Transcript Failure Analysis of Tension Members with Bolted Connections

Limit State Method
Dr S R Satish Kumar, IIT Madras
1
INTRODUCTION
Designer has to ensure the structures, he
designs are:
– Fit for their purpose
– Safe
– Economical and durable
Dr S R Satish Kumar, IIT Madras
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INTRODUCTION
Following Uncertainties affect the safety
of a structure
 about loading
 about material strength and
 about structural dimensions
 about behaviour under load
Dr S R Satish Kumar, IIT Madras
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LIMIT STATE DESIGN
Limit State: State at which one of the conditions pertaining
to the structure has reached a limiting value
Limit States
Limit States of Strength
Strength as governed by material
Buckling strength
Stability against overturning, sway
Fatigue Fracture
Brittle Fracture
Dr S R Satish Kumar, IIT Madras
Limit States of Serviceability
Deflection
Vibration
Fatigue cracks (reparable damage)
Corrosion
Fire resistance
4
RANDOM VARIATIONS
Frequency
f(S)
f(Q)
Resistance, S
Load effect, Q
Qm
Sm
Probability density functions for strength and load effect
Dr S R Satish Kumar, IIT Madras
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LIMIT STATES DESIGN
• Basis of Limit States
Design
 
 (R-Q)
S m  Qm
2
 s2   Q
f(R-Q)
(R-Q)m
R-Q<0
R-Q>0
R-Q
Fig. 1 Probability distribution of the safety margin R-Q
Dr S R Satish Kumar, IIT Madras
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PROBABILITY OF FAILURE
 R  Q m
Pf    
 R Q



  



Dr S R Satish Kumar, IIT Madras





Rm  Qm 
2
2 
 R  Q 

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SAFETY INDEX
 
S m  Qm
2
 S2   Q
Pf = [- ]

2.32
3.09
3.72
4.27
4.75
5.2
5.61
Pf =  (-)
10-2
10-3
10-4
10-5
10-6
10-7
10-8
Dr S R Satish Kumar, IIT Madras
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PARTIAL SAFETY FACTOR
Qm ( 1    qs Vq2 )  S m ( 1    sq Vs2 )

fk
Dr S R Satish Kumar, IIT Madras
Qk  Su /  m
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ALLOWABLE STRESS DESIGN (ASD)
Characteristic
Load Effects

Characteristic Strength
Factor of Safety
• Stresses caused by the characteristic loads must
be less than an “allowable stress”, which is a
fraction of the yield strength
• Allowable stress may be defined in terms of a
“factor of safety" which represents a margin for
overload and other unknown factors which could be
tolerated by the structure
Dr S R Satish Kumar, IIT Madras
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ALLOWABLE SRESS DESIGN (ASD)
Allowable stress = (Yield stress) / (Factor of
safety)
Limitations
• Material non-linearity
• Non-linear behaviour in the postbuckled state
and the property of steel to tolerate high
stresses by yielding locally and redistributing
the loads not accounted for.
• No allowance for redistribution of loads in
statically indeterminate members
Dr S R Satish Kumar, IIT Madras
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LIMIT STATES DESIGN
• “Limit States" are various conditions in which a
structure would be considered to have failed to fulfil
the purpose for which it was built.
• “Ultimate Limit States” are those catastrophic
states,which require a larger reliability in order to
reduce the probability of its occurrence to a very
low level.
• “Serviceability Limit State" refers to the limits on
acceptable performance of the structure during
service.
Dr S R Satish Kumar, IIT Madras
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General Principles of
Limit States Design
• Structure to be designed for the Limit States at
which they would become unfit for their intended
purpose by choosing, appropriate partial safety
factors, based on probabilistic methods.
• Two partial safety factors, one applied to loading
(f) and another to the material strength (m) shall
be employed.
Dr S R Satish Kumar, IIT Madras
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• f allows for;
– Possible deviation of the actual behaviour of the
structure from the analysis model
– Deviation of loads from specified values and
– Reduced probability that the various loads acting
together will simultaneously reach the characteristic
value.
Dr S R Satish Kumar, IIT Madras
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LIMIT STATES DESIGN
(Resistance
)
(Load * Load Factor) 
(Resistance Factor)
• m takes account;
– Possible deviation of the material in the
structure from that assumed in design
– Possible reduction in the strength of the
material from its characteristic value
– Manufacturing tolerances.
– Mode of failure (ductile or brittle)
Dr S R Satish Kumar, IIT Madras
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IS800 SECTION 5 LIMIT STATE DESIGN
•
•
•
•
•
5.1 Basis for Design
5.2 Limit State Design
5.3 Actions
5.4 Strength
5.5 Factors Governing the Ultimate Strength
– 5.5.1 Stability
– 5.5.2 Fatigue
– 5.5.3 Plastic Collapse
• 5.6 Limit State of Serviceability
–
–
–
–
5.6.1 Deflection
5.6.2 Vibration
5.6.3 Durability
5.6.4 Fire Resistance
Dr S R Satish Kumar, IIT Madras
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5.1 Basis for Design
• the structure shall be designed to withstand safely all
loads likely to act on it throughout its life.
• It shall also satisfy the serviceability requirements,
such as limitations of deflection and vibration.
• It shall not suffer total collapse under accidental loads
such as from explosions or impact or due to
consequences of human error to an extent beyond the
local damages.
• The objective of design is to achieve a structure that
will remain fit for use during its life with an acceptable
target reliability.
Dr S R Satish Kumar, IIT Madras
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5.1.3
The potential for catastrophic damage shall be limited or
avoided by appropriate choice of one or more of the
following:
– i) avoiding, eliminating or reducing exposure to hazards,
which the structure is likely to sustain.
– ii) choosing structural forms, layouts and details and
designing such that
• the structure has low sensitivity to hazardous conditions.
• the structure survives with only local damage even after serious
damage to any one individual element by the hazard.
Dr S R Satish Kumar, IIT Madras
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•
•
•
Conditions to be satisfied to avoid a
disproportionate collapse
building should be effectively tied together at
each principal floor level and each column should
be effectively held in position by means of
continuous ties (beams) nearly orthogonal
each storey of the building should be checked to
ensure disproportionate collapse would not
precipitate by the notional removal, one at a time,
of each column.
check should be made at each storey by
removing one lateral support system at a time to
ensure disproportionate collapse would not
occur.
Dr S R Satish Kumar, IIT Madras
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Actions
• 5.3.1 Classification of Actions 
– by their variation with time as given below:
• a) Permanent Actions (Qp): Actions due to selfweight of structural and non-structural components,
fittings, ancillaries, and fixed equipment etc.
• b) Variable Actions (Qv): Actions due to construction
and service stage loads such as imposed (live) loads
(crane loads, snow loads etc.), wind loads, and
earthquake loads etc.
• c) Accidental Actions (Qa): Actions due to
explosions, impact of vehicles, and fires etc.
Dr S R Satish Kumar, IIT Madras
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Partial Safety Factors (Actions)
Limit State of Strength
Combina
tion
LL
DL
Lead
ing
Accompa
Nying
WL
/
EL
Limit state of Serviceability
LL
AL
DL
WL
Leadi Accompan /EL
ng
ying
DL+LL+CL
1.5
1.5
1.05


1.0
1.0
1.0

DL+LL+CL
+
WL/EL
1.2
1.2
1.2
1.2
1.05
0.53
0.6
1.2

1.0
0.8
0.8
0.8
1.5
(0.9)


1.5

1.0


1.0
1.2
(0.9)
1.2







1.0
0.35
0.35

1.0




DL+WL/EL
*
DL+ER
DL+LL+AL
Dr S R Satish Kumar, IIT Madras
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PARTIAL SAFETY FACTORS (Strength)
Sl.
No
Definition
Partial Safety Factor
1
Resistance, governed by
yielding mo
1.1
2
Resistance of member to
buckling mo
1.1
3
Resistance, governed by
ultimate stress m1
1.25
4
Resistance of connection m1
Bolts-Friction Type
Bolts-Bearing Type
Rivets
Welds
Dr S R Satish Kumar, IIT Madras
Shop
Fabrication
s
1.25
1.25
1.25
1.25
Field
Fabricatio
ns
1.25
1.25
1.25
1.50
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5.5 Factors Governing the Ultimate Strength
• frame stability against overturning and sway
• Fatigue design shall be as per Section 13 of this
code. When designing for fatigue, the load factor
for action, f, equal to unity shall be used for the
load causing stress fluctuation and stress range.
• Plastic Collapse  Plastic analysis and design may
be used if the requirement specified under the
plastic method of analysis (Section 4.5) are
satisfied.
Dr S R Satish Kumar, IIT Madras
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5.6 Limit State of Serviceability
• Deflections are to be checked for the most
adverse but realistic combination of service loads
and their arrangement, by elastic analysis, using a
load factor of 1.0
• Suitable provisions in the design shall be made for
the dynamic effects of live loads, impact loads and
vibration/fatigue due to machinery operating loads.
• The durability of steel structures shall be ensured
by following recommendations of Section 15.
• Design provisions to resist fire are briefly
discussed in Section 16.
Dr S R Satish Kumar, IIT Madras
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LIMITING DEFLECTIONS under LL Only
Type of
building
Deflectio
n
Member
Live
load/Wind
load
Purlins and
Girts
Purlins and
Girts
Elastic cladding
Brittle cladding
Span / 150
Span / 180
Live load
Simple span
Elastic cladding
Span / 240
Live load
Simple span
Brittle cladding
Span / 300
Live load
Cantilever span
Elastic cladding
Span / 120
Live load
Cantilever span
Brittle cladding
Span / 150
Live load or
Wind load
Rafter
supporting
Profiled Metal
Sheeting
Span / 180
Plastered Sheeting
Span / 240
Crane load
(Manual
operation)
Gantry
Crane
Span / 500
Crane load
(Electric
operation
Dr S R Satish Kumar,over
IIT Madras
50 t)
Gantry
Crane
Span / 1000
25
Indus
trial
building
Vertical
Supporting
Maximum
Deflection
Design Load
DEFLECTION LIMITS under LL Only
Deflection
Design Load
Supporting
Column
Elastic
cladding
Height / 150
Column
Masonry/brittle
cladding
Height / 240
Crane
Gantry
(lateral)
Crane
Live load
Not
Floors & roofs
susceptible
to cracking
Span / 300
Live load
Floor & Roof
Susceptible to
cracking
Span / 360
Wind
Building
---
Height / 500
Wind
Inter storey
drift
---
Lateral
No cranes
Crane+
wind
No cranes
Vertical
Lateral
Maximum
Deflection
Member
Dr S R Satish Kumar, IIT Madras
Span / 400
Storey height /
300
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Dr S R Satish Kumar, IIT Madras
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