Nonlinear response-history analysis in design practice

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Nonlinear response-history analysis in design practice

RUTHERFORD & CHEKENE

November 2007Joe Maffei



Why do NLRH?• The code makes us. (Base isolation or

supplemental damping)

• Substantiation of non-prescriptive (“alternative”) designs.

• We want to know what happens.

What is the value of NLRH?

OutlineExample projects

Unique value of NLRH

Findings from NLRH of tall buildings

Dispersion of NLRH results

Ground motion input

Conclusions

[Modeling uncertainty]

Example projects that used NLRH



Education Tower


Buildings with supplemental damping


Waterfront pier structures


Exploratorium – Piers 15 and 17

Non-prescriptive seismic design

BASE

13th

ROOF

What is the unique value of NLRH? …

To determine what happens, not how much.

Desired mechanism


Undesirable mechanism

Findings from NLRH analyses of high-rise

buildings

Runs scaled from 0.1x MCE to 4x MCE

Runs scaled from 0.1 x MCE to 4 x MCE

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5

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15

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40

45

0 1 2 3 4

Ground-Motion Scale Factor

Pea

k L

ater

al R

oo

f D

isp

lace

men

t H

2 (f

t)

IDA H2

Core wall moment versus shear amplification

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15000

20000

25000

30000

35000

40000

45000

0 1 2 3 4


Pea

k C

ore

Sh

ear

Fo

rce

H2

(kip

-ft)

IDA H2@7th

IDA H2@1st

0

250000

500000

750000

1000000

1250000

1500000

1750000

2000000

0 1 2 3 4


Pea

k C

ore

Mo

men

t ab

ou

t H

1 (k

ip-f

t)

IDA H2@7th

IDA H2@1st

Moment to shear ratio

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20

40

60

80

100

120

140

0 1 2 3 4


Eff

ec

tive

He

igh

t M/V

(ft

)

IDA H1@7th

IDA H1@1st

IDA H2@7thMCE level

110’ at 0.6x MCE90’ at MCE57’ at 2x MCE

230’

175’

0

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Use NLRH to determine what happens, more than how much.


Coupled wall

Plastic hinge locations



Dispersion of results among 7 or 14 ground

motion records

14 NLRH RUNS

BASE

13th

ROOF

Roof Displ.

Ft.

Wall Shear at BaseKips

Wall Moment at 13th

1000xK-ft.

MinMaxMeanm+c.o.v.

2.1’6.7’4.2’5.4’0.29

76002970

01550

02220

00.43

5131080900

10900.21

Pushover

5500 760

Coupling beam rotation

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200

250

300

350

0 0.005 0.01 0.015 0.02 0.025 0.03

Plastic Rotation [rad]

Bu

ildin

g H

eig

ht

[ft]

Bhuj

El Salvador

Hector

Landers

Mexico

Nisqually

Peru

Average

Capacity

Considering dispersion“Demands for ductile actions shall be taken not less than the mean value obtained from the NLRH. Demands for low-ductility actions (e.g., axial and shear response of columns and shear response of walls) shall consider the dispersion of the values obtained from the NLRH.”

NLRH ground motion input

NLRH INPUT

7 horizontal ground motion pairs

14 response-history runs

GRN 270

GRN 180

GRN 270

GRN 180


NLRH analysis at MCE“When the ground motion components [statistically] represent site-specific fault-normal ground motions and fault-parallel ground motions, the components shall be applied to the three-dimensional mathematical analysis model according to the orientation of the fault with respect to the building. When the ground motion components represent random orientations, the components shall be applied to the model at orientation angles that are selected randomly; individual ground motion pairs need not be applied in multiple orientations. .”

NLRH analysis at MCE“Where applicable, an appropriate number of the ground motion time series shall include near fault and directivity effects such as velocity pulses producing relatively large spectral ordinates at relatively long periods.”

Conclusions

The most important value of NLRH is that it tells you what the nonlinear mechanism is, and what the overstrength forces are on elements that you want to remain elastic.


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Modeling uncertainty

Olivian

Comparison of SAP model by KPFF vs Perform model by R&C

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0.00% 0.20% 0.40% 0.60% 0.80% 1.00% 1.20% 1.40% 1.60% 1.80% 2.00%

Inter-Story Drift Ratio [%]B

uil

din

g H

eig

ht

[ft]

R&C_MAX_X

R&C_MAX_Y

EOR_MAX_X

EOR_MAX_Y

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Time [s]

Dis

pla

cem

ent

[in

]

EOR - node 2765 - X

R&C Verification - X

EQ4:

Test EQ4PGA = 0.93g

EQ4:

EQ3 and EQ4 - Experimental

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-17.5 -12.5 -7.5 -2.5 2.5 7.5 12.5 17.5

Roof Displacement [in]

Bas

e M

om

ent

[kip

-ft]

Experimental results

EQ4: Non-linear

EQ3: Essentially

linear

Blind Prediction Results - EQ3 - Shear Force EnvelopeFirst 4 teams of each category

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7

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Shear Force (kips)

Floo

r

Measured

111 Almaden Ave San Jose

-8 -6 -4 -2 0 2 4 6 8

Rotation (%)

Initiation of Shear Tab Failure

Str

eng

th

1.1

-2.0

Bottom flange fracture

Gravity Collapse

7.0-7.0

Top flange fracture

Initiation of Shear Tab Failure

Beam connection behavior

W24X76

NEUTRAL AXIS

AREA 1 = 3.06 SQ. IN.

AREA 2 = 3.06 SQ. IN.

AREA 3 = 4.96 SQ. IN.

AREA 4 = 4.96 SQ. IN.

AREA 5 = 3.06 SQ. IN.

AREA 6 = 3.06 SQ. IN.CONCSTL

5.7"

11.5"11.8"

W24X76

NEUTRAL AXIS

AREA 1 = 3.06 SQ. IN.

AREA 2 = 3.06 SQ. IN.

AREA 3 = 4.96 SQ. IN.

AREA 4 = 4.96 SQ. IN.

AREA 5 = 3.06 SQ. IN.

AREA 6 = 3.06 SQ. IN.

W24X76

NEUTRAL AXIS

AREA 1 = 3.06 SQ. IN.

AREA 2 = 3.06 SQ. IN.

AREA 3 = 4.96 SQ. IN.

AREA 4 = 4.96 SQ. IN.

AREA 5 = 3.06 SQ. IN.

AREA 6 = 3.06 SQ. IN.CONCSTL CONCSTL

5.7"

11.5"11.8"

5.7"

11.5"11.8"

Beam fiber model

RAM Model SAC_14: Force vs. displacement

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Displacement (in)

Fo

rce

(k

)

a. Model behavior b. Test behavior

RAM Model SAC_14: Force vs. displacement

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Displacement (in)

Fo

rce

(k

)

a. Model behavior b. Test behaviora. Model behavior b. Test behaviora. Model behavior b. Test behavior

Analysis model versus test results

C1.2%C1.9%

B1.8%(T) B3.1%(T)

B3.6%(T)

B4.2%(T)

B4.3%(T)

B3.5%(T)

B2.5%(T)

B1.2%(T)

C1.0%

C0.00024%

B0.05%

B0.01%

C1.9%

Roof

8th Floor

7th Floor

6th Floor

5th Floor

4th Floor

3rd Floor

2nd Floor

1st Floor

Basement

B2.4%(B)

B0.01%

B0.04%

B1.3%

B3.3%(B)

B4.2%(B)

B4.0%(B)

B3.6%(B)

B3.1%(B)

Direction of Largest Displacement (2.6% Roof Drift)

C0.00027%C1.1%

C0.00026%

DCR=0.31

DCR=0.00

DCR=0.00

DCR=0.00DCR=0.17

DCR=0.30

DCR=0.10

DCR=0.39

: Fracture: Yield

Legend:

B: Beam or C: ColumnTotal RotationT: Top flange fracture or B: Bottom flange fracture

B 2.5% (T)

DCR = Total Rotation / FEMA CP Rotation, See Table 6-2

Test Specimen

RAM Perform finite element model


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Roof Drift

Ba

se

Sh

ea

r (k

)

RAM Perform Cyclic Pushover

Envelope of test specimen hysteresis loops

Cyclic pushover results


Documents

Nonlinear response-history analysis in design practice