presentation - rc11 & rc 16_slab 1 & 2 way

43
1 1 1 1 Mongkol JIRAVACHARADET Reinforced Concrete Design Reinforced Concrete Design S U R A N A R E E INSTITUTE OF ENGINEERING UNIVERSITY OF TECHNOLOGY SCHOOL OF CIVIL ENGINEERING Two-Way Slabs Design of Two-Way Slab Moment Coefficient Method Load Transfer from Two-Way Slab Bar Detailing Design Example Slab on Ground G G B B B B B B L S (ก) () L S

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Presentation RCC Slab Design

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Page 1: Presentation - RC11 & RC 16_Slab 1 & 2 Way

1111

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

Two-Way Slabs

� Design of Two-Way Slab

� Moment Coefficient Method

� Load Transfer from Two-Way Slab

� Bar Detailing

� Design Example

� Slab on Ground

G

G

B B

B

B

B B

L

S

(ก) ������� ������ (�) ���������� �

����������� ������������������� ��������

������� ������������ �� � L � ����ก�������� ����� ����� S

Page 2: Presentation - RC11 & RC 16_Slab 1 & 2 Way

t

SL

Simple supports

on all four edges

ก�����������������ก�����������������

ก ���������ก����������������� � �ก ����� � ���! "��ก����������� ������ ����� S �$%�� �� � L

ก���ก����������ก���ก���������� ( L < 2S )( L < 2S )

L

SS

�!"������#��� $�%� tmin :

Perimeter 2 (L S)10 cm

180 180

+= ≤

d�� �� � d�� ����

1∅ ����ก������"�&ก���'!(��������

As ≥ RB 9 ≥ Temp. steel

Max. Spacing ≤ 3 t ≤ 45 cm

Min. Spacing ≥ ∅ main steel ≥ 4/3 max agg. ≥ 2.5 cm

Page 3: Presentation - RC11 & RC 16_Slab 1 & 2 Way

S/4

S/4

S/2

L/4 L/2 L/4

���ก���

�����

�����

���ก��� ����������

-Ms

-Ms

+Ms

+ML

-ML -ML

Middle strip moment: MM = CwS2

Column strip moment: MC = 2MM/3

�') ��!*���'�)'+��,!�!��-�') ��!*���'�)'+��,!�!��-

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����2!�������$����#� ����2!�������$��!�#� ����2!�������$�� $�#�

Page 4: Presentation - RC11 & RC 16_Slab 1 & 2 Way

������������� ���������� ( C )

��ก������

�� ������� �!�

������ ��� m

1.0 0.9 0.8 0.7 0.6 0.5

����*�!+����������-�������������

-����������������

���������ก���ก�������

0.033-

0.025

0.040-

0.030

0.048-

0.036

0.055-

0.041

0.063-

0.047

0.083-

0.062

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0.0410.0210.031

0.0480.0240.036

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0.0410.0210.031

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0.0490.0250.037

0.0570.0280.043

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0.0490.0250.037

������������� ���������� ( C )

��ก������

�� ������� �!�

������ ��� m

1.0 0.9 0.8 0.7 0.6 0.5

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-����������������

���������ก���ก�������

0.0580.0290.044

0.0660.0330.050

0.0740.0370.056

0.0820.0410.062

0.0900.0450.068

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-0.0470.072

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Page 5: Presentation - RC11 & RC 16_Slab 1 & 2 Way

ก�3����4"��ก5ก�������� �ก�3����4"��ก5ก�������� �

L

S

wwS/3

�� ���ก�� ��� ���� =3

wS

45o

wwS/3(3-m2)/2

�� ���ก�� ��� �� � −

=

23

3 2

wS m

ก����'!�"�&ก(��������ก����'!�"�&ก(��������

Sn

Sn / 7 Sn / 4

Sn / 4 Sn / 3

�6*����#�����

Ln

Ln / 7 Ln / 4

Ln / 4 Ln / 3

�6*����#���

Page 6: Presentation - RC11 & RC 16_Slab 1 & 2 Way

����ก����

����ก

L/5

L/5

L = �� ����� ��������

ก����'!�"�&ก�'�7.� $!%!� �ก����'!�"�&ก�'�7.� $!%!� �

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

max

0.85(240)(0.85) 6,1200.75

4,000 6,120 4,000

0.0197

ρ = +

=

Page 7: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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

As = 0.0045(100)(7.5) = 3.36 cm2

As,min = 0.0018(100)(10) = 1.8 cm2 > As OK

����2!�������$����#� (m = 0.8)

2un 2 2

M 86,600R 17.11 kg/cm

bd 0.9 100 7.5= = =φ × ×

c n

y c

0.85f 2R1 1 0.0045

f 0.85f

′ρ = − − = ′

≤ ρmax = 0.0197 OK

Select short span reinforcement DB10 @ 0.20 m (As = 3.90 cm2)

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!�������$����#� (m = 0.8)

Long span

Moment coeff. C

-M(�����������) +M -M(��������)

0.025 0.037 0.049

2un 2 2

M 66,300R 17.44 kg/cm

bd 0.9 100 7.5= = =φ × ×

c n

y c

0.85 f 2R1 1 0.0046

f 0.85 f

′ρ = − − = ′

≤ ρmax = 0.0197 OK

As = 0.0045(100)(6.5) = 2.97 cm2

As,min = 0.0018(100)(10) = 1.8 cm2 > As OK

Select short span reinforcement DB10 @ 0.20 m (As = 3.90 cm2)

Page 8: Presentation - RC11 & RC 16_Slab 1 & 2 Way

�� 5��6ก7������68���9������:��ก�4�

���� ���� ���! Vu = wuS/4 = (846)(4.0)/4

= 846 ก.ก./�.

ก$��%��%����� �����ก��� φVc = 0.85(0.53) (100)(7.5)

= 5,234 ก.ก./�. OK

240

�;�<ก����ก���3�

As,min = 0.0018(100)(10) = 1.8 cm2

Select temp. steel reinforcement DB10 @ 0.30 m (As = 2.60 cm2)

0.50

0.10

0.20 4.80 0.20

[email protected] ��������������[email protected] ��&�'&�()

[email protected] ��&�'&�()

����23��!�

0.70

1.20

1.20

1.60

0.50

0.10

0.20 3.80 0.20

[email protected] ��������������[email protected] ��&�'&�()

[email protected] ��&�'&�()

����23������

0.95

1.300.55

0.95

Page 9: Presentation - RC11 & RC 16_Slab 1 & 2 Way

��������'���������'� (Slab(Slab--OnOn--Ground)Ground)

0 5 10 15 20 30

Slab thickness, cm

0

3

6

9

Max.joint spacing,m

Range of

max. spacing

spacing

�! '"�ก �ก����� ��%��ก�����(� �ก! $���� ก� ��) � �ก. 737-2531 �� fy

= 5,000 ก.ก./5.2

1.4810.9430.943∅ 6 .× 6 ., 30 5.× 30 5.

1.7761.1311.131∅ 6 .× 6 ., 25 5.× 25 5.

2.2201.4141.414∅ 6 .× 6 ., 20 5.× 20 5.

0.6580.4190.419∅ 4 .× 4 ., 30 5.× 30 5.

0.7900.5030.503∅ 4 .× 4 ., 25 5.× 25 5.

0.9880.6290.629∅ 4 .× 4 ., 20 5.× 20 5.

1.3170.8380.838∅ 4 .× 4 ., 15 5.× 15 5.

�����+��������������

��4"��ก(กก./��.!.)

����� $"�#���(��.F!. / !.)∅∅∅∅ ������, ������ก�

���ก�����"�&ก�4��&5�6*���ก�����"�&ก�4��&5�6* (Wire mesh)(Wire mesh)

Page 10: Presentation - RC11 & RC 16_Slab 1 & 2 Way

��ก����"�&ก���'!,���') ��ก����"�&ก���'!,���') SubgradeSubgrade DragDrag

W

T

L

s s

FLWT A f

2= =

s

s

FLWA

2f=

������ T ���ก��:% ;ก�� �� �<���"$(ก���� As

= �������"$(ก��������� ก�� � 1 ��� (5.2)W = ��! "��ก������������� (ก.ก./��.)L = �� � ��������ก��� (���)F = ��?�%���@�A������ � (1.5 ก�B�������;$)fs

= "�����������'"�����"$(ก���� (ก.ก./��.5.)

ก�B�'C� Wire mesh fy = 5,000 กก./��.5. ��� fs ����'"������ 1,700 ก.ก./��.5. ��� ����

s

y y

FL(1.4W) FLWA

2f 1.43 f= =�') ก4�� :

?�� B�"$(ก����� ก�� � 1 ���

:%����� ������ T ����� ก�� � 1 ���

��! "��ก���� W = 0.12(2,400)

= 288 ก.ก./��.

s

y

FLW 1.5 6.0 288A

1.43 f 1.43 5,000

× ×= =

×

�$��ก'C� WWR ∅ 4 ..× 4 .., 30 5.× 30 5. (As= 0.419 ��.5./���) �

������� $ 9.7 :���ก����������ก���� ������<��ก! "���%�%��������� ก�� 6.0 ��� <��'C� Wire mesh �ก! $���� ก fy = 5,000 ก.ก./5.2

�') �4 �$��ก�� "� <��'C�ก� D ��� 12 5.

0 5 10 15 20 30

Slab thickness, cm

0

3

6

9

Max.joint spacing,m

Range of

max. spacing

= 0.363 ��.5./���

?�� B�"$(ก��'C�

Page 11: Presentation - RC11 & RC 16_Slab 1 & 2 Way

������QR������QR

ก���ก���������QR

-- ��'$! �!"���'$! �!"� 1010 ++ 22 F!F!..

-- (U# ��ก� �V�!��4�ก��FW!(U# ��ก� �V�!��4�ก��FW!

-- �%!V'� ��ก� �2!�("#36ก����� �%!V'� ��ก� �2!�("#36ก�����

Page 12: Presentation - RC11 & RC 16_Slab 1 & 2 Way

�������� EpoxyEpoxy ก��FW!��QRก��FW!��QR

Page 13: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 14: Presentation - RC11 & RC 16_Slab 1 & 2 Way

Types of Slab

One-way slab Two-way slabOne-way slab

Flat plate slab Flat slab Grid slab

Page 15: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 16: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 17: Presentation - RC11 & RC 16_Slab 1 & 2 Way

Framing Concepts

We can first assume that

we’ll have major girders

running in one direction

in our one-way system

Page 18: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 19: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 20: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 21: Presentation - RC11 & RC 16_Slab 1 & 2 Way

Two Load Path Options

Page 22: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 23: Presentation - RC11 & RC 16_Slab 1 & 2 Way

ExampleExample

Condo Floor PlanCondo Floor Plan

Page 24: Presentation - RC11 & RC 16_Slab 1 & 2 Way

1.0 m

LS

Main reinforcement

������������� ��������������

One-way Slab

Design of one-way slabs is like design of parallel 1m beams.

Page 25: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 26: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 27: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 28: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 29: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 30: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 31: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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] [email protected]

4.0 �.

.13 �.

1.0 �. 1.3 �[email protected]

� ���������

[email protected] [email protected] ������#$

Page 32: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 33: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 34: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 35: Presentation - RC11 & RC 16_Slab 1 & 2 Way

������������������ ������ ( C )

"��#�����

$%�����$%��&��

�)��)��*+ � m

���'�&(,���-('-/���) �� �

-/��0�)�) �� �

,���-'��12��(��3)��

1.0 0.9 0.8 0.7 0.6 0.5

0.033-

0.025

0.040-

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0.062

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-/��0�)�) �� �

,���-'��12��(��3)��

0.0410.0210.031

0.0480.0240.036

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���4�%�% �5 �� �6��,���-('-/���) �� �

-/��0�)�) �� �

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0.0490.0250.037

0.0570.0280.043

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0.0780.0390.059

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0.0490.0250.037

Page 36: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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-0.0380.057

-0.0430.064

-0.0470.072

-0.0530.080

-0.0550.083

-0.0330.050

Page 37: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 38: Presentation - RC11 & RC 16_Slab 1 & 2 Way

������������� ������

��� ����

��� ��

L/5

L/5

L = ���������������

Page 39: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 40: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 41: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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 42: Presentation - RC11 & RC 16_Slab 1 & 2 Way

����� 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 43: Presentation - RC11 & RC 16_Slab 1 & 2 Way

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