محاضرات هندسة الاساسات د. طارق نجيب p3
DESCRIPTION
محاضرات هندسة الاساسات د. طارق نجيب الجزء الثالثTRANSCRIPT
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 1
SHALLOW FOUNDATIONSSHALLOW FOUNDATIONSPART 3PART 3
الضحلة الضحلة األساسات األساسات
الثالث الثالث الجزء الجزء
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 2
DESIGN OF STRAP BEAMDESIGN OF STRAP BEAM الشداد الشداد تصميم تصميم
April 13, 2023 3Shallow Foundations, P3, Tarek Nageeb
FOUNDATION ENGINEERINGFOUNDATION ENGINEERING1- Site Investigation1- Site Investigation2- Design of Shallow Foundations:2- Design of Shallow Foundations:
a- Design of Isolated Footings.a- Design of Isolated Footings.b- Design of Isolated Footings under b- Design of Isolated Footings under
Eccentric Loads.Eccentric Loads.c- Design of Combined Footings.c- Design of Combined Footings.d- Design of Strap Beam.d- Design of Strap Beam.e- Design of Raft Foundationse- Design of Raft Foundations
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 4
Strap Beam
لربطعمود الشداد
الجار
CC22CC11 Strap BeamStrap Beam
جار جار قاعدة قاعدة
محور العمود
محور المسلح
ة
محور العادية
PropertyLine
الملكية حد
Pc2
Strap BeamStrap Beam
Pc1
April 13, 2023 5Shallow Foundations, P3, Tarek Nageeb
DESIGN OF STRAP BEAMDESIGN OF STRAP BEAMالشداد الشداد تصميم تصميم
Strap beam connects neighbor footing (at the Strap beam connects neighbor footing (at the property line) with the adjacent inner footing.property line) with the adjacent inner footing.على ( الجار قاعدة ربط فى الشداد على ( يستخدم الجار قاعدة ربط فى الشداد يستخدم
( داخلى عمود أقرب قاعدة مع الملكية ) حد داخلى عمود أقرب قاعدة مع الملكية حدلها.لها.
Resultant, R = PResultant, R = Pc1c1 + P + Pc2c2
PPtotaltotal = 1.10*(P = 1.10*(Pc1c1 + P + Pc2c2))
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 6c2c1
1c2
11c
P P
L2a
*P 2a
* P y
To determine the resultant (R) point of application from the property line, take moments at point (O)وأحمال المحصلة عزوم أخذ يتم المحصلة مكان لتحديد
نقطة حول الملكية (O)القواعد حد عند
Pc2
Strap BeamStrap Beam
PropertyLine
الملكية حد
Pc1R
L
y
2*y
O
a1
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 7
Dimensions of Plain Concrete Footings:
Assume the thickness of the plain concrete footings, tp.c.
العادية الخرسانة فرضتخانة يتم
Assume the lengths of footings F1 to be (Lp.c.1) and F2 to be (Lp.c.2), such that the resultant would approximately lie at the middle of the outer plain concrete edges.
القاعدتين إفتراضأطوال تكون (F1, F2)يتم بحيثللقاعدتين الخارجية الحدود منتصف فى المحصلة
تقريبا<Determine the reactions under the footings, R1 and R2
الفعل رد قيم تحديد فى (R1 & R2)يتم ومكانهقاعدة منتصفكل
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 8
Dimensions of Plain Concrete Footings:
To determine R1, take moments about Point (2):قيمة نقطة )(R1)لتحديد حول العزوم أخذ (:2يتم
L*10.1*P 2
L
2
aL*R c1
1.c.p11
Pc2
Strap BeamStrap Beam
PropertyLine
الملكية حد
Pc1
O LR1 R2
2
Lp.c.1 Lp.c.2
a1
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 9
Dimensions of Plain Concrete Footings:
2a
LL
L*10.1*P R
11.c.p
c11
soil all
11.c.p q
R A
1.c.p
1.c.p1.c.p L
A B
تزيد أن الحالة هذه فى تزيد يسمح أن الحالة هذه فى ( ( LLp.c.1p.c.1))عن عن ((BBp.c.1p.c.1))يسمح
RR22 = P = Ptotaltotal – R – R11
soil all
22.c.p q
R A
2.c.p
2.c.p2.c.p L
A B
- Assume t- Assume tp.c.p.c. , and x = t , and x = tp.c.p.c.
- Reinforced Concrete Dimensions:- Reinforced Concrete Dimensions:LLR.C.1R.C.1 = L = Lp.c.1p.c.1 – x, – x, BBR.C.1R.C.1 = B = BR.C.1R.C.1 – 2 x – 2 x
LLR.C.2R.C.2 = L = Lp.c.2p.c.2 – 2 x, – 2 x, BBR.C.2R.C.2 = B = BR.C.2R.C.2 – 2 x – 2 x
April 13, 2023 10Shallow Foundations, P3, Tarek Nageeb
Calculation of Ultimate Footing LoadsCalculation of Ultimate Footing Loads
PPuc1uc1 = 1.4 * (P = 1.4 * (Pc1c1+W+Wst.b./2st.b./2)) Dead + 1.6 * P Dead + 1.6 * Pc1c1 Live Live
PPuc2uc2 = 1.4 * (P = 1.4 * (Pc1c1+W+Wst.b./2st.b./2)) Dead + 1.6 * P Dead + 1.6 * Pc2c2 Live Live
Strap beam weight:Strap beam weight:WWst.b.st.b. = b = bst.b.st.b.* t* tst.b.st.b.*L**L*cc
إلى نصفه وإضافة الشداد وزن حساب إلى يتم نصفه وإضافة الشداد وزن حساب يتمعمود لكل الميت عمود الحمل لكل الميت الحمل
2L
2a
L
L*P R
1.C.R1
uc11u
RRu2u2 = P = Puc1 uc1 ++ P Puc2uc2 – R – Ru1u1
1.C.R
u11un L
R /m'f
2.C.R
u22un L
R /m'f
To get RTo get Ru1u1 take take
moments at point 2*moments at point 2*
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 11
Contact Pressure between P.C. and R.C. Footings
Pc1 Pc2
fun1/m' fun2/m'
Pc2
Strap BeamStrap Beam
PropertyLine
الملكية حد
Pc1
L
Ru1 Ru2
LR.c.1LR.c.2
a1
2*
April 13, 2023 12Shallow Foundations, P3, Tarek Nageeb
Shear Force Diagram of the Strap BeamShear Force Diagram of the Strap Beam
Pc1 Pc2
fun1/m' fun2/m'
April 13, 2023 13Shallow Foundations, P3, Tarek Nageeb
Bending Moment Diagram:Bending Moment Diagram:Pc1 Pc2
fun1 fun2
Mmax1
Mmax2
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 14
Design of Strap beam for Flexure
Pc2
Strap BeamStrap Beam
PropertyLine
الملكية حد
Pc1
L
LR.c.1LR.c.2
a1
Mmax2
M1M2
Mmax1
Two sections are designed for Mmax1 and the larger of M1 and M2
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 15
Design of Strap Beam for Shear Pc2
Strap BeamStrap Beam
PropertyLine
الملكية حد
Pc1
L
LR.c.1LR.c.2
a1
Maximum shear took place at the strap beam free span.
Qmax1
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 16
Design of Strap Beam Footings Pc2
Strap BeamStrap Beam
PropertyLine
الملكية حد
Pc1
LLR.c.1
LR.c.2
a1
Critical section for moment at the strap beam faceعلىسطح القواعد فى للعزوم الحرج القطاع
الشدادF1
CC22CC11 Strap BeamStrap BeamF2
d/2Critical Section for Shear
Critical Section for Moment
Critical section for shear at d/2 from the strap beam faceبعد على القواعد للقصفى الحرج سطح d/2القطاع
الشداد
April 13, 2023 17Shallow Foundations, P1, Tarek Nageeb
Longitudinal Reinforcements for the Strap Beamللشداد الطولى التسليح
Strap Beam Reinforcement
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 18
Reinforcement of Strap Beam Footings
F1
CC22CC11 Strap BeamStrap BeamF2
طولى بحديد القواعد تسليح يتمفقط وعرضىسفلى
April 13, 2023 Shallow Foundations, P1, Tarek Nageeb 19
Example (5): Design of Strap BeamExample (5): Design of Strap BeamFrom Dr. Mashour Ghonaim BookFrom Dr. Mashour Ghonaim Book
Design a strap beam to connect the two footings shown in figure knowing that:Allowable soil pressure = 150 kN/m2
Concrete, fcu = 25 N/mm2; Steel, fy = 360 N/mm2
April 13, 2023 20Shallow Foundations, P3, Tarek Nageeb
April 13, 2023 21Shallow Foundations, P3, Tarek Nageeb
DESIGN OF STRAP BEAMDESIGN OF STRAP BEAMResultant, R = PResultant, R = Pc1c1 + P + Pc2c2
PPc1c1 = 380 + 305 = 685.0 kN = 68.50 ton = 380 + 305 = 685.0 kN = 68.50 ton
PPc2c2 = 820 + 450 = 1270.0 kN = 127.00 ton = 820 + 450 = 1270.0 kN = 127.00 ton
R = 68.50 + 127.00 = 195.50 tonR = 68.50 + 127.00 = 195.50 ton
c2c1
1c2
11c
P P
L2a
*P 2a
* P y
m 3.43
127.0 68.50
90.425.0*127.0 0.25 *68.50 y
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 22
Choose the footings such that:Lp.c.2 = 2*[6.85 – (4.90 + 0.25)]
≈ 3.40 m, to be taken 3.35 mLp.c.1 assumed to be taken 2.20 m
Pc2=127 t
Strap BeamStrap Beam
PropertyLine
الملكية حد
Pc1 =68.50 t
O
R
4.90
3.43
2*y ≈ 6.85 m
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 23
Design of Plain Concrete Footings:
To determine R1, take moments about Point (2):قيمة نقطة )(R1)لتحديد حول العزوم أخذ (:2يتم
127.0 t
Strap BeamStrap Beam
PropertyLine
الملكية حد
68.50 t
O 4.90 mR1 R2
2
2.20 m 3.35 m
a1
2
L
2a
L
L*10.1*P R
1.c.p1
c11 ton 91.16
220.2
250.0
90.4
90.4*10.1*50.68 R1
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 24
Design of Plain Concrete Footings:
هذه فى هذه يسمح فى يسمحتزيد أن تزيد الحالة أن الحالة
((BBp.c.1p.c.1)) عن عن((LLp.c.1p.c.1 ) )
RR22 = P = Ptotaltotal – R – R1 1 = 215.05 - 91.16 = 123.89 ton= 215.05 - 91.16 = 123.89 ton
PPtotaltotal = 1.10 *(P= 1.10 *(Pc1c1 + P + Pc2c2) )
= 1.10*(68.50+127.0) = 215.05 ton= 1.10*(68.50+127.0) = 215.05 ton
2
soil all
22.c.p m 8.26
0.15
89.123
q
R A
m 2.60 2.47 35.3
26.8
L
A B
2.c.p
2.c.p2.c.p
2
soil all
11.c.p m 6.08
0.15
16.91
q
R A
m 2.80 2.76 20.2
08.6
L
A B
1.c.p
1.c.p1.c.p
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 25
Design of Reinforced Concrete Footings:
- Assume t- Assume tp.c.p.c. = 40 cm, and x = t = 40 cm, and x = tp.c.p.c. = 40 cm = 40 cm
- Reinforced Concrete Dimensions:- Reinforced Concrete Dimensions:LLR.C.1R.C.1 = L = Lp.c.1p.c.1 – x – x = 2.20 – 0.40 = 1.80 m= 2.20 – 0.40 = 1.80 m
BBR.C.1R.C.1 = B = BR.C.1R.C.1 – 2 x – 2 x = 2.80 – 0.80 = 2.00 m= 2.80 – 0.80 = 2.00 m
LLR.C.2R.C.2 = L = Lp.c.2p.c.2 – 2 x – 2 x = 3.35 – 0.80 = 2.55 m= 3.35 – 0.80 = 2.55 m
BBR.C.2R.C.2 = B = BR.C.2R.C.2 – 2 x – 2 x = 2.60 – 0.80 = 1.80 m= 2.60 – 0.80 = 1.80 m
April 13, 2023 26Shallow Foundations, P3, Tarek Nageeb
Calculation of Ultimate Footing LoadsCalculation of Ultimate Footing Loads
PPuc1uc1 = 1.4 * 41.15 + 1.6 * 30.50 = 106.41 ton = 1.4 * 41.15 + 1.6 * 30.50 = 106.41 ton
Strap beam weight:Strap beam weight:WWst.b.st.b. = b = bst.b.st.b.* t* tst.b.st.b.*L**L*cc = 2.5*0.4*1.3*4.9 = 2.5*0.4*1.3*4.9 6.3 t 6.3 t
PPc1DLc1DL = 38.0 + 6.3/2 = 41.15 ton = 38.0 + 6.3/2 = 41.15 ton
PPc2DLc2DL = 82.0 + 6.3/2 = 85.15 ton = 82.0 + 6.3/2 = 85.15 ton
PPuc2uc2 = 1.4 * 85.15 + 1.6 * 45.0 = 191.21 ton = 1.4 * 85.15 + 1.6 * 45.0 = 191.21 ton
ton 122.67
280.1
25.090.4
90.4*40.106
2L
2a
L
L*P R
1.C.R1
uc11u
April 13, 2023 27Shallow Foundations, P3, Tarek Nageeb
Calculation of Ultimate Contact PressureCalculation of Ultimate Contact Pressure
t/m'68.15 80.1
67.122
L
R /m'f
1.C.R
u11un
t/m' 68.61 55.2
95.174
L
R /m'f
2.C.R
u22un
RRu2u2 = P= Puc1 uc1 ++ P Puc2uc2 – R – Ru1u1
= 106.41 + 191.21 – 122.67 = 174.95 ton = 106.41 + 191.21 – 122.67 = 174.95 ton
April 13, 2023 28Shallow Foundations, P3, Tarek Nageeb
April 13, 2023 29Shallow Foundations, P3, Tarek Nageeb
Design of Strap Section for Maximum Moment:
April 13, 2023 30Shallow Foundations, P3, Tarek Nageeb
d = t – 7 cm = 130.0 – 7.0 = 123.0 cm
Mmax = 56.46 t.m2
scu
u
d*b*f
M R
0.037 123*40*250
10*46.56 R 2
5
Assume the strap beam has the following dimensions:Assume the strap beam has the following dimensions:ttst.b.st.b. = 130 cm = 130 cm bbst.b.st.b. = 40 cm = 40 cm
ddst.b.st.b. = 130.0 – 7.0 = 123.0 cm = 130.0 – 7.0 = 123.0 cm
From the R- chart, R = 0.037, then = 0.045
April 13, 2023 31Shallow Foundations, P3, Tarek Nageeb
d*b*f
f * A s
y
cus
2s mm1537.0 1230 *400*
360
25 *0.045 A
For such large concrete section and to make sure that the failure will not be brittle, the Egyptian Code states that the minimum area of steel will be:
كبيرة أبعاد ذو خرسانى قطاع وجود حالة فىمفاجئ إنهيار حدوث عدم من التأكد فيجب
نسبة زيادة يتم وبذلك الخرسانة، بالضغطفىحدوث من للتأكد المصرى للكود طبقا< الحديد
ممطولى إنهيار
s
y
cu
min s
A 3.1
d bf
f0.225
of smaller A
April 13, 2023 32Shallow Foundations, P3, Tarek Nageeb
steel)grade (high d b 100
0.15
steel) (mild d b 100
0.25
than largerbe houlds A min s
2s
2
y
cu
min s
mm 1998 1537.0 *1.30 A 3.1
mm 15361230*400*360
25225.0d b
f
f0.225
of smaller A
2min s mm 738 1230*400*
100
0.15 d b
100
0.15 A
As = 15.36 cm2, use 816 = 16.08 cm2
April 13, 2023 33Shallow Foundations, P3, Tarek Nageeb
Design of Strap Sec. 2: for M = 233.3 kN.m
From the R- chart, R = 0.0154, then = 0.019
0.0154 123*40*250
10*3.332 R 2
5
2s mm649.0 1230 *400*
360
25 * 0.019 A
2s
2
y
cu
min s
mm844.0 649.0 *1.30 A 3.1
mm 15361230*400*360
25225.0d b
f
f0.225
of smaller A
2min s mm 738 1230*400*
100
0.15 d b
100
0.15 A
As = 8.44 cm2, use 4-18 = 10.18 cm2
Design of Strap Beam for Shear:
April 13, 2023 34Shallow Foundations, P3, Tarek Nageeb
Qu = 16.27 ton
23
uu kg/cm 3.31
123*40
10*27.16
d * b
Q q
22cucu kg/cm9.80 N/mm 0.98
1.5
250.24
1.5
f0.24 q
2
ymin st mm 33.133200*400*
240
0.4 s*b*
f
0.4 A
Use four branches stirrups 58/m'
Ast = 4 * 50 = 200 mm2 > Ast min
Assume that the footing thickness t = 50 cm, and the depth d = 43 cm
For a 1.00 m strip at Sec. (1-1):
April 13, 2023 35Shallow Foundations, P3, Tarek Nageeb
2
R.C.1
u11u t/m 34.08
1.80*2.0
67.122
A
R f
t.m 10.91
8
4.00.2*08.34
8
b -B*f M
2
2strap1.C.Ru1
1
Design of Footings: Design for MomentFooting F1, Exterior (neighbor) Footing
Ru1 = 122.67 ton
fu1 = 34.08 t/m2
2.00
0.800.80 0.40
1
1
R = 0.024, w = 0.0284
As = 8.48 cm2
As = 516/m'
April 13, 2023 36Shallow Foundations, P3, Tarek Nageeb
Design of Footings: Design for MomentFooting F2, Interior Footing
2
R.C.2
u22u t/m 38.12
1.80*2.55
95.174
A
R f
t.m9.34
8
4.080.1*12.38
8
b -B*f M
2
2strap2.C.Ru2
2
fu2 = 38.12 t/m2
1.80
0.700.70 0.40
1
1
For a 1.00 m strip at Sec. (1-1):
Ru2 = 174.95 ton
R = 0.02, w = 0.0235
As = 7.16 cm2
As = 516/m'
April 13, 2023 Shallow Foundations, P3, Tarek Nageeb 37
Design of Footings: Design for Shear
Critical section for shear at d/2 from the strap beam faceبعد على القواعد للقصفى الحرج سطح d/2القطاع
الشداد
CC22CC11 Strap BeamStrap Beam
F2
d/2 = 0.215 m Critical Section for Shear
2.551.80
1.80
F1
2.00
0.58
5
0.48
5
0.700.80
m0.585 2
0.43 -
2
0.40 2.0 -
2
d -
2
b -B x strapR.C.1
2 For Footing F1
For Footing F2m0.485
2
0.43 -
2
0.40 -1.8
2
d -
2
b -B x strapR.C.2
2
Design of Footings: Design for Shear
The shear is safe, then check the shear for the second footing
April 13, 2023 38Shallow Foundations, P3, Tarek Nageeb
Qu1 = fu1*x2*BR.C.1 = 34.08*0.585*1.80 = 35.89 ton
For Footing F1
23
R.C.1
u11u kg/cm4.64
43*180
10*89.35
d * B
Q q
22cucu kg/cm6.50 N/mm0.65
1.5
25 0.16
1.5
f 0.16 q
qu1 (4.64 kg/cm2) < qcu (6.50 kg/cm2) O.K.
Design of Footings: Design for Shear
The shear is safe
April 13, 2023 39Shallow Foundations, P3, Tarek Nageeb
Qu2 = fu2*x2*BR.C.2 = 38.12*0.485*2.55 = 47.14 ton
For Footing F2
23
R.C.2
u2uu kg/cm 4.87
43*225
10*14.47
d * B
Q q
qu1 (4.87 kg/cm2) < qcu (6.50 kg/cm2) O.K.
Reinforcement Details of the Strap Beam
April 13, 2023 40Shallow Foundations, P3, Tarek Nageeb
Reinforcement Details of the Strap Beam
April 13, 2023 41Shallow Foundations, P3, Tarek Nageeb
Reinforcement Details of the Footings
April 13, 2023 42Shallow Foundations, P3, Tarek Nageeb