Limit State Method

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Limit State Method
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INTRODUCTION

• Designer has to ensure the structures, he
• designs are
• Fit for their purpose
• Safe
• Economical and durable

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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

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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 Limit States
  of Serviceability
• Strength as governed by material Deflection
• Buckling strength Vibration
• Stability against overturning, sway Fatigue
  cracks (reparable damage)
• Fatigue Fracture Corrosion
• Brittle Fracture Fire resistance

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RANDOM VARIATIONS

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LIMIT STATES DESIGN

• Basis of Limit States Design

Fig. 1 Probability distribution of the safety
margin R-Q
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PROBABILITY OF FAILURE
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SAFETY INDEX
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
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PARTIAL SAFETY FACTOR

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ALLOWABLE STRESS DESIGN (ASD)

• 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

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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

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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.

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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.

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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.

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LIMIT STATES DESIGN

• ?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)

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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

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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.

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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.

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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.

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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
  self-weight 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.

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Partial Safety Factors (Actions)
Combina tion Limit State of Strength Limit State of Strength Limit State of Strength Limit State of Strength Limit State of Strength Limit state of Serviceability Limit state of Serviceability Limit state of Serviceability Limit state of Serviceability
Combina tion DL LL LL WL/ EL AL DL LL LL WL/EL
Combina tion DL Lead ing Accompa Nying WL/ EL AL DL Leading Accompanying WL/EL
DLLLCL 1.5 1.5 1.05 ? ? 1.0 1.0 1.0 ?
DLLLCL 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
DLWL/EL 1.5 (0.9) ? ? 1.5 ? 1.0 ? ? 1.0
DLER 1.2 (0.9) 1.2 ? ? ? ? ? ? ?
DLLLAL 1.0 0.35 0.35 ? 1.0 ? ? ? ?
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PARTIAL SAFETY FACTORS (Strength)
Sl. No Definition Partial Safety Factor Partial Safety Factor
1 Resistance, governed by yielding ?mo 1.1 1.1
2 Resistance of member to buckling ?mo 1.1 1.1
3 Resistance, governed by ultimate stress ?m1 1.25 1.25
4 Resistance of connection ?m1 Bolts-Friction Type Bolts-Bearing Type Rivets Welds Shop Fabrications Field Fabrications
4 Resistance of connection ?m1 Bolts-Friction Type Bolts-Bearing Type Rivets Welds 1.25 1.25 1.25 1.25 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.

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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.

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LIMITING DEFLECTIONS under LL Only
Type of building Deflection Design Load Member Supporting Maximum Deflection
Indus trial building Vertical Live load/Wind load Purlins and Girts Purlins and Girts Elastic cladding Brittle cladding Span / 150 Span / 180
Indus trial building Vertical Live load Simple span Elastic cladding Span / 240
Indus trial building Vertical Live load Simple span Brittle cladding Span / 300
Indus trial building Vertical Live load Cantilever span Elastic cladding Span / 120
Indus trial building Vertical Live load Cantilever span Brittle cladding Span / 150
Indus trial building Vertical Live load or Wind load Rafter supporting Profiled Metal Sheeting Span / 180
Indus trial building Vertical Live load or Wind load Rafter supporting Plastered Sheeting Span / 240
Indus trial building Vertical Crane load (Manual operation) Gantry Crane Span / 500
Indus trial building Vertical
Indus trial building Vertical Crane load (Electric operation over 50 t) Gantry Crane Span / 1000
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DEFLECTION LIMITS under LL Only
Deflection Design Load Member Supporting Maximum Deflection
Lateral Crane wind No cranes Column Elastic cladding Height / 150
Lateral Crane wind No cranes Column Masonry/brittle cladding Height / 240
Lateral Crane wind Crane Gantry (lateral) Crane Span / 400
Lateral Crane wind
Vertical Live load Floors roofs Not susceptible to cracking Span / 300
Vertical Live load Floor Roof Susceptible to cracking Span / 360
Lateral Wind Building --- Height / 500
Lateral Wind Inter storey drift --- Storey height / 300
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Thank You