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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.
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Calculation of the effective
seismic weight “W”
𝑾 = 𝑾𝒊
𝒏
𝒊=𝟏
𝑛 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑜𝑟𝑖𝑒𝑠.
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Calculation of the seismic
response coefficient Cs
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Calculation of the seismic
response coefficient Cs
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𝑺𝑫𝟏 =𝟐
𝟑𝑺𝑴𝟏
Where, 𝑺𝑴𝟏=𝑭𝒗. 𝑺𝟏 ∗ 𝐹𝑣= 𝑡𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑡𝑎𝑏𝑙𝑒:
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∗ 𝑆1= 𝑡𝑒 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= 𝑡𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑒
𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑡𝑎𝑏𝑙𝑒:
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Calculation of 𝑆𝐷𝑆
∗ 𝑆𝑆= 𝑡𝑒 𝑚𝑎𝑝𝑝𝑒𝑑 𝑀𝐶𝐸𝑅 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑎𝑡 𝑎 𝑠𝑜𝑟𝑡 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
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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:
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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.
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Response Modification Coefficient
“R” Calculation The response modification coefficient R can be chosen
according to the following table:
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Response Modification Coefficient
“R” Calculation
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Calculation of "T" the fundamental period of the structure
Where the values of approximate period parameters 𝐶𝑡and x
are given in the following table:
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Evaluation of "TL" the mapped long −
period transition period
Where the values of mapped long-period transition period are
given in the following maps:
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Evaluation of "TL" the mapped long −
period transition period
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Evaluation of "TL" the mapped long −
period transition period
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Evaluation of "TL" the mapped long −
period transition period
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Evaluation of "TL" the mapped long −
period transition period
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Application on the IBC
2012 and ASCE 7-10
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Calculation of the effective
seismic weight “W”
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𝑺𝑴𝟏=𝑭𝒗. 𝑺𝟏 = 𝟏. 𝟓 ∗ 𝟎. 𝟗𝟏 = 𝟏. 𝟑𝟔 ∗ 𝐹𝑣= 𝑡𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑒 𝑡𝑎𝑏𝑙𝑒 11.4.2.
𝑺𝑫𝟏 =𝟐
𝟑𝑺𝑴𝟏 =
𝟐
𝟑*1.36=0.91
𝑺𝑴𝑺=𝑭𝒂. 𝑺𝑺=1*2.2=2.2
∗ 𝐹𝑎= 𝑡𝑒 𝑠𝑖𝑡𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑖𝑛 𝑡𝑒 𝑡𝑎𝑏𝑙𝑒 11.4.1.
𝑺𝑫𝑺 =𝟐
𝟑𝑺𝑴𝑺=
𝟐
𝟑∗ 𝟐. 𝟐 = 𝟏. 𝟒𝟕
Seismic Design Category SDC
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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
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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
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Response
Modification
Coefficient
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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
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Where the values of approximate period parameters 𝐶𝑡and x
are given in the following table:
Period of the Structure
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Long-Period Transition Period of the Structure
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Seismic Response Coefficient Cs
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Calculation of the seismic
response coefficient Cs
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𝑾 = 𝑾𝒊
𝒏
𝒊=𝟏
𝑛 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑜𝑟𝑖𝑒𝑠.
Effective Seismic Weight
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Base Shear & Lateral Seismic Forces
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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.
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Static Base Shear UBC97 Berkeley city seismic zone is 4 (Z=0.4) according to
the following seismic zone map of USA:
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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.
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