Page 1
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 1/19
UNITS: SI
SI 1 E = 200000 Mpa 5 m 5 m
English f'c = 20.7 Mpa
fy = 275 Mpa
Section A-A:
hf
(Panel 1) (Panel 2) 3.5 m
350 mm
clear L = 4.75 m 250 mm
Section B-B: (Panel 3) (Panel 4) 3.5 m
hf
350 mm
Ecb = 35 Mpa
clear L = 3.25 m 250 mm Ecs = 35 Mpa
bar Ø = 16 mm
Estimate I factor: (factor x Ig) Optional Values: concrete cover = 20 mm
Interior Beams: 2 Assume hf = 150 mm wDL = 3 kpa
Exterior Beams: 1.5 wu = kpa wLL = 2 kpa
Design of Slab with Beams (Direct Design Method)<Program Created by: Engr. Jeremy E. Caballes>
A A
B
B
Page 2
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 2/19
Long clear span = 4.750 m
Short clear span = 3.250 m
Assume slab thickness, hf:
Use: Ln = 4.750 m
ß = 1.462
Min. h = 96.708 mm 100 Max. h = 132.043 mm
Use hf = 150.000 mm
Effective flange projection:
(a) 5-m span (b ) 3.5-m span
h - hf = 200.000 mm h - hf = 200.000 mm
4hf = 600.000 mm 4hf = 600.000 mm
Use: 200.000 mm Use: 200.000 mm
Estimate moment of inertia of T-beams and slabs:
(a) 5-m span (b ) 3.5-m span
Interior Ib = 2 x Ig Interior Ib = 2 x Ig
= 1786458333 mm^4 = 1786458333 mm^4
Interior Is = bh³/12, slab width: b = 3500 mm 3500 Interior Is = bh³/12, slab width: b = 5000 mm
= 984375000 mm^4 = 1406250000 mm^4
Exterior Ib = 1.5 x Ig Exterior Ib = 1.5 x Ig
= 1339843750 mm^4 = 1339843750 mm^4
Exterior Is = bh³/12, slab width: b = 1875 mm 1875 Exterior Is = bh³/12, slab width: b = 2625 mm= 527343750 mm^4 = 738281250 mm^4
Calculate average α, αm:
Ecb x Ib
Ecs x Is
(a) 5-m span (b ) 3.5-m span
35(1786458333.333) 35(1786458333.333)
35(984375000) 35(1406250000)
= 1.815 = 1.270
35(1339843750) 35(1339843750)
35(527343750) 35(738281250)
= 2.541 = 1.815
Total perimeter = 2(5+3.5)
= 17 m
Panel 1, αm = (1.815+1.815+1.27+1.815)/4 Panel 2, αm = (1.815+2.541+1.27+1.815)/4
= 1.679 = 1.860
ßs = [5+2(3 5)]/17 ßs = [5+3 5]/17
Max. h =Ln(800+0.73fy)
36,000
36,000+9,000ß
Ln(800+0.73fy)
Min. h =Ln(800+0.73fy)
36,000+9,000ß
Interior α =
Exterior α =
Interior α =
ß =Long clear span
Short clear span
α = h =ßs =Length of continuous edges
Total Perimeter
Exterior α =
Page 3
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 3/19
Moment for 5-m span: (both end continuous)
hf = 150.000 mm
350 mm
wu = 1.4wDL + 1.7wLL
wu = 7.600 kpa Ln = 4.750 m 250 mm
(a) In terior (b ) Exter io r
L2 = 3.500 m L2 = 1.875 m
wuL2 = 26.600 kn/m wuL2 = 14.250 kn/m
(wuL2)(Ln)² (wuL2)(Ln)²
8 8
Mo = 75.020 kN-m Mo = 40.189 kN-m(-) M = 0.65Mo = -48.763 kN-m (-) M = 0.65Mo = -26.123 kN-m
(+) M = 0.35Mo = 26.257 kN-m (+) M = 0.35Mo = 14.066 kN-m
L2/L1 = 3.5/5 L2/L1 = 3.5/5
= 0.700 = 0.700
α1 = 1.815 α1 = 2.541
α1L2/L1 = 1.271 FALSE 1.271 α1L2/L1 = 1.779 FALSE 1.7
Column strip: Interior (-) M Column strip: Interior (-) M
0.5 0.5 0.5 0.5 0.5 0.5
L2/L1 0.5 1.0 2.0 L2/L1 0.5 1.0
75 α1L2/L1=0 75 75 75 75 75 α1L2/L1=0 75 75
90 α1L2/L1≥1 90 75 45 75 90 α1L2/L1≥1 90 75
1.0 1.0 1.0 1.0 1.0 1.0
0.5 0.700 1.0 0.5 0.700
90.0 x 75.0 90.0 x
x = 84.000 % x = 84.000 %
(-) M = 84%(-48.763) (-) M = 84%(-26.123)
= -40.961 kN-m = -21.943 kN-m
85%(-)M = -34.817 kN-m (Beam) 85%(-)M = -18.652 kN-m (Be15%(-)M = -6.144 kN-m (Slab) 15%(-)M = -3.291 kN-m (Sl
Middle strip: Interior (-) M Middle strip: Interior (-) M
(-) M = -48.763-(-40.961) (-) M = -26.123-(-21.943)
= -7.802 kN-m = -4.180 kN-m
Column strip: (+) M Column strip: (+) M
Mo = Mo =L2
Ln
Page 4
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 4/19
x = 84.000 % x = 84.000 %
(+) M = 84%(26.257) (+) M = 84%(14.066)
= 22.056 kN-m = 11.815 kN-m
85%(+)M = 18.748 kN-m (Beam) 85%(+)M = 10.043 kN-m (B15%(+)M = 3.308 kN-m (Slab) 15%(+)M = 1.772 kN-m (S
Middle strip: (+) M Middle strip: (+) M
(+) M = 26.257-(22.056) (+) M = 14.066-(11.815)
= 4.201 kN-m = 2.251 kN-m
Summary of Moments: (kN-m)
Mid. Strip
Beam Slab slab
Interior
Neg -34.817 -6.144 -7.802
Pos 18.748 3.308 4.201
Exterior
Neg -18.652 -3.291 -4.180
Pos 10.043 1.772 2.251
Design of Reinforcements: d = h - 1.5Ø - cover
Neg Pos Neg Pos Neg Pos Neg Pos
Mu -6.144 3.308 -3.291 1.772 -7.802 4.201 -4.180 2.251
b 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000
d 106.000 106.000 106.000 106.000 106.000 106.000 106.000 106.000
Rn 0.608 0.327 0.325 0.175 0.772 0.415 0.413 0.223
act ρ 0.00225 0.00120 0.00119 0.00064 0.00287 0.00153 0.00152 0.00081
min ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
use ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
As per m 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636
As temp 270 270 270 270 270 270 270 270
Use: As 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636 Col Strip (Ext): L/4 @ 500 mm,
n per m 3 3 3 3 3 3 3 3 Mid Strip (Ext): L/4 @ 500 mm
Mid. Strip
Interior Interior
Col. Strip Int.
Exterior Exterior
Col. Strip Int.
Page 5
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 5/19
Col Strip (Int) 500.000 500.000 500.000 500.000 500.000 500.000 500.000 500.000
Mid Strip (Int) 500.000 500.000 500.000 500.000 500.000 500.000 500.000 500.000
Col Strip (Int) 500.000 500.000 500.000 500.000 500.000 500.000 500.000 500.000
Moment for 5-m span: (one end continuous)hf = 150.000 mm
350 mm
wu = 1.4wDL + 1.7wLL
wu = 7.600 kpa Ln = 4.750 m 250 mm
(a) Interio r (b ) Exter ior
L2 = 3.500 m L2 = 1.875 mwuL2 = 26.600 kn/m wuL2 = 14.250 kn/m
(wuL2)(Ln)² (wuL2)(Ln)²
8 8
Mo = 75.020 kN-m Mo = 40.189 kN-m
(-) M = 0.70Mo = -52.514 kN-m (-) M = 0.70Mo = -28.133 kN-m
(+) M = 0.52Mo = 39.011 kN-m (+) M = 0.52Mo = 20.899 kN-m
ext (-) M = 0.26Mo = -19.505 kN-m ext (-) M = 0.26Mo = -10.449 kN-m
L2/L1 = 3.5/5 L2/L1 = 3.5/5
= 0.700 = 0.700
α1 = 1.815 α1 = 2.541
α1L2/L1 = 1.271 FALSE 1.271 α1L2/L1 = 1.779 FALSE 1.7
Column strip: Interior (-) M Column strip: Interior (-) M
0.5 0.5 0.5 0.5 0.5 0.5
L2/L1 0.5 1.0 2.0 L2/L1 0.5 1.0
75 α1L2/L1=0 75 75 75 75 75 α1L2/L1=0 75 75
90 α1L2/L1≥1 90 75 45 75 90 α1L2/L1≥1 90 75
1.0 1.0 1.0 1.0 1.0 1.0
0.5 0.700 1.0 0.5 0.700
90.0 x 75.0 90.0 xx = 84.000 % x = 84.000 %
(-) M = 84%(-52.514) (-) M = 84%(-28.133)
= -44.112 kN-m = -23.632 kN-m
85%(-)M = -37.495 kN-m (Beam) 85%(-)M = -20.087 kN-m (Be
15%(-)M = -6.617 kN-m (Slab) 15%(-)M = -3.545 kN-m (Sl
Middle strip: Interior (-) M Middle strip: Interior (-) M
Mo =Mo =
L2
Ln
Page 6
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 6/19
90 α1L2/L1≥1 90 75 45 75 90 α1L2/L1≥1 90 75
1.0 1.0 1.0 1.0 1.0 1.0
0.5 0.700 1.0 0.5 0.700
90.0 x 75.0 90.0 x
x = 84.000 % x = 84.000 %
(+) M = 84%(39.011) (+) M = 84%(20.899)
= 32.769 kN-m = 17.555 kN-m
85%(+)M = 27.854 kN-m (Beam) 85%(+)M = 14.922 kN-m (B
15%(+)M = 4.915 kN-m (Slab) 15%(+)M = 2.633 kN-m (S
Middle strip: (+) M Middle strip: (+) M
(+) M = 39.011-(32.769) (+) M = 20.899-(17.555)
= 6.242 kN-m = 3.344 kN-m
150 150350 350
200 200
250 250
Ecb x C Ecb x C
2Ecs x Is 2Ecs x Is
100 C = Σ(1-0.63x/y)x³y/3 C = Σ(1-0.63x/y)x³y/3
75 = 1.121E+09 mm^4 = 1.121E+09 mm
100 Is = 1.406E+09 mm^4 Is = 7.383E+08 mm
90 ßt = 0.399 < 2.5 Use 2.500 ßt = 0.759 < 2.5 Use 2.5
Column strip: Exterior (-) M Column strip: Exterior (-) M
0.5 0.5 0.5 0.5 0.5 0.5
L2/L1 0.5 1.0 2.0 L2/L1 0.5 1.0
α1L2/L1=0 ßt = 0 100 100 100 100 100 α1L2/L1=0 ßt = 0 100 100
ßt ≥ 2.5 75 75 75 75 75 ßt ≥ 2.5 75 75
α1L2/L1≥1 ßt = 0 100 100 100 100 100 α1L2/L1≥1 ßt = 0 100 100
ßt ≥ 2.5 90 75 45 75 90 ßt ≥ 2.5 90 75
1.0 1.0 1.0 1.0 1.0 1.0
0.5 0.700 1.0 0.5 0.70090.0 x 75.0 90.0 x
x = 84.000 % x = 84.000 %
(-) M = 84%(-19.505) (-) M = 84%(-10.449)
= -16.384 kN-m = -8.777 kN-m
85%(-)M = -13.926 kN-m (Beam) 85%(-)M = -7.460 kN-m (B
15%(-)M = -2.458 kN-m (Slab) 15%(-)M = -1.317 kN-m (S
ßt = ßt =
Page 7
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 7/19
Beam Slab slab
Interior
Neg Int -37.495 -6.617 -8.402
Pos 27.854 4.915 6.242
Neg Ext -13.926 -2.458 -3.121
Exterior
Neg Int -20.087 -3.545 -4.501
Pos 14.922 2.633 3.344Neg Ext -7.460 -1.317 -1.672
Design of Reinforcements: d = h - 1.5Ø - cover
Neg Int Pos Neg Ext Neg Int Pos Neg Ext Neg Int Pos Neg Ext Neg Int
Mu -6.617 4.915 -2.458 -3.545 2.633 -1.317 -8.402 6.242 -3.121 -4.501b 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000
d 106.000 106.000 106.000 106.000 106.000 106.000 106.000 106.000 106.000 106.000
Rn 0.654 0.486 0.243 0.351 0.260 0.130 0.831 0.617 0.309 0.445
act ρ 0.00243 0.00179 0.00089 0.00129 0.00095 0.00048 0.00310 0.00229 0.00113 0.00164
min ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
use ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
As per m 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636
As temp 270 270 270 270 270 270 270 270 270 270
Use: As 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636 539.636
n per m 3 3 3 3 3 3 3 3 3 3Soc 500.000 500.000 500.000 500.000 500.000 500.000 500.000 500.000 500.000 500.000
Scl 484.000 484.000 484.000 484.000 484.000 484.000 484.000 484.000 484.000 484.000
Remarks OK OK OK OK OK OK OK OK OK OK
Col. Strip Int. Mid. Strip
Interior Exterior Interior
Page 8
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 8/19
L1 = 5000 Ln1 = 4750
L2 = 3500 Ln2 = 3250
Scale = 0.0002
0.025 0.725 0.975 0.725 1.025 0.725
0.025 -0.85 0.975 -0.85 1.025 -0.85
-0.025 0.725 -0.975 0.725 -1.025 0.725
-0.025 -0.85 -0.975 -0.85 -1.025 -0.85
-1.175 0.725 -1.175 0.675 -1.175 0.025
1.025 0.725 1.025 0.675 1.025 0.025
-1.175 -0.025 -1.175 -0.675 -1.175 -0.725
1.025 -0.025 1.025 -0.675 1.025 -0.725
-0.975 1.3 -1.3 0.675 -0.975 1.3 -0.975 -1.3
-0.975 -1.3 1.3 0.675 -0.7375 1.3 -0.7375 -1.3
-0.2625 1.3 -0.2625 -1.3
-0.7375 1.3 -1.3 0.5125 -0.025 1.3 -0.025 -1.3
-0.7375 -1.3 1.3 0.5125
0.025 1.3 0.025 -1.3-0.2625 1.3 -1.3 0.1875 0.2625 1.3 0.2625 -1.3
-0.2625 -1.3 1.3 0.1875 0.7375 1.3 0.7375 -1.3
0.975 1.3 0.975 -1.3
-0.025 1.3 -1.3 0.025
-0.025 -1.3 1.3 0.025 -1.3 0.675 1.3 -0.675
-1.3 0.5125 1.3 -0.5125
0.025 1.3 -1.3 -0.025 -1.3 0.1875 1.3 -0.1875
0.025 -1.3 1.3 -0.025 -1.3 0.025 1.3 -0.025
0.2625 1.3 -1.3 -0.1875 -1.3 -0.025 1.3 0.0250.2625 -1.3 1.3 -0.1875 -1.3 -0.1875 1.3 0.1875
-1.3 -0.5125 1.3 0.5125
0.7375 1.3 -1.3 -0.5125 -1.3 -0.675 1.3 0.675
0.7375 -1.3 1.3 -0.5125
0.975 1.3 -1.3 -0.675
Slab Reinforcement Detail
Col Strip (Ext): L/4 @ 500 mm, L/2 @ 500 mm, L/4 @ 500 mm
Page 9
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 9/19
L1 = 5000 Ln1 = 4750
L2 = 3500 Ln2 = 3250
Scale = 0.0002
Extension = 0.15
f'c = 20.7 Mp -0.5 0.35 -1 0.35 -1 0.35
fy = 275 Mpa -0.5 -0.35 1 0.35 -1 0.175
bar Ø = 16 m 0.5 -0.35 -1 -0.175
concrete cov 0.5 0.35 -1 0.175 -1 -0.35
Thickness = 1 -0.5 0.35 1 0.175
1 0.35
-0.65 0.375 -1 -0.175 1 0.175
0.525 0.375 1 -0.175 1 -0.175
1 -0.35
-0.65 0.325 -1 -0.350.525 0.325 1 -0.35 -0.5 1
-0.25 1
-0.65 -0.375 -0.5 -1 0.25 1
0.525 -0.375 -0.5 1 0.5 1
-0.65 -0.325 -0.25 -1 -0.5 -1
0.525 -0.325 -0.25 1 -0.25 -1
0.25 -1
-0.525 0.375 0.25 -1 0.5 -1
-0.525 -0.525 0.25 1
-0.475 0.375 0.5 -1
-0.475 -0.525 0.5 1
0.475 0.375
0.475 -0.525
0.525 0.375
0.525 -0.525
Typical Detail on Slab
Col Strip (Ext): L/4 @ 500 mm, L/2 @ 500 mm, L/4 @ 500 mm
Mid Strip (Ext): L/4 @ 500 mm, L/2 @ 500 mm, L/4 @ 500 mm
C o l S t r i p ( E x t ) : S / 4 @ 3
3 3 m m
, S / 2 @ 3
3 3 m m ,
S / 4 @ 3
3 3 m m
M i d S t r i p ( E x t ) : S / 4 @ 3
3 3 m m
, S / 2 @ 3
3 3 m m ,
S / 4 @ 3
3 3 m
m
C
o l S t r i p ( I n t ) : S / 4 @ 3
3 3 m m , S
/ 2 @ 3
3 3 m m ,
S / 4 @ 3
3 3 m m
M i d
S t r i p ( I n t ) : S / 4 @ 3
3 3 m m , S /
2 @ 3
3 3 m m ,
S / 4 @ 3
3 3 m m
bar Ø = 16 mm
f'c = 20.7 Mpafy = 275 Mpa
bar Ø = 16 mm
concrete cover = 20 mm
Thickness = 150 mm
Page 10
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 10/19
Moment for 3.5-m span: (both end continuous)
hf = 150.000 mm
350 mm
wu = 1.4wDL + 1.7wLL
wu = 7.600 kpa Ln = 3.250 m 250 mm
(a) Interio r (b) Exterio r
L2 = 5.000 m L2 = 2.625 m
wuL2 = 38.000 kn/m wuL2 = 19.950 kn/m
(wuL2)(Ln)² (wuL2)(Ln)²
8 8
Mo = 50.172 kN-m Mo = 26.340 kN-m(-) M = 0.65Mo = -32.612 kN-m (-) M = 0.65Mo = -17.121 kN-m
(+) M = 0.35Mo = 17.560 kN-m (+) M = 0.35Mo = 9.219 kN-m
L2/L1 = 5/3.5 L2/L1 = 5/3.5
= 1.429 = 1.429
α1 = 1.270 α1 = 1.815
α1L2/L1 = 1.814 FALSE 1.814 α1L2/L1 = 2.593 FALSE 2.5
Column strip: Interior (-) M Column strip: Interior (-) M
0.5 0.5 0.5 0.5 0.5 0.5
L2/L1 0.5 1.0 2.0 L2/L1 0.5 1.0
75 α1L2/L1=0 75 75 75 75 75 α1L2/L1=0 75 75
90 α1L2/L1≥1 90 75 45 45 90 α1L2/L1≥1 90 75
1.0 2.0 2.0 1.0 2.0 2.0
0.5 1.429 2.0 0.5 1.429
90.0 x 45.0 90.0 x
x = 62.143 % x = 62.143 %
(-) M = 62.143%(-32.612) (-) M = 62.143%(-17.121)
= -20.266 kN-m = -10.640 kN-m
85%(-)M = -17.226 kN-m (Beam) 85%(-)M = -9.044 kN-m (Be15%(-)M = -3.040 kN-m (Slab) 15%(-)M = -1.596 kN-m (Sl
Middle strip: Interior (-) M Middle strip: Interior (-) M
(-) M = -32.612-(-20.266) (-) M = -17.121-(-10.64)
= -12.346 kN-m = -6.481 kN-m
Column strip: (+) M Column strip: (+) M
Mo = Mo =
L2
Ln
L2
Page 11
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 11/19
x = 62.143 % x = 62.143 %
(+) M = 62.143%(17.56) (+) M = 62.143%(9.219)
= 10.912 kN-m = 5.729 kN-m
85%(+)M = 9.275 kN-m (Beam) 85%(+)M = 4.870 kN-m (B15%(+)M = 1.637 kN-m (Slab) 15%(+)M = 0.859 kN-m (S
Middle strip: (+) M Middle strip: (+) M
(+) M = 17.56-(10.912) (+) M = 9.219-(5.729)
= 6.648 kN-m = 3.490 kN-m
Summary of Moments: (kN-m)
Mid. Strip
Beam Slab slab
Interior Neg -17.226 -3.040 -12.346
Pos 9.275 1.637 6.648
Exterior
Neg -9.044 -1.596 -6.481
Pos 4.870 0.859 3.490
Design of Reinforcements: d = h - 0.5Ø - cover
Neg Pos Neg Pos Neg Pos Neg Pos
Mu -3.040 1.637 -1.596 0.859 -12.346 6.648 -6.481 3.490
b 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000
d 122.000 122.000 122.000 122.000 122.000 122.000 122.000 122.000
Rn 0.227 0.122 0.119 0.064 0.922 0.496 0.484 0.261
act ρ 0.00083 0.00045 0.00043 0.00023 0.00344 0.00183 0.00178 0.00095min ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
use ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
As per m 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091
As temp 270 270 270 270 270 270 270 270
0 mm Use: As 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091 Col Strip (Ext): S/4 @ 333 mm,
0 mm n per m 4 4 4 4 4 4 4 4 Mid Strip (Ext): S/4 @ 333 mm
Mid. Strip
Interior Exterior
Col. Strip Int.
Interior Exterior
Col. Strip Int.
Page 12
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 12/19
Col Strip (Int) 333.333 333.333 333.333 333.333 333.333 333.333 333.333 333.333
Mid Strip (Int) 333.333 333.333 333.333 333.333 333.333 333.333 333.333 333.333
Col Strip (Int) 333.333 333.333 333.333 333.333 333.333 333.333 333.333 333.333
Moment for 3.5-m span: (one end continuous) hf = 150.000 mm
350 mm
wu = 1.4wDL + 1.7wLL
wu = 7.600 kpa Ln = 3.250 m 250 mm
(a) In ter ior (b ) Ex ter io r
L2 = 5.000 m L2 = 2.625 mwuL2 = 38.000 kn/m wuL2 = 19.950 kn/m
(wuL2)(Ln)² (wuL2)(Ln)²
8 8
Mo = 50.172 kN-m Mo = 26.340 kN-m
(-) M = 0.70Mo = -35.120 kN-m (-) M = 0.70Mo = -18.438 kN-m
(+) M = 0.52Mo = 26.089 kN-m (+) M = 0.52Mo = 13.697 kN-m
ext (-) M = 0.26Mo = -13.045 kN-m ext (-) M = 0.26Mo = -6.848 kN-m
L2/L1 = 5/3.5 L2/L1 = 5/3.5
= 1.429 = 1.429
α1 = 1.270 α1 = 1.815
α1L2/L1 = 1.814 FALSE 1.814 α1L2/L1 = 2.593 FALSE 2.5
Column strip: Interior (-) M Column strip: Interior (-) M
0.5 0.5 0.5 0.5 0.5 0.5
L2/L1 0.5 1.0 2.0 L2/L1 0.5 1.0
75 α1L2/L1=0 75 75 75 75 75 α1L2/L1=0 75 75
90 α1L2/L1≥1 90 75 45 45 90 α1L2/L1≥1 90 75
1.0 2.0 2.0 1.0 2.0 2.0
0.5 1.429 2.0 0.5 1.429
90.0 x 45.0 90.0 xx = 62.143 % x = 62.143 %
(-) M = 62.143%(-35.12) (-) M = 62.143%(-18.438)
= -21.825 kN-m = -11.458 kN-m
85%(-)M = -18.551 kN-m (Beam) 85%(-)M = -9.739 kN-m (Be
15%(-)M = -3.274 kN-m (Slab) 15%(-)M = -1.719 kN-m (Sl
Middle strip: Interior (-) M Middle strip: Interior (-) M
Mo =Mo =
LL2
Ln
Page 13
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 13/19
90 α1L2/L1≥1 90 75 45 45 90 α1L2/L1≥1 90 75
1.0 2.0 2.0 1.0 2.0 2.0
0.5 1.429 2.0 0.5 1.429
90.0 x 45.0 90.0 x
x = 62.143 % x = 62.143 %
(+) M = 62.143%(26.089) (+) M = 62.143%(13.697)
= 16.212 kN-m = 8.512 kN-m
85%(+)M = 13.780 kN-m (Beam) 85%(+)M = 7.235 kN-m (B
15%(+)M = 2.432 kN-m (Slab) 15%(+)M = 1.277 kN-m (S
Middle strip: (+) M Middle strip: (+) M
(+) M = 26.089-(16.212) (+) M = 13.697-(8.512)
= 9.877 kN-m = 5.185 kN-m
150.000 150350 350
200.000 200
250 250
Ecb x C Ecb x C
2Ecs x Is 2Ecs x Is
100 C = Σ(1-0.63x/y)x³y/3 C = Σ(1-0.63x/y)x³y/3
75 = 1.121E+09 0.375 = 1.121E+09
100 Is = 1.406E+09 0.375 Is = 7.383E+08
90 ßt = 0.399 < 2.5 Use 2.500 ßt = 0.759 < 2.5 Use 2.5
Column strip: Exterior (-) M Column strip: Exterior (-) M
0.5 0.5 0.5 0.5 0.5 0.5
L2/L1 0.5 1.0 2.0 L2/L1 0.5 1.0
α1L2/L1=0 ßt = 0 100 100 100 100 100 α1L2/L1=0 ßt = 0 100 100
ßt ≥ 2.5 75 75 75 75 75 ßt ≥ 2.5 75 75
α1L2/L1≥1 ßt = 0 100 100 100 100 100 α1L2/L1≥1 ßt = 0 100 100
ßt ≥ 2.5 90 75 45 75 90 ßt ≥ 2.5 90 75
1.0 1.0 1.0 1.0 1.0 1.0
0.5 1.429 1.0 0.5 1.42990.0 x 75.0 90.0 x
x = 62.143 % x = 62.143 %
(-) M = 62.143%(-13.045) (-) M = 62.143%(-6.848)
= -8.107 kN-m = -4.256 kN-m
85%(-)M = -6.891 kN-m (Beam) 85%(-)M = -3.618 kN-m (B
15%(-)M = -1.216 kN-m (Slab) 15%(-)M = -0.638 kN-m (S
ßt = ßt =
Page 14
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 14/19
Beam Slab slab
Interior
Neg Int -18.551 -3.274 -13.295
Pos 13.780 2.432 9.877
Neg Ext -6.891 -1.216 -4.938
Exterior
Neg Int -9.739 -1.719 -6.980
Pos 7.235 1.277 5.185Neg Ext -3.618 -0.638 -2.592
Design of Reinforcements: d = h - 0.5Ø - cover
Neg Int Pos Neg Ext Neg Int Pos Neg Ext Neg Int Pos Neg Ext Neg Int
Mu -3.274 2.432 -1.216 -1.719 1.277 -0.638 -13.295 9.877 -4.938 -6.980
b 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000 1,000.000
d 122.000 122.000 122.000 122.000 122.000 122.000 122.000 122.000 122.000 122.000
Rn 0.244 0.182 0.091 0.128 0.095 0.048 0.992 0.737 0.369 0.521
act ρ 0.00089 0.00066 0.00033 0.00047 0.00035 0.00017 0.00372 0.00274 0.00135 0.00192
min ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
use ρ 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509 0.00509
As per m 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091
As temp 270 270 270 270 270 270 270 270 270 270
Use: As 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091 621.091
n per m 4 4 4 4 4 4 4 4 4 4Soc 333.333 333.333 333.333 333.333 333.333 333.333 333.333 333.333 333.333 333.333
Scl 317.333 317.333 317.333 317.333 317.333 317.333 317.333 317.333 317.333 317.333
Remarks OK OK OK OK OK OK OK OK OK OK
Exterior Interior
Col. Strip Int. Mid. Strip
Interior
Page 15
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 15/19
Page 16
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 16/19
Page 17
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 17/19
Ln
Page 18
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 18/19
33 mm
33 mm
Page 19
7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz
http://slidepdf.com/reader/full/slab-with-beams-very-very-good-mahfuz 19/19
Ln