Lateral Load Resisting Systems
IITGN Short Course
Gregory MacRae
Many slides from 2009 Myanmar Slides of Profs Jain and Rai
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Lateral Loads
Wind
Earthquake
Lateral Load Resisting Systems
Rai, Murty and Jain
Lateral Load Resisting Elements
• Vertical Elements
• Moment-Resisting Frames
• Walls
– Bearing walls / Shear Walls / Structural Walls
•
•
•
•
•
Gravity Frame + Walls
“Dual” System (Frame + Wall)
Vertical Truss
Tube System
Bundled-Tube System
• Floor/Diaphragm
• Foundation – various types
Rai, Murty and Jain
Vertical Elements
Building Structures
• Structural Systems
Frame with Concrete
Shear Walls
Concrete Frame with
Shear Walls
Concrete Moment
Resisting Frame
Steel Braced Frame
Rai, Murty and Jain
Building Structures…
• Structural Systems…
Rai, Murty and Jain
Evolution of Systems
Vertical Elements
Moment-Resisting Frames
Walls (Bearing walls / Shear Walls / Structural Walls)
Gravity Frame + Walls
“Dual” System (Frame + Wall)
Vertical Truss
Tube System
Bundled-Tube System
Rai,
Murty
and
Jain
U.S. Buildings, Zones 3 and 4
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Sudhir K Jain
Lateral Load Resisting Elements…
Bearing/Shear Wall System
Variations in LFRS Selection among seismic countries, Zones 3 and 4
Countries – CHILE, US, PERU, COLOMBIA, MEXICO
Lateral Load Resisting Elements…
Building Frame /Shear Wall System
Variations in LFRS Selection among seismic countries, Zones 3 and 4
Countries – CHILE, US, PERU, COLOMBIA, MEXICO
Lateral Load Resisting Elements…
Moment Resisting Frame System
Variations in LFRS Selection among seismic countries, Zones 3 and 4
Countries – CHILE, US, PERU, COLOMBIA, MEXICO
Lateral Load Resisting Elements…
Wall/Frame Dual System
Variations in LFRS Selection among seismic countries, Zones 3 and 4
Countries – CHILE, US, PERU, COLOMBIA, MEXICO
Lateral Load Resisting Elements
Countries – CHILE, US, PERU, COLOMBIA, MEXICO
Bearing/Shear Wall
Building Frame/Shear Wall
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Sudhir K Jain
Lateral Load Resisting Elements
Countries – CHILE, US, PERU, COLOMBIA, MEXICO
Moment-Resisting Frame
Wall/Frame Dual Frame
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Sudhir K Jain
STRUCTURAL FORMS
Approximate Analysis of:
- Moment Frames
- Walls
Approximate analysis allows to get a simple
estimate of member sizes and to check the
magnitude of computer analysis results
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Sudhir K Jain
Moment Resisting Frame
• Components
– Beams
– Columns
– Joints
P
P/2
P/2
h
Ph / 2
Ph / 2
Ph / 2
Ph / 2
• Joints: Most frames have joints where the angle
between the connecting members in maintained,
i.e., rigid joints.
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Sudhir K Jain
Moment Resisting Frame
BMD
Frame with rigid joints and with very flexible beams.
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Sudhir K Jain
Moment Resisting Frame
Deflected shape due to
flexural deformation of
columns
Deflected shape due to
flexural deformation of
columns and beams.
Deflected shape due to
flexural deformation of
columns and beams, axial
deformation of columns.
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Sudhir K Jain
Moment Resisting Frame
BMD
Frame with rigid joints and with infinitely rigid beams
For such a frame with
different flexibility beams,
what is the range of column
base moments?
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Sudhir K Jain
Moment Resisting Frame
0.5Lbeam
Lbeam
htop
0.7htop
hmid
0.5hmid
hmid
0.5hmid
hbot
Moment Pattern
Under Lateral Forces
0.7hbot
Hinges (locations of zero
moment) – Midpoints of Beams
Aseismic Design Analysis of Buildings, by Kiyoshi Muto; Maruzen Company, Ltd.,
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Tokyo, 1974 xiv q-361 pp.
Moment Resisting Frame
Lateral Forces
Lateral Shears
Shears on Different
Columns
Exterior Columns Assumed to Carry One Half Shears of Internal Columns
Aseismic Design Analysis of Buildings, by Kiyoshi Muto; Maruzen Company, Ltd.,
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Tokyo, 1974 xiv q-361 pp.
Moment Resisting Frame
20kN
40kN
40kN
80kN
40kN
20kN
80kN
40kN
Shears on Different Columns
120kN
240kN
Lateral Forces
Lateral Shears
Exterior Columns Assumed to Carry One Half Shears of Internal Columns
Example:
If the storey shear at the top level is 120kN say, then the shear force on
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an internal column in 20kN, and on an external column is 40kN.
Moment Resisting Frame
6kN
20kN
40kN
40kN
80kN
40kN
20kN
80kN
40kN
Example:
Top right beam shear is found by
considering a free body. The beam
axial force is first computed from .
horizontal equilibrium as 20kN. Then,
by taking moments about the column
mid-height, the beam shear is
20kNx0.3*3.6m /(0.5x7.2m)= 6kN.
0.5 x 7.2m
20kN
Shears on Different Members
6kN
0.3 x 3.6m
20kN
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Moment Resisting Frame
6kN 21.6kNm
20kN
40kN
40kN
80kN
40kN
20kN
80kN
40kN
Example:
The beam moment demand is therefore
0.5 x 7.2m * 6kN = 21.6kNm due to
earthquake loads. This can be
combined with gravity loads for design.
21.6kNm
0.5 x 7.2m
20kN
Forces on Different Members
6kN
0.3 x 3.6m
20kN
A similar process may be used to obtain all moments, shears and axial forces throughout
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the frame.
Moment Resisting Frame
Seismic axial forces in columns
are generally small in the internal
columns since the shears in the
beams either side of the column
tend to cancel out. They are
generally greater in the external
columns
Forces on Different Members
Degree of Freedom in 2-D Frame
Degrees of freedom (3 per joint)
Degrees of freedom after
neglecting axial deformations
(one per joint +one per floor)
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Sudhir K Jain
Degree of Freedom in 3-D Frame
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Sudhir K Jain
Moment Resisting Frame
y
x
Plan of a three-storey building having three two-bay frame in the
y-direction, and by two four-bay frames in the x-direction
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Sudhir K Jain
Moment Resisting Frame
Plan of a three-storey building having three two-bay frame in
the y-direction, and by two four-bay frames in the x-direction
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Sudhir K Jain
Walls
•
•
•
•
•
Bearing wall / structural (shear) wall
Shear wall shear beam
Large width-to-thickness ratio; else like a column
Height-to-width
small ( 1) Mainly shear deformations
large ( 4)
Mainly flexural deformations
in-between Shear and flexural deformation
Foundation
rigid body rotation
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Sudhir K Jain
Walls
Wall with Shear
Deformation
Wall with Flexural
Deformation
Wall with both
Shear and Flexural
Deformation
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Sudhir K Jain
Example
Stiffness due to point load at the top
0.15m thick
0.4m
14m
3.6m
0.4m
0.4m
4m
Wall Section
Area = 860,000 mm2
Shear Area = 540,000 mm2 (= 0.15m x 3.6m)
Moment of Inertia = 1.867 1012 mm4
E = 25,500 MPa
G = 10,500 MPa
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Sudhir K Jain/MacRae
Example
3
3
flexure
shear
WH
W 14000
6
19
.
6
10
W mm
12
3EI
3 25,000 1.867 10
WH
W 14000
2.46 10 6 W mm
As G 540,000 10,500
Total Deflection
k wall
=
W
22.1 10 6W
flexure +
-6 W mm
=
22.1X10
shear
45,320 N mm
45,320 kN m
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MacRae/Sudhir K Jain
Rocking of Footing
4m
Shear wall
Footing
8m
Winkler’s Foundation
M
k(x ). 4dx
Sub grade modulus for some soils
k 30,000kN / m3
x
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Sudhir K Jain
Rocking of Footing
Rocking stiffness of footing
• Rocking moment M causes rotation
• Restoring moment
4
M
4m k x x dx
5.12 106 kNm
4
• Rocking stiffness of footing
M
5.12 106 kNm / rad
• Horizontal load W acting 14m above
Moment applied on footing = 14W kNm
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Sudhir K Jain
•
Rotation of footing
14W
5.12 106
•
Wall displacement at roof level
rocking
•
2.73 10 6W radians
2.73 10 6 W
14 3.83 10 5W m
Total deflection
total
rocking
flexure
5
shear
8
3.83X 10 W m 2.21X 10 W m
5
3.83X 10 W m
•
Wall stiffness
k wall
W
5
3.83X 10 W
26,110kN / m
Rocking governs deflections and stiffness!!!
It must be considered
Rocking of Footing
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Sudhir K Jain
Shear Wall with Openings
• Issues
• Stiffness calculations
• Force resultants/stresses
• Detailing
• Stiffness
Small Opening
Ignore reduction in lateral
stiffness due to opening
Large Opening
Behaves as two walls connected
with a coupling beam
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Sudhir K Jain
Shear Wall with Openings Issues
beam
Wall
beam
Imaginary
beam
Shear panels
Analysis
Model
I=∞
Column
beam
Column
I=∞
Column
Ib
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Sudhir K Jain
Example
Beam size 200 X 1100
0.15m thick
0.4m
14m
A
A
B
B
Section AA
0.4m
Section BB
Opening
4m
3m
6m
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Sudhir K Jain
Wall-Frame Systems
How does a moment-resisting frame deform?
Say, frame is generally uniform (with height)
Storey stiffness same
Storey Shear
Storey
deformation
1000
1000
5
5
1000
5
1000
5
400
1000
5
100
1400
1500
1550
7
7.5
7.75
1000
Displacement
Profile
20
15
10
5
1000
50
28.25
23.25
16.25
7.75
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Sudhir K Jain
Wall-Frame Systems
How does a wall structure deform?
The deflected shape is
 Straight line for point load at top
 Approximately a quarter cycle of sine function in case of earthquake
force.
Deformation:
Cantilever beam
Frame
(flexural beam; ignoring shear deformation)
::Large inter-storey
displacement
Zero Slope :: Small inter-storey
displacement
Zero Slope
:: Small inter-storey
displacement
What happens, if we combine the two?
Large inter-storey
displacement
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Sudhir K Jain
Wall-Frame Interaction
• Building has walls and frames which shear lateral loads
• Extreme 1 ::
Walls too rigid compared to frames
Frames deform as per walls
• Extreme 2 ::
Frames too rigid
Walls deform as per frames
• Walls and frames comparable ::
Interaction through floor diaphragm
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Sudhir K Jain
Wall-Frame Interaction
Interacting Forces
tension
Combine
compression
Rigid Frame
Shear Wall
“Shear Mode”
Deformation
Bending Mode
Deformation
Combine Deformations
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Sudhir K Jain
Wall-Frame Interaction
•
Walls :: flexural deformations
•
Frames
:: deformations are
like shear beam
Buildings must be designed
to carry interaction forces
P
This can be considered
in analysis
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Sudhir K Jain
Other Systems
Tube Systems
Bundled Tube
A
Shear lag
A Compression Columns B
Plan
B
2
Variation in axial
force
in columns
Tension Columns
Force
1
Plan
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Sudhir K Jain
Horizontal Elements
Rai, Murty and Jain
Slabs:
Cast In Situ (Common in India)
Precast:
E.g. Post-tensioned
(with topping)
Cold-Formed Steel Deck
jpcarrara.com
http://www.formstress.co.nz/products/ribtimber.html#construction
Reinforced Concrete Cast-in-Situ Slabs
•
The slab is subject to horizontal load.
t
b
• Moment of inertial for bending in its own plane
tb3
( Very large quantity!!)
I
12
• Floor is stiff for bending deformation in its own plane.
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Sudhir K Jain
Floor Diaphragm Action
L
k
b
L
k/2
k
Plan of a one-storey building
with shear walls
Springs represent lateral
stiffness walls / frames
t = floor thickness; width of the beam representing floor diaphragm
b = floor width; depth of the beam representing floor diaphragm
L = span of the beam representing floor diaphragm
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Sudhir K Jain
Floor Diaphragm Action
Lateral earthquake force, EL
Beam representing
floor diaphragm
Ibeam = tb3/12
K
K/2
K
Vertical load analogy for floor diaphragm action
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Sudhir K Jain
In-plane versus out-of-plane deformation of floor
In Plane Force
In Plane Deformation of
Floor
Out of Plane Force
Out of Plane Deformation
of Floor
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Sudhir K Jain
Floor Deformations
In-Plane Floor Deformation
Out of Plane Floor Deformation
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Sudhir K Jain
Foundations
See Prashant Presentation
Thank you!!
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