Seismic Design of Reinforced Concrete...
Transcript of Seismic Design of Reinforced Concrete...
1
Chapter 6 Seismic Design of Reinforced Concrete Buildings
Chapter 6
6.1 Introduction
6.2 Earthquake Damage in Reinforce Concrete Buildings
6.3 Structural System and Seismic Grading for Structures
6.4 Seismic design of RC frames
6.5 Seismic design of RC walls
6.6 Detailing
6.7 Dual system *
6.8 Case Study
The appropriate maximum height for R/C buildings (m)
(Table 6.1.1 in GB50011-2010)
Notes: the height in () is the value listed in GB 50011-2008
Structure Types System Seismic Fortification Intensity
6 7 8 (0.2g) 8 (0.3g) 9
Frame System 60 50 (55) 40 (45) 35 24 (25)
Frame-Wall System 130 120 100 80 50
Structural Wall System 140 120 100 80 60
Frame supported Wall System
120 100 80 50 N.A
Frame- Tube System 150 130 100 90 70
Tube in Tube System 180 150 120 100 80
Slab-Column and Wall System
80(40) 70(35) 55(30) 40 N.A
Seismic grading for reinforced concrete buildings
(Table 6.1.2 in GB50011-2010)
Types of structure Seismic fortification intensity
6 7 8 9
Fram structure
Height (m) ≤24 >24 ≤24 >24 ≤24 >24 ≤24
Frames 4th 3rd 3rd 2nd 2nd 1st 1st
Large span frames
3rd 2nd 1st 1st
Wall-Frame
structure
Height (m) ≤60 >60 ≤24 25~60 >60 ≤24 25~60 >60 ≤24 25~60
Frames 4th 3rd 4th 3rd 2nd 3rd 2nd 1st 2nd 1st
Structural walls
3rd 3rd 2nd 2nd 1st 1st
Structural wall
structure
Height (m) ≤80 >80 ≤24 25~80 >80 ≤24 25~80 >80 ≤24 25~60
Structural walls
4th 3rd 4th 3rd 2nd 3rd 2nd 1st 2nd 1st
be continued
Types of structure Seismic fortification intensity
6 7 8 9
Frame -supported
wall structure
Height (m) ≤80 >80 ≤24 25~80
>80 ≤24 25~80
Struc-tural walls
General 4th 3rd 4th 3rd 2nd 3rd 2nd
Streng-thening
3rd 2nd 3rd 2nd 1stI 2nd 1st
Frames that supporting
walls 2nd 2nd 1st 1st
Framed-tube structure
Frame 3rd 2nd 1st 1st
Tube 2nd 2nd 1st 1st
Tube in tube structure
Exterior tube 3rd 2nd 1st 1st
Interior tube 3rd 2nd 1st 1st
Slab-column-wall structure
Height (m) ≤35 >35 ≤35 >35 ≤35 >35
Columns 3rd 2nd 2nd 2nd 1st
Walls 2nd 2nd 2nd 1st 2nd 1st
(Table 6.1.2 in GB50011-2010)
Flow Chart of seismic design
simplified
m4
m3
m2
m1
K4
K3
K2
K1
Calculation of Eq. Action
Floor 1
Floor 2
Floor 3
Floor 4
D value I-Point
Shear force distribution
Response Eq. Action
Unfavorable Combinations of Some Responses
6.4 Seismic design of RC frames
Three Methods to calculate the Eq. Action
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Design of Element
Flexural Strength
Shear Strength
Flexural Strength
Shear Strength
The strength of Shear shall be stronger than flexural
columns shall be stronger than beams
Joint shear strength
joint shall be stronger than connected beams and columns
Mc,up
Mc,low
Mb,r
Mb,l
Vc,up
Vb,l
Vb,r
Nc,up
Nc,low
Vc,low Vc,low
Vc,low
Beam
Column
The strength of Shear shall be stronger than fexual
Flow Chart of seismic design 6.4.5 Design of beam-column joints
Principle: strong joints-weak members
The design of beam-column joints is primarily
aimed at:
(i) preserving the integrity of the joint so that the strength
and deformation capacity of the connected beams and
columns can be developed and substantially maintained.
(ii) preventing significant degradation of the joint stiffness
due to cracking of the joint and loss of bond between
concrete and the longitudinal column and beam
reinforcement or anchorage failure of beam reinforcement.
(1)Schematic Diagram
bc
sbo
sb
bjb
jhH
ah
ah
MV
/
/
0
1 (5.41)
bc
sbo
sb
bua
jhH
ah
ah
MV
/
/
0
115.1
(5.42)
(2) Design value of shear force
=1.5,1.35, 1.2 corresponding to grade 1, 2 and 3 for frame structurej
(6.42)
(6.43)
For Grade 1 frame structure at Intensity 9 area, it should also comply with:
strong joints - weak members
s
ahAf
b
bNhbfV sb
svjyv
c
j
jjjtj
RE
j05.01.1
1
(3) Seismic shear strength checking of joint core
s
ahAfhbfV sb
svjyvjjtj
RE
j09.0
1
( .3 )j c c j j
RE
1V 0 f b h
(6.39)
(6.40)
(6.41)
For Grade 1 frame structure at Intensity 9 area, it should also comply with:
6.5 Seismic design of reinforced concrete structural walls
Structural wall system
• Reinforced-concrete structural walls
(commonly referred to as shear walls)
are being used more and more for
resisting earthquake forces, either alone
or in conjunction with ductile moment
resisting frames.
• The reason is that shear walls stiffen a
building, and this reduces nonstructural
damage.
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• When walls are situated in advantageous position in building, they
can form an efficient lateral-force-resisting system, while
simultaneously fulfilling other functional requirements.
• The extent to which a wall will contribute to the resistance of
overturning moments, story shear forces, and story torsion depends
on its geometric configuration, orientation, and location within the
plane of the building.
6.5.1 Structural wall system
Construction of
RC-Shear Wall
Colum
Slab
Beam
Colum Beam
Main reinforcement of the colum
Stirrup
Main reinforcement of the beam
Longitudinal reinforcement of the wall
horizontal reinforcement of the wall
Strengthening rebar of the opening
• Boundary elements (边缘约束构件) are often present to
allow effective anchorage of transverse beams.
• Boundary elements are often provided
• to accommodate the principal flexural reinforcement,
• to provide stability against lateral buckling of a thin-
walled section and,
• to enable more effective confinement of the compressed
concrete in potential plastic hinges.
Boundary elements 6.5.2 Structural Analysis
Equivalent stiffness of member
• a cantilever model is used for simplicity, to derive the equivalent
flexure stiffness of structural walls.
• For structural walls with regular and uniform stiffness along the vertical
direction, the equivalent flexure stiffness E c Ieq can be obtained.
single wall
Wall with
small openings Coupled wall
a. Walls under vertical load
Where is the coefficient considering construction error
allowance, is the coefficient considering out-plane buckling.
6.5.3 Seismic design of structural walls
)( /
ysc fAAfN (5.67) (6.93)
b. Walls under combination of seismic and gravity loading
6.5.3 Seismic design of structural walls
(6.97a) 2.5 )2.0(1
wwcc
RE
hbfV
(5.68)
)15.0(1
wwcc
RE
hbfV
(5.69)
(6.98) = /( )c c
0M V h
Where the shear-span-ratio is :
(6.97b)
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• The design shear force at bottom section in strengthened regions
(底部加强区)of a structural wall
For structure walls in grade 1,2,3 frames, is 1.6, 1.4 and 1.2.
For those with Grade 1 at Intensity 9,
• Design shear force at end section of a coupling beam (连梁)
with a span depth ratio greater than 2.5
• Where is 1.3, 1.2, 1.1 for Grade 1, 2, 3
wvwVV
Gbn
r
b
l
bvb VlMMV /)(
vw
6.5.3 Seismic design of structural walls
1.1 ( / ) wua w wV M M V
vw
Load carrying capacity of normal cross section of wall under
eccentric axial loading
Walls under eccentric compressive force
)(1 //
cswssys
RE
NNAfAN
(5.74)
)
2()
2(
1/
0
// fw
csw
f
wys
RE
hhNMM
hhfAM
(5.75)
(6.105)
(6.106)
6.5.4 Shear Capacity checking of wall section
Walls with a rectangular section, subjected to a large
eccentric tensile force
wu
u
RE M
eNN 0
0
1
(5.88)
2
2/)
2(
/
0
/
0
fw
ywsw
f
wyswu
hhfA
hhfAM
(5.90)
(6.119)
(6.121)
6.5.4 Shear Capacity checking of wall section Diagonal shear resistance of structural walls under eccentric
compressive loading
Diagonal shear resistance of structural walls under eccentric
tensile loading
Seismic shear resistance of coupling beams
00 8.0)1.04.0(
5.0
11w
shyh
wwwt
RE
hs
Af
A
ANhbfV
(5.91)
00 8.0)1.04.0(
5.0
11w
shyh
wwwt
RE
w hs
Af
A
ANhbfV (5.92)
00 7.005.0
1b
svyvbbc
RE
b hs
AfhbfV
(5.93)
(6.122)
(6.123)
(6.124)
Shear strength check on the construction joints (施工缝) of structural walls
Horizontal construction joints (水平施工缝) are potential planes of weakness for structural walls.
If shear resistance of a construction joint fails to satisfy this requirement, additional steel reinforced bars are needed perpendicular to the horizontal joint, with sufficient anchorage length each side of the joint.
NAfV sy
RE
wj 8.06.01
(5.94)
6.5.5 Design of Structural Wall
Plane layout
Vertical layout
Axial-force ratio
Boundary element
Strengthening region at the bottom
Minimum ratio of reinforcement of wall
Construction requirement of tie beam
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Plane Layout
Principle:
Increase the integral lateral stiffness, but not too high;
Try to make the stiffness center superpose upon the
centric to reduce eccentricity and avoid torsion;
Avoid short-width wall;
The length of wall should be shorter than 8m and the
height-to-width should be lager than 2;
Wall should be arranged in two ways along the main axis
and the axis of wall should align to the axis of frame.
It’s inappropriate to set the frame beam onto the tie beam.
Vertical Layout
Principle:
The shear wall should be arranged continuously from bottom to
top;
Openings should be lined up in the same place. Irregular
openings should be strengthened;
Pay attention to the situation that the shear wall is set upon
beams. These beams are frame-supported beams, so their
seismic intensity should be upgraded. ;
Try to avoid weak layer. The shear force of weak layer should
multiply the amplification coefficient 1.15;
The out-of-plane stiffness should be controlled.
Bottom Strengthening Region
Purpose:
To ensure draw ability after plastic hinges appear in
the shear walls, the strengthening region at the
bottom should be reinforced.
Principle:
1/8 of the total height of shear wall,
When H>150m, 1/10
Or reinforce the two stories at the bottom
Limit of Axial-Load Ratio
principle:
Increase wall’s drawability to make the shear walls at
the bottom form plastic hingles when facing rare
earthquake, avoiding brittle failure.
Axial pressure N based on representative value of
gravity load. (different from colums)
Axial-load ratio
Ⅰ(9 degree) Ⅱ(7,8 degree) Ⅱ
N/fcA 0.4 0.5 0.6
Boundary Member
Restraining boundary member
Constructing boundary member
Principle
Restraining boundary member:the ends of Grade 1 and 2’s shear wall’ bottom-
strengthening region and the first story above;
Constructing boundary member:the rest
ends of Ⅰ,Ⅱ shear wall. The ends of Ⅲ,Ⅳ shear wall and non-seismic design wall.
Restraining Boundary Member
Length of wall: lc
Volume stirrup ratio:
Characteristic value of stirrup: v
Item Ⅰ(9 degree) Ⅰ(7,8 degree) Ⅱ
v 0.20 0.20 0.20
lc (embedded
column) 0.25hw 0.20hw 0.20hw
lc (flanking column
or column at the
end of wall)
0.20hw 0.15hw 0.15hw
cv v
yv
f
f
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Diameter of stirrup: 8mm;
Stirrup spacing value: 100mm(Ⅰ)
150mm(Ⅱ)
Longitudinal reinforcement:
range—shaded area A;
Area—1.4%, 1.2%, 1.0%;
( special Ⅰ,Ⅰ,Ⅱ shear wall respectively )
Diameter: 616, 614;
Restraining Boundary Member
约束边缘构件
约束
边缘构件截面及配筋
Constructing boundary member
Length of wall, minimum of stirrup, maximum stirrup
spacing
Strengthening portion at the bottom Other locations
Stirrups or tie bar Stirrups or tie bar
Seismic
grade of
structure
s
Minimum
amount of
longitudinal
reinforcements
(the greater value
should be used)
Minimu
m
diameter
(mm)
Max.
spacing
(mm)
Minimum
amount of
longitudinal
reinforcements
(the greater value
should be used)
Minimu
m
diameter
(mm)
Max.
spacing
(mm)
1 0.010Ac, 616 8 100 0.008Ac, 614 8 150
2 0.008Ac, 614 8 150 0.006Ac, 612 8 200
3 0.006Ac, 612
(0.005Ac, 412)
6 150 0.005Ac, 412 6 200
4 0.005Ac, 412 6 200
(150)
0.004Ac, 412 6 250
(200)
Constructing boundary member
Minimum Dimension of Shear Wall
Strength of concrete ≥C20;
Thickness of shear wall
Seismic
intensity region Embedded column Non-embedded column
Ⅰ,Ⅱ
Strengthening
region at the
bottom
H/16 200 h/12 200
The rest H/20 160 h/15 180
Ⅲ, Ⅳ
Strengthening
region at the
bottom
H/20 160 H/20 160
The rest H/25 160 H/25 180
Non-
seismic
design
all H/25 160 H/25 180
1. Non-seismic action:
2)Seismic action:
Shear-span ratio>2.5:
Shear-span ratio≤2.5:
.w c c w w0V 0 25 f b h
( . )w c c w w0
RE
1V 0 20 f b h
( . )w c c w w0
RE
1V 0 15 f b h
c
c
w0
M
V h
Minimum Dimension of Shear Wall
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Distributing reinforcements
Lateral and vertical reinforcemens:
swsw
w
A
b s
Shear wall
Seismic
intensity
Minimum ratio of
reinforcement
Maximum
spacing value
Minimum
diameter
Normal
height Ⅰ, Ⅱ, Ⅲ 0.25% 300 8
Normal
height
Ⅳ, non-seismic
design 0.20% 300 8
B height Special Ⅰ
Strengthening
region: 0.40%
The rest: 0.35%
300 8
Temperature
-stress-
increase
region
Seismic and
non-seismic
0.25%
200 ——
Design of Tie Beam
principle:
Similar to the design of RC beam;
According to the design of double-tendon section beam;
Moment and shear force should be adjusted:
Ideal elastic:6,7 degree: ×0.8,
8,9 degree: ×0.5,
Not consider the function of tie beams when meeting
rare earthquake.
Flexure capacity:
'( )y s b0M f A h a
1. non-seismic action:
2. seismic action:
Span-to depth ratio>2.5:
Span-to-depth ratio<=2.5:
. svw t b b0 yv b0
AV 0 7 f b h f h
s
( . )svb t b b0 yv b0
RE
A1V 0 42 f b h f h
s
( . . )svb t b b0 yv b0
RE
A1V 0 38 f b h 0 9 f h
s
Design of Tie Beam---Shear Capacity
Minimum dimension:
1. non-seismic action:
2. seismic action:
Shear-span ratio>2.5:
Shear-span ratio≤2.5:
.w c c w w0V 0 25 f b h
( . )w c c w w0
RE
1V 0 20 f b h
( . )w c c w w0
RE
1V 0 15 f b h
Design of Tie Beam
Strong-shear-weak-bending
Ⅰ,Ⅱ,Ⅲ,Ⅳ seismic:
9 degree:
l r
b bb vb Gb
n
M MV V
l
.l r
bua buab Gb
n
M MV 1 1 V
l
Design of Tie Beam Reinforcement of tie beams
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Exercises
Given: A 12-storey office building will be built in the area, which seismic
fortification is 7. The building is designed to use concrete (C35, fc=
16.7N/mm2). The length of the plane of the building is 48m, with the
spacing of columns is 8.0m, the width is 24m, with spacing of columns is
6.0m, meanwhile, the height for ground floor is 5.5m, and for the other floors
are all as 3.9m. The dead loads and live loads for every storey is 5.5kN/m2 and
2.5kN/m2 respectively.
Ask: 1. Please use the limitation of axial-force ratio to evaluate the section
dimension of column at bottom story.
2. Check the dimension of column according to the minimum requirement for
shear resistant.
3. According to GB 50011,2010, please give the limitation value of drift,
torsion action, minimum reinforcement ratios and maximum reinforcement
ratios of column and beam respectively.
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