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Table of contents
Table of Contents---------------------------------------------------------------------------------------1
Introduction-----------------------------------------------------------------------------------------------2
Cape Mendocino
Petrolia--------------------------------------------------------------------------------------------3
Shelter cove airport----------------------------------------------------------------------------9
Lanaja station 1---------------------------------------------------Lanaja station 2--------------------------------------------------Pineda Station 1------------------------------------------------Pineda Station 2----------------------------------------------------
Loma Prieta
Dimaano station 1---------------------------------------------------Dimaano station 2--------------------------------------------------Buyan station 1---------------------------------------------------Buyan station 2--------------------------------------------------Nabor station 1---------------------------------------------------Nabor station 2--------------------------------------------------Jumawan station 1---------------------------------------------------Janaja station 2---------------------------------------------------
1
INTRODUCTION
Comprehensive Analysis of Loma Prieta and Cape Mendocino Earthquakes using
Modified Newmark Method
Presented to: Sir Ryan James Olivo
In the realm of seismic engineering, understanding the dynamic behavior of
structures during major earthquakes is of paramount importance. The earthquakes
that struck Loma Prieta and Cape Mendocino stand as significant events in the seismic
history of California. As part of our academic exploration, this compilation delves into
a comprehensive analysis of these seismic events, employing the Modified Newmark
Method. Developed with precision using Excel and MATLAB, our study aims to unravel
the intricacies of ground motion, structural response, and the efficacy of seismicresistant measures.
The Modified Newmark Method provides a robust analytical framework,
allowing us to scrutinize the seismic performance of structures with a focus on
displacement and acceleration. Through this compilation, we embark on a journey to
decipher the nuanced characteristics of ground motion from these two seismic
episodes and evaluate their implications on structural integrity.
This work is not only a testament to our commitment to seismic engineering but
also a humble contribution to the broader understanding of earthquake engineering
principles. As we navigate through the technical intricacies, we invite the reader to join
us on this exploration into the seismic resilience of structures in the face of natural
adversities.
2
Loma Prieta
STATION NAME: APEEL 10 - Skyline
(Acceleration 00- Horizontal 1)
600
-2
-0.5
240000
1200
2
p̂
𝑢𝑖+1 = 𝑖+1
̂
𝑘
ɣ
ɣ
ɣ
ů𝑖+1 = 𝛽△𝑡(𝑢𝑖+1 − 𝑢𝑖 ) + (1 - 𝛽)ů𝑖 + △t(1 - 2𝛽)ü𝑖
ü𝑖+1 =
1
1
1
equation
(𝑢Type −
𝑢𝑖 ) - here.
ů - ( -1)ü𝑖
𝛽(△𝑡)² 𝑖+1
𝛽△𝑡 𝑖
2𝛽
a1=((1/B(deltat)²)(m))+(y/B(deltat))c
a2=((1/B(deltat))(m))+((y/B)-1)c
a3=((1/2B)-1)(m))+(deltat)((y/2b)-1)c
i=0, t=0
i=0, t=0
i=0, t=0
3
4
Acceleration,time
0,08
0,06
0,04
0,02
0
-0,02
0
5
10
15
20
25
30
35
40
45
30
35
40
45
30
35
40
45
-0,04
-0,06
-0,08
-0,1
-0,12
Displacement,time
0,03
0,02
0,01
0
0
5
10
15
20
25
-0,01
-0,02
-0,03
-0,04
velocity,time
1
0,8
0,6
0,4
0,2
0
-0,2
0
5
10
15
20
25
-0,4
-0,6
-0,8
-1
Loma Prieta
5
STATION NAME: APEEL 10 - Skyline
(Acceleration 90- Horizontal 2)
600
-2
-0.5
240000
1200
2
p̂
𝑢𝑖+1 = 𝑖+1
̂
𝑘
ɣ
ɣ
ɣ
ů𝑖+1 = 𝛽△𝑡(𝑢𝑖+1 − 𝑢𝑖 ) + (1 - 𝛽)ů𝑖 + △t(1 - 2𝛽)ü𝑖
ü𝑖+1 =
a1=((1/B(deltat)²)(m))+(y/B(deltat))c
a2=((1/B(deltat))(m))+((y/B)-1)c
a3=((1/2B)-1)(m))+(deltat)((y/2b)-1)c
1
1
1
equation
(𝑢Type −
𝑢𝑖 ) - here.
ů - ( -1)ü𝑖
𝛽(△𝑡)² 𝑖+1
𝛽△𝑡 𝑖
2𝛽
i=0, t=0
i=0, t=0
i=0, t=0
6
7
Acceleration,time
0,15
0,1
0,05
0
0
5
10
15
20
25
30
35
40
45
30
35
40
45
30
35
40
45
-0,05
-0,1
-0,15
-0,2
Displacement,time
0,06
0,04
0,02
0
0
5
10
15
20
25
-0,02
-0,04
-0,06
-0,08
Velocity,time
4
3
2
1
0
-1
0
5
10
15
20
25
-2
-3
-4
8
Loma Prieta
STATION NAME: APEEL 2E Hayward Muir Sch
(Acceleration 00- Horizontal 1)
600
-2
-0.5
240000
1200
2
p̂
𝑢𝑖+1 = 𝑖+1
̂
𝑘
ɣ
ɣ
ɣ
ů𝑖+1 = 𝛽△𝑡(𝑢𝑖+1 − 𝑢𝑖 ) + (1 - 𝛽)ů𝑖 + △t(1 - 2𝛽)ü𝑖
ü𝑖+1 =
a1=((1/B(deltat)²)(m))+(y/B(deltat))c
a2=((1/B(deltat))(m))+((y/B)-1)c
a3=((1/2B)-1)(m))+(deltat)((y/2b)-1)c
1
1
1
equation
(𝑢Type −
𝑢𝑖 ) - here.
ů - ( -1)ü𝑖
𝛽(△𝑡)² 𝑖+1
𝛽△𝑡 𝑖
2𝛽
i=0, t=0
i=0, t=0
i=0, t=0
9
10
Acceleration,time
0,2
0,15
0,1
0,05
0
-0,05
0
5
10
15
20
25
30
35
40
45
30
35
40
45
30
35
40
45
-0,1
-0,15
-0,2
Displacement,time
0,08
0,06
0,04
0,02
0
-0,02
0
5
10
15
20
25
-0,04
-0,06
-0,08
-0,1
Velocity,time
4
3
2
1
0
-1
0
5
10
15
20
25
-2
-3
-4
11
Cape Mendocino
STATION NAME: APEEL 2E Hayward Muir Sch
(Acceleration 90- Horizontal 2)
600
-2
-0.5
240000
1200
2
p̂
𝑢𝑖+1 = 𝑖+1
̂
𝑘
ɣ
ɣ
ɣ
ů𝑖+1 = 𝛽△𝑡(𝑢𝑖+1 − 𝑢𝑖 ) + (1 - 𝛽)ů𝑖 + △t(1 - 2𝛽)ü𝑖
1
1
1
equation here.
ü𝑖+1 = 𝛽(△𝑡)²(𝑢Type
𝑖+1 − 𝑢𝑖 ) - 𝛽△𝑡 ů𝑖 - (2𝛽 -1)ü𝑖
a1=((1/B(deltat)²)(m))+(y/B(deltat))c
a2=((1/B(deltat))(m))+((y/B)-1)c
a3=((1/2B)-1)(m))+(deltat)((y/2b)-1)c
i=0, t=0
i=0, t=0
i=0, t=0
12
13
Acceleration,time
0,1
0,08
0,06
0,04
0,02
0
0
-0,02
5
10
15
20
25
30
35
40
45
30
35
40
45
30
35
40
45
-0,04
-0,06
-0,08
-0,1
Displacement,time
0,03
0,025
0,02
0,015
0,01
0,005
0
-0,005 0
5
10
15
20
25
-0,01
-0,015
-0,02
-0,025
Velocity,time
0,8
0,6
0,4
0,2
0
-0,2
0
5
10
15
20
25
-0,4
-0,6
-0,8
14