En Curs09 Dsis

8/12/2019 En Curs09 Dsis

1/11

1

Structural Dynamics and Earthquake

Engineering

Course 9

Seismic-resistant design of structures (1)

Seismic action

Methods of elastic analysis

Course notes are available for download at

http://www.ct.upt.ro/users/AurelStratan/

Seismic-resistant design of structures

P100-1/2013 "Cod de proiectare seismic P100 Partea I -

Prevederi de proiectare pentru cldiri"

Eurocode 8 "Design of structures for earthquake

resistance - Part 1: General rules, seismic actions and

rules for buildings"

Fundamental requirements:

Life safety: sufficient safety margin over local or global collapseof the structure

P100-1/2013: associated earthquake: 225 years return period

Eurocode 8: associated earthquake: 475 years return period

Damage limitation. NO occurrence of damage and the associated

limitations of use, with disproportionately high cost in

comparison with the costs of the structure itself

P100-1/2013: associated earthquake: 40 years return period

Eurocode 8: associated earthquake: 95 years return period


2/11

2

Ultimate limit states

Fundamental requirements (life safety and damagelimitation) are verified by checking the structure for two

limit states:

Ultimate Limit State (ULS)

associated to collapse and other forms of structural degradation

that may endanger human lives

verification of ULS implies a balance between strength and

ductility

Serviceability Limit State (SLS)

associated to degradations, that lead to limitation of use

limitation of structural and non-structural damage generally, check for SLS involves limitation of interstorey drifts, in

order to protect non-structural elements, equipments, etc.

Seismic action: elastic response spectrum

National territory: divided in zones of constant seismic

hazard

Seismic hazard for design is expressed by horizontal

peak ground acceleration ag (determined for the return

period associated to ULS)


3/11

3

Elastic response spectrum

Seismic action on the ground surface expressed bypseudo-acceleration response spectra

2 horizontal components

1 vertical component

Local site conditions affect:

amplification of acceleration

frequency content of the ground motion

Control periods

TC, s 0.7 1.0 1.6TB, s 0.14 0.20 0.32

TD, s 3.0 3.0 2.0

Elastic spectrum: control period TC

P100-1/2006: TCspecified at a macroseismic scale


4/11

4

Elastic spectrum: normalized form (T)

Elastic response spectrum:

Normalized form of the response spectrum:

Ta)T(S ge

Elastic spectrum: normalized form (T)


5/11

5

Local site conditions: Eurocode 8

Behaviour factorq

Most structures are able to survive a major earthquake

without collapse, but with important structural

degradations due to:

ductility of the structure (capacity to deform in the inelastic range)

overstrength

design of structures for a fraction of the strengthnecessary for an elastic response(behaviour factor - q)

Design codes: a single force reduction factor depending

on material and structural typology

D

F

Fe

Fy

De=DmDy

DRy

1

1

R

F

q Ry


6/11

6

Force reduction factors

1V

Vy

V

Vd

Ve

q

q

q

R

Sd

qS

qraspunsul real

raspunsul idealizat

raspunsul

infinit elastic

uy e

Fi

V


u- ultimate displacement of the system y- displacement at global yield Ve - base shear force corresponding to an infinitely

elastic response

Vy - yield base shear force

V1 base shear force at first yield in the structure

Vd - design base shear force

Global ductility of the structure

u y


7/11

7


Ductility-related force reduction factor

Overstrength:

redundancy

design governed by non-seismic loads

limitation of the number of different cross-sections use to

simplify fabrication and erection

a real strength larger than the nominal one

Total reduction factor (behaviour factor):

e yq V V

S y d

q V V S R Sd q q q

1R y

q V V

1Sd dq V V

S Sd R q q q q q q


Force reduction factors: period dependent

To simplify, qcan be considered constant In reality, qdepends on:

properties of the ground motion (TC), in relation with

period of vibration of the structure

q

S

q

q

1


8/11

8

Design response spectrum for elastic analysis

0TTB:0 1

( ) 1d g

B

qS T a T

T

T> TB:( )

( )d gT

S T aq

0 1 2 3 40

0.2

0.4

0.6

0.8

T, s

pseudo-a

cceleratie,

g

P100-1/2013, TC

=1.6 s, ag=0.30g

Se

Sd, q=6

Elastic design methods

In design: elastic analysis

Alternatives:

lateral force method (equivalent static force method)

modal response spectrum analysis (spectral analysis)


9/11

9

The equivalent static force method

Can be used for structures that: can be modeled using two planar models for each principal

direction and

whose seismic response is not influenced significantly by higher

modes of vibration (structures with T11.5 sec, regular in

elevation, and with height less than 30 m)

A simplified spectral analysis, that considers the

contribution of the fundamental mode only

(Vb1 Fb;A1 I,eSd(T1); M1* m )

*

bn n nV M A , 1b I e d F S T m


Base shear force (P100-1/2013):

Sd(T1) - ordinate of the design response spectrum

corresponding to fundamental period T1

m - total mass of the structure

I,e importance factor of the building - correction factor (contribution of the fundamental

mode of vibration using the concept of effective modal

mass):

= 0.85if T1 TC and the structure is higher than twolevels, and

= 1.0in all other cases

, 1b I e d F S T m


10/11

10


Equivalent static force at storey iin mode n:

where

using the expression

in n i in nf m A 12

1

N

i in

in N

i in

i

m

m

2

1*

2

1

N

i in

i

n N

i in

i

m

M

m

*

n bn nA V M

2

1 1

22

1 11

N N

i in i ini i i in

in n i in n i in bn bnN nN

i in i ini in

i ii

m mmf m A m V V

m mm


Equivalent static forces

Lateral force at storey i (P100-1/2013):

Fb -base shear force in the fundamental mode of vibration

si- displacement of the mass iin the fundamental mode shape

n - number of storeys in the structure

mi-storey mass

1

i ii b N

i i

i

m sF F

m s

1

i inin bn N

i in

i

mf V

m


11/11

11


Fundamental mode shape can be approximated by ahorizontal displacements increasing linearly with height

Preliminary design of

structures with height

En Curs09 Dsis

Documents

Transcript of En Curs09 Dsis