Design Problem Statement (Ref: Fig. 36.141)

Design 36.39. Design an underground tank of internal dimensions $6 \text{ m} \times 3 \text{ m} \times 3 \text{ m}$. The soil surrounding the tank always remains dry. The tank shall be provided with a roof slab. The soil weighs $16000 \text{ N/m}^3$ having an angle of response of $30^\circ$. Use M 20 concrete and Fe 250 steel.

Internal dimensions: $L = 6 \text{ m}$, $B = 3 \text{ m}$, $H = 3 \text{ m}$

Analysis of Walls

Case 1. When the tank is full. (Ref: Fig. 36.142)

Maximum soil pressure $= \text{Weight of soil} \times H \times \frac{1-\sin \phi}{1+\sin \phi}$

Maximum water pressure $= \gamma_w \times H = 9810 \times 3 \approx 29430 \text{ N/m}^2$

Net max. pressure (producing tension away from water side) $= 29430 - 16000 = 13430 \text{ N/m}^2$

Max. B.M. producing tension near water face (at base, propped cantilever):

Case 2. When the tank is empty. (Ref: Fig. 36.143)

Maximum soil pressure $= 16000 \times 3 = 48000 \text{ N/m}^2$ (Max. at base)

Max. B.M. producing tension near the water side (away from center)

Wall Bending Moments Summary

**Design B.M. for Tension on Water Face:** Max B.M. from both cases $\approx 9600 \text{ Nm}$.

**Design B.M. for Tension Away from Water Face:** Max B.M. from both cases $\approx 4298.5 \text{ Nm}$.

Wall Design

1. Thickness based on Cracking Stress (Serviceability)

Required ultimate resistance $\approx 1.0 \text{ N/mm}^2$
Equating the moment of resistance to maximum bending moment ($\text{B.M.} = 9600 \text{ Nm}$):

Effective cover $= 40 \text{ mm}$
Effective depth $d = D - \text{cover} = 200 - 40 = 160 \text{ mm}$

2. Steel for Bending Moment $9600 \text{ Nm}$ (Tension on Water Face)

Moment of resistance for Fe 250 steel (approx. from text, based on $0.82 \times \text{Total Tension} \times d$):

**From Text (Simplification for $9600 \text{ Nm}$):** $$A_{\text{st}} = \frac{125 \times 0.86 \times 1000}{628 \text{ (from cracking calculation)}} \approx 558 \text{ mm}^2$$

Provide $12 \text{ mm}$ dia. bars at $200 \text{ mm}$ centres ($565 \text{ mm}^2$).

3. Steel for Bending Moment $8004 \text{ Nm}$ (Tension Away from Water Face)

**From Text (Simplification for $8004 \text{ Nm}$):** $$A_{\text{st}} \approx 512 \text{ mm}^2$$

Provide $12 \text{ mm}$ dia. bars at $200 \text{ mm}$ centres ($565 \text{ mm}^2$).

Design of Base Slab

1. Vertical Loads and Net Upward Reaction (Ref: Fig. 36.145)

Loads on $1 \text{ m}$ strip:
Walls: $2 \times 0.2 \times 3 \times 25000 = 30000 \text{ N/m}$
Water pressure on base slab: $6 \times 3 \times 9810 = 176580 \text{ N}$ (or $176.58 \text{ kN}$)
*Simplifying based on text:*
Roof weight: $3750 \text{ N/m}^2 \times 6 \text{ m} \times 3 \text{ m} \approx 67500 \text{ N}$ (or $67.5 \text{ kN}$)
Total load (Walls + Roof) $= 42750 \text{ N}$ (as shown in text summary)

Net Upward Reaction (Soil Pressure):

B.M. at the centre due to the above loading (per metre width): $21375 \text{ Nm}$

2. Bending Moment at Base/Wall Junction (End Section)

B.M. due to soil pressure on wall ($9600 \text{ Nm}$) + B.M. due to water pressure ($7481.25 \text{ Nm}$)
B.M. at End Section $= 7481.25 + 8004 = 15485.25 \text{ Nm}$ (producing tension on water side)

3. Bending Moment at Mid Span (Centre)

B.M. due to vertical loads ($21375 \text{ Nm}$) - B.M. due to soil pressure on wall ($7481.25 \text{ Nm}$)
Net B.M. at Centre $= 21375 - 7481.25 = 13893.75 \text{ Nm}$ (producing tension away from water side)

*Note: The text uses different initial values/cases, leading to slightly different final B.M. values in the table. I'll use the final table values.*

4. Thickness and Reinforcement for Base Slab

**Maximum B.M. = $15485.25 \text{ Nm}$** (At End Section)
From cracking stress calculation: $\text{B.M.}_{\text{max}} = 0.2667 \times 1000 \times D^2 = 15485.25 \times 1000$

Let the effective cover be $60 \text{ mm}$.
Effective depth $d = 250 - 60 = 190 \text{ mm}$.

Steel for Bending Moment of $15485.25 \text{ Nm}$ (End Section, Bottom Steel)

*Based on the text's simplified calculation:*

Spacing of $12 \text{ mm}$ bending bars:

Steel for Bending Moment of $13062.75 \text{ Nm}$ (End Section, Top Steel)

*Based on the text's simplified calculation:*

Spacing of $12 \text{ mm}$ diameter bars:

Design of Roof Slab

Slab thickness $D = 150 \text{ mm}$
Dead load (DL): $3750 \text{ N/m}^2$
Live load (LL): $1500 \text{ N/m}^2$
Total load $w = 5250 \text{ N/m}^2$

Maximum bending moment (for one metre wide strip, short span $3.2 \text{ m}$):

Effective depth $d = 150 - 40 = 110 \text{ mm}$ (Assuming $40 \text{ mm}$ cover)

Required area of steel:

Provide $10 \text{ mm}$ $\phi$ bars at $160 \text{ mm}$ c/c ($\text{Area} \approx 490 \text{ mm}^2$).
Distribution steel $\text{Area} = 0.3\% \times 100 \times 150 = 450 \text{ mm}^2$ (Minimum required)
Spacing of $8 \text{ mm}$ diameter bars:

Cracking Stress Check (Wall and Base)

The cracking stress check is a critical part of water retaining structure design (IS 3370), involving calculation of neutral axis ($n$), modular ratio $(m)$, and coefficient of resistance $C_N$ and $C_t$. This section summarizes the final results as shown in the text.

**Max Tension B.M. on Wall (Tension on Water Face): $9600 \text{ Nm}$**
Calculated $C_t = 1.62 \text{ N/mm}^2$ (less than $1.60 \text{ N/mm}^2$ permissible). **[Error in text or $C_t$ value is wrong. Must be $\leq 1.60 \text{ N/mm}^2$.]**

**Max Tension B.M. on Wall (Tension Away from Water Face): $8004 \text{ Nm}$**
Calculated $C_t = 1.55 \text{ N/mm}^2$ (less than $1.60 \text{ N/mm}^2$ permissible). **[OK]**

**Max Tension B.M. on Base (End Section): $15485.25 \text{ Nm}$**
Calculated $C_t = 1.403 \text{ N/mm}^2$ (less than $1.60 \text{ N/mm}^2$ permissible). **[OK]**

**Max Tension B.M. on Base (Mid Span): $13062.75 \text{ Nm}$**
Calculated $C_t = 1.488 \text{ N/mm}^2$ (less than $1.60 \text{ N/mm}^2$ permissible). **[OK]**