Download - P8 AM Structuralanalyismethods
Seismic Design of Multi-storey Buildings: IS-1893 vs. Eurocode-8
Structural Analysis Methods
Abdelghani Meslem, PhD & Dominik Lang, PhD
Department of Earthquakes and the Environment NORSAR, Kjeller, Norway
IS-1893-1:2002 - NE 1998-1:2004
EN 1998-1: 2004
IS 1893-1: 2002
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Criteria for earthquake resistant design of structures
Part 1: General provisions and buildings
IS-1893 Provisions
Eurocode-8 Provisions Design of structures for earthquake resistance
Part 1: General rules, seismic actions and rules for buildings
Table of contents
EN 1998-1: 2004
IS 1893-1: 2002
IS 1893-1:2002 vs. EN 1998-1:2004
Dynamic Characteristics
Seismic Masses Fundamental Natural Period
Methods of analysis
Design Lateral Force Method Modal Response Spectrum Method Linear Time History Method
Components of seismic action
Accidental/Torsional Effects
Second-order Effects (P-Δ effects)
Select and Scale Earthquake Records
Contribution of Joint Regions
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Percentage of imposed load (IL) to be considered in seismic weight calculation (IS-1893-1:2002, Table 8)
the seismic weight of each floor (k) is its full Dead Load (DL) plus appropriate amount of
Imposed Load (IL).
Imposed Uniformity Distributed Floor Loads (kN/m2)
Percentage of Load
Up to and icluding 3,0 25
Above 3,0 50
∑k (DLk + ILk )
DLk + ILk
the seismic weight of the whole building is the sum of the seismic weights of all the floors.
the imposed load shall also be considered for roof.
IS 1893-1: 2002, 7.4
Dynamic Characteristics: Seismic Masses IS 1893-1:2002
DL + IL
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Dynamic Characteristics: Seismic Masses EN 1998-1:2004
Gk + ∑i (ΨEi QKi)
with: ΨEi - combination coefficient for variable action
Ψ2i - occupancy type coefficient φ - load type coefficient
composed of permanent and participating live loads
Occupancy type Ψ2
Residential, office 0.30
Public, commercial (shops), parking 0.60
Roof with snow 0.20
Archives, libraries, staircases 0.80
Storey φ
Roof 1.00
storeys with correlated occupancies 0.80
Interdependently occupied storeys 0.50
Archives 1.00
ΨEi = φ Ψ2i
EN 1998-1:2004, 3.2.4
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
for moment-resisting frame building without brick infill panels:
750
750
0850
0750
.
.
a
H,
H, T
for RC frame building
for steel frame building
H: Height of building, in m. This excludes the basement stories, where basement walls are
connected with the ground floor deck or fitted between the building columns. But it
includes the basement stories, when they are not so connected.
Approximate Ta, in seconds, of all other buildings, including moment-resisting frame
buildings with brick infill panels, may be estimated by the empirical expression:
HTa d
0,09
d: Base dimension of the building at the plinth level, in m, along the considered direction
of the lateral force.
IS 1893-1: 2002, 7.6
Dynamic Characteristics: Fundamental Natural Period IS 1893-1:2002
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Dynamic Characteristics: Fundamental Natural Period EN 1998-1:2004
EN 1998-1:2004, 4.3.3.2
based on any equation coming from structural mechanics (e.g. Rayleigh method)
for building heights H 40 m :
75.0t1 HCT with: Ct - structural coefficient
H - building height (in [m]) from foundation or top of a rigid basement
Ct = 0.085 for moment-resistant steel frames
0.075 for moment-resistant concrete frames and eccentrically braced steel frames
0.050 for all other structures
Ct = 0.075 / √Ac for building with concrete or masonry shear walls
with Ac:
)(2.0( 2/H)lAA wiic
with: Ac - total effective area of the shear walls in the first storey (in [m2])
Ai - effective cross-sectional area of shear wall i (in [m2])
lwi - length of shear wall i parallel to applied forces
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Regularity Model type
Plan Elevation
● ● planar (2D)
● ○
○ ● spatial (3D)
○ ○
if regular in plan, planar (2D) models may be used for each direction X and Y
Ideally, the building should be modelled as three-dimensional. In some cases the analyst may wish to use two-dimensional (planar) in order to reduce the calculation effort. However, this later may be acceptable for buildings with regular geometries where the response in each orthogonal direction is independent and torsional response is not significant.
Modeling Specifications: Planar (2D) & Spatial (3D)
Regular/Irregular Configurations
EN 1998-1:2004, 4.2.3
IS 1893-1:2002, 7.1
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
m3
m2
m1
m4
k
k
k*
k
m3
m2
m1
m4
if floor diaphrams are rigid in plane, masses and moments of inertia may be lumped at the
centre of gravity
EN 1998-1:2004, 4.3.1
Modeling Specifications: Masses Lumped System
A floor diaphragm shall be considered rigid if horizontal displacements at
any point do not exceed more than 10 % of the rigid diaphragm
assumption. EN 1998-1:2004, 4.3.1
A floor diaphragm shall be considered to be flexible, if it deforms such that
the maximum lateral displacement measured from the chord of the deformed
shape at any point of the diaphragm is more than 1,5 times the average
displacement of the entire diaphragm. IS 1893-1:2002, 7.7.2
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Modeling Specifications: Masses Lumped System
Buildings with regular, or nominally irregular plan configurations may be modeled as a
system of masses lumped at the floor levels. IS 1893-1:2002, 7.8.4.5
m3
m2
m1
m4
k
k
k*
k
m3
m2
m1
m4
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Methods of Analysis
Analysis methods specified in IS 1893-1:2002 and EN 1998-1:2004
EN 1998-1:2004, 4.3.3.2 (1) Design Lateral Force Method
(2) Response Spectrum Method
(3) Linear Time History Method
EN 1998-1:2004, 4.3.3.3
low complexity of computation
high complexity of computation
IS 1893-1:2002, 7.8.3
IS 1893-1:2002, 7.8.4
IS 1893-1:2002, 7.7
EN 1998-1:2004, 4.3.3.3
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
This approach defines a series of forces acting on a building to represent the effect of
earthquake ground motion, typically defined by a seismic design response spectrum.
(1) Design Lateral Force Method
Buildings shall be deisgned and constructed to resist the effects of design lateral force
as a MINIMUM IS 1893-1:2002, 7.5
Criteria :
shall be applied to buildings whose response is principally dominated by the 1st mode:
and that are regular in elevation
sec 0,2
41
CTT EN 1998-1:2004, 4.3.3.2
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
This approach defines a series of forces acting on a building to represent the effect of
earthquake ground motion, typically defined by a seismic design response spectrum.
Buildings shall be deisgned and constructed to resist the effects of design lateral force
as a MINIMUM IS 1893-1:2002, 7.5
Criteria (cont'd):
and that are regular in elevation
Regularity Allowed simplification in modeling Plan Elevation
● ● planar
○ ● spatial
(1) Design Lateral Force Method
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Steps:
Step 1: the design lateral force shall first be computed for the building as a whole
Step 2: this deisgn lateral force shall then be distributed to the various floor levels
Step 3: the overall design seismic force thus obtained at each floor level, shall
then be distributed to individual lateral load resisting elements depending on
the floor diaphgram action
(1) Design Lateral Force Method
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(1) Design Lateral Force Method
IS 1893-1:2002, 7.5
Design base shear VB :
Total design lateral force shall be determined for each horizontal
direction by the following expresssion:
WAV hB
with: Ah - design horizontal seismic coefficient for the structure, using the fundamental period Ta
W - seismic weight of the building.
VB
g
S
R
IZA a
h
2 IS 1893-1:2002, 6.4.2
Z = seismic zone factor (given in Table 2 Clause 6.4.2);
I = importance factor depending upon the functional use of the structure (given in Table 6 Clause 6.4.2 );
R = response reduction factor depending on the perceived seismic damage performance of the structure (given in Table 7 Clause 6.4.2);
Sa/g = average response acceleration coefficient.
IS 1893-1:2002
IS 1893-1: 2002, 6.4.1
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(1) Design Lateral Force Method IS 1893-1:2002
For rocky, or hard soil sites
0,00 ≤ T ≤ 0,10
0,10 ≤ T ≤ 0,40
0,40 ≤ T ≤ 4,00
T,
,
T
g
Sa
001
502
151
For medium soil sites
0,00 ≤ T ≤ 0,10
0,10 ≤ T ≤ 0,55
0,55 ≤ T ≤ 4,00
T,
,
T
g
Sa
361
502
151
For soft soil sites
0,00 ≤ T ≤ 0,10
0,10 ≤ T ≤ 0,67
0,67 ≤ T ≤ 4,00
T,
,
T
g
Sa
671
502
151
Horizontal components of the seismic action:
The design acceleration spectrum for vertical motions, when required, may be taken as two-thirds of the design horizontal acceleration spectrum.
For the purpose of determining seismic forces,
the country is classified into four seismic zones
IS 1893-1: 2002, 6.4.1
Calculation of average acceleration coefficient at T=Ta:
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(1) Design Lateral Force Method IS 1893-1:2002
Calculation of average acceleration coefficient at T=Ta:
For rocky, or hard soil sites
0,00 ≤ Ta ≤ 0,10
0,10 ≤ Ta ≤ 0,40
0,40 ≤ Ta ≤ 4,00
a
a
a
T
T
g
S
00,1
50,2
151
For medium soil sites
0,00 ≤ Ta ≤ 0,10
0,10 ≤ Ta ≤ 0,55
0,55 ≤ Ta ≤ 4,00
a
a
a
T
T
g
S
36,1
50,2
151
For soft soil sites
0,00 ≤ Ta ≤ 0,10
0,10 ≤ Ta ≤ 0,67
0,67 ≤ Ta ≤ 4,00
a
a
a
T
T
g
S
67,1
50,2
151
Ta
IS 1893-1: 2002, 6.4.1
Example: 4-story building
For medium soil site (Soil Type II)
Ta = 0,4 sec → 0,10 ≤ Ta ≤ 0,55
→ Sa/g = 2,5
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Vertical distribution of base shear to different floor levels:
calculation of horizontal design forces Qi to all storey levels can be done as per the
following expression
n
j
jj
iiBi
hW
hWVQ
1
2
2
Q3
Q2
Q1
W3
W2
W1
h3
h2
h1 IS 1893-1:2002, 7.7
Qi = design lateral force at floor i;
Wi = seismic weight of floor i;
hi = height of floor i measured from base; and
n = number of storeys in the building (the number of levels ayt which the masses are located).
(1) Design Lateral Force Method IS 1893-1:2002
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Base shear force Fb :
shall be calculated for each horizontal direction
m)T(SF 1db
with:
Sd (T1) = ordinate of the design spectrum at T1
M = total mass of the building
= correction factor = 0.85 if T1 2TC and the building has more than 2 storeys.
Otherwise = 1.0
Fb EN 1998-1:2004, 4.3.3.2
EN 1998-1:2004 (1) Design Lateral Force Method
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Calculation of design spectral acceleration Sa,d :
dependent on soil class and behavior factor q
for 0 ≤ T1 ≤ TB :
for TB ≤ T1 ≤ TC :
for TC ≤ T1 ≤ TD :
for TD ≤ T1 ≤ 4 s :
)
q
.(
T
TSa)T(S
B
gd,a3
252
3
2 11
q
.Sa)T(S gd,a
521
1
1
52
T
T
q
.Sa)T(S C
gd,a
2
1
1
52
T
TT
q
.Sa)T(S DC
gd,a
EN 1998-1:2004, 4.3.3.2
EN 1998-1:2004 (1) Design Lateral Force Method
Period T [sec]
Spec
tral
acc
eler
atio
n S
a,d
q = 1
q = 2
q = 4
TB TC TD T1
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Distribution of horizontal seismic forces:
calculation of horizontal forces Fi to all storey levels can be done by two ways
Type A (dependent on height of masses):
jj
iibi
mz
mzFF
F3
F2
F1
m3
m2
m1
z3
z2
z1
Type B (dependent on absolute horizontal displacement of masses):
jj
iibi
ms
msFF
with: zi height of the respective mass i
with: si lateral displacement of mass i in the 1st mode
F3
F2
F1
m3
m2
m1
s3
s2
s1
EN 1998-1:2004, 4.3.3.2
EN 1998-1:2004, 4.3.3.2
EN 1998-1:2004 (1) Design Lateral Force Method
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
3-story RC frame building (residential use)
m3
m2
m1
3 x 3.5 m
Ground type C
Level G [kN] Q [kN] G+ Ψ Q [kN] Mass mi [tons]
3 260 120 289 29.44
2 350 140 384 39.10
1 750 300 822 83.79
Total seismic mass m 152.33 2s
mkg1N1
N1000kN1
Units:
1. Seismic masses:
residential use → ΨEi = φ Ψ2i = 0.8 0.3 = 0.24
Gk + ∑i (ΨEi QKi)
Tutorial 1
(1) Design Lateral force Nethod: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
- base shear force Fb:
(since T1 < 2 TC → = 0.85) → Fb = Sa,d (T1) m = 2.12 152.33 0.85 = 274 kN
2. Base shear force Fb :
- fundamental period:
(with Ct = 0.075 for RC frames) → T1 = Ct H 0.75 = 0.075 10.5 0.75 = 0.44 s
- design spectral acceleration:
residential use → γI = 1.0
ground motion agR = 0.3 g → ag = agR I = 2.943 m/s2
behavior factor q = 4.0 → Sa,d = ag S 2.5/q = 2.12 m/s2
Period T [sec]
Spec
tral
acc
eler
atio
n S
a
TB TC TD T1
Tutorial 1
(1) Design Lateral force Method: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
3. Load distribution and moment calculation:
Level Height z [m] Mass mk [tons] zk mk [mtons] Force Fk [kN] Moment = Fk zk [kNm]
3 10.5 29.44 309.12 96.68 1015.1
2 7.0 39.10 273.70 85.60 599.2
1 3.5 83.79 293.27 91.72 321.0
Totals 152.33 876.09 274.0 1935.3
4. Effective height of the resultant lateral force:
m..
.
F
Mh
res
reseff 067
0274
31935
m3
m2
m1 heff
Fres
Mres
m3
m2
m1
F3
F2
F1
jj
iibi
mz
mzFF
Tutorial 1
(1) Design Lateral force Method: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response spectrum method
This approach permits the multiple modes of response of a building to be taken into
account.
the Response spectrum method shall be performed using the design spectum, or by a site-
specific design spectrum mentioned.
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response Spectrum method
Criteria:
shall be performed for the following buildings:
• Regular buildings – those greater than 40 m in height in Zone IV and V, and those
greater than 90 m in height in Zones II and III.
• Irregular buildings – all framed buildings heigher than 12 m in Zones IV and V, and
those greater than 40 m in height in Zones II and III.
the resulted design base shear (VB) shall be compared with a base shear (𝑉𝐵) calculated
using a fundamental period TB.
• Where VB is less than 𝑉𝐵 , all the response quantities (e.g. Member forces,
displacements, story forces, story shears and base reactions) shall be multiplied by
𝑉𝐵 /VB.
IS 1893-1:2002, 7.8.4
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response Spectrum method
Criteria (cont'd):
the number of modes to be used in the analysis should be such that:
The sum total of modal masses
of all modes considered
90 % of the total seismic mass and
missing mass correction beyond 33 % ≥
IS 1893-1:2002, 7.8.4
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response Spectrum method
Criteria:
Regularity Allowed simplification
Plan Elevation Model
● ○ planar
○ ○ spatial
shall be applied if the criteria for analysis method (1) are not
fulfilled, this means if:
Fb
1st mode
sec 0,2
41
CTT
EN 1998-1:2004, 4.3.3.3
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response Spectrum method
Criteria (cont'd):
response of all modes shall be considered that contribute significantly to the global
building response (i.e., important for buildings of a certain height)
those modes shall be considered for which:
(1) the sum of the modal masses is at least 90% of the total
building mass
or
(2) the modal mass is larger than 5% of the total building mass
mi ≥ 0.9 mtot
mi ≥ 0.05 mtot
EN 1998-1:2004, 4.3.3.3
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response Spectrum method
if the '90%' and the '5%' criteria is not fulfilled (e.g. for buildings prone to torsional
effects), those modes shall be considered for which:
with: k - number of modes taken into account
n - story number (from above foundation to top)
Tk - period of vibration of mode k
n = 4
k ≥ 3 √n
and
Tk ≤ 0.20 s
Mode shape: 1 2 3 4
Period Tk : 0.27 s 0.23 s 0.16 s 0.02 s
Example: 4-story building
k ≥ 3 √4 = 6 and T12 = 0.002 s ≤ 0.20 s → six modes shall be
considered !!
Criteria (cont'd): EN 1998-1:2004, 4.3.3.3
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response Spectrum method
Obtain natural periods, mode shapes & modal participating factors:
undamped free vibration analysis of the entire building to obtain natural periods
and mode shapes for the modes of vibration that need to be considered;
Differential equation:
Assumption: [C] = zero matrix ! – Undamped system
0uKuCuM
i
3
2
1
m000
0m00
00m0
000m
M
nn1n
33
22
n111
c....c
..c....
....c..
c....c
C
nn1n
33
22
n111
k....k
..k....
....k..
k....k
K with:
0uKuCuM
modal segmentation: =>
derive circular frequencies i / periods Ti and mode shapes i
0MK 2 mk
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response Spectrum method
Obtain natural periods, mode shapes & modal participating factors:
Given: - circular frequencies i / periods Ti
- mode shapes i
1,n
1,1j
1,j
1
n,1
j+1,1
j,1
T1
n
j
ijj
n
j
ijj
i
W
W
P
1
2
,
1
,
n
j
ijj
n
j
ijj
i
m
m
1
2
,
1
,
EN 1998-1:2004, 4.3.3.3 IS 1893-1:2002, 7.8.4
Modal participation factor of mode k:
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Effective masses
Mode. T mx' my' mz' [-] [s] [%] [%] [%] 1 0.398 0 52.1 0 2 0.316 52 0.7 0 3 0.264 8 0.7 0 4 0.19 0 0 39.2 5 0.17 0.5 0 1.4 6 0.137 0 0 2.6 7 0.136 0 0 6 8 0.134 0 0 0 9 0.129 0 0.6 7
10 0.124 0 0 0 11 0.118 0 3.7 4.7 12 0.116 0 28.5 0 13 0.113 0 3.8 2.8 14 0.11 0 0 0 15 0.105 14.1 0 0 16 0.104 5.5 0 0 17 0.103 8.5 1.9 0 18 0.098 0 0 1.6 19 0.096 0.6 0 0 20 0.096 0 0 0 21 0.095 0 0 0 22 0 1 0 2.5 23 0.092 3.5 0 0 24 0.092 2.6 0 0 25 0.09 0 0 0 26 0.088 0 0 0 27 0.086 0 0 0 28 0.084 0 0 4.4 29 0.081 0 0 0 30 0.08 0 0 1
building response
’purely ’ translational
first eigenmode is
translational
Tutorial 2.1 Example 1.1 - Modal analysis results:
(2) Response Spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
response of all modes
shall be considered
that contribute
significantly to the
global building
response
Effective masses
Mode. T mx' my' mz' [-] [s] [%] [%] [%] 1 0.398 0 52.1 0 2 0.316 52 0.7 0 3 0.264 8 0.7 0 4 0.19 0 0 39.2 5 0.17 0.5 0 1.4 6 0.137 0 0 2.6 7 0.136 0 0 6 8 0.134 0 0 0 9 0.129 0 0.6 7
10 0.124 0 0 0 11 0.118 0 3.7 4.7 12 0.116 0 28.5 0 13 0.113 0 3.8 2.8 14 0.11 0 0 0 15 0.105 14.1 0 0 16 0.104 5.5 0 0 17 0.103 8.5 1.9 0 18 0.098 0 0 1.6 19 0.096 0.6 0 0 20 0.096 0 0 0 21 0.095 0 0 0 22 0 1 0 2.5 23 0.092 3.5 0 0 24 0.092 2.6 0 0 25 0.09 0 0 0 26 0.088 0 0 0 27 0.086 0 0 0 28 0.084 0 0 4.4 29 0.081 0 0 0 30 0.08 0 0 1
Example 1.1 - Modal analysis results: Tutorial 2.1
(2) Response Spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
those modes shall be
considered for which:
or
Effective masses
Mode. T mx' my' mz' [-] [s] [%] [%] [%] 1 0.398 0 52.1 0 2 0.316 52 0.7 0 3 0.264 8 0.7 0 4 0.19 0 0 39.2 5 0.17 0.5 0 1.4 6 0.137 0 0 2.6 7 0.136 0 0 6 8 0.134 0 0 0 9 0.129 0 0.6 7
10 0.124 0 0 0 11 0.118 0 3.7 4.7 12 0.116 0 28.5 0 13 0.113 0 3.8 2.8 14 0.11 0 0 0 15 0.105 14.1 0 0 16 0.104 5.5 0 0 17 0.103 8.5 1.9 0 18 0.098 0 0 1.6 19 0.096 0.6 0 0 20 0.096 0 0 0 21 0.095 0 0 0 22 0 1 0 2.5 23 0.092 3.5 0 0 24 0.092 2.6 0 0 25 0.09 0 0 0 26 0.088 0 0 0 27 0.086 0 0 0 28 0.084 0 0 4.4 29 0.081 0 0 0 30 0.08 0 0 1
Sum 91.6 90.0
mi ≥ 0.9 mtot
mi ≥ 0.05 mtot
Example 1.1 - Modal analysis results: Tutorial 2.1
(2) Response Spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
building strongly prone
to torsional response
first eigenmode is
torsional:
Effective masses
Mode T mx' my' mz' [-] [s] [%] [%] [%] 1 0.302 1.7 2 0 2 0.183 0 0.5 12.6 3 0.15 0 55.3 0.9 4 0.144 0 2.6 0 5 0.142 0 11.6 3.2 6 0.14 0 0 0 7 0.138 0 5 13.1 8 0.131 0 0 0 9 0.123 0 0 0
10 0.122 0 0 0 11 0.118 0 0 0 12 0.117 0 0 1.2 13 0.114 0 0.8 10.7 14 0.111 11 0 1.7 15 0.11 4.3 0 0 16 0.109 53.2 0 0.8 17 0.106 0.8 0 0 18 0.1 7 0 0 19 0.096 0 0 0 20 0.095 0 0 0.5 21 0.094 0 0 1 22 0.093 0 0 0 23 0.092 0 0 0 24 0.087 0 0 0 25 0.084 0 0 0 26 0.083 0 0 0 27 0.082 0 0 0 28 0.078 0 0 0 29 0.077 0 0 2.9 30 0.077 0 0 1.8 … … … … …
Example 1.2 - Modal analysis results: Tutorial 2.2
(2) Response Spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
response of all modes shall be
considered that contribute
significantly to the global
building response
Effective masses
Mode T mx' my' mz' [-] [s] [%] [%] [%] 1 0.302 1.7 2 0 2 0.183 0 0.5 12.6 3 0.15 0 55.3 0.9 4 0.144 0 2.6 0 5 0.142 0 11.6 3.2 6 0.14 0 0 0 7 0.138 0 5 13.1 8 0.131 0 0 0 9 0.123 0 0 0
10 0.122 0 0 0 11 0.118 0 0 0 12 0.117 0 0 1.2 13 0.114 0 0.8 10.7 14 0.111 11 0 1.7 15 0.11 4.3 0 0 16 0.109 53.2 0 0.8 17 0.106 0.8 0 0 18 0.1 7 0 0 19 0.096 0 0 0 20 0.095 0 0 0.5 21 0.094 0 0 1 22 0.093 0 0 0 23 0.092 0 0 0 24 0.087 0 0 0 25 0.084 0 0 0 26 0.083 0 0 0 27 0.082 0 0 0 28 0.078 0 0 0 29 0.077 0 0 2.9 30 0.077 0 0 1.8 … … … … …
Example 1.2 - Modal analysis results: Tutorial 2.2
(2) Response Spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Effective masses
Mode T mx' my' mz' [-] [s] [%] [%] [%] 1 0.302 1.7 2 0 2 0.183 0 0.5 12.6 3 0.15 0 55.3 0.9 4 0.144 0 2.6 0 5 0.142 0 11.6 3.2 6 0.14 0 0 0 7 0.138 0 5 13.1 8 0.131 0 0 0 9 0.123 0 0 0
10 0.122 0 0 0 11 0.118 0 0 0 12 0.117 0 0 1.2 13 0.114 0 0.8 10.7 14 0.111 11 0 1.7 15 0.11 4.3 0 0 16 0.109 53.2 0 0.8 17 0.106 0.8 0 0 18 0.1 7 0 0 19 0.096 0 0 0 20 0.095 0 0 0.5 21 0.094 0 0 1 22 0.093 0 0 0 23 0.092 0 0 0 24 0.087 0 0 0 25 0.084 0 0 0 26 0.083 0 0 0 27 0.082 0 0 0 28 0.078 0 0 0 29 0.077 0 0 2.9 30 0.077 0 0 1.8 … … … … …
Sum 77.2 76.5
those modes shall be
considered for which:
or
mi ≥ 0.9 mtot
mi ≥ 0.05 mtot
Example 1.2 - Modal analysis results: Tutorial 2.2
(2) Response Spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
since both criteria are
not fulfilled, those
modes shall be
considered for which:
k ≥ 3 √n
and
Tk ≤ 0.20 sec
k ≥ 3 √4 = 6 modes
Example 1.2 - Modal analysis results: Effective masses
Mode T mx' my' mz' [-] [s] [%] [%] [%] 1 0.302 1.7 2 0 2 0.183 0 0.5 12.6 3 0.15 0 55.3 0.9 4 0.144 0 2.6 0 5 0.142 0 11.6 3.2 6 0.14 0 0 0 7 0.138 0 5 13.1 8 0.131 0 0 0 9 0.123 0 0 0
10 0.122 0 0 0 11 0.118 0 0 0 12 0.117 0 0 1.2 13 0.114 0 0.8 10.7 14 0.111 11 0 1.7 15 0.11 4.3 0 0 16 0.109 53.2 0 0.8 17 0.106 0.8 0 0 18 0.1 7 0 0 19 0.096 0 0 0 20 0.095 0 0 0.5 21 0.094 0 0 1 22 0.093 0 0 0 23 0.092 0 0 0 24 0.087 0 0 0 25 0.084 0 0 0 26 0.083 0 0 0 27 0.082 0 0 0 28 0.078 0 0 0 29 0.077 0 0 2.9 30 0.077 0 0 1.8 … … … … …
Tutorial 2.2
(2) Response Spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Define Masses Seismic...G + 0.3 ∙ Q
Example 2.1 – 3-Story RC Frame System SAP2000
(2) Response Spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Define Number of Modes
(2) Response Spectrum analysis: EN 1998-1:2004 SAP2000
select the number of
modes to be considered
Example 2.1 – 3-Story RC Frame System
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Run Model Analysis
(2) Response Spectrum analysis: EN 1998-1:2004 SAP2000 Example 2.1 – 3-Story RC Frame System
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Deformed shape....
Mode 1 Mode 2 Mode 3
(2) Response Spectrum analysis: EN 1998-1:2004 SAP2000 Example 2.1 – 3-Story RC Frame System
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Modal Information....
first torsional
mode is 3rd
Σ = 0,90 0,98
(2) Response Spectrum analysis: EN 1998-1:2004 SAP2000 Example 2.1 – 3-Story RC Frame System
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
first eigenmode
is torsional
SAP2000
(2) Response Spectrum analysis: EN 1998-1:2004
Example 2.2 – 3-Story RC Dual System
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
first eigenmode is
torsional
Σ = 0,83 0,74
SAP2000
(2) Response Spectrum analysis: EN 1998-1:2004
Example 2.2 – 3-Story RC Dual System
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Modal Response spectrum method
Steps:
Step 1: for each mode of vibration, a response is read from the design spectrum,
based on the modal frequency and the modal mass, for each floor;
Step 3: modal combination of the resulted peak response quantities (e.g.
displacements, story forces, story shears and base reactions) to obtain the
total response of the structure (total response at each floor).
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Procedure:
Period T [sec]
Spec
tral
acc
eler
atio
n S
a
T2 T1 T3
Sa,d (T1)
Sa,d (T2)
Sa.d (T3)
Design spectral accelerations Sa(Ti )/g for each mode i :
Design seismic coefficient for each mode i:
Mode shape i: 1 2 3 n,1
j+1,1
j,1
n,2
j+1,2
j,2
n,3
j+1,3
j,3
g
TS
R
IZA ia
i
2
IS 1893-1:2002 (2) Modal Response spectrum method
IS 1893-1:2002, 7.8.4
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
IS 1893-1:2002 (2) Modal Response spectrum method
Procedure: Design lateral force at each floor in each mode – the peak lateral force (Qj,i) at floor j in
mode i is given by:
where
jiijiij WPAQ ,,
n
i
iki
n
i
iki
k
W
W
P
1
2
1
Qn,1
Qj+1,1
Qj,1
Qn,2
Qj+1,2
Qj,2
Qn,3
Qj+1,3
Qj,3
IS 1893-1:2002, 7.8.4
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
IS 1893-1:2002 (2) Modal Response spectrum method
Procedure:
IS 1893-1:2002, 7.8.4
Story shear forces in each mode – the peak shear force (Vj,i) acting in story j in mode i is
given by:
n
ij
ijij QV1
,,
Story shear forces due to all modes considered– the peak story shear force (Vj) in story j
due to all modes considered is obtained by combining those due to each mode
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
IS 1893-1:2002 (2) Modal Response spectrum method
Procedure:
Modal Combination
the peak response quantities (e.g. Member forces, displacements, story forces,
story shears and base reactions) shall be combined as per Complete Quadratic
Combination (CQC) method (here the modes are assumed to be closely-spaced):
r
i
r
j
jiji
1 1
Number of modes being considered,
Cross-modal coefficient,
Response quantity in mode i (including sign),
Response quantity in mode j (including sing), j
i
ij
r
IS 1893-1:2002, 7.7
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
IS 1893-1:2002 (2) Modal Response spectrum method
Procedure:
Modal Combination
the If the buildings does not have closely-spaced modes, then the peak response
quantities due to all modes considered shall be combined using the following
expresssion:
r
k
k
1
2 IS 1893-1:2002, 7.7
roofroof VF
1 jjj VVF
Lateral forces at each story due to all modes considered – the design lateral forces, Froof
and Fj, at roof and at floor j:
IS 1893-1:2002, 7.8.4
Lateral Forces at each Story due to all modes considered
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
IS 1893-1:2002 (2) Modal Response spectrum method
Procedure:
IS 1893-1:2002, 7.8.4
Story shear forces in each mode – the peak shear force (Vj,i) acting in story j in mode i is
given by:
n
ij
ijij QV1
,,
Story shear forces due to all modes considered– the peak story shear force (Vj) in story j
due to all modes considered is obtained by combining those due to each mode
roofroof VF
1 jjj VVF
Lateral forces at each story due to all modes considered – the design lateral forces, Froof
and Fj, at roof and at floor j:
IS 1893-1:2002, 7.8.4
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
EN 1998-1:2004 (2) Modal Response spectrum method
Procedure:
Design spectral accelerations Sa(Ti )/g for each mode i :
Mode shape i: 1 2 3 n,1
j+1,1
j,1
n,2
j+1,2
j,2
n,3
j+1,3
j,3
EN 1998-1:2004, 4.3.3.3
Period T [sec]
Spec
tral
acc
eler
atio
n S
a
T2 T1 T3
Sa,d (T1)
Sa,d (T2)
Sa.d (T3)
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
EN 1998-1:2004 (2) Modal Response spectrum method
Procedure: )T(SmF id,aii,jji,j
Fn,1
Fj+1,1
Fj,1
Fn,2
Fj+1,2
Fj,2
Fn,3
Fj+1,3
Fj,3
Mode shape i: 1 2 3 n,1
j+1,1
j,1
n,2
j+1,2
j,2
n,3
j+1,3
j,3
resulting shear forces Fb,m : 2i,m,b
n
1im,b FF
EN 1998-1:2004, 4.3.3.3
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
3-story RC frame building (residential use)
behavior factor q = 4
ground motion: agR = 0.3 g
residential use: γI = 1.0
structural parameters:
E = 2.1 108 kN/m2 I = 2.679 10-5 m4
h = 3.0 m k = 12 EI/h3
m = 50 tons = 50 kNs2/m
1. Setting up the differential equation of motion:
m3 = m
m2 = 1.5m
m1 = 2m
h
h
h
k3 = k
k2 = 2k
k1 = 3k
0uKuCuM if [C] = 0 : 0uKuM
100
05.10
002
m
m00
0m0
00m
M
3
2
1
110
132
025
k
kk0
kkkk
0kkk
K
33
3322
221
Tutorial 2.3
(2) Response spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
2. Modal segmentation:
0MK 2
0
mkk0
km5.1k3k2
0k2m2k5
2
2
2
3. Modal circular frequencies ωi and periods Ti :
1 = 4.19 s-1 → T1 = 1.50 sec 2 = 8.97 s-1 → T2 = 0.70 sec 3 = 13.3 s-1 → T3 = 0.47 sec
4. Eigenmodes:
00.1
644.0
30.0
1
00.1
601.0
676.0
2
00.1
57.2
47.2
3
Tutorial 2.3
(2) Response spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
5. Modal participation factors i :
1 = 100 0.3 + 75 0.644 + 50 1.0 = 128.3 kNs2/m
2 = –100 0.676 – 75 0.601 + 50 1.0 = -62.7 kNs2/m 3 = 100 2.47 – 75 2.57 + 50 1.0 = 104.3 kNs2/m M1
* = 100 0.32 + 75 0.6442 + 50 1.02 = 90.0 kNs2/m M2
* = 100 0.6762 + 75 0.6012 + 50 1.02 = 122.8 kNs2/m M3
* = 100 2.472 + 75 2.572 + 50 1.02 = 1155.0 kNs2/m → 1 = 128.3 / 90.0 = 1.426 → 2 = -62.7 / 122.8 = –0.511 → 3 = 104.3 / 1155.0 = 0.090
*
i
in
1j
2i,jj
n
1ji,jj
iM
m
m
Tutorial 2.3
(2) Response spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
6. Design spectral accelerations Sa(Ti ) for each mode i :
T1 = 1.50 sec :
Check: Sa,d (T) = 0.846 m/s2 ≥ β ∙ ag = 0.20 ∙ 2.943 = 0.5886 m/s2
T2 = 0.70 sec :
Check: Sa,d (T) = 1.813 m/s2 ≥ β ∙ ag = 0.20 ∙ 2.943 = 0.5886 m/s2
T3 = 0.47 sec :
2
1
Cgd,a s/m846.0
50.1
6.0
0.4
5.215.1)0.1943.2(
T
T
q
5.2Sa)T(S
2
1
Cgd,a s/m813.1
7.0
6.0
0.4
5.215.1)0.1943.2(
T
T
q
5.2Sa)T(S
2gd,a s/m115.2
0.4
5.215.1)0.1943.2(
q
5.2Sa)T(S
Tutorial 2.3
(2) Response spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
5. Lateral story loads Fj,i :
F1,1 = 100 0.30 1.426 0.846 = 36.2 kN
F2,1 = 75 0.644 1.426 0.846 = 58.3 kN
F3,1 = 50 1.00 1.426 0.846 = 60.3 kN
F1,2 = 100 (–0.676) (–0.511) 1.813 = 62.6 kN
F2,2 = 75 (–0.601) (–0.511) 1.813 = 41.8 kN
F3,2 = 50 1.00 (–0.511) 1.813 = –46.3 kN
F1,3 = 100 2.47 0.090 2.115 = 47.0 kN
F2,3 = 75 (–2.57) 0.090 2.115 = –36.7 kN
F3,3 = 50 1.00 0.090 2.115 = 9.5 kN
)T(SmF id,aii,jji,j F3,1= 60.3
F2,1 = 58.3
F1,1 = 36.2
F3,2 = –46.3
F2,2 = 41.8
F1,2 = 62.6
F3,3 = 9.5
F2,3 = –36.7
F1,3 = 47.0
Tutorial 2.3
(2) Response spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
5. Maximum shear forces Fb :
60.3
118.6
154.8
-46.3
-4.5
58.1
9.5
-27.2
19.8
76.6
121.7
166.5
2i,m,b
n
1im,b FF
Tutorial 2.3
(2) Response spectrum analysis: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Define Response Spectrum to be used
SAP2000 – 3-Story RC Frame System SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
SAP2000 – 3-Story RC Frame System
Define Response Spectrum to be used
Acceleration is in g unit
we can move the cursor on
the grave to obtain the
coordinartes at any point
SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Define Load case to include the Response Spectrum Analysis
SAP2000 – 3-Story RC Frame System SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Define Load case to include the Response Spectrum Analysis
A number of ways to combine modes given direction including CQC, SRSS,..and others...
Response spectrum will be applied as an acceleration in U1 (UX) direction using the
previously defined curve EC-8-B
SAP2000 – 3-Story RC Frame System SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Run Analysis
SAP2000 – 3-Story RC Frame System SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Display Base Reactions for the Response Spectrum (RS) case
SAP2000 – 3-Story RC Frame System SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Moments, Shear Forces, Axial Forces...for the Response Spectrum (RS) case
SAP2000 – 3-Story RC Frame System SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Moments, Shear Forces, Axial Forces...for the Response Spectrum (RS) case
SAP2000 – 3-Story RC Frame System SAP2000
(2) Modal Response spectrum analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(3) Linear time history analysis
Linear time history method of analysis, when used, shall be based on an appropriate
ground motion and shall be performed using accepted principles of dynamics.
The result of a response spectrum analysis using the response spectrum from a ground
motion is typically different from that which would be calculated directly from a linear
dynamic analysis using that ground motion directly, since phase information is lost in
the process of generating the response spectrum.
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
IS 1893-1:2002, 7.8.4
shall be performed for the following buildings:
• Regular buildings – those greater than 40 m in height in Zone IV and V, and those
greater than 90 m in height in Zones II and III.
• Irregular buildings – all framed buildings heigher than 12 m in Zones IV and V, and
those greater than 40 m in height in Zones II and III.
the resulted design base shear (VB) shall be compared with a base shear (𝑉𝐵) calculated
using a fundamental period TB.
• Where VB is less than 𝑉𝐵 , all the response quantities (e.g. Member forces,
displacements, story forces, story shears and base reactions) shall be multiplied by
𝑉𝐵 /VB.
IS 1893-1:2002 (3) Linear time history analysis
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
SAP2000 – 3-Story RC Frame System SAP2000
(3) Linear time history analysis
Define ground motion to be used Linear Time History analysis in UX direction (LTH_UX)
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
SAP2000 – 3-Story RC Frame System SAP2000
(3) Linear time history analysis
Define ground motion to be used Linear Time History analysis in UX direction (LTH_UX)
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
SAP2000 – 3-Story RC Frame System SAP2000
(3) Linear time history analysis
Define ground motion to be used Linear Time History analysis in UX direction (LTH_UX)
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
When the analysis is conducted the actions of the orthogonal components of ground motions shall be combined using approximate equations.
a) Horizontal components: Step 1: Compute the structural response of the structure under each component separately
- Analysis in Y direction - – Analysis in X direction – Compute Ey Compute Ex
Combination of effects of seismic action
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Load factors for design of steel structures: The following combination shall be accounted for:
IS 1893-1:2002, 6.3
Combination of effects of seismic action: ISN 1893-1:2002
ELILDL1,3 )3
ELDL1,7 )2
ILDL1,7 )1
Load factors for design of reinforced concrete and prestressed concrete structures: The following combination shall be accounted for:
ELDL
5,10,9 )4
ELDL1,5 )3
ELILDL1,2 )2
ILDL1,5 )1
The terms DL, IL, and EL stand for the response quantities due to Dead Load, Imposed Load and Earthquake Load.
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Combination of effects of seismic action: ISN 1893-1:2002
IS 1893-1:2002, 6.3 Design horizontal earthquake load :
When the lateral load resisting elements are oriented along orthogonal horizontal
direction, the structure shall be designed for the effects due to full design earthquake
load in one horizontal direction at time.
Example:
Case of steel building, and where lateral load resisting elements are oriented along UX direction. The building should be deisgned for:
xELILDL1,3 )3
xELDL1,7 )2
ILDL1,7 )1
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Combination of effects of seismic action: ISN 1893-1:2002
IS 1893-1:2002, 6.3 Design horizontal earthquake load :
When the lateral load resisting elements are not oriented along orthogonal horizontal
direction, the structure shall be designed for the effects due to full design earthquake
load in one horizontal direction PLUS 30% of the design earthquake load in the other
direction
Example:
Case of steel building, and where lateral load resisting elements are not oriented along UX direction. The building should be deisgned for:
yEL3,0xELILDL1,3 )3
yEL3,0xELDL1,7 )2
ILDL1,7 )1
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Combination of effects of seismic action: ISN 1893-1:2002
IS 1893-1:2002, 6.3
Combination for two or three component motion:
When responses from the three earthquake components are to be considered, the
responses due to each component may be combined using the assumption that when
response from one component are 30% of their maximum.
The response due earthquake force (EL) is the maximum of the following three cases:
zELyELxEL
zELyELxEL
zELyELxEL
3.03.0 )3
3.03.0 )2
3.03.0 )1
Alternatively, the response (EL) due to the combined effect of the three components
can be obtained on the basis of Square Root of the sum of the Square (SRSS):
222
zyx ELELELEL
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
a) Horizontal components: Step 2: Combine the response quantities using SRSS method:
2y
2x EEE
Alternatively, the response quantities can be combined as:
xy
yx
E3.0EE
E3.0EE
Exception: For buildings satisfying the regularity criteria in plan and in which walls or independent bracing systems in the two main horizontal directions are the only primary seismic elements, the seismic action may be assumed to act separately and without combinations.
EN 1998-1:2004, 4.3.3.5
Combination of effects of seismic action: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
b) Vertical components: If avg is greater than 0.25g, the vertical of the seismic action should be taken into account for the following cases:
• for horizontal or nearly horizontal structural members spanning 20 m or more.
• for horizontal or nearly horizontal cantilever components longer than 5 m. • for horizontal or nearly horizontal pre-stressed components • for beams supporting columns • in base-isolated structures
The analysis for determining the effects of the vertical component of the seismic action may be based on a partial model of the structure, which includes the aforementioned elements.
The effects of 2 horizontal and vertical components will be combined by:
zyx
zyx
zyx
EE3.0E3.0E
E3.0EE3.0E
E3.0E3.0EE
EN 1998-1:2004, 4.3.3.5
Combination of effects of seismic action: EN 1998-1:2004
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Torsional effects created in a simple building configuration: Torsion is occuring because a uniformly distributed force is not resisted by a uniformly distributed lateral resistant.
Accidental/Torsional Effects
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
SAP2000 – 3-Story RC Dual System
Mode 1
UX = 0,144
UY = 0
RZ = 0,61726
Mode 1
UX = 0
UY = 0
RZ = 0,7735
Mode 1
UX = 0,73509
UY = 0
RZ = 0
Mode 1
UX = 0,08906
UY = 0,15627
RZ = 0,54874
Modal Participating Mass Ratios
Accidental/Torsional Effects
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Accidental/Torsional Effects
isi
isi
dibeor
bee
05,0
05,05,1
the design eccentricity, edi to be used at floor i shall be taken as:
bi - Floor plan dimension of floor i, perpendicular to seismic action;
esi – Static eccentricity at floor i defined as the distance between centre of mass and centre of
rigidity.
IS 1893-1:2002, 7.9
IS 1893-1:2002
M
edi bi
x
y
direction of seismic action x
z
Qi,j - lateral force acting on story i in direction j
Mdi - torsional moment applied at story i about
its vertical axis z
jididi QeM ,
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Accidental/Torsional Effects
Irregular Buildings
In case of highly irregular buildings modeled as a system of
lumped masses at the floor levels (with each mass having
one degree of freedom), additive shears will be
superimposed for a statically applied eccentricity of ±0,05bi,
with respect to the centre of rigidity.
m3
m2
m1
m4
IS 1893-1:2002
IS 1893-1:2002, 7.9
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(1) Spatial models (3D):
displace the theoretical center of mass M at story i by an accidental eccentricity eai
for both directions of seismic motion/general building axes j of the structural
model
eai,j = 0.05 ∙ Li
Li - floor dimension (length, width)
perpendicular to seismic action
Mai = eai,j ∙ Fi,j
Fi,j - lateral force acting on story i in direction j
Mai - torsional moment applied at story i about its vertical axis z
M
eai, y Ly
x
y
direction of seismic action x
z
to account for torsional effects predominantly depends on the model type (planar or spatial)
EN 1998-1:2004, 4.3.2
EN 1998-1:2004 Accidental/Torsional Effects
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
(2) Planar models (2D):
→ theoretically, torsion cannot be considered in planar models
→ to overcome this, action effects for each individual lateral force-resisting element are
increased by a factor d :
i
e
ii F)L
x6.01(FF d
Ly
direction of seismic action
x
M
→ if two planar models are used:
(1) increase accidental eccentricity eai by a factor of 2 or
(2) double the factor d, so that: i
e
ii F)L
x2.11(FF d
EN 1998-1:2004, 4.3.3.2.4
to account for torsional effects predominantly depends on the model type (planar or spatial)
EN 1998-1:2004 Accidental/Torsional Effects
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Structures in real life are flexible and can exhibit large
lateral displacements in unusual circumstances. The lateral
displacements can be caused by wind or seismically
induced inertial forces.
Gravity loading will influence structural response under
significant lateral displacement.
P-Δ may contribute to loss of lateral resistance, ratcheting
of residual deformations, and dynamic instability.
Second-order Effects (P-Δ effects)
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Second-order effects (P-∆ effects) need not be taken into account if the following
condition is fulfilled in all storeys:
EN 1998-1:2004 Second-order Effects (P-Δ effects)
EN 1998-1:2004, 4.4.2.2
10,0
hV
dP
tot
rtot
h
V
d
P
tot
r
tot
= is the interstorey drift sensitivity coefficient;
= is the total gravity load at and above the storey considered in the seismic design
situation;
= is the design interstorey drift, evaluated as the difference of the average lateral
displacements ds at the top and bottom of the storey under consideration and
calculated in accordance with Chapter 4.3.4;
= is the total seismic storey shear; and
= is the interstorey height.
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Second-order effects (P-∆ effects) need not be taken into account if the following
condition is fulfilled in all storeys:
EN 1998-1:2004 Second-order Effects (P-Δ effects)
EN 1998-1:2004, 4.4.2.2
10,0
hV
dP
tot
rtot
If 0,1 < θ≤0,2, the second-order effects may approximately be taken into account by
multiplying the relevant seismic action effects by a factor equal to 1/(1 - θ).
value of the coefficient θ shall not exceed 0,3
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Second-order Effects (P-Δ effects)
Use P-Delta in SAP2000
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Second-order Effects (P-Δ effects)
To mitigate second-order effects: two-story X-bracing or zipper columns are recommended
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Select and Scale Earthquake Records EN 1998-1:2004
The suite of recorded or simulated/artificial accelerograms should observe the following rules:
• A minimum of 3 accelerograms should be used;
• The duration of the accelerograms shall be consistent with the magnitude and the other relevant features of the seismic event underlying the establishment of ag;
• The values are scaled to the value of ag.S for the zone under consideration;
• in the range of periods between 0,2T1 and 2T1, where T1 is the fundamental period of the structure in the direction where the accelerogram will be applied;
• no value of the mean 5% damping elastic spectrum, calculated from all time histories, should be less than 90% of the corresponding value of the 5% damping elastic response spectrum;
A. Meslem & D. Lang © NORSAR – Kjeller (Norway) 2014
Select and Scale Earthquake Records EN 1998-1:2004
The parameters (that have the most influence on ground motion spectral shape) that need to be considered in selecting records :
• Magnitude range of anticipated significant event;
• Distance range of the site from the causative fault;
• Site Condition (i.e. looking at the average shear velocity);
• Basin effect (if basin exists)
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Contribution of Joint Regions
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SAP2000 – 3-Story RC Frame System
not considered
considered
Contribution of Joint Regions
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