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Design of Reinforced Concrete Structure

Prepared by:Ghanashyam Prajapati (13cv88)

LIMIT STATE METHOD

INTRODUCTION

Designer has to ensure the structures, he designs are:

Fit for their purpose Safe Economical and durable

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INTRODUCTIONFollowing 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 DESIGNLimit State: State at which one of the conditions pertaining

to the structure has reached a limiting value

Limit StatesLimit States of Strength Limit States of Serviceability

Strength as governed by material DeflectionBuckling strength VibrationStability against overturning, sway Fatigue cracks (reparable

damage)Fatigue Fracture CorrosionBrittle Fracture Fire resistance 4

RANDOM VARIATIONS

5Resistance, SLoad effect, Q

f(S)f(Q)

Qm

Frequency

Probability density functions for strength and load effect

Sm

LIMIT STATES DESIGN Basis of Limit States

Design2Q

2s

mm QS

6Fig. 1 Probability distribution of the safety margin R-Q

PROBABILITY OF FAILURE

2Q

2R

mm

QR

mf

QR

QRP

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SAFETY INDEX

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

2Q

2S

mm QS

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Pf = [- ]

PARTIAL SAFETY FACTOR

)V1(S)V1(Q 2ssqm

2qqsm

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mukfk SQ /

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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CharacteristicLoad Effects

Characteristic Strength Factor of Safety

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)

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

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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)

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. 17

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

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)

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Combination

Limit State of Strength Limit state of Serviceability

DLLL WL

/EL

AL DLLL

WL/ELLead

ingAccompa

NyingLeadi

ngAccompan

ying

DL+LL+CL 1.5 1.5 1.05 1.0 1.0 1.0

DL+LL+CL+WL/EL

1.21.2

1.21.2

1.050.53

0.61.2 1.0 0.8 0.8 0.8

DL+WL/EL1.5

(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

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 TypeBolts-Bearing Type

RivetsWelds

Shop Fabrication

s

Field Fabricatio

ns1.251.251.251.25

1.251.251.251.50

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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

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Type of building

Deflection Design Load Member Supporting Maximum

Deflection

Industrial

buildingVertical

Live load/Wind load

Purlins and GirtsPurlins and Girts

Elastic claddingBrittle cladding

Span / 150Span / 180

Live load Simple span Elastic cladding Span / 240Live load Simple span Brittle cladding Span / 300Live load Cantilever span Elastic cladding Span / 120Live load Cantilever span Brittle cladding Span / 150

Live load or Wind load

Rafter supporting

Profiled Metal Sheeting Span / 180

Plastered Sheeting Span / 240Crane load(Manual operation)

Gantry Crane Span / 500

Crane load(Electric operationover 50 t)

Gantry Crane Span / 1000

DEFLECTION LIMITS UNDER LL ONLYDeflection Design Load Member Supporting Maximum

DeflectionLateral

Crane+ wind

No cranes Column Elastic cladding Height / 150

No cranes Column Masonry/brittle cladding Height / 240

Crane Gantry (lateral) Crane Span / 400

VerticalLive 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 26

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