13-Design of Flat Slab-slab With Drop Panel

‫ﻣﺬﻛﺮة‬ ‫رﰴ )‪(13‬‬

‫‪Reinforced Concrete‬‬ ‫اﳋﺮﺳـــــــﺎﻧــــــــــــــــــﺔ اﳌﺴـﻠﺤـــــــــــــﺔ‬ ‫‪Third Civil Year‬‬ ‫اﻟﻔﺮﻗـــــــــــــــﺔ اﻟﺜﺎﻟﺜــــــــﺔ ﻣﺪﻧـــــــــــــــﻲ‬

‫‪Flat slab with drop panel‬‬

3rd Civil year – Reinforced Concrete - Notes No (13)

Flat slab with drop panel For the shown floor plan given that: - fcu= 300 kg/cm2

- fy= 4000 kg/cm2

- Live load = 800 kg/m2

-Covering = 150 kg/m2

- walls= 150 kg/m2 - Column dimensions (30*60)cm -no of stories =4 -story height = 3.0m Required to: (a) Make complete design of the reinforced concrete flat slab in both directions and draw reinforcement details? (b) Check punching shear for interior column (C1) and exterior column (C2). (C) Design the column (C1) and draw its details of reinforcement to scale 1 :10.

page No(- 1 -)


page No(- 2 -)


Solution 1- slab theicknes (ts)

‫ ﺣﺴﺎب ﲰﻚ اﻟﺒﻼﻃﺔ‬-1

- ts =

flat slab with drop panel

=

=20.84 cm take ts = 22.0cm

-Dimension of drop panel: -take

td =ts/2= 22/2=11.0cm l1=7.50 m

for slab : -take

&

l2=6.0 m

ld= l2/2 = 6.0/2 =3.0m ‫اﺑﻌﺎد اﻟﺴﻘﻮط ﻣﺮﺑﻌﺔ‬

2- laods (wsu): -Wdl = ts*rc +(

‫ ﺣﺴﺎب الاﺣﲈل ﻋﲇ اﻟﺒﻼﻃﺎت‬-2 ∗ ∗

)*rc (‫)وزن اﻟﺴﻘﻮط‬+ covering + walls

∗

Wdl = 0.22 * 2.50 +(

. ∗ . ∗ . .

∗ .

)*2.50 + 0.15 +0.15

= 0.90 t/m 2 -Wll = 800 kg/m2 = 0.80 t/m2 . (given) - ultimate slab loads :

> 0.75

Wsu = (1.40 wdl + 1.60 wll ) = 1.40 *0.90 +1.60 *0.80 = 2.54 t/m 2 .

page No(- 3 -)


3- Width of column strip & field strip: l1= 7.5m (‫ & )اﻟﻄﻮل اﻟﻜﺒﲑ‬l2= 6.0m (‫)اﻟﻄﻮل اﻟﺼﻐﲑ‬ -width of column strip (C.s) = -width of field strip (F.s) :

.

=

=3.0 m ‫ﰲ الاﲡﺎﻫﲔ‬

-in(X) direction =l2-

=6. 0 -

.

=3.0 m

-in (y) direction =l1-

=7.5 -

.

=4.5 m

page No(- 4 -)


4-total bending moment in (X & y) direction: -in(X) direction ∗

Mx=

(lx- D)2

D=b =0.30m  Mx=

.

∗ .

for slab without column head ‫ﻋﺮض اﻟﻌﻤﻮد‬

(6.0 - *0.30)2 =80.10 t.m

-in(y) direction M y=

∗

(ly- D)2 =

.

∗ .

(7.50 - *0.30)2 =101.52 t.m

5-distribution of total moment between column and field strip:

: (6-48) ‫ﻗﲓ اﻟﺘﻮزﻳﻊ ﻣﻮﺟﻮدﻩ ﰲ اﻟﻜﻮد اﳌﴫي ﺻــ‬ for slab without marginal beam: ‫ ﰲ ﺣﺎةل اﻟﺒﻼﻃﺔ ﺑﺪون ﳈﺮة ﻋﲇ اﶈﻴﻂ اﳋﺎريج‬-in(X) direction : Mx=80.10 t.m

page No(- 5 -)


-in(y) direction : My=101.52 t.m ∗

-Mc=

* l ‫اﻟﻌﺰم ﻋﲇ اﻟﲀﺑﻮﱄ‬

where: lc : ‫ﻃﻮل اﻟﲀﺑﻮﱄ‬ Mc=

.

∗ .

&

l : ‫اﻟﻄﻮل اﻟﻌﻤﻮدي ﻋﲇ اﻟﲀﺑﻮﱄ‬

* 6.0 = 30.48 t.m : ‫ﻳﱲ ﺗﻮزﻳﻊ ﻋﺰم اﻟﲀﺑﻮﱄ ﻋﲇ ﴍﳛﺔ اﻟﻌﻤﻮد وﴍﳛﺔ اﻟﻮﺳﻂ ﺑﻨﺴـﺒﺔ‬

(Mc)c.s =0.75 *Mc = 0.75 *30.48 =22.86 t.m (Mc)f.s =0.25 *Mc = 0.25 *30.48 =7.62 t.m

page No(- 6 -)


6-Design critical sections in (X & y) direction: ‫ ﻳﱲ ﺗﺼﻤﲓ ﻗﻄﺎﻋﲔ ﻧﻈﺮا ﻻﺧﺘﻼف ﲰﻚ اﻟﺒﻼﻃﺔ‬: ‫ﺗﺼﻤﲓ اﻟﻘﻄﺎﻋﺎت اﳊﺮﺟﺔ ﰲ الاﲡﺎﻫﲔ‬ Section (1): ‫ٔاﻛﱪ ﻋﺰم ﺳﺎﻟﺐ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد ﰲ الاﲡﺎﻩ اﻟﻄﻮﻳﻞ‬ Mu=50.76 t.m at support ‫ ابﻟﻨﺴـﺒﺔ ﻟﻠﻌﺰم اﻟﺴﺎﻟﺐ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد‬: ‫ﻻﺣﻆ‬ ‫ ﲰﻚ اﻟﺴﻘﻮط‬+ ‫ﲰﻚ اﻟﺒﻼﻃﺔ = ﲰﻚ اﻟﺒﻼﻃﺔ اﻟﻌﺎدﻳﺔ‬ t = ts+td=22+11=33cm 1- d = C1

.

....(1)

& d = t - cover (2.0 cm)

 d = 33.0 - 2.0 = 31 cm

B (width of column strip)=300cm C1 ‫ ﻟﻠﺤﺼﻮل ﻋﲇ‬.....1 ‫ابﻟﺘﻌﻮﻳﺾ ﰲ‬ .

 31 = C1

∗

^

get C1 = 4.13

∗

from table (shaker 401) using C1 = 4.13 get 2- As =

=

.

∗ ∗ .

^

∗

j = 0.808

= 50.66 cm2 / strip (3.0 m) .

As / m’ = As /3.0=50.66 /3.0=16.89 cm2 / m’ Take As = 7 Ø 18 / m’ .

page No(- 7 -)

‫)‪3rd Civil year – Reinforced Concrete - Notes No (13‬‬

‫ٔاﻛﱪ ﻋﺰم ﻣﻮﺟﺐ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد ﰲ الاﲡﺎﻩ اﻟﻄﻮﻳﻞ )‪-Section (2‬‬ ‫‪Mu=30.46 t.m at mid span‬‬ ‫ﻻﺣﻆ ‪ :‬ابﻟﻨﺴـﺒﺔ ﻟﻠﻌﺰم اﳌﻮﺟﺐ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد ‪ :‬ﲰﻚ اﻟﺒﻼﻃﺔ = ﲰﻚ اﻟﺒﻼﻃﺔ اﻟﻌﺎدﻳﺔ‬ ‫‪t = ts=22cm‬‬ ‫)‪....(1‬‬

‫‪.‬‬

‫‪1- d = C1‬‬

‫‪& d = 22 - 2.0 =20cm‬‬ ‫‪B (width of column strip)=300cm‬‬ ‫ابﻟﺘﻌﻮﻳﺾ ﰲ ‪ .....1‬ﻟﻠﺤﺼﻮل ﻋﲇ ‪C1‬‬ ‫^‬

‫‪get C1 = 3.44‬‬ ‫‪j = 0.777‬‬

‫∗‬

‫‪.‬‬

‫‪ 20 = C1‬‬

‫∗‬

‫‪from table (shaker 401) using C1 = 3.44 get‬‬

‫‪= 49.0 cm2 / strip (3.0 m) .‬‬

‫^‬

‫∗‬

‫∗‬ ‫‪∗ .‬‬

‫‪.‬‬

‫=‬

‫= ‪2- As‬‬

‫’‪As / m’ = As /3.0=49.0 /3.0=16.34 cm2 / m‬‬ ‫‪Take As = 7 Ø 18 / m’ .‬‬ ‫‪‬ﻳﱲ ﺗﻨﺴﻴﺐ ابﰶ اﻟﻘﻄﺎﻋﺎت ﻟﻠﻘﻄﺎﻋﲔ اذلي ﰎ ﺗﺼﻤﳰﻬﲈ ﻣﻊ ﻣﺮاﻋﺎة‪:‬‬ ‫‪ -1‬اﻟﻌﺰوم اﻟﺴﺎﻟﺒﺔ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد ﰲ الاﲡﺎﻫﲔ ﻳﱲ ﺗﻨﺴﻴﳢﻢ ﻟﻠﻘﻄﺎع اﱄ ﻋﻨﺪ اﻟﺴﻘﻮط اﱄ ﻋﻨﺪﻩ )‪(t=33cm‬‬ ‫‪ -2‬اﻟﻌﺰوم اﳌﻮﺟﺒﺔ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد ﰲ الاﲡﺎﻫﲔ واﻟﻌﺰوم اﻟﺴﺎﻟﺒﺔ واﳌﻮﺟﺒﺔ ﰲ ﴍﳛﺔ اﻟﻮﺳﻂ ﰲ الاﲡﺎﻫﲔ ﻳﱲ ﺗﻨﺴﻴﳢﺎ‬ ‫ﻟﻠﻘﻄﺎع اﱄ ﰲ ﻧﺼﻒ اﻟﺒﺎﻛﻴﺔ ﺑﺪون ﺳﻘﻮط اﱄ ﻋﻨﺪﻩ )‪.(t=22cm‬‬ ‫)‪page No(- 8 -‬‬


(Mu=40.05 t.m) :(x) ‫ اﻟﻌﺰم اﻟﺴﺎﻟﺐ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد ﰲ اﲡﺎﻩ‬: 1‫ﻣﺜﺎل‬ Ex: Mu = 50.76 t.m use As= 16.89 cm2 / m’ Mu = 40.05t.m need As=?? cm2 / m’  As=16.89 *40.05/50.76 =13.33 cm2/m’ =7 Ø 16 / m’ (Mu=24.03 t.m) :(x) ‫ اﻟﻌﺰم اﳌﻮﺟﺐ ﰲ ﴍﳛﺔ اﻟﻌﻤﻮد ﰲ اﲡﺎﻩ‬: 2‫ﻣﺜﺎل‬ Ex: Mu = 30.46 t.m use As= 16.34 cm2 / m’ Mu = 24.03t.m need As=?? cm2 / m’  As=16.34 *24.03t /30.46 =12.89 cm2/m’ =7 Ø 16 / m’ (y) Direction

(X) Direction

page No(- 9 -)


7-Draw reinforcement details in (X & y) direction:

page No(- 10 -)


page No(- 11 -)


2-Check punching shear stresses: ‫( ﻣﻦ وش اﻟﻌﻤﻮد وﻗﻄﺎع ﻋﲇ‬d/2) ‫ ﻗﻄﺎع ﻋﲇ ﺑﻌﺪ‬- ‫ ﻳﻮﺟﺪ ﻗﻄﺎﻋﲔ ﻟﻠﻘﺺ اﻟﺜﺎﻗﺐ‬: ‫ ﰲ ﺣﺎةل اﻟﺒﻼﻃﺔ ﺑﺴﻘﻮط‬: ‫ﻻﺣﻆ‬ . ‫( ﻣﻦ وش اﻟﺴﻘﻮط‬d/2) ‫ﺑﻌﺪ‬  Column (C1): interior column:

page No(- 12 -)


Section (1-1) -d=t-2.0=33.0-2.0=31.0cm -lx=t+d=0.60+0.31=0.91m -ly=b+d=0.30+0.31=0.61m - β = 1.15

internal column

-Qu=wsu*(l1*l2 -lx*ly)=2.54(7.50*6.0 - 0.91*0.61)=112.89 t

-bo = 2(lx+ly)=2(0.91 +0.61)=3.04m =304.0cm -qu = β

.

- qcup=

.

=1.15 * =

. .

∗

^

. ∗

.

=12.32 kg/cm2

=14.14 kg/cm2

qu < qcup Safe

-Section (2-2) -d=t-2.0=22.0-2.0=20.0cm -lx= ly = ld+d=3.0+0.20=3.20m -Qu=wsu*(l1*l2 -lx*ly) =2.54(7.50*6.0 - 3.20*3.20)=88.29 t

-bo = 2(lx+ly) =2(3.20+3.20)=12.80m =1280 cm -qu = β

.

=1.15 *

.

∗

^

∗

.

=3.96 kg/cm2

qu < qcup Safe

page No(- 13 -)


3- Design of column  Column (C1): -No of story =4 - story height =3.0m -Column section (30*60)cm pu=(wsu*Area +Column weight) *No. of stories. -Column weight =1.40(b*t*h*rc) =1.40 *0.30*0.60*3.0*2.5=1.89 t Internal column:  pu =(2.54*7.0*6.0 +1.89) *4 =428 ton Moment transfer from slab to column (C1): -in(X) direction : (internal col.): Mc=0.50 *M-ve Col. strip in (x) direction Mc= 0.50 *40.05 * 0.50 (‫ =)ﲻﻮد ﻋﻠﻮي وﺳﻔﲇ‬10.0 t.m -in(y) direction : (internal col.): Mc=0.50 *M-ve Col. strip in (y) direction =0.50 *50.76 * 0.50 (‫=)ﲻﻮد ﻋﻠﻮي وﺳﻔﲇ‬12.69 t.m Design column on: pu=428 ton & Mx=12.69 t.m

& My=10.0 t.m : ‫ﻳﱲ اﻛﲈل اﻟﺘﺼﻤﲓ ﻋﺎدي ﺟﺪا‬

1-Check column buckling. 2-get final moment. 3-Design section. page No(- 14 -)

13-Design of Flat Slab-slab With Drop Panel

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