Lateral Load Resisting Systems
IITGN Short Course Gregory MacRae
Many slides from 2009 Myanmar Slides of Profs Jain and Rai
1
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
9
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
14
Sudhir K Jain
Lateral Load Resisting Elements Countries – CHILE, US, PERU, COLOMBIA, MEXICO
Moment-Resisting Frame
Wall/Frame Dual Frame
15
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
16
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. 17
Sudhir K Jain
Moment Resisting Frame
BMD
Frame with rigid joints and with very flexible beams. 18
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.
19
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?
20
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., 21 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., 22 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 23 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
24
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 25 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)
27
Sudhir K Jain
Degree of Freedom in 3-D Frame
28
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 29
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 30
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
31
Sudhir K Jain
Walls
Wall with Shear Deformation
Wall with Flexural Deformation
Wall with both Shear and Flexural Deformation 32
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
33
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
34
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 35
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
36
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
37
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 38
Sudhir K Jain
Shear Wall with Openings Issues
beam Wall
beam
Imaginary beam Shear panels
Analysis Model
I=∞
Column
beam
Column
I=∞ Column
Ib
39
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
40
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
41
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 42 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 43
Sudhir K Jain
Wall-Frame Interaction Interacting Forces
tension
Combine compression
Rigid Frame
Shear Wall
“Shear Mode” Deformation
Bending Mode Deformation
Combine Deformations
44
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
45
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
46
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. 49
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
50
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
51
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 52
Sudhir K Jain
Floor Deformations
In-Plane Floor Deformation
Out of Plane Floor Deformation
53
Sudhir K Jain
Foundations See Prashant Presentation
Thank you!! 55
