penjelasan sni 1726 2012

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prepared by Djoni Simanta, Unpar, Bandung, 2013 1

BEBAN GEMPA

UNTUK

STRUKTUR GEDUNG TAHAN GEMPA

MENURUT SNI 1726‐201X

Djoni Simanta

Fakultas Teknik

Universitas Katolik Parahyangan

2013

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KESIMPULAN

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Kesimpulan

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/ /

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Building Model

SNI 1726 Code Based Response Spectrum Analysis Procedure

I. Shear Building Model

12.E .I

SDOF

HIc

m

qL

c cL 3

. .K =4.

H

t

mW =m.g T=2.π

K

presented by Djoni Simanta, Ir., MT

s

o s t

plot tospectra curve to get C

baseshear V =C .W

Building Model

In Code Based Response Spectrum Analysis Procedure


SDOF

sL n2

n n

s L

r t ontro

a.Lateraldisplacement:

C .g 2πq = ω =

ω T b.Drift control

Δ =q


s

s

Δservicedrift ratio=

H

C .Δultimatedrift ratio=

I .H

d

e

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Scale Factor xf 1 a t

f a a

a f μ f

f μ a μ a

T =T ; T = C .H

if T T T=TT < T C .T T =C T

a


DS e D1 es

11 smin DS e

e

smin DS

ASCE 7-10/SNI 1726:

S . I S .IC =min ;

R R.T

Si f S 0 ,6 C =max 0 ,0 44 .S . I ; 0 ,0 1; 0,5.

R/ I

o therwise C =max 0,044.S .I

e ;0,01


DS e D1 es smin

s s t t

sD

o

S . I S .Iand C =max C ;min ;R T.R

V = C . W ; W = m .g

Scale Factor:

ζ.Vf =max ;1,0 ; ζsni=0,85

V

Building Model


I. Shear Building ModelSDOF

Gross Responses

.

.

s o D

o s

o s

Equivalent Design Lateral Force f V f

Design Base Shear V f

Overturning Design Moment M f H


Building Model


II. Plane Frame Model

HIc

m

qL

L

1

2 3

q1

q2

q3

q4 q5 0 5 5

1 1 32 2 4

0 0 0 M


3 0 0

4 0 0

Building Model


, ,

STATIC CONDENSATION

0m m m n m

nn m n n n

K K U

F K K U

, ,

, ,

, ,

1, ,

1

, , , ,

0

Rearrange . .

Pluginto

m m m m n n

n m m n n n n

m m m m n n

n n n n m m m m n n n

K U K U

K U K U F

U K K U

K U K K K U F

presented by Djoni Simanta, Ir., MTpresented by Djoni Simanta, Ir., MT

, , , ,

,

Simplify ( )

(

n n n m m m m n n n

n n n

K K K K U F

K K K

1, , , )m m m m nK K

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Building Model


LK =2.K ; thereare2 frames

Drift Control

a.Lateraldisplacement:

II. Plane

Frame

Model

t

L

s

o s t

mW =m.g T=2.π

K

plot tospectra curve to get C

baseshear V =C .W

sL 5 n2

n n

s L 5

s

.q =q = ω =

ω T

b.Drift control

Δ =q

Δservicedrift ratio=

H

q


s.

ultimatedrift ratio= I .Hd

e

Scale Factor:

x

f 1 a t

f a a

a f μ f

f μ a μ a

T =T ; T =C .H

if T T T=T

T < T C .T T =C T

StaticCode BaseShear

a

II. Plane Frame Model

DS e D1 es

11 smin DS e

e

smin DS

ASCE 7-10/SNI 1726:

S . I S .IC =min ;

R R.T

Sif S 0 ,6 C =max 0,044.S . I ;0 ,01;0,5.

R/I

otherwise C =max 0,044.S .I

e ;0,01


DS e D1 es smin

s s t t

sD

o

. .

and C =max C ;min ;R T.R

V =C .W ; W = m.g

ScaleFactor:

ζ.Vf =max ;1,0 ;ζsni=0,85

V

Building Model


.s o D

o s

Equivalent Design Lateral Force f V f

Design Base Shear V f

Gross Response

II. Plane Frame Model SDOF

.o sOverturning Design Moment M f H

Each frame response

5 5

1

1

. Dq q f

qq


2

2 1

, , 5 3

3

4

4

5

. . ; .i i i i im m m m m nq

q U K K q q q D d f k d q

qq

q

Building Model


MDOF1

m2

H2

5 6 7 8 q1814

2

3

4

Typical Frame

m1

H1

L L L

1 2 3 4 q17

1 2 14

1 2 3 4


18 DOF with 2 dynamic DOFNotes:

q17=U1

q18=U2

17 17 ....... 0

1 3 .... .. ..13

2 4 ........14

0 0 ........ 0

0 0 ........ 15

0 0 ........ 16

M

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Building Model


, ,

STATIC CONDENSATION0m m m n mK K U

F K K U

, ,

, ,

, ,

1

, ,

1

, , , ,

0

Rearrange . .

Pluginto

m m m m n n

n m m n n n n

m m m m n n


K U K U

K U K U F

U K K U

K U K K K U F

presented by Djoni Simanta, Ir., MTpresented by Djoni Simanta, Ir., MTpresented by Djoni Simanta, Ir., MT

, , , ,

,

Simplify ( )

(

n n n m m m m n n n

n n n

K K K K U F

K K K

1

, , , )m m m m nK K

Building Model


1. Mass

Matrix

1

2

0

0

m M

m

MDOF

2. Lateral Stiffness Matrix

2.1. Structural stiffness Matrix of each frame

( ) ( ) 16,6 18,18 18,18

1

eachframe NE

ii i F

i

K K K K

2.2. Lateral Stiffness Matrix of each frame

1condensation to lateralstiffness F K K

m2 q18=u2


, , L

2.3. Total Lateral Stiffness Matrix of Building

1 2 3 4

2,2 2,2 2,2 2,2 2,2

F F F F

L L L L LK K K K K

m1 q17=u1

2.4. Eigen Analysis

Building Model


to find eigen values and eigen vectors

2. 0K M

MDOF

2

n n n

n

11 12

21 22

foreach mode-n:

2πeigenvalue ω ;ω ;T =

ω

eigenvector (modeshape): and can benormalized t o M = 1,T

n n n

a aa M

a a


11 1 221 22 2

1

andnormalizedmodeshape

.

ij

ij j

k kj

k

m a

Building Model


2.5. Spectral values:

For each mode‐n period Tn, plot to Nominal Spectra, and get Cn

spectral matrix

MDOF

1

2

1

2

22

.0

.0

c g

SAc g

2.6. Modal Participation Factors


. . 1

. .

; for normalized modeshapes

T

n n

T

n n n

nn n n

n

L a M

M a M a

L L

M

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Building Model


3. Response

Spectra

Analysis

For each mode‐n :

3.1. Lateral Displacements

MDOF

2 2

2

.. .

. .

in total matrixform:

an nnnn n Dn n Dn

n n

ann n n

n

S c gY S u a Y with S

S u a


17,1 17,211 1221 22 18,1 18,2

. . for this 2dofscaseq qu uu a SAu u q q

Building Model


3.2. Lateral Drift Control

11 12 11 12

ServiceCondition:

u u

MDOF

21 22 21 11 22 1 2

2 3/2

12 12 112 21 122 2 2

12 12 12 2

1

( ) ( )

ModalCombinationswith"CQC Method":

8 (1 ).;

[(1 ) 4 . (1 ) ]

service drift ateachstory:

/

s

s

u u u u

ratio

2 2

11 12 12 11 12 11 2 . . / hh


2 22 2 21 22 12 21 22 2

1 1

2 2

/ 2 . . /

ultimatedrift ratio ateach story

. / ( . )should beless thanallowable drift ratio

. / ( . )

s

sd e

sd e

h h

C I h

C I h

presented by Djoni Simanta, Ir., MT presented by Djoni Simanta, Ir., MT

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3.3. Lateral Forces & Base Shear

Building Model


2.elasticlateralforces foreachmode-n:

n n nu u

MDOF

2 2

2

11 12

. .( ). .( ). .

.( ). . . . . .

for all mode:

. . .

nsn n n n n n

sn n n n Dn n n an

s s

s

f M u M u M a Y

f M a S M a S

f f f M a SA


:

1 1 .o s

Base Shear

V f 11 12

2 2

11 12 12 11 122. . .

o o

o o o o o

V V

V V V V V

3.4. Scale Factor

x

f 1 a t

f a a

a f μ f

f μ a μ a

T =T ; T = C .H

if T T T=TT < T C .T T =C T

a

DS e D1 es

11 smin DS e

e

smin DS

a c o e ase ear

ASCE 7-10/SNI 1726:

S . I S .IC =min ;

R R.T

Sif S 0 ,6 C =max 0,044.S . I ;0 ,01;0,5.

R/I

otherwise C =max 0,044.S .I

e ;0,01


DS e D1 es smin

s s t t

sD

o

S .I S .Iand C =max C ;min ;R T.R

V =C .W ; W = m.g

ScaleFactor:

ζ.Vf =max ;1,0 ; ζsni=0,85

V

Building Model


3.5. Gross Responses

3.5.a. Lateral Design Forces and Design Base Shear

for all mode:

f f

MDOF

s s

s D

s 21 s 22

2 2

s11 s12 12 s11 s12sCQC

2 2

s21 s22 12 s21 s22

f = M . a . τ . SA .f =f f

CQCModalCombinations:

f +f +2ρ .f . f f =

f +f +2ρ .f . f

Design BaseShear:


o s o11 o12V = 1 1 . f = V V

CQCModal

2 2

oCQC o11 o12 12 o11 o12

Combinations:

V = V +V +2.ρ .V .V

Building Model


DesignOverturning Moment:

3.5.b. Design Overturning Moment

MDOF

o 1 1 2 s o11 o12

2 2

oCQC o11 o12 12 o11 o12

M = h (h +h ) . f = M M

CQCModalCombinations:

M = M +M +2.ρ .M .M


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Building Model


, ,

STATIC CONDENSATION0m m m n mK K U

F K K U

, ,

, ,

, ,

1

, ,

1

, , , ,

0

Rearrange . .

Pluginto

m m m m n n

n m m n n n n

m m m m n n


K U K U

K U K U F

U K K U

K U K K K U F


, , , ,

,

Simplify ( )

(

n n n m m m m n n n

n n n

K K K K U F

K K K

1, , , )m m m m nK K

Building Model


3.6. Design Internal Forces in each frame

17,1 17,211 12

21 22 18,1 18,2

. . . for this 2dofscasen D

q qu uU a SA f

u u q q

MDOF

1,1 1, 2

17,1 17,21 1

, , , ,

18,1 18,2

1 6,1 1 6, 2

. .. . . .

. .m m m m n n m m m n

q q

q qU K K U K K

q q

q q

q q


, ,

6,2 6,2 6,2 6,6 6,2

1 8,1 1 8, 2

. .. ;n=2for thiscase

. .

i i i i iq D d f k d

q q

emen orces

Building Model


3.6. Design Internal Forces in each frame

(contionued)

InternalFrame ElementForces

:CQC Modal Combinations

MDOF

2 2

11 12 12 11 122 . .

.....................................

.....................................

.....................................

..............

i

CQC

f f f f

f

.......................


2 2

61 62 12 61 622 . . f f f f

Loading CombinationsLoading Combinations

Accidental Torsion

12

1‐axis & 2‐axis are principle axes

from mode‐1 and mode‐2 translation

directions

b1b2

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Accidental Torsion (continued)

Loading CombinationsLoading Combinations

T1 1 i1 d11 i1

T2 1 i1 d21 i1

ra :

E1 =>(-0,05.b ).F =e .F

E1 =>(+0,05.b ).F =e .F

Arah 2:

T1 2 i2 d12 i2

T2 2

E2 =>(-0,05.b ).F =e .F

E2 =>(+ 0,05.b ) iy d22 i 2.F =e .F

Dynamic Loading

Combinations,

Horizontal

EQ,

LRFD

Directional Combinations

Scale Absolute Sum Method, with scale factor= 0,3:

Comb1= E1 + 0,3 E2

Comb2= E2 + 0,3 E1

Comb3= E1 + E1T1 + 0,3 E2

Comb4= E1 + E1T2 + 0,3 E2

Comb5= E2 + E2T1 + 0,3 E1

om = + + ,

E = max

[ Comb1,

Comb2,………..,

Comb6]

max = envelope command in etabs

1. Beam Flexural Design 2. Column/WALL Flexural Design

KombinasiKombinasi HasilHasil AnalisisAnalisis DinamisDinamis

1,4 DL 1,4 DL

1,2 DL + 1,6 LL 1,2 DL + 1,6 LL

1,2 DL + 0,5 LL ± E 1,2 DL + 0,5 LL ± E

0,9 DL ± E 0,9 DL ± E

Total 6 kombinasi

Total

18

kombinasi

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Desain Struktur Gedung Beton Bertulang Tahan Gempa

berdasarkan

‐

Desain Struktur Gedung Baja Tahan Gempa

berdasarkan

Spesifikasi Umum untuk Gedung Baja Struktur

Ketentuan Desain

Tahan

Gempa

untuk

Struktur

Gedung

Baja

penjelasan sni 1726 2012

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