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Using the Ultimate Limit Design Method
byEng.MO. Azima
Structural Engineering Dept.Faculty of Engineering - Azhar University
* Calculation of coefficients* Design of slabs* Design of flat slabs* Check Punching* Design of beams* Design Compression Steel* Design of sections under M,N* Design for torsion* Design of rectangular columns* Design of circular columns* Design of isolated footings* Design of isolated footings under moment* Design of combined footings* Design of strap footings* Design of retaining walls* Deflection of cantilevers* Deflection of simples
Reinforced Concrete Design©
Concrete design according to the Egyptian code 1995.
By: Eng. MO.Azima
* Calculation of Coeffecients
Yc= 1.5 Ys=
check shear
Fy Fcu Ec
2400 kg/cm2 180 kg/cm2 25.49 kg/cm2 187829.7 kg/cm2 24.1 kg/cm2 8.2 kg/cm2
2800 kg/cm2 200 kg/cm2 26.87 kg/cm2 197989.9 kg/cm2 25.4 kg/cm2 8.7 kg/cm2
3600 kg/cm2 250 kg/cm2 30.04 kg/cm2 221359.4 kg/cm2 28.4 kg/cm2 9.7 kg/cm2
4000 kg/cm2 300 kg/cm2 32.91 kg/cm2 242487.1 kg/cm2 31.1 kg/cm2 10.6 kg/cm2
4500 kg/cm2 350 kg/cm2 35.55 kg/cm2 261916.0 kg/cm2 33.6 kg/cm2 11.5 kg/cm2
400 kg/cm2 38.00 kg/cm2 280000.0 kg/cm2 35.9 kg/cm2 12.2 kg/cm2
450 kg/cm2 40.31 kg/cm2 296984.8 kg/cm2 38.1 kg/cm2 13.0 kg/cm2
500 kg/cm2 42.49 kg/cm2 313049.5 kg/cm2 40.2 kg/cm2 13.7 kg/cm2
550 kg/cm2 44.56 kg/cm2 328329.1 kg/cm2 42.1 kg/cm2 14.4 kg/cm2
600 kg/cm2 46.54 kg/cm2 342928.6 kg/cm2 44.0 kg/cm2 15.0 kg/cm2
Hollow Slabs:
AreaWeb breadth Spacing Thick Slab th F.C
b (cm) e (cm) t (cm)1 12 40 32 7 1502 12 40 27 7 1503 12 40 30 5 1504 12 40 32 7 1505 12 40 32 7 150
Slabs:
Fctr= 1.9ÖFcu qumax= 2.2e(Fcu/Yc)
q cu= 0.75Ö(Fcu/Yc)
ts (cm) (kg/m2)
Concrete design according to the Egyptian code 1995.
By: Eng. MO.Azima
AreaLong span Short span Code of practice
Span (m) contin. Span (m) contin. a
1 6 1 2 1 1.350
2 5 1 4 1 0.475
3 5 1 4 1 0.475
4 5 1 4 1 0.475
5 5 1 4 1 0.475
6 5 1 4 1 0.475
7 5 1 4 1 0.475
8 5 1 4 1 0.475
9 5 1 4 1 0.475
10 5 1 4 1 0.475
Beams:
AreaLoad on Long Short Load coeff.
span (m) span (m) shear moment1 0.85 5 4 0.600 0.7872 0.85 5 4 0.600 0.7873 0.85 5 4 0.600 0.7874 0.85 5 4 0.600 0.7875 0.85 5 4 0.600 0.7876 0.85 5 4 0.600 0.7877 0.85 5 4 0.600 0.7878 0.85 5 4 0.600 0.7879 0.85 5 4 0.600 0.787
10 0.85 5 4 0.600 0.787
c1 j
c/d c1 j
0.125 4.854 0.8260.1375 4.64 0.821
0.15 4.455 0.8170.1625 4.291 0.8130.175 4.146 0.808
0.1875 4.016 0.8040.2 3.899 0.8
0.2125 3.793 0.7950.225 3.697 0.791
0.2375 3.608 0.7860.25 3.526 0.782
0.2625 3.451 0.7780.275 3.81 0.773
slab (t/m2)
Concrete design according to the Egyptian code 1995.
By: Eng. MO.Azima
1.15
check tension
2.1 kg/cm2
2.2 kg/cm2
2.5 kg/cm2
2.7 kg/cm2
2.9 kg/cm2
3.1 kg/cm2
3.3 kg/cm2
3.5 kg/cm2
3.6 kg/cm2
3.8 kg/cm2
L.L One way Two way
200 1.237 1.385 25 104200 1.129 1.250 20 104200 1.169 1.318 25 104200 1.237 1.385 25 104200 1.237 1.385 25 104
q tu= 0.19Ö(Fcu/Yc)
(kg/m2) Wu (t/m`) Wu (t/m2)
Concrete design according to the Egyptian code 1995.
By: Eng. MO.Azima
Code of practice Marcus Grashoff
b a b a b
0.039 0.790 0.010 0.988 0.012 3
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
0.224 0.568 0.232 0.709 0.291 1.25
Load distribution for
shear (t/m`) moment (t/m`)1.020 1.337 1.251.020 1.337 1.251.020 1.337 1.251.020 1.337 1.251.020 1.337 1.251.020 1.337 1.251.020 1.337 1.251.020 1.337 1.251.020 1.337 1.251.020 1.337 1.25
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
Check Punching according to ECP
* Project :
fcu= 25 MpaRegular Irregular
العمود Q pu d Type perim. perim act. α1 41 ton 400 mm 400 mm 170 mm Interior 2280 mm 2280 mm 4
2 17 ton 300 mm 300 mm 145 mm Edge(b) 1190 mm 1190 mm 3
300 mm 600 mm 140 mm Interior 2360 mm 2360 mm 4
51 ton 400 mm 400 mm 200 mm Interior 2400 mm 2400 mm 4
20 ton 400 mm 400 mm 220 mm Edge(b) 1640 mm 1640 mm 3
300 mm 700 mm 200 mm Interior 2800 mm 2800 mm 4
300 mm 700 mm 200 mm Interior 2800 mm 2800 mm 4
300 mm 700 mm 200 mm Interior 2800 mm 2800 mm 4
300 mm 800 mm 200 mm Interior 3000 mm 3000 mm 4
300 mm 800 mm 200 mm Interior 3000 mm 3000 mm 4
300 mm 800 mm 200 mm Interior 3000 mm 3000 mm 4
300 mm 900 mm 200 mm Interior 3200 mm 3200 mm 4
300 mm 1000 mm 200 mm Interior 3400 mm 3400 mm 4
InteriorEdge(a)Edge(b) Edge(b) Corner
Corner Edge(a)
Interior
a Smaller B Bigger
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
qp qcp Check
1.22 kg/cm2 1.29 kg/cm2 safe
1.28 kg/cm2 1.29 kg/cm2 safe
0.00 kg/cm2 1.29 kg/cm2 safe
1.22 kg/cm2 1.29 kg/cm2 safe
0.72 kg/cm2 1.29 kg/cm2 safe
0.00 kg/cm2 1.20 kg/cm2 safe
0.00 kg/cm2 1.20 kg/cm2 safe
0.00 kg/cm2 1.20 kg/cm2 safe
0.00 kg/cm2 1.13 kg/cm2 safe
0.00 kg/cm2 1.13 kg/cm2 safe
0.00 kg/cm2 1.13 kg/cm2 safe
0.00 kg/cm2 1.08 kg/cm2 safe
0.00 kg/cm2 1.03 kg/cm2 safe
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
* Design of Beams
* Project :
0.0125
250 9.68
3600 28.4019
2400 0.194 kg/cm2
T sec
Sec.Ult. Moment Breadth Comp.fl. width
C1 Check C1 JAs
Rft.b (cm) B (cm) t (cm)
1 5 12 100 40 7.826 safe 0.826 4.80 1.28 3 f 16
1 10 25 100 40 5.534 safe 0.826 9.61 2.67 5 f 16
1 8 12 100 50 7.955 safe 0.826 5.98 1.65 3 f 16
1 16 25 100 50 5.625 safe 0.826 11.96 3.44 6 f 16
1 7 12 100 60 10.394 safe 0.826 4.28 2.02 3 f 16
1 18 25 100 60 6.482 safe 0.826 11.01 4.20 6 f 16
R sec1 4.7 12 12 40 2.796 safe 0.720 5.18 1.28 3 f 16
1 9.9 25 25 40 2.781 safe 0.717 10.95 2.67 6 f 16
1 7.5 12 12 50 2.846 safe 0.726 6.38 1.65 4 f 16
1 15.5 25 25 50 2.858 safe 0.727 13.15 3.44 7 f 16
1 7 12 12 60 3.601 safe 0.787 4.49 2.02 3 f 16
1 16 25 25 60 3.438 safe 0.778 10.39 4.20 6 f 16
M max = kg/cm2
Concrete Fcu = kg/cm2 qcu = kg/cm2
Steel Fy = kg/cm2 qu max = kg/cm2
Steel Fystr = kg/cm2 R max =
Asmin
Mu (m.t) (cm2) (cm2)
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
Vertical Stirrups Bent Bars
check s n a nb n s11 26.19 safe 8.19 2 13 f 8 45 1 2 2 20
24 27.43 safe 10.01 2 10 f 10 45 1 2 2 20
15 27.78 safe 8.76 2 12 f 8 45 1 2 2 20
31 27.56 safe 9.95 2 11 f 10 45 1 2 2 20
18 27.27 safe 8.96 2 12 f 8 45 1 2 2 20
39 28.36 safe 6.15 2 17 f 8 45 1 2 2 20
11 26.19 safe 9.41 2 11 f 8 45 1 2 2 20
24 27.43 safe 10.01 2 10 f 10 45 1 2 2 20
15 27.78 safe 8.76 2 12 f 8 45 1 2 2 20
31 27.56 safe 9.95 2 11 ff 10 45 1 2 2 20
18 27.27 safe 8.96 2 12 f 8 45 1 2 2 20
39 28.36 safe 6.15 2 17 ff 8 45 1 2 2 20
qu=Qu/(b*d)
qsu=qu - .5*qcu
qsub=qsu - qsus
Qu tonequ Vertical
Stirrups. Rft. /m
sina+cosa or
sina(kg/cm2)
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
Bent Bars
f Rft.
8 8.74 12.61 1.69 1 f 16
8 4.19 18.39 5.14 3 f 16
8 8.74 14.2 2.45 2 f 16
8 4.19 18.52 6.66 4 f 16
8 8.74 13.69 2.89 2 f 16
8 4.19 19.33 8.49 5 f 16
8 8.74 12.61 1.69 1 f 16
8 4.19 18.39 5.14 3 f 16
8 8.74 14.2 2.45 2 f 16
8 4.19 18.52 6.66 4 f 16
8 8.74 13.69 2.89 2 f 16 Axe 3
8 4.19 19.33 8.49 5 f 16
qsus qsub Asb (cm2)(kg/cm2)(kg/cm2)
Axe , ب هـ
Axe , ج د
Axe , ب هـ
Axe , ج د
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
* Design Compression Steel
* Project : Dr F
250 kg/cm2 0.194 kg/cm23600 kg/cm2 0.0125 kg/cm2
secUlt. Load Breadth Width chek
chekmoment moment
Mu (m.ton) B (cm) T (cm)
1 8 12 40 2.143 4.75 3.25
1 16.5 25 40 2.154 9.90 6.60
1 13.4 12 50 2.129 7.86 5.54
1 28.1 25 50 2.122 16.37 11.73
1 20.3 12 60 2.114 11.74 8.56
Concrete Fcu = Rmax =Steel Fy = M max =
c1 Mmax (t.m) ∆m (t.m)
use compressi
on steel
use compressi
on steel
use compressi
on steel
use compressi
on steel
use compressi
on steel
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
Dr F
compressionReinforcement
2 f 163.46safe
4 f 167.03safe
3 f 164.43safe
5 f 169.37safe
3 f 165.47
As/(cm2)
Concrete Design using the ultimate limit design method.
By: Eng. Mo.Azima
* Design of Circular Columns
* Project : Dr Fatma Mahmoud Ali
250 kg/cm2
3600 kg/cm2
Col.Ult. Load desired AC Req Dia Req Diamter As
Reinforcement %m D (cm) D (cm)
0.8 964.46 35 40 10.05 6 f 16
1 103 1 922.77 34 35 9.62 5 f 161.2 884.55 34 35 11.54 6 f 16
0.8 1666.73 46 50 15.70 8 f 16
2 178 1 1594.70 45 50 19.63 10 f 161.2 1528.63 44 45 19.08 10 f 16
0.8 0.00 0 0 0.00 1 f 16
3 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
0.8 0.00 0 0 0.00 1 f 16
4 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
0.8 0.00 0 0 0.00 1 f 16
5 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
0.8 0.00 0 0 0.00 1 f 16
6 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
0.8 0.00 0 0 0.00 1 f 16
7 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
0.8 0.00 0 0 0.00 1 f 16
8 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
0.8 0.00 0 0 0.00 1 f 16
9 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
0.8 0.00 0 0 0.00 1 f 16
10 0 1 0.00 0 0 0.00 1 f 161.2 0.00 0 0 0.00 1 f 16
1 0.00 0 0 0.00 1 f 16
11 0 1.3 0.00 0 0 0.00 1 f 16
Concrete Fcu =
Steel Fy =
Nu (ton) (cm2) (cm2)
Concrete Design using the ultimate limit design method.
By: Eng. Mo.Azima
1.6 0.00 0 0 0.00 1 f 16
Concrete Design Using The Ultimate Limit Design Method.
By: Eng. MO.Azima
250 kg/cm2 NO of Floor = 12
3600 kg/cm2
Col.Ult. Load desired dim of column AC As
Reinforcement2--3
Reinforcement %m b (cm) t (cm) b t
1 2500.65
25100 2500.0 16.25 8 f 16
25 75 101 90 2250.0 22.50 12 f 161.2 85 2125.0 25.50 12 f 16
2 2520.8
2595 2375.0 19.00 16 f 12
25 75 101 90 2250.0 22.50 12 f 161.2 90 2250.0 27.00 14 f 16
3 3350.8
25125 3125.0 25.00 22 f 12
25 100 121 120 3000.0 30.00 14 f 161.2 115 2875.0 34.50 18 f 16
4 3350.8
25125 3125.0 25.00 22 f 12
25 100 121 120 3000.0 30.00 14 f 161.2 115 2875.0 34.50 18 f 16
* Design of Rectangular short Columns
* Project : كامل\ على ياسر م
Fcu =
Fy =
Nu (ton) (cm2) (cm2)
Concrete Design Using The Ultimate Limit Design Method.
By: Eng. MO.Azima
Reinforcement4--5
Reinforcement6--7
Reinforcement8--9
Reinforcementb t b t b t
f 16 25 60 8 f 16 20 55 6 f 16 20 40 4
f 16 25 60 8 f 16 20 60 6 f 16 20 40 4
f 16 25 80 10 f 16 20 75 8 f 16 20 50 4
f 16 25 80 10 f 16 20 75 8 f 16 20 50 4
Concrete Design Using The Ultimate Limit Design Method.
By: Eng. MO.Azima
Reinforcement10--11
Reinforcementb t
f 16 20 20 2 f 16
f 16 20 20 2 f 16
f 16 20 25 2 f 16
f 16 20 25 2 f 16
Concrete design using the ultimate limit design method.
By: Eng. MO Azima
* Design of Isolated footings
* Project :
250 kg/cm2
3600 kg/cm2
1.50 kg/cm2
Column working load column dim. extension
foot b (cm) t (cm) of P.C (cm)
F1 30 30 40 10
Dims. of P.C : B (cm) L (cm) t (cm)
20000 140 150 1021000
Dims. of R.C : B (cm) L (cm) t (cm)
15600 120 130 40
2.89 31
Notes
2.28 safe 6.46
Notes
3.17 safe 12.91
Long Rft. : Mu ton.m/B c1 j
3 3.60 10.10 0.826
Short Rft. : Mu ton.m/L c1 j
3 3.90 10.10 0.826
Calculation of Rft. : (long) As (cm) /m'
2.90 5.25
Calculation of Rft. : (short) As (cm) /m'
2.88 2.90 5.25
Long Rft. : no. f total no.
4.64437 12 /m 6
Fcu =
Fy =
Bearing capacity qall =
Nw (ton)
q bearing :qu(kg/cm2)= Q punch applied (ton)=
Shear stress (kg/cm2) qscu (kg/cm2)
Punching stress (kg/cm2) qpcu (kg/cm2)
Asmin cm2
Asmin cm2
Concrete design using the ultimate limit design method.
By: Eng. MO Azima
Short Rft. : no. f total no.
4.64437 12 /m 7
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
* Design of Combined footings
* Project :
250 kg/cm2 6.45
3600 kg/cm2
1.50 kg/cm2
25cm
Column working load column dim. (cm) extension
Col trans. long. of P.C (cm)
biger 443 45 120 45
small 190 25 90 45
Distance from c.g to c.g: 2.83 m
Resultant of 2 loads is at: 0.85 m from big column
Dims. of P.C : B (cm) L (cm) t (cm)Area req = 42.20 m2 538.61 783.499 50
Area chosen = 26.95 m2 385 700Dims. of R.C : B (cm) L (cm) t (cm)
295 610 100BIG COLUMN
5.28 11.3
Notes
Longitudinal direction: 7.80 safeSMALL COLUMN
Notes 10.05
6.47 unsafe Notes
Top Rft. : 3.06 safec1 j
9.29 0.826 As (cm2) /m'
9.45 13.95no. f total no.
6.942 16 /m 21
Bottom Rft R. :
c1 j As (cm2) /m'
4.20 0.811 47.06 28.42
Fcu = qscu = (kg/cm2)
Fy =
Bearing capacity qall =
Nw (ton)
q bearing :qu(kg/cm2)= qpcu =(kg/cm2)
Punching stress (kg/cm2)
Shear stress (kg/cm2) qpcu =(kg/cm2)
Punching stress (kg/cm2)
Asmin cm2
Asmin cm2
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
no. f total no.
9.591 25 /m 29
Bottom Rft L. :
c1 j As (cm2) /m'
8.65 0.826 10.91 14.18no. f total no.
7.058 16 /m 21
Transverse direction:
Bottom Rft L. : As (cm2) /m'
Mu = (ton.m/L) 293.29894 17.41 22.64c1 j no. f total no.
4.76 0.825 5.958 22 /m 18
Asmin cm2
Asmin cm2
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
90 cm 120 cm
45cm
190 t 2.83 443 t
m
190 t 443 t
total no.
1556.56 kg/cm/340cm
24.90 t 65.99 t
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
total no.
119.75 t 177.45 t
199 cm 327 cm
16 cm 114 cm
total no. 122 77.12 m.t
cm
89.01 m.t 376.88 m.t
total no. MOMENT@ZEROO SHER= -87.2339126
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
* Design of Retaining Walls
* Project :
250
3600
2.00 0.70 ###
2.00 1.14 t/m' force
Cohesion of soil C = 0.00 ###
30 degree ###
0.3
6.6
0
6.6
0
###
###
0.00 0.80 3.50 ###
###
0.60 ###
0.10 ###5.00 ###5.00 ###
######
Factor of safety against sliding = 2.26
Factor of safety against overturning = 3.85
Max. stress on soil = 2.03 Unsafe stress No tension on soil ###
Min. stress on soil = 0.78 Safe stress No tension on soil ###
Calculation of Rft. :###
C1 J ###
For wall 54.30 4.55 0.820 27.45 10.05 8 f 22For Base 9.27 9.03 0.826 5.67 8.25 5 f 16
Concrete Fcu = kg/cm2
Steel Fy = kg/cm2
Bearing capacity qall = kg/cm2
Soil density g = ton/m3
kg/cm2
Angle of friction d =
Coeff. of earth pressure Ka =
kg/cm2
kg/cm2
Mu (m.t) As (cm2) As min
R.C
P.C
Concrete design using the ultimate limit design method.
By: Eng. MO.Azima
األعـمـال م بنـود عـــددوحـدةبياناألبعـاد
عـرضطـول
الحفر 1 ــــــــــ11598.20ااعمال211.601.50701.201.10
2211.601.50701.201.10
1283.600.25السمالت
4813.580.30103.580.25
5سعد سامى ــــــــــــ12046.55سقف
1467.000.25130.440.12
6
ــــــــــ215.50ـــــــــ703.62
ــــــــــ1283.60السمالتاالعمده 910.501.40رقاب
الردم 7 1775.201.80ااعمال
8
أ ــــــــــــ1130.50حج ـــــــــــــ1130.50ح
ـــــــــــــ112.30ـــــــــــــ112.30
9
أ ــــــــــــ2141.30ح
ج ـــــــــــــ2141.30ح
ـــــــــــــ213.30ـــــــــــــ213.30
ــــــــــــ1011948.00
12ط ــــــــــــ12913.30م
13أبواب
4.00ـــــــــــــــ1
3.00ـــــــــــــ12.00ـــــــــــــــ20شبابيك
1833.0 m2
النطرون وادي امات مصنع لكميات "With internal column Prestressed"دراسة
3م اعمالالخرسانةالعادية للقواعد
3م1ق3م2ق
اعمالالخرسانةالمسلحةللقواعد
3م1ق3م2ق
3م اعمالالخرسانةالمسلحةلالعمدة
3م1ع3م2ع
اعمالالخرسانةالمسلحةللسقف
2م3م60*25كمر3م60*12كمر
العزل اعمالللرطوبه
2م1ق2م2ق
2م2م3م
أعمالبلوك المباني
اسمنتى
2م2م
2م1ح2م25ح
أعمالالمحاره
2م
2م
2م1ح2م25ح اعمال
خرسانةاالرضيات
2م
العزل اعمالالفواصل
أعمالاالبواب
2م
2م2م
المنشا = مساحة
م/ 390.1 2جنيه