Problem:
Design a circular tank with fixed base for a given capacity in litres.
- Draw cross section of tank showing reinforcement details of dome, tank walls and floor slabs
- Draw plan of tank showing reinforcement details.
Design steps:
- Capacity of circular water tank ( V ) in liters.
- Depth of water ( h ) in m.
- Free board ( f ) in mm.
- Strength of concrete (ex : M20, M35)
- Strength of steek in (ex : Fe415, Fe-500)
IS: 3370 (Part II) Table 1, Clause 3.3.1 and IS: 456-2000, Clause B-2.1.1 and Table 21.
- Unit weight of water , γ = 9.8 kN/m3.
- Permissible tensile stress in concrete , σct
- Permissible stress in concrete , σcbc.
- Permissible tensile stress in steel , σst.
D = Diameter of water tank. This can be found out using following equation.
\[V = \frac{{\pi \times {D^2}}}{4} \times h\]
Diameter of water tank is found out using below equation.
\[D = \sqrt {\frac{{V \times 4}}{{\pi \times h}}}\]
Choose required diameter of water tank.
Total height tank = depth of the tank + Free board
H = h + f
Calculate modular ratio.
\[m = \frac{{280}}{{3 \times {\sigma _{cbc}}}}\]
Neutral axis depth factor.
\[n = \frac{{m \times {\sigma _{cbc}}}}{{m \times {\sigma _{cbc}} + \times {\sigma _{st}}}}\]
Lever arm.
\[j = 1 - \frac{n}{3}\]
Moment of resistance.
\[k = \frac{1}{2} \times {\sigma _{cbc}} \times j \times n\]
Cantilever action steel is provided in vertical direction.
Height of cantilever action above the base slab.
\[{h_{cantilever}} = \frac{H}{3}\]
Calculate cantilever moment.
\[{M_{cantilever}} = \frac{1}{2} \times \gamma \times H \times h \times \frac{h}{3}\]
Calculate balanced depth.
\[{d_{balance}} = \sqrt {\frac{M}{{k \times b}}}\]
Keep section sufficiently under reinforced.
\[{d_{sufficient}} = \frac{4}{3} \times {d_{balance}}\]
Provide minimum thickness of 150mm to avoid leakage.
Consider D = d + effective cover.
calculate area of steel
\[{A_{st}} = \frac{M}{{{\sigma _{st}} \times j \times d}}\]
Consider the bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{As{t_{required}}}} \times 1000\]
Provide diameter of bar at distance C/C.
Hoop reinforcement is provided in horizontal direction.
Maximum hoop tension is given by.
\[T = \gamma \times \left( {H - h} \right) \times \frac{D}{2}\]
Calculate area of steel for hoop stress.
\[{A_{sh}} = \left( {\frac{{T \times 1000}}{{{\sigma _{st}}}}} \right)\]
Consider the bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{As{t_{required}}}} \times 1000\]
Provide diameter of bar at distance C/C.
\[{A_{sh}}provided = \left( {\frac{{{A_{provided}} \times 1000}}{{{S_V}}}} \right)\]
Increase the spacing from h/3 to top of the tank.
Check for permissible tensile stress in concrete is within limits.
\[{\sigma _{ct}} = \frac{{T \times 1000}}{{1000 \times t + \left( {m - 1} \right) \times {A_{sh}}provided}}\]
Only minimum reinforcement is required.
\[{A_{st}} = 0.3\% \times {t_{wall}} \times 1000\]
Consider the bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{As{t_{required}}}} \times 1000\]
Provide diameter of bar at distance C/C.
The base slab is laid on 75mm thick lean conrete mix. Provide thickness of 150 mm or more to avoid leakage of water.
Provide minimum nominal reinforcement in both direction.
\[{A_{st}} = 0.3\% \times {t_{base}} \times 1000\]
Consider the bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{As{t_{required}}}} \times 1000\]
Provide diameter of bar at distance C/C.
Reinforcement details of sectional elevation and plan are shoen below.
Indian standard code IS 3370-Part ( 2 ).
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