Seismic Design of New R.C. Structures Prof. Stephanos E. Dritsos University of Patras, Greece.

Pisa, March 2015

Seismic Design Philosophy Main Concepts

 Energy dissipation  Ductility  Capacity design  Learning from Earthquakes

Energy Dissipation

3

Ductility and Ductility Factors •

Ductility is the ability of the system to undergo plastic deformation. The structural system deforms before collapse without a substantial loss of strength but with a significant energy dissipation.

• The system can be designed with smaller restoring forces, exploiting its ability to undergo plastic deformation. • Ductility factor (δu/δy): Ratio of the ultimate deformation at failure δu to the yield deformation δy. * δu is defined for design purposes as the deformation for which the material or the

structural

element

loses

a

predefined percentage of its maximum strength. 4

Ductility Factors

δu µδ = δy

δu: ultimate deformation at failure δy: yield deformation

• In terms of rotations: (for members)

θu µθ = θy

θu: ultimate rotation at failure θy: yield rotation

• In terms of curvatures: (for members)

ϕu µϕ = ϕy

φu: ultimate curvature at failure φy: yield curvature

• In terms of displacements:

5

Behaviour q Factor The q factor corresponds to the reduction in the level of seismic forces due to nonlinear behaviour as compared with the expected elastic force levels.

Ductility and Behaviour Factor q Vel . Definition q = Vinel

Flexible Structures T ≥ Tc : Rule of equal dispacement

V1max δ u 2 = = = µδ q V2max δ y 2

δy2

δu2

δ

7

Ductility and Behaviour Factor q Stiff Structures T≤Tc

for T=0 q=1 for T=Tc q=μδ

q

μδ 1 δy

δu2

Rule of equal dissipating energy

q

Vel V1max = = (2 µδ − 1)1/ 2 Vinel V2max

δ

Τc

Τ

T q= 1 + ( µδ − 1) (Eurocode 8) Tc

8

Design spectrum for linear analysis • The capacity of structural systems to resist seismic actions in the non-linear range permits their design for resistance to seismic forces smaller than those corresponding to a linear elastic response. • The energy dissipation capacity of the structure is taken into account mainly through the ductile behavior of its elements by performing a linear analysis based on a reduced response spectrum, called design spectrum. This reduction is accomplished by introducing the behavior factor q.

9

Design spectrum for linear analysis (Eurocode 8) • For the horizontal components of the seismic action the design spectrum, Sd(T), shall be defined by the following expressions: ag is the design ground acceleration on type A ground (ag = γI.agR); γI=importance factor TB is the lower limit of the period of the constant spectral acceleration branch; TC is the upper limit of the period of the constant spectral acceleration branch; TD is the value defining the beginning of the constant displacement response range of the spectrum; S is the soil factor Sd(T) is the design spectrum; q is the behaviour factor; β is the lower bound factor for the horizontal design spectrum, 10 recommended β=0,2

Importance Classes (Eurocode 8)

11

Behaviour Factor (Eurocode 8) • The upper limit value of the behavior factor q, introduced to account for energy dissipation capacity, shall be derived for each design direction as follows: q = qo∙kw ≥ 1,5 Where qo is the basic value of the behavior factor, dependent on the type of the structural system and on its regularity in elevation; kw is the factor reflecting the prevailing failure mode in structural systems Pr evailing wall aspect ratio = Σhwi / Σ wi (1 + ao ) / 3 ≤ 1 and ≥ 0,5 ao = with walls: ku =

• Low Ductility Class (DCL): Seismic design for low ductility , following EC2 without any additional requirements other than those of § 5.3.2, is recomended only for low seismicity cases (see §3.2.1(4)).

12

Behaviour Factor (Eurocode 8) A behaviour factor q of up to 1,5 may be used in deriving the seismic actions, regardless of the structural system and the regularity in elevation. • Medium (DCM) and High Ductility Class (DCH):

For buildings which are not regular in elevation, the value of qo should be reduced by 20% 13

au/a1 in behaviour factor of buildings designed for ductility: due to system redundancy & overstrenght

Structural Regularity (Eurocode 8) • For seismic design, building structures in all modern codes are separated in two categories: a) regular buildings b) non-regular buildings • This distinction has implications for the following aspects of the seismic design: − the structural model, which can be either a simplified planar model or a spatial model ; − the method of analysis, which can be either a simplified response spectrum analysis (lateral force procedure) or a modal one; − the value of the behavior factor q, which shall be decreased for buildings non-regular in elevation 15

Structural Regularity (Eurocode 8)

16

Criteria for Regularity in Elevation (Eurocode 8) • All lateral load resisting systems, such as cores, structural walls, or frames, shall run without interruption from their foundations to the top of the building or, if setbacks at different heights are present, to the top of the relevant zone of the building. • Both the lateral stiffness and the mass of the individual storeys shall remain constant or reduce gradually, without abrupt changes, from the base to the top of a particular building. • When setbacks are present, special additional provisions apply.

17

STRUCTURE OF EN1998-1:2004

How q is achieved? • Specific requirements in detailing (e.g. confining actions by well anchored stirrups) • Avoid brittle failures • Avoid soft storey mechanism • Avoid short columns • Provide seismic joints to protect from earthquake induced pounding from adjacent structures • …..

Material limitations for primary seismic elements“

Capacity Design

Avoid weak column/strong beam frames

Capacity Design Provide strong column/weak beam frames or wall equivalent dual frames, with beam sway mechanisms, trying to involve plastic hinging at all beam ends

Capacity Design (Eurocode 8)

column 1

beam 1

beam 2

column 2

Exceptions: see EC8 §5.2.3.3 (2)

Shear Capacity Design (Eurocode 8) Avoid Brittle failure

∆Μ V= M M ∆x 2 1 M 2 − Μ1 V= Column moment distribution  12 2

1

+

+E

1

M1,d

1

-E

-

M1,d

-

+

or 2

Vmax,c

-

M2,d

M 1,+d + Μ −2,d ,  12  clear =  12

+

Vmax,c = −

2

+

M2,d

M 2,+ d + Μ1,− d  12

Shear Capacity Design of Columns (Eurocode 8) +

M1,d

γRd·MRc,1+ , when ΣΜRb > ΣΜRc ,

weak columns

γRd·MRc,1+ ·(ΣΜRd,b\ ΣΜRd,c) , when ΣΜRb < ΣΜRc , weak beams: (moment developed in the column when beams fail)

Similarly -

M1,d

γRd·MRc,1- , when ΣΜRb < ΣΜRc γRd·MRc,1- ·(ΣΜRd,b\ ΣΜRd,c)

Also similarly for M2,d+, M2,dΣΜRb , ΣΜRc for the corresponding direction of seismic action (+E or -E) • In DC H γRd=1.3 • In DC M γRd=1.1

Shear Capacity Design of Beams (Eurocode 8) 2

1

M2

=

+

2

1

VM

Determination of VM

M1,d

+

M2,d

1

-E

2

-

[M]

or

+

M2,d

1

2

M1,d

M 2,+ d + Μ1,− d  12

• In DC H γRd=1.2 • In DC M γRd=1.0

[M]

-

[V]

+

VM max,b =

M1

+

+E

2

1

Vg+ψq

VCD

+

M1

[V]

-

VM max,b = −

M 1,+d + Μ −2,d  12

M2

Shear Capacity Design of Beams (Eurocode 8) +

M1,d

γRd·MRb,1+ , when ΣΜRb < ΣΜRc ,

weak beams

γRd·MRb,1+ ·(ΣΜRd,c\ ΣΜRd,b) , when ΣΜRb > ΣΜRc , weak columns: (moment developed in the column when beams fail)

Similarly -

M1,d

γRd·MRb,1- , when ΣΜRb < ΣΜRc γRd·MRb,1- ·(ΣΜRd,c\ ΣΜRd,b)

Also similarly for M2,d+, M2,dΣΜRb , ΣΜRc for the corresponding direction of seismic action (+E or -E) • In DC H γRd=1.3 • In DC M γRd=1.1

Local Ductility Conditions  Relation between q and μδ

= µδ q if T1 ≥ Tc , µδ =+ 1 (q − 1) Tc / T1 if T1 < Tc ;  Relation between μδ and μφ

1 + 3( µφ − 1) Lpl / Ls (1 − 0.5 Lpl / Ls ); where Lpl:plastic hinge length, Ls: shear span µδ =

 Relation of Lpl & Ls for typical RC beams, columns & walls

(considering = : ε cu* 0.0035 + 0.1aωw ) Lpl ≈ 0.3 Ls and for safety factor 2 : L pl ≈ 0.15 Ls Then : µφ ≈ 2 µδ − 1  For T1≥Tc µφ = 2µδ − 1= 2q − 1 Tc Tc µ = 2 µ − 1 = 2[1 + ( − 1) ] − 1 = 1 + 2( − 1) q q For T1≤Tc φ δ T1 T1

In EC8 qo is used instead of q concervatively to include irregular buildings (q 0.65 for DCM and vd > 0.55 for DCH

Confined Concrete Model σc περισφιγμένο με FRP

περισφιγμένο με χαλύβδινα στοιχεία

*

fc fc 0,85 fc

According to EC2

f c*

ε co ε * c u ε co

0

β= f c ε co* β 2 ε co

Adopting β ≈1 + 3, 7  p   fc 

0.86

ε*

cu

ε

p When hoops are used ≈ 0.5 a ωw fc ωw= Mechanical volumertic ratio of hoops

(Newman K. & Newnan J.B. 1971)

 p p β ≈ min 1 + 5 , 1.125 + 2.5  fc fc  

ε cu* 0.0035 + 0.2

p fc

α=Confinement effectiveness factor, Therefore β= min (1 + 2.5 aωw , 1.125 + 1.25aωw ) = ε cu* 0.0035 + 0.1aωw

a = as an

Detailing of primary beams for local ductility EN 1998-1:2004 (Ε) § 5.4.3.1.2 For Tension Reinforcement

For Comression Reinforcement

= ρ 2 ρ 2req + 0.5ρ

 More detailing rules for DCH

Detailing of primary beams for local ductility for DCM  cr = hw for DCH  cr =1.5hw

Within ℓcr transverse reinforcement in critical regions of beams: 

dbw ≥ 6mm

s ≤

hw / 4 24 dbw 8 dbL

( DCM ) or 6 dbL ( DCH ) 225mm ( DCM ) or 175mm ( DCH )

Detailing of primary seismic columns for local ductility EN 1998-1:2004 (Ε) § 5.4.3.2.2

Everywhere 6 mm dbw ≥ 1 dbL ,max 4  more restrictions for DCH critical regions In critical regions for DCM

s

s≤

For  cr / hc < 3.0 →  cr =  cl

for DCH

s≤

bo / 2 8 dbL ,min 175 mm bo / 3 6 dbL ,min 125 mm

Detailing of primary seismic columns for local ductility EN 1998-1:2004 (Ε) § 5.4.3.2.2

c d

Normilised Axial Load vd ≤ 0.65 for DCM vd ≤ 0.55 for DCH

dw bo =bc − 2(c + ) 2 bi ≤ 200 mm for DCM bi ≤150 mm for DCH At least 3 bars in every slide

Astot ρtot = bu

min ρtot =1% max ρtot = 4%

Detailing of primary seismic columns for local ductility for DCM & DCH in critical region at column base

EN 1998-1:2004 (Ε) § 5.4.3.2.2

ωw ≥ 0.08 for DCM

ωw ≥ 0.12 for DCH

Beam-Column Joints 

DCM

- Horizontal hoops as in critical region of columns - At least one intermediate column bar at each joint slide 

DCH Specific rules in § 5.5.33

Types of Dissipative Walls

Ductile Walls w hcr = max

hw / 6

hw

hcr ≤ hcr

2 w hs 2hs

ℓw

for n ≤ 6 storeys for n ≥ 7 storeys

hs = clear storey height

µφ after qo′ = qo M Ed / M Rd M Ed / M Rd at the base Normilised axial load for DCM vd > 0.40 and for DCH vd > 0.35

No strong column/weak beam capacity design required in wall or wallequivallent dual systems (