2. Limit state method of Design
PRESENTED BY
Name : Avik Ghorai
Roll No : 18201321019
Paper Name : DESIGN OF RC STRUCTURES
Paper Code : CE(PC)501
Semester : 5th
Department : Civil engineering
CA1 Examination For Odd Semester-2022
Institute of Science &
Technology
2
4. INTRODUCTION
Designer has to ensure the structures, he
designs are:
Fit for their purpose
Safe
Economical and durable
4
5. 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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6. 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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8. LIMIT STATES DESIGN
Basis of Limit States Design
2
Q
2
s
m
m Q
S
8
Fig. 1 Probability distribution of the safety margin R-Q
R-Q
R-Q<0 R-Q>0
(R-Q)m
f(R-Q)
(R-Q)
9. PROBABILITY OF FAILURE
2
Q
2
R
m
m
Q
R
m
f
Q
R
Q
R
P
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12. 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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Characteristic
Load Effects
Characteristic Strength
Factor of Safety
13. 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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ALLOWABLE SRESS DESIGN (ASD)
14. 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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15. 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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16. 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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17. LIMIT STATES DESIGN
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(Load * Load Factor)
(Resistance )
(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)
18. 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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19. 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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20. 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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21. 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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22. Actions
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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23. Partial Safety Factors (Actions)
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Combina
tion
Limit State of Strength Limit state of Serviceability
DL
LL
WL/
EL
AL DL
LL
WL/
EL
Lead
ing
Accompa
Nying
Leading
Accompanyin
g
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
24. 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
Shop Fabrications Field
Fabrications
1.25
1.25
1.25
1.25
1.25
1.25
1.25
1.50
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25. 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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26. 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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27. LIMITING DEFLECTIONS under LL
Only
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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
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
28. 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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