roumieh - wassim joseph elias€¦ · static base shear ubc97 = .𝑰. = 𝑲 𝒑𝒔. * the soil...

LEBANESE UNIVERSITY

FACULTY OF ENGINEERING

BRANCH II - ROUMIEH

1

Evaluation of the Static Seismic Base

Shear Using IBC 2012 and ASCE 7-10

Prepared by

Eng. Wassim J. Elias

Supervised by

Dr. Michel F. Khouri

2

Introduction

The purpose of the earthquake

provisions herein is primarily to

safeguard against major structural

failures and loss of life, not to limit

damage or maintain function.

The seismic base shear V in a given

direction shall be determined in

accordance with the following equation:

V = Cs . W

Cs = the seismic response coefficient.

W = the effective seismic weight.

3

Base Shear Distribution The lateral seismic force “Fx"

induced at any level shall be determined

from the following equations:

𝑭𝒙 = 𝑪𝒗𝒙 . 𝑽 𝑪𝒗𝒙 =𝒘𝒙. 𝒉𝒙

𝒌

𝒘𝒊𝒉𝒊𝒌𝒏

𝒊=𝟏

𝒌 = 𝟎. 𝟕𝟓 + 𝟎. 𝟓. 𝑻, 𝐟𝐨𝐫 𝐬𝐭𝐫𝐮𝐜𝐭𝐮𝐫𝐞𝐬 𝐡𝐚𝐯𝐢𝐧𝐠 𝐚 𝐩𝐞𝐫𝐢𝐨𝐝 "𝑻" 𝐛𝐞𝐭𝐰𝐞𝐞𝐧

𝟎. 𝟓 𝐬 𝐚𝐧𝐝 𝟐. 𝟓 𝐬.

4

Calculation of the effective

seismic weight “W”

𝑾 = 𝑾𝒊

𝒏

𝒊=𝟏

𝑛 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑜𝑟𝑖𝑒𝑠.

5

Calculation of the seismic

response coefficient Cs

6



7

𝑺𝑫𝟏 =𝟐

𝟑𝑺𝑴𝟏

Where, 𝑺𝑴𝟏=𝑭𝒗. 𝑺𝟏 ∗ 𝐹𝑣= 𝑡𝑕𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑕𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑡𝑎𝑏𝑙𝑒:

8

∗ 𝑆1= 𝑡𝑕𝑒 𝑚𝑎𝑝𝑝𝑒𝑑 𝑀𝐶𝐸𝑅 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑎𝑡 𝑎 𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 1𝑠.

User Note: Electronic values of mapped acceleration

parameters, and other seismic design parameters, are

provided at the USGS web site at:

http://geohazards.usgs.gov/designmaps/ww/.

or through the SEI Web site at:

http://content.seinstitute.org.

9

Calculation of 𝑆𝐷𝑆

𝑺𝑫𝑺 =𝟐

𝟑𝑺𝑴𝑺

Where, 𝑺𝑴𝑺=𝑭𝒂. 𝑺𝑺 ∗ 𝐹𝑎= 𝑡𝑕𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑕𝑒

𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑡𝑎𝑏𝑙𝑒:

10

Calculation of 𝑆𝐷𝑆

∗ 𝑆𝑆= 𝑡𝑕𝑒 𝑚𝑎𝑝𝑝𝑒𝑑 𝑀𝐶𝐸𝑅 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑎𝑡 𝑎 𝑠𝑕𝑜𝑟𝑡 𝑝𝑒𝑟𝑖𝑜𝑑𝑠.

User Note: Electronic values of mapped acceleration

parameters, and other seismic design parameters, are

provided at the USGS web site at:

http://geohazards.usgs.gov/designmaps/ww/.

or through the SEI Web site at:

http://content.seinstitute.org.

11

Site Classification

The site soil shall be classified in accordance with the

following table:

𝑣𝑠𝑖 =𝐺𝑖𝜌𝑠𝑖

𝐺𝑖 =𝐸𝑖

2(1 + 𝜗𝑖)

∗ 𝐺𝑖= Soil Shear Modulus.

∗ 𝜌𝑠𝑖= Soil Density. ∗ 𝜗𝑖= Poisson Coefficient. 12

Site Classification

13

Risk Category of Structures The risk category of buildings and other structures for flood,

wind, snow, earthquake and ice loads can be chosen

according to the following table:

14

Importance Factor and Seismic Design Category

SDC Calculation The importance factor by risk category of buildings and other structures for snow,

ice and earthquake loads can be chosen according to the following table:

The Seismic Design Category SDC can be chosen according to the following

table:

SDC=E when 𝑆1 ≥ 0.75 for risks categories I, II or III.

SDC=F when 𝑆1 ≥ 0.75 for risks categories IV.

15

Response Modification Coefficient

“R” Calculation The response modification coefficient R can be chosen

according to the following table:

16


“R” Calculation

17


“R” Calculation

18


“R” Calculation

19


“R” Calculation

20


“R” Calculation

21


“R” Calculation

22


“R” Calculation

23


“R” Calculation

24


“R” Calculation

25

Calculation of "T" the fundamental period of the structure

Where the values of approximate period parameters 𝐶𝑡and x

are given in the following table:

26

Evaluation of "TL" the mapped long −

period transition period

Where the values of mapped long-period transition period are

given in the following maps:

27



28



29



30



31

Application on the IBC

2012 and ASCE 7-10

32

34

Calculation of the effective

seismic weight “W”

𝑺𝑴𝟏=𝑭𝒗. 𝑺𝟏 = 𝟏. 𝟓 ∗ 𝟎. 𝟗𝟏 = 𝟏. 𝟑𝟔 ∗ 𝐹𝑣= 𝑡𝑕𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑕𝑒 𝑡𝑎𝑏𝑙𝑒 11.4.2.

𝑺𝑫𝟏 =𝟐

𝟑𝑺𝑴𝟏 =

𝟐

𝟑*1.36=0.91

𝑺𝑴𝑺=𝑭𝒂. 𝑺𝑺=1*2.2=2.2

∗ 𝐹𝑎= 𝑡𝑕𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑕𝑒 𝑡𝑎𝑏𝑙𝑒 11.4.1.

𝑺𝑫𝑺 =𝟐

𝟑𝑺𝑴𝑺=

𝟐

𝟑∗ 𝟐. 𝟐 = 𝟏. 𝟒𝟕

Seismic Design Category SDC

38

The Risk Category is II & Seismic Design Category

SDC=E, can be chosen according to the following tables 1.5-1 &

11.6-1,2:

Seismic Design Category SDC

39

SDC=E when 𝑆1 ≥ 0.75 for risks categories I, II or III. SDC=F when 𝑆1 ≥ 0.75 for risks categories IV.

Seismic

Design

Category

SDC

&

Risk

Category

40

Response

Modification

Coefficient

41

The importance factor by risk category of buildings and other structures for snow,

ice and earthquake loads can be chosen according to the following table:

Importance Factor

42

Where the values of approximate period parameters 𝐶𝑡and x

are given in the following table:

Period of the Structure

43

Long-Period Transition Period of the Structure

44

Seismic Response Coefficient Cs

45



46

𝑾 = 𝑾𝒊

𝒏

𝒊=𝟏

𝑛 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑜𝑟𝑖𝑒𝑠.

Effective Seismic Weight

47

Base Shear & Lateral Seismic Forces

48

Base Shear Distribution The lateral seismic force “Fx" induced at

any level shall be determined from the

following equations:

𝑭𝒙 = 𝑪𝒗𝒙 . 𝑽 𝑪𝒗𝒙 =𝒘𝒙. 𝒉𝒙

𝒌

𝒘𝒊𝒉𝒊𝒌𝒏

𝒊=𝟏

𝒌 = 𝟎. 𝟕𝟓 + 𝟎. 𝟓. 𝑻, 𝐟𝐨𝐫 𝐬𝐭𝐫𝐮𝐜𝐭𝐮𝐫𝐞𝐬 𝐡𝐚𝐯𝐢𝐧𝐠 𝐚 𝐩𝐞𝐫𝐢𝐨𝐝 "𝑻" 𝐛𝐞𝐭𝐰𝐞𝐞𝐧

𝟎. 𝟓 𝐬 𝐚𝐧𝐝 𝟐. 𝟓 𝐬.

49

Static Base Shear UBC97 Berkeley city seismic zone is 4 (Z=0.4) according to

the following seismic zone map of USA:

50

Static Base Shear UBC97

𝑽𝑼𝑩𝑪𝟗𝟕 =𝑪𝑽.𝑰.𝑾

𝑹.𝑻 =𝟎.𝟔𝟒∗𝟏∗𝟗𝟔𝟓𝟓

𝟖.𝟓∗𝟎.𝟓𝟖= 𝟏𝟐𝟓𝟑 𝑲𝒊𝒑𝒔.

* The soil profile is Sd the seismic coefficient Cv=0.64*Nv (Table

16-R) where Nv=1 (Table 16-T) for a seismic source type A≥ 15 𝐾𝑚.

* The occupancy Category is I=1 (Table 16-K).

* W= Total Structure Construction Weight = 9655 Kips.

* T= the structure period =𝐶𝑡 . 𝑕𝑛34 =0.03* 52

34 =0.58 s.

* 𝐶𝑡=0.030 for reinforced concrete moment resisting frames and

eccentrically braced frames.

* R=Coefficient of the inherent over strength and global ductility = 8.

5 for SMRF (Table 16-N).

𝑽𝑰𝑩𝑪𝟐𝟎𝟏𝟐 = 𝑪𝑺.𝑾 =0.18*9655 =1738 Kips.

51

roumieh - wassim joseph elias€¦ · static base shear ubc97 = .𝑰. = 𝑲 𝒑𝒔. * the soil...

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