Limit state method

1. 1
Design of Reinforced Concrete Structure
Prepared by:
Ghanashyam Prajapati (13cv88)
LIMIT STATE METHOD

2. INTRODUCTION
Designer has to ensure the structures, he designs are:
 Fit for their purpose
 Safe
 Economical and durable
2

3. INTRODUCTION
Following Uncertainties affect the safety of a structure
 about loading
 about material strength and
 about structural dimensions
 about behaviour under load
3

4. 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 4

5. RANDOM VARIATIONS
5
Resistance, S
Load effect, Q
f(S)
f(Q)
Qm
Frequency
Probability density functions for strength and load effect
Sm

6. LIMIT STATES DESIGN
 Basis of Limit States Design
2
Q
2
s
mm QS
σσ
β
+
−
=
6
Fig. 1 Probability distribution of the safety margin
R-Q

7. PROBABILITY OF FAILURE
( )










+
−
−=







 −
−=
−
2
Q
2
R
mm
QR
m
f
QR
QR
P
σσ
Φ
σ
Φ
7

8. SAFETY INDEX
β 2.32 3.09 3.72 4.27 4.75 5.2 5.61
Pf
= φ (-β) 10-2
10-3
10-4
10-5
10-6
10-7
10-8
2
Q
2
S
mm QS
σσ
β
+
−
=
8
Pf =Φ [- β]

9. PARTIAL SAFETY FACTOR
)V1(S)V1(Q 2
ssqm
2
qqsm αβαβ −<+
9
mukfk SQ γγ /≤∑

10. 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
10
Characteristic
Load Effects
Characteristic Strength
Factor of Safety
≤

11. 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
11
ALLOWABLE SRESS DESIGN (ASD)

12. 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.
12

13. 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 (γf) and
another to the material strength (γm) shall be employed.
13

14.  γf 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.
14

15. LIMIT STATES DESIGN
15
Σ(Load * Load Factor)
≤
(Resistance )
(Resistance Factor)
∀ γm 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)

16. 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
16

17. 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.
17

18. 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.
18

19. 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.
19

20. 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.
20

21. PARTIAL SAFETY FACTORS (ACTIONS)
21
Combina
tion
Limit State of Strength Limit state of Serviceability
DL
LL WL
/
EL
AL DL
LL
WL
/ELLead
ing
Accompa
Nying
Leadi
ng
Accompan
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
DL+WL/EL
1.5
(0.9)
*
  1.5  1.0   1.0
DL+ER
1.2
(0.9)
1.2       
DL+LL+AL 1.0 0.35 0.35  1.0    

22. PARTIAL SAFETY FACTORS (STRENGTH)
Sl.
No Definition Partial Safety Factor
1 Resistance, governed by
yielding γmo
1.1
2 Resistance of member to
buckling γmo
1.1
3 Resistance, governed by
ultimate stress γm1
1.25
4 Resistance of connection γm1
Bolts-Friction Type
Bolts-Bearing Type
Rivets
Welds
Shop
Fabrication
s
Field
Fabricatio
ns
1.25
1.25
1.25
1.25
1.25
1.25
1.25
1.50
22

23. 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, γf, 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.
23

24. 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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25. LIMITING DEFLECTIONS UNDER LL ONLY
25
Type of
building
Deflectio
n
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
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
over 50 t)
Gantry Crane Span / 1000

26. DEFLECTION LIMITS UNDER LL ONLY
Deflection
Design Load Member Supporting
Maximum
Deflection
Lateral
Crane+
wind
No cranes Column
Elastic
cladding
Height / 150
No cranes Column
Masonry/brittle
cladding
Height / 240
Crane
Gantry
(lateral)
Crane Span / 400
Vertical
Live load Floors & roofs
Not
susceptible
to cracking
Span / 300
Live load Floor & Roof
Susceptible to
cracking
Span / 360
Lateral Wind Building --- Height / 500
Wind
Inter storey
drift
---
Storey height
/ 300
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27. 27