COST Action TU0601, February 4-5, 2008, Zurich, Switzerland
Design for Robustness
Prof. Thomas Vogel
2Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Content
Introduction
Simple examples
Elements of robustness
Evaluation of some design provisions in codes
What happens with real structures?
3Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Definition for RobustnessAbility of a structure and its members to keep the amount
of deterioration or failure within reasonable limits in
relation to the cause.[SIA 260]
The ability of a structure to withstand events like fire,
explosions, impact or the consequences of human error,
without being damaged to an extent disproportionate to
the original cause.[EN 1991-1-7]
4Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Which design is more robust?
Multiple choice
4 Examples
Distribute sheets
5Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (1)A: 1 bolt B: 2 bolts
RN 2 · 0.5 RN
N N N N
Which design is more robust?
6Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (1)A: 1 bolt B: 2 bolts
RN
N N N N
t
S, R
N2
RN
t
N1
N20.5 RN
S, R
more robust, ifN < 0.5 RN
N1
7Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (1)A: 1 bolt B: 2 bolts
N N N N
safer, if variation coefficient σ/μof bolts constant
[User Manual VaP 1.6] A
RARBR
BR μ=μ⋅=μ⋅=μ 5.022 ,
( )AR
ARRR σμ= , ( ) ( )A
RAR
BR
BRRR σμ=σμ= 5.0,,
AR
AR
AR
BRBRBR
σ=⎟⎟⎠
⎞⎜⎜⎝
⎛ σ+⎟⎟
⎠
⎞⎜⎜⎝
⎛ σ
=σ+σ=σ
5.022
22
2,
2,
8Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (1)A: 1 bolt B: 2 bolts
N N N N
imperfect fit δ0
N
δδ
N
δ0δ
N
δ0
ductility reduced by imperfect fit
9Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (2)A: 2 bolts aside each other B: 2 bolts in a row
2 · 0.5 RN
N N N N
2 · 0.5 RN
Which design is more robust?
10Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (2)A: 2 bolts aside each other B: 2 bolts in a row
N NN N
N
δ
N
δN2
N1
N2
N1
δ1 δ2δ1 δ2
more robust for imposed deformations
more robust for imposed loads
11Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (3)A: 2 bolts aside each other B: 3 bolts aside each other
3 · 0.333 RN
N N
2 · 0.5 RN
N N
Which design is more robust?
12Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (3)A: 2 bolts aside each other B: 3 bolts aside each other
3 · 0.333 RN
N N
2 · 0.5 RN
N N
statically determinate statically indeterminate, distribution of forces depending on fit and shear stiffness of gusset plate
13Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (4)A: 3 bolts B: 2 bolts
3 · 0.33 RN2 · 0.5 RN
N N N N
Which design is more robust?
14Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Bolted connection in tension (4)A: 3 bolts B: 2 bolts
N N
Ae2 · 0.5 A
c [kN/mm]
EAceDecisive
parameter
Weak bolts ce/EA = 0.075
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1 2 3 4 5 6 7
No of bolts
Shar
e of
tens
ion
forc
e
3 bolts4 bolts5 bolts6 bolts7 bolts
Stiff bolts ce/EA = 0.3
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1 2 3 4 5 6 7
No of bolts
Shar
e of
tens
ion
forc
e
3 bolts4 bolts5 bolts6 bolts7 bolts
15Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Elements of robustness (1)
NH number of hazards Hi
ND number of direct (local) damages Dj
NS number of types of follow up behaviour Sk
p(Hi) probability of occurrence of hazard Hi
p(Dj|Hi) probability of the occurrence of direct damage Dj due to hazard Hi
p(Sk|Dj) probability of the occurrence of structural behaviour Sk due to direct damage Dj
C(Sk) (monetarized) consequences of structural behaviour Sk
( ) ( ) ( ) ( )kjk
N
j
N
kij
N
ii SCDSpHDpHpR
D SH
||1 11
∑ ∑∑= ==
=
16Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Elements of robustness (2)
Reduce the probability of occurrence of an accidental eventand its magnitude.Reduce the probability of local damage due to an accidental eventReduce the probability of progressive collapse in the case oflocal damageReduce the consequences of the collapseReduce the number of different accidental events NH
Reduce the number of possible induced damages NS
( ) ( ) ( ) ( )kjk
N
j
N
kij
N
ii SCDSpHDpHpR
D SH
||1 11
∑ ∑∑= ==
=
17Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Elements of robustness (4)Direct approaches
Event control
Specific load
resistance method
Alternate path
method
Reduction of conse-quences
Monitoring x
Provide continuity x
Capacity design x
Sacrificial and protective devices
x x
Compartimentisation x
x
Provide strength x x
Provide ductility x x
Second line of defence x
Indirect approaches
18Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Code provisions improving robustnessProvisions for ductility
...Capacity design for shelters
Uneven distribution of internal forcesReduction of shear resistance for long bolted connections
Second line of defencePrevention of collapse due to punching shear
Provisions for the failure of a single elementExternally bonded reinforcement Impact on bridge piersCable stayed bridges
19Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Capacity design for shelters (1) [TWK 1994]
Plan view:
Failure modes:
Section:
Bending failure Shear failure
20Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Capacity design for shelters (2) [TWK 1994]
Plan view:
Failure modes:
Section:
Bending failure Shear failure
qacc ⇒ md < mRd ⇒ qR,b ⇒ vR ≥ v(qR,b)
qacc qR,b
21Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Reduction of shear resistance for long bolted connections
[Steel structures, SIA 263]
22Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Prevention of collapse due to punching shear
In order to prevent the slab from totally collapsing after a possible punching, some reinforcement shall be provided on the flexural compression side. The reinforcement shall be extended over the supported area and dimensioned as follows:
[Concrete structures, SIA 262]
23Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Externally bonded reinforcement... Two types of hazard scenarios can be distinguished:
hazard scenarios which result from the intended use;failure of the externally bonded reinforcement as an accidental design situation.
For the hazard scenario Failure of plate bonding the design value [...] is calculated as follows:
( )ddkiidkkd aXQAPGEE ,,,,, 2ψ=
[SIA 166]
24Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Design criteria for impact loads
Distance from obstacle to rail axis
Required provision
< 3.00 m "normally" not allowed
> 3.00 m QA║ = 2'000 kNQA┴ = 1'000 kN
< 5.00 m Protection of pier by guiding device or dimensioning of bridge with missing pier
[Guideline Swiss Railways, 1983 ]
25Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Cable stayed bridgesFailure / replacement of a stay (together with full or part of the traffic load) is an ordinary design situation
Chesapeak-Delaware-Canal Bridge, USA
26Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Code provisions preventing robustnessShear capacity of solid slab bridges
Punching shear capacity of flat slabs
Design criteria for impact loads
Ambitious requirements for post-tensioning
27Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Shear capacity of solid slab bridges
Beam or slab?Beam ⇒ stirrups requiredSlab ⇒ shear resistance without stirrups
design criterion:vR
d
without stirrups
with minimal stirrups
reasonable range
28Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Punching shear capacity of flat slabs
Usual code provisions:Increase of punching shear capacity with increased bending reinforcement(but reduction of ductility)Punching reinforcement allows for a further increase (but is expensive)
The designers optimize the slab depth, aiming at
no punching reinforcementnecessary bending reinforcement
29Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Design criteria for impact loads
Distance from obstacle to rail axis
Required provision
< 3.00 m "normally" not allowed
> 3.00 m QA║ = 2'000 kNQA┴ = 1'000 kN
< 5.00 m Protection of pier by guiding device or dimensioning of bridge with missing pier
5.00 m
30Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Ambitious requirements for post-tensioning[Guideline
ASTRA/SBB2007]
31Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
What happens with real structures?What has already happened?
What can we consider?
What could happen in future?
32Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Rock fall gallery subject to train impact 05.01.07
33Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Avalanche gallery subject to rock fall 29.04.2003
34Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Charles de Gaulle Airport Roissy/Paris 23.5.04
35Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
FE-method
Actions forces due toinertia and gravity
Sudden failure of a column
Robustness of Reinforced Concrete Flat Slab Structures(PhD thesis of Ingo Müllers)
Structural analysis
36Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Size of the FE model
Model for ground floor, 1st and 2nd upper floor
37Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Modelled structure
Plan view 1st upper floor
38Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
0
100
200
300
400
500
600
700
800
900
1 000
1 100
1 200
0.0 0.2 0.4 0.6 0.8Zeit [s]
Pun
chin
g fo
rce
colu
mn
D2
[kN
]
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
0.0 0.2 0.4 0.6 0.8
time [s]
Def
lect
ions
sla
b ed
ge c
lose
to A
2[m
m]
Action effects – Slab over ground floorafter failure of corner column B2
Model GF
Model GF, 1st & 2nd UF
Model GF(static)
Model GF +deflections 1st UF
39Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Failure modes
Breaking or buckling of bending reinforcement
Punching above columns, wall corners and wall ends
Shear failure in slabs or edge beams
Buckling of adjacent columns
40Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Robustness of large roofs? (1)[www.structurae.de ]
41Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Robustness of large roofs? (2)
Spatial structures (shells, …)generally robust structures, unlessbuckling in compressionprogressive failure of textile membranes in tension
Uniaxial structures (beams, arches, cantilevers, …)local failure possiblewhat means local?
Critical structural elementstension & compression ringssupportive structures
[www.structurae.de ]
42Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Tension & compression rings (1)
[K. Göppert, SEI 4/2007]
New Commerzbank ArenaFrankfurt, Germany
43Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Tension & compression rings (2)
44Workshop COST Action TU0601, February 4-5, 2008, Zurich, Switzerland Thomas Vogel, ETH Zürich
Supportive structures
[D. A. Nethercot / T. Ruffell, SEI 4/2007]
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