Shear Wall IS13920

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1
Ductile Detailing of
RC Structures
:: IS:13920-1993
Ductile Detailing of Ductile Detailing of
RC Structures RC Structures
:: IS:13920 :: IS:13920- -1993 1993
Short Course on Seismic Design of RC Structures
Durgesh C. Rai
Department of Civil Engineering, IIT Kanpur
The material contained in this lecture handout is a property of
Professors Durgesh C. Rai, Sudhir K. Jain and C.V.R.Murty of IIT Kanpur, and
is for the sole and exclusive use of the participants enrolled in the short course on
“Seismic Design of RC Structures” conducted at Ahmedabad during Nov 25-30,
2012. It is not to be sold, reproduced or generally distributed.
Seismic Seismic Seismic Seismic Behaviour Behaviour Behaviour Behaviour of of of of
RC Shear Walls RC Shear Walls RC Shear Walls RC Shear Walls
Seismic Seismic Seismic Seismic Behaviour Behaviour Behaviour Behaviour of of of of
RC Shear Walls RC Shear Walls RC Shear Walls RC Shear Walls
4
• Three common lateral load resisting
systems in RC Buildings
Shear Wall Braced Frame Moment Resistant Frame
Front Views
of Buildings
Top Views
of Buildings
RC Building SYSTEMS RC Building SYSTEMS
55
shear wall shear wall
• What is a Shear Wall?
– Vertical plate-like RC Walls
– Generally starts at foundation
– Goes through full building height
RC
Shear
Wall
Foundation
C
o
l
u
m
nBeam
Slab
6
• RC Shear Wall Building
– Shear Walls also called Structural Walls
RC
Walls
Plan
SHEAR WALLS... SHEAR WALLS...
RC
Shear
Wall
Foundation
C
o
l
u
m
nBeam
Slab
2
7
• Principal attributes
– Large Strength
– High Stiffness
– Ductility
– Shear wall can be detailed to have large ductility
7
SHEAR WALLS... SHEAR WALLS...
0
Strength
Deformability
H
RC Shear Wall
Building
RC Frame
Building

8
• Role of Shear Walls
– Smooth transfer of seismic forces
– Vertically oriented
wide beams
Earthquake-generated
forces at floor levels
Cumulative horizontal
force from above
increases downward
Floor Slab
F
3
F
2
F
1
F
3
F
2
F
1
F
3
F
3
Shear
Wall
F=F
1
+F
2
+F
3
SHEAR WALLS... SHEAR WALLS...
Shear
Wall
9
• Advantages of Shear Walls
– Very good earthquake performance,
if properly designed
– In past earthquakes
•Large number of RC frame buildings damaged or
collapsed
•Shear wall buildings performed very well
SHEAR WALLS... SHEAR WALLS...
“We cannot afford to build concrete buildings meant
to resist severe earthquakes without shear walls”
:: Mark Fintel, a noted earthquake engineer in USA
“We cannot afford to build concrete buildings meant
to resist severe earthquakes without shear walls”
:: Mark Fintel, a noted earthquake engineer in USA
10
• Advantages of Shear Walls…
– Easy to construct
•Straight-forward reinforcement detailing
Easily implemented at site
– Effective in
•Reducing construction cost
•Minimising earthquake damage to
Structural elements
Non-Structural elements
E.g., Glass Windows, Building Contents
SHEAR WALLS... SHEAR WALLS...
11
• Advantages of Shear Walls…
– Lesser lateral displacement than frames
– Lesser Damage to structural and non-structural
elements
Shear Wall
small large
Moment Resistant Frame
SHEAR WALLS... SHEAR WALLS...
12
• Current Use of Shear Walls
– Popular choice in many earthquake prone countries
•Chile, Canada, USA and New Zealand
– In general, used in medium and high rise buildings
•10 storeys and higher
SHEAR WALLS... SHEAR WALLS...
3
13
• Walls must be preferably in both directions
– in plan
If provided only in one direction,
a proper moment resisting frame
must be provided in the other direction.
Architectural Aspects Architectural Aspects
14
• If provided only in one direction, a proper
moment resisting frame must be provided
in the other direction.
Architectural Aspects... Architectural Aspects...
A D
1
4
B C
3
2
Frame
Frame
Shear
Wall
Shear
Wall
Frame
Frame
15
• Shear wall can extend over the full width
of building, or even over partial width
RC Wall of
partial width
Architectural Aspects... Architectural Aspects...
RC Wall of
full width
16
• Walls should be throughout the height
– Cannot be interrupted in lower levels
Best Option:
Wall all through!!
RC Wall
Discontinuity of
wall not desirable
RC Wall
Architectural Aspects... Architectural Aspects...
17
• Walls should be throughout the height
– Cannot be interrupted in upper levels
Architectural Aspects... Architectural Aspects...
Best Option:
Wall all through!!
RC Wall
Discontinuity of
wall not desirable
RC Wall
18
• Walls should be along perimeter of building
– Improves resistance to twist
Shear walls along
perimeter
are more efficient
Shear walls close to
center of building
are less efficient
Architectural Aspects... Architectural Aspects...
4
19
• Walls must be symmetrically placed in plan
Unsymmetric
location of
shear walls
not desirable
Symmetric
location of
shear walls
desirable
Shear Walls only
along one direction
of the building
Symmetry of building in
plan about one axis
Symmetry of building in
plan about both axes
Architectural Aspects... Architectural Aspects...
20
• Shear wall building should not be narrow
– Earthquakes cause significant overturning effects
– Special care is required in design of their foundations
Soil
Architectural Aspects... Architectural Aspects...
Local failure
of soil
Soil
21
• Openings in walls must be
– As few as possible
– As small as possible
– As symmetric as possible
Small and symmetrically
placed openings allowed
RC Wall
Large and randomly placed
openings not allowed
RC Wall
Architectural Aspects... Architectural Aspects...
22
Sliding
Failure
• Undesirable Modes of Failure
Vertical
Uplift
Horizontal
Slide
Inclined
Crack
Overturning
Failure
Shear
Failure
Seismic Seismic Behaviour Behaviour
23
• Undesirable Mode of Failure
Crushing
of
Concrete
Flexure
Compression
Failure
Seismic Seismic Behaviour Behaviour... ...
24
• Desirable Mode of Failure
Horizontal
cracks and
yielding of
steel bars
Flexure
Tension
Failure
Seismic Seismic Behaviour Behaviour... ...
5
25
• Shear demand is more in lower storeys
Earthquake-generated
forces at floor levels
Cumulative
horizontal force
from above
increases
downward
Floor
Slab
Shear
Wall
Direct force flow
through the wall
Seismic Seismic Behaviour Behaviour... ...
26
• Shear demand is more in lower storeys…
Earthquake-induced
horizontal force
at floor levels
Total Horizontal
Force
B
u
i
l
d
i
n
g

H
e
i
g
h
t
Seismic Seismic Behaviour Behaviour... ...
27
• At each section along the height,
shear wall carries
– Axial Force P
– Shear Force V
– Bending Moment M
Seismic Seismic Behaviour Behaviour... ...
P
V
V
M
M
28
• Region of Ductile Detailing
L
w
H
w
Ductile Response
Region:
Larger of Lw and Hw/6,
but need not be more
than 2Lw
(b) Yielding of
vertical steel bars
Actions in Ductile
Response Region
(a) Formation of
horizontal cracks
T
e
n
s
i
o
n
C
o
m
p
r
e
s
s
i
o
n
Seismic Design of RC Walls Seismic Design of RC Walls… …
29
• Possible Geometry of Walls
Hollow::
Walls around Elevators
C-Shaped
L-Shaped
Rectangular
Seismic Design of RC Walls Seismic Design of RC Walls… …
Flanged
30
• Possible Geometry of Walls…
Wall with two columns
built together
Wall with more than two
columns built together
Seismic Design of RC Walls Seismic Design of RC Walls… …
Barbell-Shaped
6
31
• Primary Reinforcement in Walls
Maximum spacing
of vertical
reinforcement not
more than L
w
/5, t
w
or 450mm
Maximum
spacing of
horizontal
reinforcement
not more than
L
w
/5, t
w
or
450mm
Proper anchoring
of vertical
reinforcement into
foundation
Seismic Design of RC Walls Seismic Design of RC Walls… …
32
• Lapping of Vertical Reinforcement Bars
L
w
H
w
Region over which
lapping should be
avoided:
Larger of L
w
and H
w
/6,
but need not be more
than 2L
w
Staggering lapping of
adjacent vertical bars:
Minimum of 600mm
Seismic Design of RC Walls Seismic Design of RC Walls… …
33
• Detailing of Vertical and Horizontal Bars
Closely spaced
confining
reinforcement in
boundary
elements
Max. spacing of
vertical
reinforcement not
more than L
w
/5, t
w
or 450mm
Max. spacing
of horizontal
reinforcement
not more than
L
w
/5, t
w
or
450mm
Seismic Design of RC Walls Seismic Design of RC Walls… …
34
• Confining Steel in Boundary Elements
t
w
L
w
Two curtains of reinforcement
Single curtain of reinforcement
Confining
reinforcement in
boundary elements:
135° hooks, closely
spaced ties
Anchoring of wall reinforcement
in boundary element
Seismic Design of RC Walls Seismic Design of RC Walls… …
35
• Confining Wall Concrete
Open-leg Ties
Anchoring of ties around
both vertical and horizontal
wall reinforcement
Closed stirrups with
135° hook ends
Seismic Design of RC Walls Seismic Design of RC Walls… …
Closed Loop Ties
36
• Curtains of Reinforcement
– One
– Two
Wall thickness t
w
Wall length L
w
Two curtains of reinforcement
Single curtain of reinforcement
Seismic Design of RC Walls Seismic Design of RC Walls… …
7
37
Tension Compression
• Boundary Elements
Two curtains of reinforcement
Single curtain of reinforcement
Confining reinforcement in
boundary elements:
135° hooks, closely spaced ties
Anchoring of wall
reinforcement in
boundary element
Boundary
Element
Two curtains of reinforcement
Single curtain of reinforcement
Boundary Elements
without increased thickness
Boundary Elements
with increased thickness
Boundary
Element
Seismic Design of RC Walls Seismic Design of RC Walls… …
38
• Boundary Elements…
Seismic Design of RC Walls Seismic Design of RC Walls… …
Boundary
Element
Boundary
Element
39
• Seismic behaviour is controllable through
design
Vertical
Uplift
Overturning
Failure
Horizontal
Slide
Sliding
Failure
Inclined
Crack
Shear
Failure
Horizontal
Cracks
Flexure
Failure
Seismic Design of RC Walls Seismic Design of RC Walls… …
40
• Influence of Boundary Elements on Strength
– For same amount of concrete and steel
•Strength of Section 2 > Strength of Section 1
Boundary
Element
1
1
2
2
Slender and Squat Walls Slender and Squat Walls… …
41
• Effect of Axial Load on flexural strength
– Just as in columns
0
P
M
Slender and Squat Walls Slender and Squat Walls… …
42
Coupled Shear Walls Coupled Shear Walls
• Size of opening
Coupling
Beam
P
V
M
8
43 43
• Coupling Beam
– Span-to-depth ratio is small
• Shear deformations are significant
– Ends have large rotational and vertical displacement
• Require very high ductility
Coupled Shear Walls Coupled Shear Walls… …
44 44
• Coupling Beam…
– Shear failure should not precede flexural yielding
– Diagonal reinforcement more effective
– Provide confinement throughout the beam
– Good anchorage of main bars into walls on either side
Coupled Shear Walls Coupled Shear Walls… …
45
• Coupling Beam…
– Diagonal and parallel reinforcement
Coupled Shear Walls Coupled Shear Walls… …
Special confining
reinforcement spacing
> 100 mm centers Wall reinforcement not shown
Wall reinforcement not shown
1.5 ld
1.5 ld
1.5 ld
1.5 ld
46
9.1 General Requirements 9.1 General Requirements
• 9.1.2 Thickness ≥ ≥≥ ≥ 150 mm (preferably)
– Thinner walls have a tendency to buckle out of plane
Wall thickness t
w
Wall length L
w
47
• 9.1.3. Effective flange width,
beyond face of web, smaller of
– Half distance to next wall web
– 1/10 of total wall height
9.1 General Provisions... 9.1 General Provisions...
48
• 9.1.4 Minimum reinforcement in walls
– Vertical and horizontal direction 0.25% of gross area
9.1 General Provisions... 9.1 General Provisions...
9
49
• 9.1.4 Minimum reinforcement in walls…
0.25% of
Gross Area
0.25% of
Gross Area
0.25% of
Gross Area
0.25% of
Gross Area
Vertical
Horizontal
9.1 General Provisions... 9.1 General Provisions...
Both faces
together
Both faces
together
50
• 9.1.5 Two curtains of reinforcement, if
– Factored shear stress > 0.25 ; or
– Wall thickness > 200 mm
•Two curtains reduce fragmentation and early
deterioration of concrete under cyclic response.
ck
f
9.1 General Provisions... 9.1 General Provisions...
51
9.1 General Provisions... 9.1 General Provisions...
• 9.1.5 Two curtains of reinforcement…
t
w
L
w
Two curtains of reinforcement
Single curtain of reinforcement
mm 200 t
or f 25 0
w
ck v
>
> , . τ
52
• 9.1.6 Diameter of bars ≤ ≤≤ ≤ 1/10th wall thickness
9.1 General Provisions... 9.1 General Provisions...
t
w
L
w
d
b
53
• 9.1.7 Maximum reinforcement spacing ≤ ≤≤ ≤


– 450 mm
5 l
w
9.1 General Provisions... 9.1 General Provisions...
w
t 3
54
• 9.1.7 Maximum reinforcement spacing…
Maximum spacing of
vertical reinforcement
not more than
L
w
/5, t
w
or 450mm
Maximum spacing of
vertical reinforcement
not more than
L
w
/5, t
w
or 450mm
Vertical
Horizontal
9.1 General Provisions... 9.1 General Provisions...
Maximum spacing of
vertical reinforcement
not more than
L
w
/5, t
w
or 450mm
Maximum spacing of
vertical reinforcement
not more than
L
w
/5, t
w
or 450mm
10
55
9.2 Shear Strength 9.2 Shear Strength
56
9.2 Shear Strength... 9.2 Shear Strength...
57
• • 9.2.1 to 9.2.5 provide same shear design 9.2.1 to 9.2.5 provide same shear design
provisions as in IS:456 provisions as in IS:456- -2000 for beams 2000 for beams
9.2 Shear Strength... 9.2 Shear Strength...
Section Redesign
ent Reinforcem Design
nforcement MinimumRei
max ,
max ,
v c
c v c
c v
τ τ
τ τ τ
τ τ
<
< <
<
58
• 9.2.6 Uniformly distributed vertical
reinforcement ≥ ≥≥ ≥ Horizontal reinforcement
calculated for shear
– Particularly important for walls with height-to-width
ratio of 1.0 or less
9.2 Shear Strength... 9.2 Shear Strength...
H
W
59
• 9.3.1 Flexural strength similarly calculated
as for columns under axial loads (IS:456).
– Can use Annex A equations for assessing
flexural strength under uniform distribution of
reinforcement
9.3 Flexural Strength 9.3 Flexural Strength
60
• 9.3.1 Flexural strength…
≡ ≡≡ ≡ +
9.3 Flexural Strength... 9.3 Flexural Strength...
11
61
9.3 Flexural Strength... 9.3 Flexural Strength...
• 9.3.1 Flexural strength…
– Annex A
0 0.04 0.08 0.12
0.1
0.2
0.3
0.4
0.5
0.6
0.7
th f
P
ck
u
2
ck
u
th f
M
ε
c
= 0.0035
62
• 9.3.2 Cracked flexural strength >
Uncracked flexural strength
– Avoid brittle behaviour
9.3 Flexural Strength... 9.3 Flexural Strength...
63
• 9.3.3 If no boundary elements
– Provide 4 bars of 12 mm diameter
– In two layers at either end
•Good to have more reinforcement near wall ends
9.3 Flexural Strength... 9.3 Flexural Strength...
64
9.4 Boundary Elements 9.4 Boundary Elements
• 9.4 Boundary elements improve
– Flexural strength
– Shear strength
– Ductility
Boundary
Element
Boundary
Element
65
9.4 Boundary Elements... 9.4 Boundary Elements...
66
• 9.4.1 Boundary elements required
– When extreme fiber compressive stress > 0.2f
ck
– May discontinue boundary element
•When extreme fiber compressive stress < 0.2f
ck
>0.2fck
<0.2fck
9.4 Boundary Elements... 9.4 Boundary Elements...
No
boundary
element
No
boundary
element
Boundary
element
Boundary
element
12
67
9.4 Boundary Elements... 9.4 Boundary Elements...
68
• 9.4.2 Boundary element to carry axial
– Gravity load P
w
(its own share proportional to area)
– Vertical load P
eq
induced by EQ
•Vertical force couple caused by EQ overturning
moment
9.4 Boundary Elements... 9.4 Boundary Elements...
P
eq
= (M
u
-M
uw
)/C
w
69
– M
u
resisted by web = 6,000 kNm
– M
ub
resisted by boundary elements
= 10,000 - 6,000 = 4,000 kNm
– C/c distance of boundary element = 5 m
– Axial force induced by 4,000 kNm moment =
10,000 kNm ±50 kN Seismic
-
400 kN Gravity
Moment M
u
on
entire wall
Axial Load P on
boundary element
4 000
800
5
± = ± ± = ± ± = ± ± = ±
,
kN
9.4 Boundary Elements... 9.4 Boundary Elements...
• Example
– Given
70
• 9.4.3 When gravity load adds to strength
– Load factor is 0.8 (as against 1.2 or 1.5)
Example:
•Let load factor be 1.2 for gravity.
•Design factored axial force
Compression: 1.2(400+50+800)=1,500kN
Tension: (0.8×400)-(1.2 ×50)-(1.2 ×800)=-700kN
9.4 Boundary Elements... 9.4 Boundary Elements...
71
• 9.4.4 Vertical reinforcement in boundary
element
≥ 0.8 % gross area of boundary element
≤ 6% (practically 4%)
─Just like a column
9.4 Boundary Elements... 9.4 Boundary Elements...
72
• 9.4.5 Confinement reinforcement required
throughout height of boundary element
9.4 Boundary Elements... 9.4 Boundary Elements...
13
73
• 9.4.5 Confinement reinforcement…
9.4 Boundary Elements... 9.4 Boundary Elements...
Closely spaced
confining
reinforcement in
boundary
elements
74
• 9.4.6 If entire wall is confined, boundary
element not required.
9.4 Boundary Elements... 9.4 Boundary Elements...
Open-leg
Ties
Anchoring of ties around
both vertical and horizontal
wall reinforcement
Closed stirrups with
135° hook ends
Closed
Loop
Ties
75
• 9.5.1 Coupling beams to be ductile
– When shear stress in coupling beam exceeds given
value, entire seismic shear and flexure to be taken by
diagonal reinforcement (preferably).
9.5 Coupled Shear Walls 9.5 Coupled Shear Walls
76
• 9.5.1 Coupling beams to be ductile…
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
77
• 9.5.1 Coupling beams to be ductile…
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
Special confining
reinforcement spacing
> 100 mm centers
Wall reinforcement not shown
Wall reinforcement not shown
1.5 ld
1.5 ld
78
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
14
79
• 9.5.2 C
u
and T
u
intersect at mid-span
– Moment resisted at mid-span by diagonal bars is zero
C
u
C
u
T
u
T
u
M
u
V
u
V
u
M
u
T
u
V
u
C
u
α
α
α
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
80
• 9.5.2 ...
α sin .
sd y u
A f 74 1 V = ∴
α sin .
y
sd
f 74 1
Vu
A =
C
u
C
u
T
u
T
u
M
u
V
u
V
u
M
u
T
u
V
u
C
u
α
α
α
sd y u
u u
A f 87 0 T
T 2 V
.
sin
=
= α
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
81
• 9.5.3 Diagonal/horizontal bars
– Anchored in wall by 1.5L
dt
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
82
• 9.5.3 Diagonal/horizontal bars…
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
1.5 ld
1.5 ld
1.5 ld
1.5 ld
83
• ACI 318 – 11: Coupling Beams
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
< 4
n
l
h
Diagonal reinforcement effective
< 2
n
l
for
h
necessary to reinforced with two intersecting group of diagonally
placed bars
84
• ACI 318 – 11: Diagonal/horizontal bars
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
Detailing option 1
Confinement of individual diagonals
15
85
• ACI 318 – 11: Diagonal/horizontal bars
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
Detailing option 1
86
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
Detailing option 2
Full confinement of diagonally reinforced beam section
• ACI 318 – 11: Diagonal/horizontal bars…
87
• ACI 318 – 11: Diagonal/horizontal bars
9.5 Coupled Shear Walls... 9.5 Coupled Shear Walls...
Detailing option 2
88
• 9.6.1 Shear strength to be checked along
planes passing through openings
9.6 Openings in Walls 9.6 Openings in Walls
Critical Section
Critical Section
89
• 9.6.2 Reinforcement interrupted by opening
to be provided along edges
– Vertical edge reinforcement to extend full storey height
– Horizontal edge reinforcement to have development
length in tension
9.6 Openings in Walls... 9.6 Openings in Walls...
90
• 9.6.2 Reinforcement at openings…
9.6 Openings in Walls... 9.6 Openings in Walls...
Interrupted bars
Interrupted bars
Replacement steel
Replacement steel
L
dt
16
91
9.7 Discontinuous Walls 9.7 Discontinuous Walls
• 9.7 Special confinement reinforcement
required over full height of columns
supporting walls
92
• 9.7 Special confinement reinforcement…
Special confining reinforcement:
closely spaced transverse ties
throughout the short column
Development length of
longitudinal bar in column
Region over which special
confining reinforcement must
extend into the column above
Regular floor
RC Wall
9.7 Discontinuous Walls... 9.7 Discontinuous Walls...
93
• 9.8 Minimum vertical reinforcement across
the construction joint
9.8 Construction Joints 9.8 Construction Joints
94
• 9.8 Construction Joints…
9.8 Construction Joints... 9.8 Construction Joints...
Construction Joint
Construction Joint
Vertical bars across
construction joint
Vertical bars across
construction joint
95
9.9 9.9 Development, Splice & Anchorage Requirement Development, Splice & Anchorage Requirement
96
• 9.9.2 Splicing of vertical reinforcement to
be avoided in critical regions
9.9 Development, Splice & Anchorage Req.... 9.9 Development, Splice & Anchorage Req....
L
w
H
w
Region over which
lapping should be
avoided:
Larger of L
w
and H
w
/6,
but need not be more
than 2L
w
Staggering lapping of
adjacent vertical bars:
Minimum of 600mm
17
97
• 9.9.3 Lateral tie requirements for lapped
spliced bars
9.9 Development, Splice & Anchorage Req.... 9.9 Development, Splice & Anchorage Req....
98
• 9.9.4 Welded splices and mechanical
connections as per IS:456.
9.9 Development, Splice & Anchorage Req.... 9.9 Development, Splice & Anchorage Req....
99
Example: RC Shear Example: RC Shear Example: RC Shear Example: RC Shear
Wall Design Wall Design Wall Design Wall Design
Example: RC Shear Example: RC Shear Example: RC Shear Example: RC Shear
Wall Design Wall Design Wall Design Wall Design
100
• Design a shear wall for a two-storey building as shown in
Figure. The materials are M20 concrete and Fe415 steel.
The example shows design for load combination 1.2(DL +
LL +EL) only. In practice all other combinations should
also be considered. The unfactored forces in the panel
between the ground level and first floor are obtained by
analysis as
Example Example
IITK GSDMA: Explanatory Examples for Ductile Detailing of RC Buildings
101
Example Example… …
102
• Factored bending moment on the section,
– M
u
= 1.2 × (577.5 + 4830.9) = 6490 kNm
• The maximum factored shear force,
– V
u
=1.2 × (19.7 + 699.1) = 863 kN
• Effective depth
– d
e
= 3380+(380/2)+(380/2) = 3760 mm

• Let the minimum vertical reinforcement = 0.25% provided
in the web
, 0.998 Shear stress τ = =
×
u
v
e w
V
d t
Example Example… …
18
103
• As per Table 19 of IS: 456-2000, τ
c
= 0.36 N/mm
2
.
• Shear carried by concrete,
• Shear to be resisted by horizontal reinforcement,
V
us
= V
u
- V
uc
= (863 – 311) = 552 kN
• Minimum horizontal reinforcement (0.25%) requires this
ratio to be 0.575
• For t
w
> 200 mm, the reinforcement shall be in 2 layers
• Provide horizontal reinf. of 8mm dia. bars at 175 mm c/c in
2 layers
311 kN τ = × × =
uc c e
V d t
Shear DESIGN Shear DESIGN… …
0 87 .
=
y h e
us
v
f A d
V
S
0 41 . ⇒ =
h
v
A
S
104
• Effective depth of wall on each side of opening
= (1090+380/2) = 1280 mm
→τ
v
=1.47 N/mm
2
• Shear to be resisted by reinforcement on each side of
opening
V
us
= 326 kN.
Provide 8 mm diameter 2-legged stirrups at 140 mm c/c on
each side of opening
Shear DESIGN at opening Shear DESIGN at opening… …
105
• Vertical reinf. in web is 0.25 percent
• L
w
= 4140 mm and t
w
= 230 mm
• Axial compression will increase moment capacity of wall
Factored axial force
- P
u
= 0.8 × 1922.9 +1.2 × 255.7 = 1845 kN
Assuming this axial load to be uniformly distributed,
load on web = 0.574 × 1845 = 1059 kN
• The moment of resistance of a slender rectangular shear
wall section with uniformly distributed vertical reinf. can
be estimated as per IS 13920: 1993 (Annex A)
Flexural Strength of web Flexural Strength of web… …
106
where
(1)
Flexural Strength of web Flexural Strength of web… …
107
Value of x
u
/ l
w
calculated from the quadratic equation
where
(2)
Flexural Strength of web Flexural Strength of web… …
108
• As x
u
/l
w
< x
u
*/l
w
,
– we get the value as:
λ= 0.056, φ = 0.045, x
u
/l
w
= 0.233,
x
u
*/l
w
= 0.660, and β = 0.516
• Moment of resistance of the web
– M
uv
= 3296 kNm
• Remaining moment will be resisted by reinf. in boundary
elements
– (M
u
- M
uv
) = (6490 - 3296) = 3194 kNm
Flexural Strength of web Flexural Strength of web… …
19
109
• Due to combined axial load and bending, axial compression
at the extreme fibre = 6.81 N/mm
2
> 0.2f
ck
→Boundary elements are mandatory
• Center to center dist. b/w the boundary elements, C
w
= 3760 mm
• Axial force on the boundary element due to earthquake
loading
= (M
u
-M
uv
)/C
w
= 3194/3.76 = 849 kN
• Maximum factored compression on the boundary element
[849 + 0.213 × 1.2 × (1922.9 + 255.7)] = 1406 kN
• Factored tension on the boundary element,
[0.213 × (0.8 × 1922.9 - 1.2 × 255.7) -849] = -587 kN
Boundary elements Boundary elements… …
Cl. 9.4.1
IS 13920
Cl. 9.4.1
IS 13920
110
• Assuming short column action
– the axial load capacity of the boundary element with
min. reinf. of 0.8% = 2953 kN
• 12 bars of 16 mm diameter will be adequate to take the
compression as well as tension
• Also, provide special confining reinf. as per Cl. 9.4.5
Boundary elements Boundary elements… …
Cl. 9.4.4
IS 13920
Cl. 9.4.4
IS 13920
111
• Opening size = 1200 mm by 1200 mm
• Area of vertical and horizontal reinforcement in the web
(0.25%) that is interrupted by it is 690 mm
2
– Provide area of bars equal to the
respective interrupted bars
• Thus, one bar of 16 mm diameter should be provided per
layer of reinforcement on each side of the opening
– The vertical bar should extend for the full storey height
– The horizontal bar should be provided with development length
in tension beyond the sides of the opening
Reinforcement Around opening Reinforcement Around opening… …
Cl. 9.6.2
IS 13920
Cl. 9.6.2
IS 13920
Cl. 9.6.2
IS 13920
Cl. 9.6.2
IS 13920
112
Reinforcement Details Reinforcement Details… …
Thank you…

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