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

//upload.wikimedia.org/wikipedia/en/d/d4/Iitroorkee.jpg

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

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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


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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


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


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


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


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


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


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


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


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


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



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




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


(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:



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


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).



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


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


Period T [sec]

Spec

tral

acc

eler

atio

n S

a,d

q = 1

q = 2

q = 4

TB TC TD T1


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



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


- 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


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


(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.


(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



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



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



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



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



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



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:


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


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


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




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 … … … … …




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 … … … … …




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


or

mi ≥ 0.9 mtot

mi ≥ 0.05 mtot




since both criteria are

not fulfilled, those

modes shall be


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



Define Masses Seismic...G + 0.3 ∙ Q

Example 2.1 – 3-Story RC Frame System SAP2000



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


Run Model Analysis

(2) Response Spectrum analysis: EN 1998-1:2004 SAP2000 Example 2.1 – 3-Story RC Frame System


Deformed shape....

Mode 1 Mode 2 Mode 3



Modal Information....

first torsional

mode is 3rd

Σ = 0,90 0,98



first eigenmode

is torsional

SAP2000


Example 2.2 – 3-Story RC Dual System


first eigenmode is

torsional

Σ = 0,83 0,74

SAP2000


Example 2.2 – 3-Story RC Dual System


(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).


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



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



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



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



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



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


EN 1998-1:2004 (2) Modal Response spectrum method

Procedure:

Design spectral accelerations Sa(Ti )/g for each mode i :


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)


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


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


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


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



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



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



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



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



Define Response Spectrum to be used

SAP2000 – 3-Story RC Frame System SAP2000

(2) Modal Response spectrum analysis


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



Define Load case to include the Response Spectrum Analysis




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




Run Analysis




Display Base Reactions for the Response Spectrum (RS) case




Moments, Shear Forces, Axial Forces...for the Response Spectrum (RS) case




(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.


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



(3) Linear time history analysis

Define ground motion to be used Linear Time History analysis in UX direction (LTH_UX)


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


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.



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



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



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) 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


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


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.



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




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 ,



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


(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


(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


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-∆ 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.


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



Use P-Delta in SAP2000



To mitigate second-order effects: two-story X-bracing or zipper columns are recommended


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;


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)


SAP2000 – 3-Story RC Frame System

not considered

considered



Abdelghani Meslem, PhD NORSAR, Kjeller

[email protected] Phone: (+47) 974 10 740

Web: www.norsar.no

p8 am structuralanalyismethods

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