Multi modal response spectrum analysis implemented in OpenSEESlese.fe.up.pt/OSDPt2014/New/Apresent/D2_009_Simon_… · · 2017-02-09Budapest University of Technology and Economics

Budapest University of Technology and Economics

Department of Structural Engineering

Multi modal response spectrum analysis

implemented in OpenSEES

OpenSeesDays Portugal

July 03-04, 2014, Porto

József Simon

László Gergely Vigh

27/11/2014 TDK konferencia 2011 22014.07.04. OpenSeesDays - Porto

Introduction

Research project:

Seismic analysis of bridges in moderate seismic regions

Database of existing bridges

Pre-Eurocode era – lack of seismic design

Seismic behavior is not known

Thousands of structures

Parametric study to recognize vulnerable configurations

Fast analysis method is needed

Multi modal response spectrum analysis


Introduction

Response spectrum analysis:

Most widely used

Well-known

Relatively fast (compared to other methods)

Suitable for parametric study or sensitivity analysis

Linear method, but

Can be used with non-linear elements (effective stiffness

and iterative solution)

Overestimates (generally) the internal forces

Thus, gives an upper limit for the responses


𝒑𝑖 = 𝒎 𝜱𝑖

𝜱𝑖𝑇𝒎 𝜾

𝜱𝑖𝑇𝒎 𝜱𝑖

𝑆𝑑 𝑇𝑖

Theoretical background


• Based on modal analysis (eigenvectors and eigenvalues)

• Importance of a mode characterized by the modal mass:

𝑚𝑖∗ =

𝜱𝑖𝑇𝒎 𝜾 2

𝜱𝑖𝑇𝒎 𝜱𝑖

• Load vector for each mode:

• Quasi-static loading, static analysis

• Combination of the responses from each mode:

𝐸𝐴𝐵𝑆𝑆𝑈𝑀 = 𝐸𝑖 , 𝐸𝑆𝑅𝑆𝑆 = 𝐸𝑖 𝟐 , 𝐸𝐶𝑄𝐶 = 𝐸𝑖 𝜌𝑖𝑗 𝐸𝑗

𝒋𝒊


RSA modul in OpenSees

proc RSA {ag soiltype eqtype ξ q qd sumtype elelist nodelist}

Written in TCL

3D analysis of any structure

ag peak ground acceleration [m/s2]

soiltype (A, B, C, D or E)

eqtype (1 or 2)

ξ damping ratio

q behavior factor

qd needed to calculate displacements

sumtype (ABSSUM, SRSS, CQC) comb. method

elelist

nodelist

Defines the shape of the

standard spectrum

Only results of listed nodes and elements are

stored and combined



Modal analysis > eigen command (Φi)

Mass matrix compilation > nodeMass command (m)

Note: mass has to be defined in nodes!

Modal mass calculation (m*i)

Necessary number of modes (e.g. 90% rule)

Load vector compilation (pi)

Static analyses

Storing responses (nodelist and eleslist)

Note: only eleResponse $e_num forces!

Combination of responses (sumtype)

Combined responses > global variables



Output:

Global variables

Global coordinate system!! (displacements and forces as well)

3·3=9 global list variables for displacements

3·2·6=36 global list variables for element internal forces


Ex.1 - Equivalent linear analysis of girder bridges with seismic isolators

EC8-2 Section 7

1. Non-linear behavior approximated by bi-linear characteristic. NLTHA

2. Equivalent linear stiffness and effective damping.LRSA

ITERATION NEEDED!!

ξ = ?? • EC - AASHTO

• JPWRI

• CALTRANS 94

• CALTRANS 96

Five standard methods:

Continous girder bridges

With isolation bearing in the longitudinal direction

Comparison of two analysis methods (non-linear elements!)



Three dimensional numerical model in OpenSees

No energy dissipation is expected in the piers!!



In TCL (automatic iteration) with RSA



Three continous girder bridges (concrete, composite, steel)

Only one fixed/isolation bearing!

Two soil types (C,E), two peak ground acc. (1.0 and 1.4 m/s2)

C

ag=1.4 m/s2

Compared to NLTHA:

The accuracy of the internal

forces (pier moments,

isolator forces) is ± 25%


Ex.2 - Seismic assessment of M0 Highway bridge at Háros, Hungary

0

50

100

150

200

250

300

350

P2 P3 P4 P5 P6 P7 P8 P9

Mxlo

ngit

ud

inal m

om

ents

[M

Nm

]

Pier number

RSA

THA

Comparison of RSA and LTHA

results

Upper-limit for the responses!


Ex.3 – Parametric seismic analysis of multi-girder bridges

Number of supports: 2-5

Spans: 4-8-12-16-20-24 m

Outer/inner span ratio: 0.75-1.00

Pier height: 2-6-10-14 m

Pier cap cross-section: 1.20x1.00 m

Pier: 0.60x0.90 m

Abutment: 1.00x2.00 m (14 m wide)

Number of piers in the lateral direction: 4 (distributed in every 3 m)

Piles: D=80 cm 1x5 (abutment) – 2x5 (piers)

Fixed parameters:

Nearly half of the higher level

road bridges!!!


Superstructure:

ElasticBeamColoumn

Pier: ElasticBeamColoumn

Abutments: ElasticBeamColoumn

Rigid links

Rigid links

Foundation and backfill: linear springs




Superstructure

Abutments

Backfill soil

Superstructure-abutment

Superstructure-pier joints

Piers

Pier foundations

H p (m) 4 8 12 16 20 24

2 0.56 1.13 1.77 2.11 3.04 3.73

6 0.47 0.85 1.27 1.75 2.27 2.98

10 0.64 0.94 1.26 1.63 2.10 2.68

14 1.31 1.60 1.80 2.15 2.62 3.05

Támaszköz méterben

Critical components at longer

bridges

Components found to be adequate

Spans (m)

D/C ratio for piers

(4 span bridges)


Concluding remarks


Linear method, but

Can be used with non-linear elements (Ex.1)

Overestimates (generally) the internal forces

Thus, gives an upper limit for the responses (Ex. 2)

Relatively quick,

Suitable for parametric study or sensitivity analysis (Ex. 3)

Also it provides solid base for:

detailed seismic assessment

retrofit planning

development of design concepts for new bridges


Concluding remarks

RSA should be implemented in the soure code:

Mass matrix can be constructed even with discontinuous,

unlumped masses

During the combination of the responses, the element type

can be recognized and specific responses can be queried,

stored

Any structure can be analyzed in 2D or 3D as well

187/11/2014 TDK konferencia 2011

Thank you for your attention!

Acknowledgement :This presentation was supported by the János Bolyai Research Scholarship of the Hungarian

Academy of Sciences.

Documents

Multi modal response spectrum analysis implemented in OpenSEESlese.fe.up.pt/OSDPt2014/New/Apresent/D2_009_Simon_… · · 2017-02-09Budapest University of Technology and Economics