Example 6 1 Rectangular Water Tank Design

HAWASSA UNIVERSITY IOTECH SCHOOL OF CIVIL AND URBAN ENGINEERING ADVANCED STRUCTURAL DESIGN (CENG 5721) EXAMPLES FOR CHAPTER 6

Example 1 A rectangular R.C water tank with an open top is required to store 80000 liters of water. The inside dimensions of tank may be taken as 6mx4m. Design the side walls of the tank using C-20 concrete and steel of class I. Assume free board of 15cm.

𝐸𝑐𝑚 = 9.5 𝑚=

8 + 𝑓𝑐𝑘

1 3

= 9.5 8 + 16

1/3

= 27.4𝐺𝑝𝑎

𝐸𝑠 200 𝑚 7.3 = = 7.3 , 𝑛 = = = 0.34, 𝜎 100 𝐸𝑐𝑚 27.4 𝑚 + 𝜎 𝑠𝑡 7.3 + 𝑐𝑏𝑐 7

𝑗= 1−

𝑛 = 0.89, 3

𝑄 = 0.5𝜎𝑐𝑏𝑐 𝑛𝑗 = 0.5 ∗ 7 ∗ 0.34 ∗ 0.89 = 1.06

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Example 2 A reinforced concrete water tank resting on ground is 6mx2m with a maximum depth of 2.5m. Using C-20 concrete and Grade I steel design the tank walls. 1. Data Size of tank=6mx2m Depth of tank=2.5m C-20 concrete and steel with Class 1 2. Permissible stresses 𝜎𝑐𝑏𝑐 = 7𝑁/𝑚𝑚2 𝜎𝑠𝑡 = 100𝑁/𝑚𝑚2 𝑜𝑛 𝑓𝑎𝑐𝑒𝑠 𝑛𝑒𝑎𝑟 𝑤𝑎𝑡𝑒𝑟 𝑓𝑎𝑐𝑒 𝜎𝑠𝑡 = 125𝑁/𝑚𝑚2 𝑜𝑛 𝑓𝑎𝑐𝑒𝑠 𝑎𝑤𝑎𝑦 𝑓𝑟𝑜𝑚 𝑤𝑎𝑡𝑒𝑟 𝑓𝑎𝑐𝑒 𝑚=

200 = 7.3 27.4

7.3 = 0.34 𝜎𝑠𝑡 = 100 𝑚+𝜎 7.3 + 𝑐𝑏𝑐 7 𝑛 0.34 𝑗= 1− = 1− = 0.89 3 3 𝑄 = 0.5𝜎𝑐𝑏𝑐 𝑛𝑗 = 0.5 ∗ 7 ∗ 0.34 ∗ 0.89 = 1.06 3. Dimension of tank L=6m; B=2m 𝑛=

𝑚

𝐿 6 = =3>2 𝐵 2 ∴Long walls are Designed as vertical cantilevers and short walls as slabs spanning horizontally between long walls. 4. Design of Long walls 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑏𝑒𝑛𝑑𝑖𝑛𝑔 𝑚𝑜𝑚𝑒𝑛𝑡 𝑎𝑡 𝑏𝑎𝑠𝑒 𝑜𝑓 𝐿𝑜𝑛𝑔 𝑤𝑎𝑙𝑙: 𝑤𝐻 3 10 ∗ 2.53 = = = 26.04𝐾𝑁. 𝑚 6 6 𝑡𝑕𝑒 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑕𝑖𝑐𝑘 𝑛𝑒𝑠𝑠 𝑜𝑓 𝑤𝑎𝑙𝑙 𝑑 𝑠𝑕𝑜𝑢𝑙𝑑 𝑏𝑒 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑑=

𝑀 = 𝑄𝑏

26.04 ∗ 106 = 156.74𝑚𝑚 1.06 ∗ 1000

Using 16mm diameter bars and 25mm effective cover up to center of rebar Over all Depth D=d+ cover = 156.74+25=181.74𝑚𝑚 Take t=D=185mm Effective depth d=185-25= 160mm

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𝑀 26.04 ∗ 106 = = 1828.65𝑚𝑚2 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 𝑤𝑖𝑑𝑡𝑕 𝜎𝑠𝑡 𝑗 𝑑 100 ∗ 0.89 ∗ 160 1000 ∗ 201 𝑠𝑝𝑎𝑐𝑖𝑛𝑔 𝑜𝑓 16 𝑚𝑚 𝑏𝑎𝑟𝑠 𝑆 = = 109.92 ∴

𝐴𝑠𝑡 =

1828.65

Provide 16 mm diameter bars at 100mm c/c spacing. Intensity of pressure at H/4 or 1m whichever is greater H/4 =2.5/4 =0.63 or 1m At h = 1m from base is the largest 𝑃 = 𝑤 𝐻 − 𝑕 = 10 ∗ 2.5 − 1 = 15𝐾𝑁/𝑚2 Direct tension in Long walls 1 15 ∗ 2 𝑇 = 𝑤 𝐻−𝑕 ∗𝐵 = = 15 𝐾𝑁 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 𝑤𝑖𝑑𝑡𝑕 2 2 𝑇 15 ∗ 1000 ∴ 𝐴𝑠𝑡 = = = 150𝑚𝑚2 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 𝑤𝑖𝑑𝑡𝑕 𝜎𝑠𝑡 100 But minimum area Ast min =0.3% Ag 0.3 Ast min = 0.3% Ag = ∗ 185 ∗ 1000 = 555 𝑚𝑚2 100 1000 ∗ 79 spacing of 10mm diameter bars S = = 142.34𝑚𝑚 555 since steel is provided on both faces, provide 10 mm diameter bars at 280 mm c/c on both faces. 5. Design of short walls P = 15 KN/mm2 effective span of horizontal slab B = 2+0.185=2.185 Bending Moment at corner section 𝑃𝐵 2 15 ∗ 2.1852 𝑀= = = 5.97𝐾𝑁𝑚 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 𝑙𝑒𝑛𝑔𝑡𝑕 12 12 𝑇𝑒𝑛𝑠𝑖𝑜𝑛 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑒𝑑 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 𝑕𝑒𝑖𝑔𝑕𝑡 𝑜𝑓 𝑠𝑕𝑜𝑟𝑡 𝑤𝑎𝑙𝑙 = 𝑃 𝐻 − 𝑕 ∗ 1 = 15𝐾𝑁 185 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑜𝑚 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑤𝑎𝑙𝑙 𝑡𝑜 𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡 𝑥 = 160 − = 67.5𝑚𝑚 2 𝑀 − 𝑇𝑥 𝑇 5.89 ∗ 106 − 15 ∗ 67.5 15 ∗ 1000 ∴ 𝐴𝑠𝑡 = + = + = 563.55𝑚𝑚2 > 𝐴𝑠 𝑚𝑖𝑛 𝜎𝑠𝑡 𝑗 𝑑 𝜎𝑠𝑡 100 ∗ 0.89 ∗ 160 100 1000 ∗ 79 𝑆𝑝𝑎𝑐𝑖𝑛𝑔 𝑜𝑓 10𝑚𝑚 𝑏𝑎𝑟𝑠 𝑆 = = 140.18 563.55

Provide 10mm bars at 140 mm c/c. Bending Moment at mid section 𝑃𝐵 2 15 ∗ 2.172 𝑀= = = 2.94𝐾𝑁𝑚 𝑝𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 𝑙𝑒𝑛𝑔𝑡𝑕 24 24 T=15KN ∴ 𝐴𝑠𝑡 =

𝑀 − 𝑇𝑥 𝑇 2.94 ∗ 106 − 15 ∗ 67.5 15 ∗ 1000 𝐴𝑠 𝑚𝑖𝑛 + = + = 285.11𝑚𝑚2 > = 277.5 𝜎𝑠𝑡 𝑗 𝑑 𝜎𝑠𝑡 125 ∗ 0.89 ∗ 160 125 2

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1000 ∗ 79 = 277.09𝑚𝑚 285.11 Hence at mid span provide minimum horizontal reinforcements on inner face and Provide 10mm diameter bars c/c 275mm on outer faces. 6. Design of cantilevering effect of short wall 1 1 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐵. 𝑀 = ∗ 𝑤𝐻𝑕2 = ∗ 10 ∗ 2.5 ∗ 12 = 4.17𝐾𝑁𝑚 6 6 Effective depth using 10mm bars= 185-25-5=155mm 𝑀 4.17 ∗ 106 ∴ 𝐴𝑠𝑡 = = = 302.28𝑚𝑚2 𝜎𝑠𝑡 𝑗 𝑑 100 ∗ 0.89 ∗ 155 1000 ∗ 79 𝑆𝑝𝑎𝑐𝑖𝑛𝑔 𝑜𝑓 10𝑚𝑚 𝑏𝑎𝑟𝑠 S = = 261.35𝑚𝑚 302.28 𝑆𝑝𝑎𝑐𝑖𝑛𝑔 𝑜𝑓 10𝑚𝑚 𝑏𝑎𝑟𝑠 S =

Hence Provide 10mm diameter bars c/c 260mm on inner faces and minimum rebar on the outer faces in the vertical direction.

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Example 6 1 Rectangular Water Tank Design

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