slab with beams very very good mahfuz

7/29/2019 Slab With Beams VERY VERY GOOD Mahfuz

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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



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:


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


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 =



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



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.



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 = 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


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



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


Mo =Mo =

L2

Ln



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


(+) 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 =



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


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



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



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



Moment for 3.5-m span: (both end continuous)

hf = 150.000 mm

350 mm


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


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



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


(-) 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



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


(+) 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


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.



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 = 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


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



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


Mo =Mo =

LL2

Ln



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


(+) 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 =



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


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



Ln



33 mm

33 mm



Ln

slab with beams very very good mahfuz

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