2. Dead loads

Consider one meter of barrel: Depth of dry earth over barrel Depth of saturated earth Weight of dry and saturated earth

 254 254  253.2 53.25 5  0.7 0.75 m

Weight of top slab (0.3 m thick)

 0.3  2.4  0.72t

 253. 253.25 25  251. 251.4 4  1.85 1.85 m

1.6  1.85  2   0.75 1.6

Weight on the top slab including its own weight

4.9t m 2

m2

= 4.9  0.72  5.62t m 2

Weight of barrels per meter of length



Total dead load/   m of length of barrels

 15.6  4.9  6.9  49.4 t

Uplift per one meter length

6.9  31.05 .05t  4.5 6.9

Net vertical load acting on foundation

49.4  31.0 31.05 5  18.3 18.35 5t  49.4

Pressure on foundation soil (Soil reaction)



 4  3.3  3 2.8  0.3 2.4  15.6t

18.35



m

m m

2.66 t m 2

6.9 =Soil reaction 2  2.66  4.5  7.16 t m

Pressure acting on the base slab + uplift Net upward pressure on the base slab

 7.16 .16  0.7 0.72  6.44 6.44t

Say 6.5t m 2

2

m

2

m

 Hydraulic Structures  –  Structural Design of Syphon

3. Earth pressure

The earth pressure shall comprise of the t he following: a. Dry earth pressure above saturation line (from  R.L. 253.25 m to R.L. 254.00 m) b. Saturated earth pressure (from R.L. 253.25 m to R.L. 248.45 m). Corresponding to    30 , c p



1  sin   1  sin  



1 3

Pressure at A = Surcharge due to dry earth+ surcharge due to saturated earth

 254  253.25  c

 c p  

Pressure at D

1 3

1.6  0. 0.75 

 3.07  c p  s  3.07 

1 3

1 3

p 

s253.25  251.25    253.25  251.25

1.0  2  1  2  3.07 t

m

2

 251.25  248.45    251.25  248.45

1 2.8  1 2.8  6.8t

2

m

4. Fixing moments 2

a. On span b. On span CD

w AB 12 



5.62 5.62  3.3 3.32

6.5 6.5  3.3 3.32 12

 5.1 

12

t m

 5.9 t  m

c. On span AD 2

M

 AD

3.07  2.8 12

2



2

M

 DA

3.07  2.8 12

3.73  2.8 2.8 30

 2.985 

t m

 3.475 

t m

2



3.73  2.8

3

20

 Hydraulic Structures  –  Structural Design of Syphon

Joint Member D. factor F.E.M. Balance C.O. Balance C.O. Balance C.O. Balance

C CD -5.9

D DC 0.46 +5.9 -1.115

DA 0.54 -3.475 -1.31 +0.57 -0.3078 +0.177 -0.096 +0.042 -0.023 -4.423

-0.5575 -0.2622 -0.1311 -0.081 -0.041 -6.630

A

-0.019 +4.423 +4.42 3

AD 0.54 +2.985 +1.142 -0.655 +0.3537 -0.1539 +0.083 -0.048 +0.026 +3.733

AB 0.46 -5.1 +0.973

B BA +5.1 +0.485

+0.3013 +0.151 +0.0708 +0.035 +0.022 -3.733

+5.771

5. Design moments a. Span AB Net moments at center and face of span  AB

Sagging moment at face 

5.62  3.3 2 3.15

 0.15 

5.62  0.152 2

 1.33t  m

 5.771  3.73  5.68t  m 3.3 .68 1.33 1.33  4.35 .35 t  m Net fixing moments at face  5.68

Fixing moment at face  3.73 

Sagging moment at center 

5.62 5.62  3.3 3.32

8 3.73 3.73  5.77 5.771 1

 7.65t  m

 4.75t  m 2 .75  2.9t  m Net sagging moment at center  7.65  4.75

Fixing moment at center 

b. Span CD Sagging moment at face 

6.5  3.3 2

2

 0.15 

3.15

6.5  0.15 2

 1.54 t  m

 6.63  4.423  6.529 t  m 3.3 .529 1.54 1.54  4.98 4.98t  m Net fixing moment at face  6.529

Fixing moment at face  4.423 

4

 Hydraulic Structures  –  Structural Design of Syphon

6.5 6.5  3.3 3.32

Sagging moment at center  Fixing moment at center 

 8.85t  m

8 6.63 6.63  4.42 4.423 3

 5.53t  m 2 Net sagging moments at center  8.85 .85  5.53 5.53  3.32 .32 t  m

c. Span AD Sagging moment at face: i. Due to rectangular portion 3.07  0.15

2

 0.15  2 2 Due to triangular portion 

ii.

3.07  2.8

2.8  R D



 R D



3.73  2.8 2 3.73 3.73 2.8 2.8



2 3

 0.61t  m

 2.8

3 Sagging moment

3.73  2.8

3.53  0.152

 0.15   0.483t  m 3 2 0.61 0.48 0.483 3  1.09 1.09t  m Total sagging moments  0.61 

2.65

 4.423  3.73  4.39t  m 2.8 .39  1.09 .09  3.3t  m Net fixing moment at face  4.39

Fixing moment at face  3.73 

Sagging moment at center i. ii.

Due to rectangular portion 

3.07 3.07  2.8 2.82 8

 3.01t  m

Due to triangular portion 2.8  R A



 R A



3.7 3.73  2.8 2.8 2 3.73 3.73 2.8 2.8 6 3.73  2.8



3

2.8

1.865  1.4 1.4

  1.83 6 2 2 3 3.01 1.8 1.83  4.84 .84 t  m Total Sagging moment at center center  3.01  C M





4.42 4.423 3  3.73 3.73

 4.08t  m 2 Net sagging moment at center  4.84 .84  4.08 4.08  0.76 .76 t  m

Fixing moment at center 

5



t m

 Hydraulic Structures  –  Structural Design of Syphon

Span Fixing moment (-ve) at face ( t.m) Sagging moment (+ve) at center ( t.m) AB 4.35 2.9 16 mm bars@ 12.5cm c/c (up) 12 mm bars@ 10 cm c/c (down) CD 4.98 3.32 16 mm bars@ 11.25 cm c/c 16 mm bars@ 16.25 cm c/c AD 3.3 0.76 16 mm bars@ 16.25 cm c/c 12 mm bars@ 25 cm c/c

6. Thickness of members Maximum moment in the barrels=4.98 t.m The minimum effective thickness ( d ) required for bending moment is d  



 M  bQ

4.98 4.981000 1000 100 100 100 100  9.18 9.18



23.29cm

Adopt 27.5 cm effective depth and 30 cm overall thickness for all members. 7. Reinforcement a. Span AB and BE  At face (hogging moment, -ve steel) 

4.35 4.35 1000 1000 100 100 2 A cm  15.38 6 1200   27.5 7 Provide 16 mm bars @ 12.5 cm c/c (up) At center (sagging moment, +ve steel) t 





2.9 2.9 1000 1000 100 100 2 A cm  10.25 6 1200   27.5 7 Provide 12 mm bars @ 10 cm c/c (down) t 



b. Span CD and CF  At face 4.98 4.981000 1000 100 100 2   17.6 A cm t  6 1200   27.5 7 Provide 16 mm bars @ 11.25 cm c/c At center 3.32 3.32 1000 1000 100 100 2 A cm   11.74 t  6 1200   27.5 7 Provide 16 mm bars @ 16.25 cm c/c 



c. Span AD and EF  6

 Hydraulic Structures  –  Structural Design of Syphon





At face 3.3 3.3 1000 1000 100 100 2 A cm  11.7 t   6 1200   27.5 7 Provide 16 mm bars @ 16.25 cm c/c At center 0.76 0.764 4 1000 1000 100 100 2  2.70 A cm t   6 1200   27.5 7 Provide 12 mm bars @ 25 cm c/c Table: Cross-sectional area for steel bars of different diameters Diameter   (mm) Cross-sectional area 12 14 16 18

1.13 1.54 2.01 2.54

7

s

A 

 2 4





c2m