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CE162P (CO2)

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Prepared By
ENGR. YOSHIAKI C. MIKAMI, BSCE RMP
WALL FOOTING
EXAMPLE:
design a wall footing that carries a 250mm thick wall with a
service load of 𝑀𝐷𝐿 = 60 π‘˜π‘ π‘š and 𝑀𝐿𝐿 = 35 π‘˜π‘ π‘š. The bottom of
the footing is 1.1m below the NGL where: 𝑓′𝑐 = 21 π‘€π‘ƒπ‘Ž ,
𝑓𝑦 = 420 π‘€π‘ƒπ‘Ž, π›Ύπ‘ π‘œπ‘–π‘™ = 17 π‘˜π‘ π‘š3, π›Ύπ‘π‘œπ‘›π‘ = 24 π‘˜π‘ π‘š3, π‘žπ‘Žπ‘™π‘™π‘œπ‘€ = 150 π‘˜π‘ π‘š2
Use temp=12mmØ bars and main=12mmØ
a)
b)
c)
d)
e)
f)
Initial thickness
Effective soil bearing pressure
Area of footing
Ultimate soil bearing pressure
Solve for effective depth
Design reinforcement
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
1. Initial thickness
𝑑 = 20% 𝑓𝑑𝑔. π‘‘π‘–π‘šπ‘’π‘›π‘ π‘–π‘œπ‘› + 75π‘šπ‘š
𝑑 = 0.20 ∗ 1π‘š + 0.075π‘š
𝒕 = 𝟎. πŸπŸ•πŸ“π’Ž
2. Effective soil bearing pressure
π‘žπ‘’π‘“π‘“ = π‘žπ‘Žπ‘™π‘™π‘œπ‘€ − Σπ›Ύβ„Ž
π‘žπ‘’π‘“π‘“ = 150 π‘˜π‘
24 π‘˜π‘
𝒒𝒆𝒇𝒇 =
π’ŽπŸ
π‘š2 −
πŸπŸπŸ—. πŸ‘πŸ•πŸ“ π’Œπ‘΅
π‘š3
∗ 0.275π‘š − 17 π‘˜π‘
π‘š3
∗ 0.825π‘š
3. Required area of footing
𝐴𝑓𝑑𝑔 =
π‘’π‘›π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘’π‘‘ π‘™π‘œπ‘Žπ‘‘
π‘žπ‘’π‘“π‘“
=
60π‘˜π‘ π‘š+35π‘˜π‘ π‘š ∗1π‘š
129.375π‘˜π‘/π‘š2
𝐴𝑓𝑑𝑔 = 0.7343π‘š2 = 𝐡𝐿 = 𝐡(1π‘š)
𝐡 = 0.7343π‘š π‘ π‘Žπ‘¦ 𝟎. πŸ–π’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
4. Ultimate bearing stress
π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘’π‘‘ π‘™π‘œπ‘Žπ‘‘
1.2𝐷𝐿+1.6𝐿𝐿
π‘žπ‘’π‘™π‘‘ =
=
𝐴𝑓𝑑𝑔
π‘žπ‘’π‘™π‘‘ =
𝐴𝑓𝑑𝑔
1.2 60π‘˜π‘ π‘š +1.6 35π‘˜π‘ π‘š ∗1π‘š
0.8π‘š∗(1π‘š)
𝒒𝒖𝒍𝒕 = πŸπŸ”πŸŽ π’Œπ‘΅
π’ŽπŸ
5. Footing depth
Beam Shear:
𝑉𝑒𝑙𝑑 = ∅𝑉𝑐
∅𝑉𝑐 = ∅0.17λ 𝑓′𝑐 ∗ 𝑏𝑀 ∗ 𝑑
∅𝑉𝑐 = 0.75 ∗ 0.17(1) 21
𝑁
π‘šπ‘š2
∗ 1000π‘šπ‘š ∗ 𝑑
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
5. Footing depth
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 = 0.160 𝑁
0.160 𝑁
π‘šπ‘š2 ∗ 1000π‘šπ‘š ∗
π‘šπ‘š2 ∗ 1000π‘šπ‘š ∗
0.75 ∗ 0.17(1) 21
𝑁
π‘šπ‘š2
800π‘šπ‘š−250π‘šπ‘š
2
800π‘šπ‘š−250π‘šπ‘š
2
−𝑑
−𝑑 =
∗ 1000π‘šπ‘š ∗ 𝑑
𝐝 = πŸ“πŸ—. πŸπŸπ’Žπ’Ž
Note: as per provision 415.8, minimum d=150mm for footing
on soil
𝒅 = πŸπŸ“πŸŽπ’Žπ’Ž
𝑑 = 150π‘šπ‘š + 75π‘šπ‘š + 0.5 12π‘šπ‘š
𝑑 = 231π‘šπ‘š π‘ π‘Žπ‘¦ πŸπŸ“πŸŽπ’Žπ’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
5. Footing depth
check:
π‘žπ‘’π‘“π‘“ = 150 π‘˜π‘
𝒒𝒆𝒇𝒇 =
𝐴𝑓𝑑𝑔 =
𝐴𝑓𝑑𝑔 =
π‘š2 − 24
πŸπŸπŸ—. πŸ“πŸ“ π’Œπ‘΅ π’ŽπŸ
π‘˜π‘
π‘š3
∗ 0.25π‘š − 17 π‘˜π‘
π‘š3
∗ 0.85π‘š
60π‘˜π‘ π‘š+35π‘˜π‘ π‘š ∗1π‘š
129.55π‘˜π‘/π‘š2
0.7333π‘š2 = 𝐡(1π‘š)
𝐡 = 0.7333π‘š π‘ π‘Žπ‘¦ 𝟎. πŸ–π’Ž
𝑑𝑛𝑒𝑀 = 250π‘šπ‘š − 75π‘šπ‘š − 0.5 π‘šπ‘š
π’…π’π’†π’˜ = πŸπŸ”πŸ—π¦π¦
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
𝑀 = π‘žπ‘’π‘™π‘‘ ∗ 𝐡 = 160 π‘˜π‘
𝑙=
0.8π‘š−0.25π‘š
2
𝑀𝑒𝑙𝑑 =
𝑀𝑙 2
2
=
π‘š2
∗ 1π‘š = 160 π‘˜π‘
π‘š
= 0.275π‘š
160π‘˜π‘ π‘š∗(0.275π‘š)2
2
𝑴𝒖𝒍𝒕 = πŸ”. πŸŽπŸ“π’Œπ‘΅ βˆ™ π’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
𝑀𝑒𝑙𝑑 = ∅𝑀𝑛 = 0.9 𝑓′𝑐 𝑏𝑑 2 πœ” 1 − 0.59πœ”
6.05π‘₯106 𝑁 βˆ™ π‘šπ‘š =
0.9(21 𝑁 π‘šπ‘š2)(1000π‘šπ‘š) 169π‘šπ‘š 2 πœ”(1 − 0.59πœ”)
𝝎 = 𝟎. πŸŽπŸπŸπŸπŸ–
𝜌=
πœ”π‘“′𝑐
𝑓𝑦
=
0.01128(21π‘€π‘ƒπ‘Ž)
420π‘€π‘ƒπ‘Ž
𝝆 = 𝟎. πŸŽπŸŽπŸŽπŸ“πŸ”
𝜌=
𝐴𝑠
;
𝑏𝑑
𝐴𝑠 = πœŒπ‘π‘‘
𝐴𝑠 = 0.00056 1000π‘šπ‘š 169π‘šπ‘š
𝑨𝒔 = πŸ—πŸ“. πŸ‘πŸπ’Žπ’ŽπŸ
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
𝐴𝑠_π‘šπ‘–π‘› = 0.0018𝐴𝑐 = 0.0018𝐡𝑑
𝐴𝑠_π‘šπ‘–π‘› = 0.0018 1000π‘šπ‘š 250π‘šπ‘š
𝑨𝒔_π’Žπ’Šπ’ = πŸ’πŸ“πŸŽπ’Žπ’ŽπŸ > 𝑨𝒔 = 𝟏𝟎𝟏. πŸ’π’Žπ’ŽπŸ
∴ 𝒖𝒔𝒆 𝑨𝒔 = πŸ’πŸ“πŸŽπ’Žπ’ŽπŸ
𝑛 = 𝐴𝑠
πœ‹
(𝑑 )2
4 𝑏
𝑛 = 3.98
= 450π‘šπ‘š
2
πœ‹
(12π‘šπ‘š)2
4
π‘π‘Žπ‘Ÿπ‘ 
π‘š
π‘ π‘π‘Žπ‘π‘–π‘›π‘” =
1000π‘šπ‘š
3.97π‘π‘Žπ‘Ÿπ‘  π‘š
π‘ π‘π‘Žπ‘π‘–π‘›π‘” = 251.3257π‘šπ‘š
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
3 ∗ β„Ž = 3(250π‘šπ‘š)
π‘ π‘šπ‘Žπ‘₯ =
450π‘šπ‘š
π‘ π‘šπ‘Žπ‘₯ = 450π‘šπ‘š
π‘ π‘”π‘œπ‘£π‘› = 251.33π‘šπ‘š π‘ π‘Žπ‘¦ 250π‘šπ‘š
𝐴𝑠_π‘‘π‘’π‘šπ‘ = 0.0018 800π‘šπ‘š 250π‘šπ‘š
𝐴𝑠_π‘‘π‘’π‘šπ‘ = 360π‘šπ‘š2
360π‘šπ‘š2
𝑛=πœ‹
4
(12π‘šπ‘š)2
𝑛 = 3.1831 π‘ π‘Žπ‘¦ πŸ’ − πŸπŸπ’Žπ’ŽØ π’ƒπ’‚π’“π’”
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
EXAMPLE:
design a wall footing that carries a 325mm thick wall with a
service load of 𝑀𝐷𝐿 = 200 π‘˜π‘ π‘š and 𝑀𝐿𝐿 = 180 π‘˜π‘ π‘š and a
moment load 𝑀𝐷𝐿 = 60 π‘˜π‘ π‘š π‘š and 𝑀𝐿𝐿 = 50 π‘˜π‘ π‘š π‘š. The bottom
of the footing is 1.9m below the NGL where: 𝑓′𝑐 = 20.7 π‘€π‘ƒπ‘Ž,
𝑓𝑦 = 345 π‘€π‘ƒπ‘Ž , π›Ύπ‘ π‘œπ‘–π‘™ = 18 π‘˜π‘ π‘š3 , π›Ύπ‘π‘œπ‘›π‘ = 23.5 π‘˜π‘ π‘š3 , π‘žπ‘Žπ‘™π‘™π‘œπ‘€ =
185 π‘˜π‘ π‘š2
Use temp=12mmØ bars and main=20mmØ
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
1. Initial thickness
𝑑 = 20% 𝑓𝑑𝑔. π‘‘π‘–π‘šπ‘’π‘›π‘ π‘–π‘œπ‘› + 75π‘šπ‘š
𝑑 = 0.20 ∗ 1π‘š + 0.075π‘š
𝒕 = 𝟎. πŸπŸ•πŸ“π’Ž
2. Effective soil bearing pressure
π‘žπ‘’π‘“π‘“ = π‘žπ‘Žπ‘™π‘™π‘œπ‘€ − Σπ›Ύβ„Ž
π‘žπ‘’π‘“π‘“ = 185 π‘˜π‘
𝒒𝒆𝒇𝒇 =
π‘š2 − 23.5
πŸπŸ’πŸ—. πŸπŸ— π’Œπ‘΅ π’ŽπŸ
π‘˜π‘
π‘š3
∗ 0.275π‘š − 18 π‘˜π‘
π‘š3
∗ 1.625π‘š
3. Required area of footing
𝑃
6𝑀
π‘žπ‘’π‘“π‘“ = + 2
𝐿𝐡
149.29 π‘˜π‘
𝐿𝐡
π‘š2
=
(200π‘˜π‘ π‘š+180π‘˜π‘ π‘š)(1π‘š)
6(60π‘˜π‘βˆ™π‘š π‘š+50π‘˜π‘βˆ™π‘š π‘š)(1π‘š)
+
1π‘š 𝐡
(1π‘š)𝐡2
B = 3.73π‘š π‘ π‘Žπ‘¦ πŸ‘. πŸ–π’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
4. Ultimate bearing stress
π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘’π‘‘ π‘™π‘œπ‘Žπ‘‘
6(π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘’ π‘šπ‘œπ‘šπ‘’π‘›π‘‘)
π‘žπ‘’π‘™π‘‘ =
+
2
𝐡𝐿
π‘žπ‘’π‘™π‘‘ =
𝐿𝐡
(1.2βˆ™200π‘˜π‘ π‘š+1.6βˆ™180π‘˜π‘ π‘š)(1π‘š)
±
1π‘š (3.8π‘š)
6(1.2βˆ™60π‘˜π‘βˆ™π‘š π‘š+1.6βˆ™50π‘˜π‘βˆ™π‘š π‘š)(1π‘š)
(1π‘š)(3.8π‘š)2
𝒒𝒖𝒍𝒕_π’Žπ’‚π’™ = 𝟐𝟎𝟐. 𝟏𝟏 π’Œπ‘΅
𝒒𝒖𝒍𝒕_π’Žπ’Šπ’ = πŸ•πŸ“. πŸ•πŸ— π’Œπ‘΅
π’ŽπŸ
π’ŽπŸ
5. Footing depth
Beam Shear:
𝑉𝑒𝑙𝑑 = ∅𝑉𝑐
∅𝑉𝑐 = ∅0.17λ 𝑓′𝑐 ∗ 𝑏𝑀 ∗ 𝑑
∅𝑉𝑐 = 0.75 ∗ 0.17(1) 20.7
𝑁
π‘šπ‘š2
∗ 1000π‘šπ‘š ∗ 𝑑
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
5. Footing depth
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
5. Footing depth
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 =
π‘žπ΄ +0.2021𝑁 π‘šπ‘š2
2
∗ 1000π‘šπ‘š ∗
3800π‘šπ‘š−325π‘šπ‘š
2
−𝑑
π‘žπ΄ −0.0758𝑁 π‘šπ‘š2
0.2021𝑁 π‘šπ‘š2−0.0758𝑁 π‘šπ‘š2
=
1737.5π‘šπ‘š+325π‘šπ‘š+𝑑
3800π‘šπ‘š
π‘žπ΄ − 0.0758 𝑁 π‘šπ‘š2 = 3.327π‘₯10−5 𝑁 π‘šπ‘š3 2062.5π‘šπ‘š
π‘žπ΄ = 3.327π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 + 0.144 𝑁 π‘šπ‘š2
+𝑑
3.327π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 +0.144𝑁 π‘šπ‘š2 +0.2021𝑁 π‘šπ‘š2
βˆ™ 1000π‘šπ‘š βˆ™
2
1737.5π‘šπ‘š − 𝑑 = 0.75 ∗ 0.17(1) 20.7 𝑁 π‘šπ‘š2 βˆ™ 1000π‘šπ‘š
βˆ™π‘‘
𝒅 = πŸ’πŸπŸ. πŸ“πŸ– π’Žπ’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
5. Footing depth
check:
𝑑𝑛𝑒𝑀 = 411.58π‘šπ‘š + 75π‘šπ‘š + 0.5 20π‘šπ‘š
𝑑𝑛𝑒𝑀 = 496.58 π‘šπ‘š π‘ π‘Žπ‘¦ πŸ“πŸŽπŸŽ π’Žπ’Ž
𝑑𝑛𝑒𝑀 = 500π‘šπ‘š − 75π‘šπ‘š − 0.5 20π‘šπ‘š
π’…π’π’†π’˜ = πŸ’πŸπŸ“ π’Žπ’Ž
π‘žπ‘’π‘“π‘“ = 185 π‘˜π‘
𝒒𝒆𝒇𝒇 =
π‘š2 − 23.5
πŸπŸ’πŸ–. πŸŽπŸ“ π’Œπ‘΅ π’ŽπŸ
π‘žπ‘’π‘“π‘“ =
𝑃
𝐿𝐡
148.05 π‘˜π‘
+
π‘˜π‘
π‘š3 (0.5π‘š)
− 18 π‘˜π‘
π‘š3 (1.4π‘š)
6𝑀
𝐿𝐡2
π‘š2
=
(200π‘˜π‘ π‘š+180π‘˜π‘ π‘š)(1π‘š)
6(60π‘˜π‘βˆ™π‘š π‘š+50π‘˜π‘βˆ™π‘š π‘š)(1π‘š)
+
1π‘š 𝐡
(1π‘š)𝐡2
B = 3.75π‘š π‘ π‘Žπ‘¦ πŸ‘. πŸ–π’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
π‘žπ΅ −0.0758𝑁 π‘šπ‘š2
0.2021𝑁 π‘šπ‘š2−0.0758𝑁 π‘šπ‘š2
=
1737.5π‘šπ‘š+325π‘šπ‘š
3800π‘šπ‘š
π‘žπ΅ = 0.144 𝑁 π‘šπ‘š2
1737.5 π‘šπ‘š
1000π‘šπ‘š +
π‘šπ‘š2
2
1
2
(0.2021 𝑁 π‘šπ‘š2 − 0.144 𝑁 π‘šπ‘š2)(1737.5π‘šπ‘š)( 1737.5π‘šπ‘š )(1000π‘šπ‘š)
2
3
𝑴𝒖𝒍𝒕 = πŸπŸ•πŸ“. πŸ–πŸ‘π’™πŸπŸŽπŸ” 𝑡 βˆ™ π’Žπ’Ž
𝑀𝑒𝑙𝑑 = 0.144 𝑁
1737.5π‘šπ‘š
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
𝑀𝑒𝑙𝑑 = ∅𝑀𝑛 = 0.9 𝑓′𝑐 𝑏𝑑 2 πœ” 1 − 0.59πœ”
275.83π‘₯106 𝑁 βˆ™ π‘šπ‘š =
0.9(20.7 𝑁 π‘šπ‘š2)(1000π‘šπ‘š) 415π‘šπ‘š 2 πœ”(1 − 0.59πœ”)
𝝎 = 𝟎. πŸŽπŸ—πŸŽπŸ–πŸ’
𝜌=
πœ”π‘“′𝑐
𝑓𝑦
=
0.09084(20.7π‘€π‘ƒπ‘Ž)
345π‘€π‘ƒπ‘Ž
𝝆 = 𝟎. πŸŽπŸŽπŸ“πŸ’πŸ“
𝜌=
𝐴𝑠
;
𝑏𝑑
𝐴𝑠 = πœŒπ‘π‘‘
𝐴𝑠 = 0.00545 1000π‘šπ‘š 415π‘šπ‘š
𝑨𝒔 = πŸπŸπŸ”πŸ. πŸ•πŸ“ π’Žπ’ŽπŸ
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
𝐴𝑠_π‘šπ‘–π‘› = 0.002𝐴𝑐 = 0.002𝐡𝑑
𝐴𝑠_π‘šπ‘–π‘› = 0.002 1000π‘šπ‘š 500π‘šπ‘š
𝑨𝒔_π’Žπ’Šπ’ = πŸπŸŽπŸŽπŸŽπ’Žπ’ŽπŸ > 𝑨𝒔 = πŸπŸπŸ”πŸ. πŸ•πŸ“π’Žπ’ŽπŸ
∴ 𝒖𝒔𝒆 𝑨𝒔 = πŸπŸπŸ”πŸ. πŸ•πŸ“π’Žπ’ŽπŸ
𝑛 = 𝐴𝑠
πœ‹
(𝑑 )2
4 𝑏
𝑛 = 7.2
= 2261.75π‘šπ‘š
2
πœ‹
(20π‘šπ‘š)2
4
π‘π‘Žπ‘Ÿπ‘ 
π‘š
π‘ π‘π‘Žπ‘π‘–π‘›π‘” =
1000π‘šπ‘š
7.2π‘π‘Žπ‘Ÿπ‘  π‘š
π‘ π‘π‘Žπ‘π‘–π‘›π‘” = 138.8π‘šπ‘š
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
WALL FOOTING
SOLUTION:
6. Design reinforcement
3 ∗ β„Ž = 3(475π‘šπ‘š)
π‘ π‘šπ‘Žπ‘₯ =
450π‘šπ‘š
π‘ π‘šπ‘Žπ‘₯ = 450π‘šπ‘š
π‘ π‘”π‘œπ‘£π‘› = 138.8π‘šπ‘š π‘ π‘Žπ‘¦ 125π‘šπ‘š
𝐴𝑠_π‘‘π‘’π‘šπ‘ = 0.002 3800π‘šπ‘š 500π‘šπ‘š
𝐴𝑠_π‘‘π‘’π‘šπ‘ = 3800π‘šπ‘š2
3800π‘šπ‘š2
𝑛=πœ‹
4
(12π‘šπ‘š)2
𝑛 = 33.6 π‘ π‘Žπ‘¦ πŸ‘πŸ’ − πŸπŸπ’Žπ’ŽØ π’ƒπ’‚π’“π’”
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
EXAMPLE:
a rectangular column footing is to support a 450mmx450mm
square tied column that carries a dead load of 950 kN and live
load of 550 kN. The column is reinforced with a 6-20mmØ bars.
The base of the footing is 1.8m below the natural grade line
where the allowable soil pressure is 210 kPa. Using 𝑓′𝑐 =
20.7 π‘€π‘ƒπ‘Ž, 𝑓𝑦 = 420 π‘€π‘ƒπ‘Ž, π›Ύπ‘ π‘œπ‘–π‘™ = 17 π‘˜π‘ π‘š3, π›Ύπ‘π‘œπ‘›π‘ = 23.5 π‘˜π‘ π‘š3
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
1. Initial thickness
𝑑 = 20% 𝑓𝑑𝑔. π‘‘π‘–π‘šπ‘’π‘›π‘ π‘–π‘œπ‘› + 75π‘šπ‘š
𝑑 = 0.20 ∗ 2200π‘šπ‘š + 75π‘šπ‘š
𝒕 = πŸ“πŸπŸ“π’Žπ’Ž
2. Effective soil bearing pressure
π‘žπ‘’π‘“π‘“ = π‘žπ‘Žπ‘™π‘™π‘œπ‘€ − Σπ›Ύβ„Ž
π‘žπ‘’π‘“π‘“ = 210 π‘˜π‘
𝒒𝒆𝒇𝒇 =
π‘š2 − 23.5
πŸπŸ•πŸ”. πŸŽπŸ“ π’Œπ‘΅ π’ŽπŸ
π‘˜π‘
π‘š3 (0.515π‘š)
− 17 π‘˜π‘
π‘š3 (1.285π‘š)
3. Required area of footing
𝑃
6𝑀
π‘žπ‘’π‘“π‘“ = + 2
𝐡𝐿
176.05 π‘˜π‘
𝐡𝐿
π‘š2
=
950π‘˜π‘+550π‘˜π‘
2.2π‘š 𝐿
L = 3.87π‘š π‘ π‘Žπ‘¦ πŸ‘. πŸ—π’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
4. Ultimate bearing stress
π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘’π‘‘ π‘™π‘œπ‘Žπ‘‘
π‘žπ‘’π‘™π‘‘ =
π‘žπ‘’π‘™π‘‘ =
𝐡𝐿
1.2βˆ™950π‘˜π‘+1.6βˆ™550π‘˜π‘
2.2π‘š (3.9π‘š)
𝒒𝒖𝒍𝒕 = πŸπŸ‘πŸ“. πŸ’πŸ‘ π’Œπ‘΅
π’ŽπŸ
5. Footing depth
Beam Shear:
a) along short span (2.2m)
𝑉𝑒𝑙𝑑 = ∅𝑉𝑐
∅𝑉𝑐 = ∅0.17λ 𝑓′𝑐 ∗ 𝑏𝑀 ∗ 𝑑
∅𝑉𝑐 = 0.75 ∗ 0.17(1) 20.7
𝑁
π‘šπ‘š2
∗ 2200π‘šπ‘š ∗ 𝑑
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 = 0.23543 𝑁
0.23543 𝑁
π‘šπ‘š2 ∗ 2200π‘šπ‘š ∗
π‘šπ‘š2 ∗ 2200π‘šπ‘š ∗
0.75 ∗ 0.17(1) 20.7
𝑁
π‘šπ‘š2
3900π‘šπ‘š−450π‘šπ‘š
2
3900π‘šπ‘š−450π‘šπ‘š
2
−𝑑
−𝑑 =
∗ 2200π‘šπ‘š ∗ 𝑑
𝒅𝒔𝒉𝒐𝒓𝒕 𝒔𝒑𝒂𝒏 = πŸ’πŸ—πŸ•. πŸ—πŸ— π’Žπ’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
b) along long span (3.9m)
𝑉𝑒𝑙𝑑 = ∅𝑉𝑐
∅𝑉𝑐 = 0.75 ∗ 0.17(1) 20.7
𝑁
π‘šπ‘š2
∗ 3900π‘šπ‘š ∗ 𝑑
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 = 0.23543 𝑁
0.23543 𝑁
π‘šπ‘š2 ∗ 3900π‘šπ‘š ∗
π‘šπ‘š2 ∗ 3900π‘šπ‘š ∗
0.75 ∗ 0.17(1) 20.7
𝑁
π‘šπ‘š2
2200π‘šπ‘š−450π‘šπ‘š
2
2200π‘šπ‘š−450π‘šπ‘š
2
−𝑑
−𝑑 =
∗ 3900π‘šπ‘š ∗ 𝑑
π’…π’π’π’π’ˆ 𝒔𝒑𝒂𝒏 = πŸπŸ“πŸ. πŸ”πŸŽ π’Žπ’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
Punching Shear:
∅𝑉𝑐 = ∅0.33λ 𝑓′𝑐 ∗ π‘π‘œ ∗ 𝑑
∅𝑉𝑐 = 0.75 ∗ 0.33(1) 20.7
𝑁
π‘šπ‘š2
4 450π‘šπ‘š + 𝑑 (𝑑)
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 = 0.23543 𝑁
0.23543 𝑁
π‘šπ‘š2
π‘šπ‘š2
2200π‘šπ‘š βˆ™ 3900π‘šπ‘š − 450π‘šπ‘š + 𝑑
2200π‘šπ‘š βˆ™ 3900π‘šπ‘š − 450π‘šπ‘š + 𝑑
0.75 ∗ 0.33(1) 20.7
𝑁
π‘šπ‘š2
2
2
=
4 450π‘šπ‘š + 𝑑 (𝑑)
𝒅𝒑𝒖𝒏𝒄𝒉 = πŸ’πŸ“πŸŽ. πŸ•πŸ– π’Žπ’Ž
π‘‘π‘”π‘œπ‘£π‘› = π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š(π‘‘π‘ β„Žπ‘œπ‘Ÿπ‘‘ π‘ π‘π‘Žπ‘› , π‘‘π‘™π‘œπ‘›π‘” π‘ π‘π‘Žπ‘› , π‘‘π‘π‘’π‘›π‘β„Ž )
π‘‘π‘”π‘œπ‘£π‘› = π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š(497.99π‘šπ‘š, 252.60π‘šπ‘š, 450.78π‘šπ‘š)
π’…π’ˆπ’π’—π’ = πŸ’πŸ—πŸ•. πŸ—πŸ—π’Žπ’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
check:
𝑑𝑛𝑒𝑀 = 497.99π‘šπ‘š + 75π‘šπ‘š + 1.5 20π‘šπ‘š
𝑑𝑛𝑒𝑀 = 602.99 π‘šπ‘š π‘ π‘Žπ‘¦ πŸ”πŸπŸ“ π’Žπ’Ž
𝑑𝑛𝑒𝑀 = 625π‘šπ‘š − 75π‘šπ‘š − 1.5 20π‘šπ‘š
π’…π’π’†π’˜ = πŸ“πŸπŸŽ π’Žπ’Ž
π‘žπ‘’π‘“π‘“ = 210 π‘˜π‘
𝒒𝒆𝒇𝒇 =
π‘š2 − 23.5
πŸπŸ•πŸ“. πŸ‘πŸ’ π’Œπ‘΅ π’ŽπŸ
π‘žπ‘’π‘“π‘“ =
𝑃
𝐡𝐿
175.34 π‘˜π‘
π‘š2
=
π‘˜π‘
π‘š3 (0.625π‘š)
− 17 π‘˜π‘
π‘š3 (1.175π‘š)
950π‘˜π‘+550π‘˜π‘
2.2π‘š 𝐿
L = 3.89π‘š π‘ π‘Žπ‘¦ πŸ‘. πŸ—π’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along long span)
𝑀𝑒𝑙𝑑 = 0.23543 𝑁
π‘šπ‘š2
1725π‘šπ‘š
1725π‘šπ‘š
2
2200π‘šπ‘š
𝑴𝒖𝒍𝒕 = πŸ•πŸ•πŸŽ. πŸ”πŸπ’™πŸπŸŽπŸ” 𝑡 βˆ™ π’Žπ’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along long span)
𝑀𝑒𝑙𝑑 = ∅𝑀𝑛 = 0.9 𝑓′𝑐 𝑏𝑑 2 πœ” 1 − 0.59πœ”
770.61π‘₯106 𝑁 βˆ™ π‘šπ‘š =
0.9(20.7 𝑁 π‘šπ‘š2)(2200π‘šπ‘š) 520π‘šπ‘š 2 πœ”(1 − 0.59πœ”)
𝝎 = 𝟎. πŸŽπŸ•πŸπŸ”πŸ“
𝜌=
πœ”π‘“′𝑐
𝑓𝑦
=
0.07265(20.7π‘€π‘ƒπ‘Ž)
420π‘€π‘ƒπ‘Ž
𝝆 = 𝟎. πŸŽπŸŽπŸ‘πŸ“πŸ–
𝜌=
𝐴𝑠
;
𝑏𝑑
𝐴𝑠 = πœŒπ‘π‘‘
𝐴𝑠 = 0.00358 2200π‘šπ‘š 520π‘šπ‘š
𝑨𝒔 = πŸ’πŸŽπŸ—πŸ”. 𝟐𝟏 π’Žπ’ŽπŸ
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along long span)
𝐴𝑠_π‘šπ‘–π‘› = 0.0018𝐴𝑐 = 0.0018𝐡𝑑
𝐴𝑠_π‘šπ‘–π‘› = 0.0018 2200π‘šπ‘š 625π‘šπ‘š
𝑨𝒔_π’Žπ’Šπ’ = πŸπŸ’πŸ•πŸ“π’Žπ’ŽπŸ < 𝑨𝒔 = πŸ’πŸŽπŸ—πŸ”. πŸπŸπ’Žπ’ŽπŸ
∴ 𝒖𝒔𝒆 𝑨𝒔 = πŸ’πŸŽπŸ—πŸ”. 𝟐𝟏 π’Žπ’ŽπŸ
𝑛 = 𝐴𝑠
πœ‹
(𝑑 )2
4 𝑏
= 4096.21π‘šπ‘š
2
πœ‹
(20π‘šπ‘š)2
4
𝑛 = 13.04 π‘ π‘Žπ‘¦ πŸπŸ’ − πŸπŸŽπ’Žπ’ŽØ π’ƒπ’‚π’“π’” π’‚π’π’π’π’ˆ π’π’π’π’ˆ 𝒔𝒑𝒂𝒏
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along short span)
𝑀𝑒𝑙𝑑 = 0.23543 𝑁
π‘šπ‘š2
875π‘šπ‘š
875π‘šπ‘š
2
3900π‘šπ‘š
𝑴𝒖𝒍𝒕 = πŸ‘πŸ“πŸ. πŸ’πŸ—π’™πŸπŸŽπŸ” 𝑡 βˆ™ π’Žπ’Ž
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along short span)
𝑀𝑒𝑙𝑑 = ∅𝑀𝑛 = 0.9 𝑓′𝑐 𝑏𝑑 2 πœ” 1 − 0.59πœ”
351.49π‘₯106 𝑁 βˆ™ π‘šπ‘š =
0.9(20.7 𝑁 π‘šπ‘š2)(3900π‘šπ‘š) 520π‘šπ‘š 2 πœ”(1 − 0.59πœ”)
𝝎 = 𝟎. πŸŽπŸπŸ–πŸŽπŸ–
𝜌=
πœ”π‘“′𝑐
𝑓𝑦
=
0.01808(20.7π‘€π‘ƒπ‘Ž)
420π‘€π‘ƒπ‘Ž
𝝆 = 𝟎. πŸŽπŸŽπŸŽπŸ–πŸ—
𝜌=
𝐴𝑠
;
𝑏𝑑
𝐴𝑠 = πœŒπ‘π‘‘
𝐴𝑠 = 0.00089 3900π‘šπ‘š 520π‘šπ‘š
𝑨𝒔 = πŸπŸ–πŸŽπŸ’. πŸ—πŸ π’Žπ’ŽπŸ
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along short span)
𝐴𝑠_π‘šπ‘–π‘› = 0.0018𝐴𝑐 = 0.0018𝐿𝑑
𝐴𝑠_π‘šπ‘–π‘› = 0.0018 3900π‘šπ‘š 625π‘šπ‘š
𝑨𝒔_π’Žπ’Šπ’ = πŸ’πŸ‘πŸ–πŸ•. πŸ“ π’Žπ’ŽπŸ > 𝑨𝒔 = πŸπŸ–πŸŽπŸ’. πŸ—πŸ π’Žπ’ŽπŸ
∴ 𝒖𝒔𝒆 𝑨𝒔 = πŸ’πŸ‘πŸ–πŸ•. πŸ“π’Žπ’ŽπŸ
𝑛 = 𝐴𝑠
πœ‹
(𝑑 )2
4 𝑏
= 4387.5π‘šπ‘š
2
πœ‹
(20π‘šπ‘š)2
4
𝑛 = 13.97 π‘ π‘Žπ‘¦ πŸπŸ’ − πŸπŸŽπ’Žπ’ŽØ π’ƒπ’‚π’“π’” π’‚π’π’π’π’ˆ 𝒔𝒉𝒐𝒓𝒕 𝒔𝒑𝒂𝒏
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
7. Band Width
π‘π‘π‘Žπ‘Ÿ π‘π‘’π‘›π‘‘π‘Ÿπ‘Žπ‘™ π‘π‘Žπ‘›π‘‘ π‘€π‘–π‘‘π‘‘β„Ž
π‘π‘‡π‘œπ‘‘π‘Žπ‘™
=
2
;
𝛽+1
=
2
1.77+1
𝛽=
𝐿
𝐡
𝛽 = 3.9π‘š
2.2π‘š = 1.77
π‘π‘π‘Žπ‘Ÿ π‘π‘’π‘›π‘‘π‘Ÿπ‘Žπ‘™ π‘π‘Žπ‘›π‘‘ π‘€π‘–π‘‘π‘‘β„Ž
13
𝑁𝑐𝑏𝑀 = 9.39 π‘ π‘Žπ‘¦ 𝟏𝟎 𝒃𝒂𝒓𝒔
𝑁𝑙𝑒𝑓𝑑 = 14 − 10 = 4 π‘π‘Žπ‘Ÿπ‘  (π‘π‘œπ‘‘π‘’: π‘Žπ‘‘π‘‘ 1 π‘“π‘œπ‘Ÿ π‘ π‘¦π‘šπ‘šπ‘’π‘‘π‘Ÿπ‘¦)
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
SOLUTION:
8. Development Length
𝑙𝑑
π‘‘π‘π‘Žπ‘Ÿ
=
9
10
βˆ™
𝑓𝑦
𝑓′𝑐
βˆ™
𝛼𝛽𝛾λ
𝑐+π‘˜π‘‘π‘Ÿ
𝑑𝑏
;
𝑐+π‘˜π‘‘π‘Ÿ
𝑑𝑏
≤ 2.5
20π‘šπ‘š
= 85π‘šπ‘š
2
2200π‘šπ‘š−2 75π‘šπ‘š −20π‘šπ‘š
𝑐2 =
= 145π‘šπ‘š
15−1
9
414π‘€π‘ƒπ‘Ž
1 1 (1)(1)
= 20π‘šπ‘š
βˆ™
βˆ™ 85π‘šπ‘š+0
10
20.7π‘€π‘ƒπ‘Ž
20π‘šπ‘š
𝑐1 = 75π‘šπ‘š +
𝑙𝑑
𝑙𝑑 = 655.16π‘šπ‘š
𝑙𝑑𝑠𝑒𝑝𝑝𝑙𝑖𝑒𝑑 =
2200π‘šπ‘š−450π‘šπ‘š
2
= 875π‘šπ‘š > 𝑙𝑑 ∴ π‘Žπ‘‘π‘’π‘žπ‘’π‘Žπ‘‘π‘’
DON’T PRACTICE UNTIL YOU GET IT RIGHT. PRACTICE
RECTANGULAR FOOTING
EXAMPLE:
design the footing for a rectangular column 400mmx600mm
which is to carry 𝑃𝐷𝐿 = 780 π‘˜π‘, 𝑀𝐷𝐿 = 340 π‘˜π‘ βˆ™ π‘š, 𝑃𝐿𝐿 = 650 π‘˜π‘,
𝑀𝐿𝐿 = 280 π‘˜π‘ βˆ™ π‘š. The footing dimension is limited to 3 m. the
bottom of footing is 1.5m below the NGL with an allowable
bearing capacity of π‘žπ‘Žπ‘™π‘™π‘œπ‘€ = 160 π‘˜π‘ π‘š2. Using 𝑓′𝑐 = 27.5 π‘€π‘ƒπ‘Ž, 𝑓𝑦 =
275 π‘€π‘ƒπ‘Ž, π›Ύπ‘ π‘œπ‘–π‘™ = 16 π‘˜π‘ π‘š3, π›Ύπ‘π‘œπ‘›π‘ = 23.5 π‘˜π‘ π‘š3 , 25mmØ bars
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RECTANGULAR FOOTING
SOLUTION:
1. Initial thickness
𝑑 = 20% 𝑓𝑑𝑔. π‘‘π‘–π‘šπ‘’π‘›π‘ π‘–π‘œπ‘› + 75π‘šπ‘š
𝑑 = 0.20 ∗ 3000π‘šπ‘š + 75π‘šπ‘š
𝒕 = πŸ”πŸ•πŸ“π’Žπ’Ž
2. Effective soil bearing pressure
π‘žπ‘’π‘“π‘“ = π‘žπ‘Žπ‘™π‘™π‘œπ‘€ − Σπ›Ύβ„Ž
π‘žπ‘’π‘“π‘“ = 160 π‘˜π‘
𝒒𝒆𝒇𝒇 =
π‘š2 − 23.5
πŸπŸ‘πŸŽ. πŸ—πŸ’ π’Œπ‘΅ π’ŽπŸ
π‘˜π‘
π‘š3 (0.675π‘š)
− 16 π‘˜π‘
π‘š3 (0.825π‘š)
3. Required area of footing
𝑃
6𝑀
π‘žπ‘’π‘“π‘“ = + 2
𝐡𝐿
130.94 π‘˜π‘
𝐡𝐿
π‘š2
=
780π‘˜π‘+650π‘˜π‘
3π‘š 𝐿
+
6(340π‘˜π‘βˆ™π‘š+280π‘˜π‘βˆ™π‘š)
(3π‘š)𝐿2
L = 5.396π‘š π‘ π‘Žπ‘¦ πŸ“. πŸ’π’Ž
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RECTANGULAR FOOTING
SOLUTION:
4. Ultimate bearing stress
π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘’π‘‘ π‘™π‘œπ‘Žπ‘‘
6(π‘“π‘Žπ‘π‘‘π‘œπ‘Ÿπ‘’ π‘šπ‘œπ‘šπ‘’π‘›π‘‘)
π‘žπ‘’π‘™π‘‘ =
+
2
π‘žπ‘’π‘™π‘‘ =
𝐡𝐿
1.2βˆ™780π‘˜π‘+1.6βˆ™650π‘˜π‘
3π‘š (5.4π‘š)
𝒒𝒖𝒍𝒕_π’Žπ’‚π’™ = πŸπŸ–πŸŽ. πŸ”πŸ— π’Œπ‘΅
𝒒𝒖𝒍𝒕_π’Žπ’Šπ’ = πŸ”πŸ‘. πŸπŸ” π’Œπ‘΅
±
𝐿𝐡
6(1.2βˆ™340π‘˜π‘βˆ™π‘š+1.6βˆ™280π‘˜π‘βˆ™π‘š)
(3π‘š)(5.4π‘š)2
π’ŽπŸ
π’ŽπŸ
5. Footing depth
Beam Shear:
a) along short span (3m)
𝑉𝑒𝑙𝑑 = ∅𝑉𝑐
∅𝑉𝑐 = ∅0.17λ 𝑓′𝑐 ∗ 𝑏𝑀 ∗ 𝑑
∅𝑉𝑐 = 0.75 ∗ 0.17(1) 27.5
𝑁
π‘šπ‘š2
∗ 3000π‘šπ‘š ∗ 𝑑
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 =
π‘žπ΄ +0.18069𝑁 π‘šπ‘š2
2
∗ 3000π‘šπ‘š ∗ 2400π‘šπ‘š − 𝑑
π‘žπ΄ −0.06326𝑁 π‘šπ‘š2
0.18069𝑁 π‘šπ‘š2−0.06326𝑁 π‘šπ‘š2
=
2400π‘šπ‘š+600π‘šπ‘š+𝑑
5400π‘šπ‘š
π‘žπ΄ − 0.06326 𝑁 π‘šπ‘š2 = 2.17π‘₯10−5 𝑁 π‘šπ‘š3 3000π‘šπ‘š
π‘žπ΄ = 2.17π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 + 0.12849 𝑁 π‘šπ‘š2
+𝑑
2.17π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 +0.12849𝑁 π‘šπ‘š2 +0.18069𝑁 π‘šπ‘š2
βˆ™ 3000π‘šπ‘š βˆ™
2
2400π‘šπ‘š − 𝑑 = 0.75 ∗ 0.17(1) 27.5 𝑁 π‘šπ‘š2 βˆ™ 3000π‘šπ‘š
βˆ™π‘‘
𝒅𝒔𝒉𝒐𝒓𝒕 𝒔𝒑𝒂𝒏 = πŸ’πŸ”πŸ. πŸ“πŸ π’Žπ’Ž
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
b) along long span (5.4m)
𝑉𝑒𝑙𝑑 = ∅𝑉𝑐
∅𝑉𝑐 = 0.75 ∗ 0.17(1) 27.5
𝑁
π‘šπ‘š2
∗ 5400π‘šπ‘š ∗ 𝑑
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 =
0.18069𝑁 π‘šπ‘š2+0.06326𝑁 π‘šπ‘š2
2
∗ 5400π‘šπ‘š ∗ 1300π‘šπ‘š − 𝑑
0.18069𝑁 π‘šπ‘š2+0.06326𝑁 π‘šπ‘š2
∗ 5400π‘šπ‘š ∗
2
0.75 ∗ 0.17(1) 27.5 𝑁 π‘šπ‘š2 βˆ™ 5400π‘šπ‘š
1300π‘šπ‘š − 𝑑 =
βˆ™π‘‘
π’…π’π’π’π’ˆ 𝒔𝒑𝒂𝒏 = 𝟐𝟎𝟎. πŸ“πŸ• π’Žπ’Ž
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
Punching Shear:
∅𝑉𝑐 = ∅0.33λ 𝑓′𝑐 ∗ π‘π‘œ ∗ 𝑑
∅𝑉𝑐 = 0.75 ∗ 0.33(1) 27.5 𝑁
2 600π‘šπ‘š + 𝑑 + 400π‘šπ‘š + 𝑑 (𝑑)
π‘šπ‘š2
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
π‘žπ΅ −0.06326𝑁 π‘šπ‘š2
0.18069𝑁 π‘šπ‘š2−0.06326𝑁 π‘šπ‘š2
=
2400π‘šπ‘š−0.5𝑑
5400π‘šπ‘š
π‘žπΆ −0.06326𝑁 π‘šπ‘š2
0.18069𝑁 π‘šπ‘š2−0.06326𝑁 π‘šπ‘š2
2400π‘šπ‘š+600π‘šπ‘š+0.5𝑑
=
5400π‘šπ‘š
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
π‘žπ΅ = 2.17π‘₯10−5 𝑁
π‘žπ΅ =
π‘šπ‘š3 2400π‘šπ‘š − 0.5𝑑 + 0.06326
−1.085π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 + 0.11534 𝑁 π‘šπ‘š2
π‘žπΆ = 2.17π‘₯10−5 𝑁
π‘žπΆ =
π‘šπ‘š3 3000π‘šπ‘š + 0.5𝑑 + 0.06326
1.085π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 + 0.12849 𝑁 π‘šπ‘š2
𝑁
𝑁
π‘šπ‘š2
π‘šπ‘š2
𝑉𝑒𝑙𝑑 = π‘žπ‘’π‘™π‘‘ ∗ 𝐴
𝑉𝑒𝑙𝑑 =
π‘žπ΅ +π‘žπΆ
2
0.18069𝑁 π‘šπ‘š2+0.06326𝑁 π‘šπ‘š2
2
3000π‘šπ‘š βˆ™ 5400π‘šπ‘š −
(600π‘šπ‘š + 𝑑) βˆ™ (400π‘šπ‘š + 𝑑)
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
0.18069𝑁 π‘šπ‘š2+0.06326𝑁 π‘šπ‘š2
2
3000π‘šπ‘š βˆ™ 5400π‘šπ‘š −
−1.085π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 +0.11534𝑁 π‘šπ‘š2 + 1.085π‘₯10−5 𝑁 π‘šπ‘š3 𝑑 +0.12849𝑁 π‘šπ‘š2
2
(600π‘šπ‘š + 𝑑) βˆ™ (400π‘šπ‘š + 𝑑) =
0.75 ∗ 0.33(1) 27.5 𝑁
2 600π‘šπ‘š + 𝑑 + 400π‘šπ‘š + 𝑑 (𝑑)
π‘šπ‘š2
𝒅𝒑𝒖𝒏𝒄𝒉 = πŸ’πŸŽπŸ. πŸ‘πŸ” π’Žπ’Ž
π‘‘π‘”π‘œπ‘£π‘› = π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š(π‘‘π‘ β„Žπ‘œπ‘Ÿπ‘‘ π‘ π‘π‘Žπ‘› , π‘‘π‘™π‘œπ‘›π‘” π‘ π‘π‘Žπ‘› , π‘‘π‘π‘’π‘›π‘β„Ž )
π‘‘π‘”π‘œπ‘£π‘› = π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š(462.51π‘šπ‘š, 200.57π‘šπ‘š, 401.36π‘šπ‘š)
π’…π’ˆπ’π’—π’ = πŸ’πŸ”πŸ. πŸ“πŸ π’Žπ’Ž
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RECTANGULAR FOOTING
SOLUTION:
5. Footing depth
check:
𝑑𝑛𝑒𝑀 = 462.51π‘šπ‘š + 75π‘šπ‘š + 1.5 25π‘šπ‘š
𝑑𝑛𝑒𝑀 = 575.01 π‘šπ‘š π‘ π‘Žπ‘¦ πŸ”πŸŽπŸŽ π’Žπ’Ž
𝑑𝑛𝑒𝑀 = 600π‘šπ‘š − 75π‘šπ‘š − 1.5 25π‘šπ‘š
π’…π’π’†π’˜ = πŸ’πŸ–πŸ•. πŸ“π’Žπ’Ž
π‘žπ‘’π‘“π‘“ = 160 π‘˜π‘
− 23.5 π‘˜π‘
𝒒𝒆𝒇𝒇 =
π’ŽπŸ
π‘š2
πŸπŸ‘πŸ. πŸ“ π’Œπ‘΅
6𝑀
𝐡𝐿2
780π‘˜π‘+650π‘˜π‘
131.5 π‘˜π‘ π‘š2 =
3π‘š 𝐿
π‘žπ‘’π‘“π‘“ =
𝑃
𝐡𝐿
π‘š3 (0.6π‘š)
− 16 π‘˜π‘
π‘š3 (0.9π‘š)
+
+
6(340π‘˜π‘βˆ™π‘š+280π‘˜π‘βˆ™π‘š)
(3π‘š)𝐿2
L = 5.38π‘š π‘ π‘Žπ‘¦ πŸ“. πŸ’π’Ž
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RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along long span)
π‘žπ· −0.06326𝑁 π‘šπ‘š2
0.18069𝑁 π‘šπ‘š2−0.06326𝑁 π‘šπ‘š2
=
2400π‘šπ‘š+600π‘šπ‘š
5400π‘šπ‘š
π‘žπ· = 0.12849 𝑁 π‘šπ‘š2
2400π‘šπ‘š
3000π‘šπ‘š +
π‘šπ‘š2
2
1
2
(0.18069 𝑁 π‘šπ‘š2 − 0.12849 𝑁 π‘šπ‘š2)(2400π‘šπ‘š)( 2400π‘šπ‘š )(3000π‘šπ‘š)
2
3
𝑴𝒖𝒍𝒕 = πŸπŸ’πŸπŸŽ. πŸ–πŸ‘π’™πŸπŸŽπŸ” 𝑡 βˆ™ π’Žπ’Ž
𝑀𝑒𝑙𝑑 = 0.12849 𝑁
2400π‘šπ‘š
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RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along long span)
𝑀𝑒𝑙𝑑 = ∅𝑀𝑛 = 0.9 𝑓′𝑐 𝑏𝑑 2 πœ” 1 − 0.59πœ”
1410.83π‘₯106 𝑁 βˆ™ π‘šπ‘š =
0.9(27.5 𝑁 π‘šπ‘š2)(3000π‘šπ‘š) 487.5π‘šπ‘š 2 πœ”(1 − 0.59πœ”)
𝝎 = 𝟎. πŸŽπŸ–πŸ’πŸπŸ‘
𝜌=
πœ”π‘“′𝑐
𝑓𝑦
=
0.08413(27.5π‘€π‘ƒπ‘Ž)
275π‘€π‘ƒπ‘Ž
𝝆 = 𝟎. πŸŽπŸŽπŸ–πŸ’πŸ
𝜌=
𝐴𝑠
;
𝑏𝑑
𝐴𝑠 = πœŒπ‘π‘‘
𝐴𝑠 = 0.00841 3000π‘šπ‘š 487.5π‘šπ‘š
𝑨𝒔 = πŸπŸπŸπŸ—πŸ—. πŸ”πŸ‘π’Žπ’ŽπŸ
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RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along long span)
𝐴𝑠_π‘šπ‘–π‘› = 0.002𝐴𝑐 = 0.002𝐡𝑑
𝐴𝑠_π‘šπ‘–π‘› = 0.002 3000π‘šπ‘š 600π‘šπ‘š
𝑨𝒔_π’Žπ’Šπ’ = πŸ‘πŸ”πŸŽπŸŽπ’Žπ’ŽπŸ < 𝑨𝒔 = πŸπŸπŸπŸ—πŸ—. πŸ”πŸ‘π’Žπ’ŽπŸ
∴ 𝒖𝒔𝒆 𝑨𝒔 = πŸπŸπŸπŸ—πŸ—. πŸ”πŸ‘π’Žπ’ŽπŸ
𝑛 = 𝐴𝑠
πœ‹
(𝑑 )2
4 𝑏
= 12299.63π‘šπ‘š
2
πœ‹
(25π‘šπ‘š)2
4
𝑛 = 25.06 π‘ π‘Žπ‘¦ πŸπŸ” − πŸπŸ“π’Žπ’ŽØ π’ƒπ’‚π’“π’” π’‚π’π’π’π’ˆ π’π’π’π’ˆ 𝒔𝒑𝒂𝒏
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RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along short span)
𝑀𝑒𝑙𝑑 =
0.06326𝑁 π‘šπ‘š2+0.18069𝑁 π‘šπ‘š2
2
5400π‘šπ‘š 1300π‘šπ‘š
1300π‘šπ‘š
2
𝑴𝒖𝒍𝒕 = πŸ“πŸ“πŸ”. πŸ“πŸ•π’™πŸπŸŽπŸ” 𝑡 βˆ™ π’Žπ’Ž
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RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along short span)
𝑀𝑒𝑙𝑑 = ∅𝑀𝑛 = 0.9 𝑓′𝑐 𝑏𝑑 2 πœ” 1 − 0.59πœ”
556.57π‘₯106 𝑁 βˆ™ π‘šπ‘š =
0.9(27.5 𝑁 π‘šπ‘š2)(5400π‘šπ‘š) 487.5π‘šπ‘š 2 πœ”(1 − 0.59πœ”)
𝝎 = 𝟎. πŸŽπŸπŸ•πŸ•πŸ
𝜌=
πœ”π‘“′𝑐
𝑓𝑦
=
0.01771(27.5π‘€π‘ƒπ‘Ž)
275π‘€π‘ƒπ‘Ž
𝝆 = 𝟎. πŸŽπŸŽπŸπŸ•πŸ•
𝜌=
𝐴𝑠
;
𝑏𝑑
𝐴𝑠 = πœŒπ‘π‘‘
𝐴𝑠 = 0.00177 5400π‘šπ‘š 487.5π‘šπ‘š
𝑨𝒔 = πŸ’πŸ”πŸ“πŸ—. πŸ“πŸ‘ π’Žπ’ŽπŸ
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RECTANGULAR FOOTING
SOLUTION:
6. Design reinforcement (along short span)
𝐴𝑠_π‘šπ‘–π‘› = 0.002𝐴𝑐 = 0.002𝐿𝑑
𝐴𝑠_π‘šπ‘–π‘› = 0.002 5400π‘šπ‘š 600π‘šπ‘š
𝑨𝒔_π’Žπ’Šπ’ = πŸ”πŸ’πŸ–πŸŽπ’Žπ’ŽπŸ > 𝑨𝒔 = πŸ’πŸ”πŸ“πŸ—. πŸ”πŸ‘π’Žπ’ŽπŸ
∴ 𝒖𝒔𝒆 𝑨𝒔 = πŸ”πŸ’πŸ–πŸŽπ’Žπ’ŽπŸ
𝑛 = 𝐴𝑠
πœ‹
(𝑑 )2
4 𝑏
= 6480π‘šπ‘š
2
πœ‹
(25π‘šπ‘š)2
4
𝑛 = 13.2 π‘ π‘Žπ‘¦ πŸπŸ’ − πŸπŸ“π’Žπ’ŽØ π’ƒπ’‚π’“π’” π’‚π’π’π’π’ˆ 𝒔𝒉𝒐𝒓𝒕 𝒔𝒑𝒂𝒏
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RECTANGULAR FOOTING
SOLUTION:
7. Band Width
π‘π‘π‘Žπ‘Ÿ π‘π‘’π‘›π‘‘π‘Ÿπ‘Žπ‘™ π‘π‘Žπ‘›π‘‘ π‘€π‘–π‘‘π‘‘β„Ž
π‘π‘‡π‘œπ‘‘π‘Žπ‘™
=
2
;
𝛽+1
=
2
1.8+1
𝛽=
𝐿
𝐡
𝛽 = 5.4π‘š
3π‘š = 1.8
π‘π‘π‘Žπ‘Ÿ π‘π‘’π‘›π‘‘π‘Ÿπ‘Žπ‘™ π‘π‘Žπ‘›π‘‘ π‘€π‘–π‘‘π‘‘β„Ž
13
𝑁𝑐𝑏𝑀 = 9.29 π‘ π‘Žπ‘¦ 𝟏𝟎 𝒃𝒂𝒓𝒔
𝑁𝑙𝑒𝑓𝑑 = 14 − 10 = 4 π‘π‘Žπ‘Ÿπ‘  (π‘›π‘œπ‘‘π‘’: π‘Žπ‘‘π‘‘ 1 π‘“π‘œπ‘Ÿ π‘ π‘¦π‘šπ‘šπ‘’π‘‘π‘Ÿπ‘¦)
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RECTANGULAR FOOTING
SOLUTION:
8. Development Length
𝑙𝑑
π‘‘π‘π‘Žπ‘Ÿ
=
9
10
βˆ™
𝑓𝑦
𝑓′𝑐
βˆ™
𝛼𝛽𝛾λ
𝑐+π‘˜π‘‘π‘Ÿ
𝑑𝑏
;
𝑐+π‘˜π‘‘π‘Ÿ
𝑑𝑏
≤ 2.5
25π‘šπ‘š
= 87.5π‘šπ‘š
2
3000π‘šπ‘š−2 75π‘šπ‘š −25π‘šπ‘š
𝑐2 =
= 100.89π‘šπ‘š
29−1
9
275π‘€π‘ƒπ‘Ž
1 1 (1)(1)
= 25π‘šπ‘š
βˆ™
βˆ™ 87.5π‘šπ‘š+0
10
27.5π‘€π‘ƒπ‘Ž
25π‘šπ‘š
𝑐1 = 75π‘šπ‘š +
𝑙𝑑
𝑙𝑑 = 471.96π‘šπ‘š
𝑙𝑑𝑠𝑒𝑝𝑝𝑙𝑖𝑒𝑑 =
3000π‘šπ‘š−400π‘šπ‘š
2
= 1300π‘šπ‘š > 𝑙𝑑 ∴ π‘Žπ‘‘π‘’π‘žπ‘’π‘Žπ‘‘π‘’
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