16 reinforced concrete design design of slabs -...
TRANSCRIPT
![Page 1: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/1.jpg)
1616
� Types of Slabs
� Load Paths and Framing Concepts
� One-way Slabs
� Two-way Slabs
Mongkol JIRAVACHARADET
Reinforced Concrete DesignReinforced Concrete Design
S U R A N A R E E INSTITUTE OF ENGINEERING
UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL ENGINEERING
Design of Slabs
![Page 2: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/2.jpg)
Types of Slab
One-way slab Two-way slabOne-way slab
Flat plate slab Flat slab Grid slab
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Think we’ll need some additional framing members???
Load Path / Framing Possibilities
Ln = 4.4 m
Ln = 8.2 m
Ln = 3.2 m
Ln = 3.6 m
![Page 4: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/4.jpg)
Plan
Framing Concepts
Let’s use a simple example
for our discussion…
Think about relating it to your
design project.
Column spacing 8 m c-c
![Page 5: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/5.jpg)
Framing Concepts
We can first assume that
we’ll have major girders
running in one direction
in our one-way system
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Framing Concepts
We can first assume that
we’ll have major girders
running in one direction
in our one-way system
If we span between girders
with our slab, then we have
a load path, but if the spans
are too long…
![Page 7: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/7.jpg)
But we need to support the
load from these new beams,
so we will need additional
supporting members
Framing Concepts
We will need to shorten up
the span with additional beams
![Page 8: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/8.jpg)
We again assume that we’ll
have major girders running in
one direction in our one-way
system.
Framing Concepts
Now let’s go back through with
a slightly different load path.
This time, let’s think about
shortening up the slab span by
running beams into our girders.
Our one-way slab will transfer our load to the beams.
![Page 9: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/9.jpg)
Two Load Path Options
![Page 10: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/10.jpg)
Framing Concepts - Considerations
For your structure:
Look for a “natural” load path
Assume walls are not there for structural support, but
consider that the may help you in construction (forming)
Identify which column lines are best suited to having
major framing members (i.e. girders)
![Page 11: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/11.jpg)
ExampleExample
Condo Floor PlanCondo Floor Plan
![Page 12: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/12.jpg)
1.0 m
LS
Main reinforcement
������������� ��������������
One-way Slab
Design of one-way slabs is like design of parallel 1m beams.
![Page 13: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/13.jpg)
Design of One-way Slab (L > 2S)
S
L 1 m
������������� ��������� 1 ���
S
w
Minimum Thickness (ACI)
Simply
supported
One end
continuous
Both ends
continuousCantilever
L/20 L/24 L/28 L/10
*multiplied by 0.4 + fy/7,000 for steel other than SD40
![Page 14: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/14.jpg)
ACI Design ProvisionACI Design Provision
Shrinkage and temperature reinforcement
Spacing ≤≤≤≤ 5 t ≤≤≤≤ 45 cm
Main Steel (short direction):
As ≥ ∅ 6 mm
Max. Spacing ≤ 3 t ≤ 45 cm
Min. Spacing ≥ f main steel ≥ 4/3 max agg. ≥ 2.5 cm
For structural slabs only; not intended for soil-supported slabs on grade
Ratio of reinforcement As to gross concrete area Ag : As/Ag
RB24 (fy = 2,400 ksc) . . . . . . . . . . . . . . . . . 0.0025
DB30 (fy = 3,000 ksc) . . . . . . . . . . . . . . . . . 0.0020
DB40 (fy = 4,000 ksc) . . . . . . . . . . . . . . . . . 0.0018
DB (fy > 4,000 ksc) . . . . . . . . . . . . . . . . . . . 0.0018 4,0000.0014
yf
×≥
![Page 15: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/15.jpg)
Effect of column width
b b
L
b/212
2wL
2
wL
A′A
b/2
B
w
Moment at A’:
( )
+−−=
−
+−=
8412
2
2/
2212
22
22
wbwLbwL
bwbwLwL
( )
+−−=
−−=
1261212
222wbwLbwLbLw
M
If A’ and B’ are fiexed against rotation,
B′
12
2wL
2
wL
![Page 16: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/16.jpg)
Typical reinforcement in a oneTypical reinforcement in a one--way slabway slab
Exterior span
Bottom bars
Top bars at
exterior beams
Top bars at
exterior beams
Interior span
Temperature bars
(a) Straight top and bottom bars
Exterior span
Bottom bars
Bent bar Bent bars
Interior span
Temperature bars
(b) Alternate straight and bent bars
![Page 17: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/17.jpg)
3 @
8 m
= 24 m
4 @ 12 m = 48 m
G1
A AS1 S2 S3
Example: Design one-way slab as shown below to carry the live
load 500-kg/m2 fc’ = 210 kg/cm2, fy = 2,400 kg/cm
2
0.4 + 2400/7000 = 0.74
min h = 400(0.74)/24 = 12.3 cm
USE h = 13 cm
DL = 0.13×2400 = 312kg/m2
wu = 1.4(312) + 1.7(500) = 1,286.8 kg/m2
clear span = 4 - 0.3 = 3.7 m
Mu = (1,286.8)(3.7)2/10 = 1,762 kg-m
ρmax = 0.75ρb = 0.75(0.0454) = 0.0341
![Page 18: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/18.jpg)
USE RB9 with 2 cm covering: d = 13-2-0.45 = 10.55 cm
ksc 6.1755.101009.0
100176222=
××
×==
bd
MR u
n φ
0077.085.0
211
85.0'
'
=
−−=
c
n
y
c
f
R
f
fρ < ρmax OK
As = ρbd = 0.0077(100)(10.55) = 8.16 cm2/m
Select [email protected] (As = 9.28 cm2/m)
Temp. steel = 0.0025(100)(13) = 3.25 < 9.28 cm2/m OK
Select [email protected] (As = 3.53 cm2/m)
![Page 19: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/19.jpg)
Detailing of one-way slab
3
1L
4
1L
8
1L
L1
Temp. steel
4.0 �.
.13 �.
1.0 �. 1.3 �.
[email protected] [email protected]
4.0 �.
.13 �.
1.0 �. 1.3 �[email protected]
� ���������
[email protected] [email protected] ������#$
![Page 20: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/20.jpg)
Design of Two-way Slab (L < 2S)
L
S
Min. Thickness:
t ≥ 9 cm ≥ Perimeter/180 = 2(L+S)/180
Reinforcement Steel:
As ≥ φ 6 mm ≥ Temp. steel
Max. Spacing ≤ 3 t ≤ 45 cm
Min. Spacing ≥ φ main steel ≥ 4/3 max agg. ≥ 2.5 cm
![Page 21: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/21.jpg)
Load transfer from two-way Slab
45o 45o
45o 45o
A
D C
B
S
L
Short span (BC):
Floor load = w kg/sq.m
Tributary area = S2/4 sq.m
Load on beam = wS/4 wS/3 kg/m
Long span (AB): Span ratio m = S/L
Tributary area = SL/2 - S2/4 = sq.m
Load on beam kg/m
−m
mS 2
4
2
−2
3
3
2mwS
![Page 22: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/22.jpg)
Moment Coefficient Method
S/4
S/4
S/2
L/4 L/2 L/4
%&'�(��
%&'��
%&'��
%&'�(�� %&'��%&'��
-Ms
-Ms
+Ms
+ML
-ML-ML
Middle strip moment: MM = CwS2
Column strip moment: MC = 2MM/3
![Page 23: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/23.jpg)
������������������ ������ ( C )
"��#�����
$%�����$%��&��
�)��)��*+ � m
���'�&(,���-('-/���) �� �
-/��0�)�) �� �
,���-'��12��(��3)��
1.0 0.9 0.8 0.7 0.6 0.5
0.033-
0.025
0.040-
0.030
0.048-
0.036
0.055-
0.041
0.063-
0.047
0.083-
0.062
0.033-
0.025
���4�%�% �5 �6��67&�,���-('-/���) �� �
-/��0�)�) �� �
,���-'��12��(��3)��
0.0410.0210.031
0.0480.0240.036
0.0550.0270.041
0.0620.0310.047
0.0690.0350.052
0.0850.0420.064
0.0410.0210.031
���4�%�% �5 �� �6��,���-('-/���) �� �
-/��0�)�) �� �
,���-'��12��(��3)��
0.0490.0250.037
0.0570.0280.043
0.0640.0320.048
0.0710.0360.054
0.0780.0390.059
0.0900.0450.068
0.0490.0250.037
![Page 24: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/24.jpg)
������������������ ������ ( C )
"��#�����
$%�����$%��&��
�)��)��*+ � m
���4�%�% �5 ����6��,���-('-/���) �� �
-/��0�)�) �� �
,���-'��12��(��3)��
1.0 0.9 0.8 0.7 0.6 0.5
0.0580.0290.044
0.0660.0330.050
0.0740.0370.056
0.0820.0410.062
0.0900.0450.068
0.0980.0490.074
0.0580.0290.044
���4�%�% �5 ��756��,���-('-/���) �� �
-/��0�)�) �� �
,���-'��12��(��3)��
-0.0330.050
-0.0380.057
-0.0430.064
-0.0470.072
-0.0530.080
-0.0550.083
-0.0330.050
![Page 25: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/25.jpg)
Bar detailing in slab
L1 L2
L1/7 L1/4
L1/3
L2/4
L2/3����������������
Bar detailing in beam
L1 L2
L1/8
L1/3 L2/3
L1/8
![Page 26: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/26.jpg)
������������� ������
��� ����
��� ��
L/5
L/5
L = ���������������
![Page 27: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/27.jpg)
Example: Design two-way slab as shown below to carry the live
load 300-kg/m2 fc’ = 240 kg/cm2, fy = 2,400 kg/cm
2
3.80
4.00
4.805.00
Floor plan
0.10
0.50
0.20 0.20
Cross section
Min h = 2(400+500)/180 = 10 cm
DL = 0.10(2,400) = 240 kg/m2
wu = 1.4(240)+1.7(300) = 846 kg/m2
m = 4.00/5.00 = 0.8
As,min = 0.0018(100)(10) = 1.8 cm2/m
![Page 28: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/28.jpg)
Short span
Moment coeff. C
-M(������������) +M -M(���������)
0.032 0.048 0.064
Max.M = C w S 2 = 0.064 × 846 × 4.02 = 866 kg-m/1 m width
d = 10 - 2(covering) - 0.5(half of DB10) = 7.5 cm
2
2 2
86,60017.11 kg/cm
0.9 100 7.5
un
MR
bdφ= = =
× ×
0.85 21 1 0.0045
0.85
c n
y c
f R
f fρ
′= − − = ′
As = 0.0045(100)(7.5) = 3.36 4�.2 > As,min
(� �63��(7�1���8� [email protected] (As=3.90 4�.2)
![Page 29: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/29.jpg)
Long span
Moment coeff. C
-M(������������) +M -M(���������)
0.025 0.037 0.049
Max.M = C w S 2 = 0.049 × 846 × 4.02 = 663 kg-m/1 m width
d = 10 - 2(covering) - 1.5(half of DB10) = 6.5 cm
2
2 2
66,30017.44 kg/cm
0.9 100 7.5
un
MR
bdφ= = =
× ×
0.85 21 1 0.0046
0.85
c n
y c
f R
f fρ
′= − − = ′
As = 0.0046(100)(6.5) = 2.97 4�.2 > As,min
(� �63��(7�1���8� [email protected] (As=3.90 4�.2)
![Page 30: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/30.jpg)
����� 8�9�"����8:��;� � �� ��7�
%��9� 9(2�: Vu = wuS/4 = (846)(4.0)/4
= 846 ��./�.
�<�(8��8'%��9� � ��2� φVc = 0.85(0.53) (100)(7.5)
= 5234 ��./�. OK
240
![Page 31: 16 Reinforced Concrete Design Design of Slabs - .xyzlibvolume3.xyz/.../designofslabs/designofslabstutorial2.pdf · 16 Types of Slabs Load Paths and Framing Concepts One-way Slabs](https://reader033.vdocuments.mx/reader033/viewer/2022061323/5a792d577f8b9ae93a8b7b3b/html5/thumbnails/31.jpg)
0.50
0.10
0.20 4.80 0.20
[email protected] � ���������[email protected] ������#$
[email protected] ������#$
���6��&��
0.70
1.20
1.20
1.60
0.50
0.10
0.20 3.80 0.20
[email protected] � ���������[email protected] ������#$
[email protected] ������#$
���6�����
0.95
1.300.55
0.95