54
مبادرة
#تواصل_تطوير
المحاضرة الرابعة والخمسون من المبادرة مع
الاستاذ الدكتور /ناجي أبو شادي
استاذ الهندسة الإنشائية بالولايات المتحدة الأمريكية
بعنوان
" Advanced Seismic Analysis of Buildings"
التاسعة مساء توقيت مكة المكرمة الأربعاء09سبتمبر2020
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--
3. 2
Advanced Seismic Analysis and
Design of Buildings (1)
Nagi Abo-Shadi, PhD, PE, SE, PEng
Structural Engineering Center, Inc
4. Seismic Analysis of Structures (Buildings)
This is about the determination of the expected
deformation of structures and the developed forces,
strains and stresses during an earthquake event.
3
5. 4
Seismic Performance of Buildings is based on:
Site
- Seismicity (location)
- Soil properties
Building
- Structural system
- Size and weight of building
- Construction materials
9. 8
Multi Degree of Freedom System (MDOF)
Single Degree of Freedom System (SDOF)
Single Degree of Freedom System (SDOF)
Building
10. Equation of Motion (E.O.M.)
Equations describing dynamic equilibrium of a system
in terms of D.O.F.s
𝐹 = 0 = 𝐹𝐼 + 𝐹𝑠𝑝
0 = 𝑚 𝑥 + 𝑘 𝑥
𝑀 = 𝑚 and 𝐾 = 𝑘
E.O.M. → 0 = 𝑀 𝑥 + 𝐾 𝑥 ( Undamped Free Vibration)
9
𝑥
𝑥
𝐹 𝐷
𝐹 𝐷 is ignored here
11. 10
0 5 10 15 20 25 30 35 40
Time (sec)
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Displacement(in)
T
Damped SDOF
Undamped SODF
= 5%
= 20%
Xn Xn+1
Single Degree of Freedom System (SDOF)
12. 11
In general, take the undamped free vibration form of
the E.O.M.
0 = 𝑀 𝑥 + 𝐾 𝑥
1
𝑀
0 = 𝑥 +
𝐾
𝑀
𝑥
0 = 𝑥 + 𝜔 𝑛
2
𝑥
𝜔 𝑛 =
𝐾
𝑀
(Note that 𝐾 ≠ 𝑘 always, and M ≠ 𝑚 always)
13. 12
Fundamental Period (𝑻 𝒏)
Represents the time for one complete cycle of
vibration (s)
𝑇𝑛 =
2𝜋
𝜔 𝑛
= 2 𝜋
𝑀
𝐾
Frequency
𝑓𝑛 =
1
𝑇𝑛
=
1
2 𝜋
𝐾
𝑀
14. 13
0 10 20 30 40 50 60
Time (sec)
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
Acceleration(g)
1940 El-Centro-270
o
PGA = 0.35g
0 10 20 30 40 50 60
Time (sec)
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
Acceleration(g)
1940 El-Centro-270
SDOF - T=0.7 sec
o
Sa = 0.69 g
= 5 %
0 10 20 30 40 50 60
Time (sec)
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
Acceleration(g)
1940 El-Centro-270
SDOF - T=1.0 sec
o
Sa = 0.51 g
= 5 %
Response Spectra
El-Centro Ground Acceleration
Structural Response for
T = 0.7 Sec and = 5%
Structural Response for
T = 1.0 Sec and = 5%
15. 14
Response Spectra for = 5%
F = m x Sa
Where:
m = Structure mass
Sa = Spectral acceleration
F = Elastic force
Spectral force
Unreduced force
16. 15
Seismic Design of Buildings
Seismic design of buildings follows the following codes:
2018 International Building Code, IBC
2019 California Building Code, CBC
2020 City of Los Angeles Building Code, LABC
2020 County of Los Angeles Building Code, LACBC
which adopts the ASCE7-16 document for the design forces
18. 17
Stiff Bracing Elements:
Appropriate for controlling the building drift.
- Concentric Braced Frames
- Eccentric Braced Frames
- Steel shear walls
- Reinforced concrete shear walls
- Masonry shear walls
- Light-framed shear walls (wood or sheet metal)
19. 18
Concentric Braced Frames
For the concentric braced frames, the energy dissipation occurs
in the brace itself through the compression reversals. These
compression forces cause buckling of the frame braces.
Concentric braced frames with K-Bracing are prohibited in high
seismic zones since losing one brace will result in column failure..
21. 20
Eccentric Braced Frames
The link beam in the eccentric braced frames is exposed to high
shear forces and dissipates the energy through shear yielding.
26. 25
Concrete Confinement
Concrete confinement is provided at specific locations of the
seismic force resisting member. These locations are exposed
to high strains beyond that can be taken by the unconfined
concrete.
The purpose of providing
the confinement is to
enhance the concrete
properties including the
strength, f’c and the
ultimate concrete strain,
εcu.
32. 31
The pre-Northridge earthquake connection demonstrated poor
performance. The weld at the interface between the beam and
column fractured. The figure below shows fractured weld at the
interface between the frame beam and frame column.
33. 32
The figure shows a
pre-Northridge
earthquake moment
frame connection at
which the maximum
moment and hence
the maximum strain
occurs at the beam-
column interface.
42. 41
)I/R(
S
C DS
s
)I/R(T
S
C 1D
maxs
Equivalent Lateral Force Procedure (ASCE 12.8)
The ASCE 7-16 includes static equivalent lateral force procedure to
determine the earthquake forces on building structures as follows:
V = CS W (ASCE 12.8-1)
Cs-min = 0.044 SDS I
Seismic Weight (ASCE 12.7.2)
W = D (self weight) + 1) 25% of the storage load
2) Partition wt. or 10 psf min.
3) Permanent equipment A/C, generators, etc.
4) 0.2 snow load if snow load Pf > 30 psf
55. 54
Tallest Concrete Shear Wall Building in the West Coast
Height = 220 feet (code permits 160 feet)
21 stories: Two 18-story residential towers atop 3
levels of partially enclosed parking
556 Residential Units
723,000 sf (residential)
264,000 sf (parking)
85,000 sf (plaza)
$150 million
56. 55
Structural System
Specially Reinforced Concrete Bearing
Wall
8-inch and 6-inch shear walls spaced at
12 to 16 feet
Cast-in-Place concrete with tunnel form
construction
Support a 5½-inch one way slab
57. Advantages of Using Tunnel Form Construction
Faster Completion
High Quality Construction
Reduced Maintenance & Insurance Expense
Reliable Completion Dates
Cost Savings on Construction
Built-In Accuracy and Tolerances
Noise Reduction & Fire Resistance
https://www.youtube.com/watch?v=5vD62cZN4LE
https://www.youtube.com/watch?v=Me0uouvePG8
58.
59.
60. 0.00 1.00 2.00 3.00 4.00 5.00 6.00
Period (sec)
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80Acceleration(g)
1.7 (El-Centro 270 )
El-Centro, 270
Site Specta
o
o
61. 0.00 1.00 2.00 3.00 4.00 5.00 6.00
Period (sec)
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80Acceleration(g)
2.0 (El-Centro 180 )
El-Centro, 180
Site Specta
o
o