Limit State Method Dr S R Satish Kumar

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 2

INTRODUCTION Following Uncertainties affect the safety of a structure Ø about loading Ø about material strength and Ø about structural dimensions Ø about behaviour under load Dr S R Satish Kumar, IIT Madras 3

LIMIT STATE DESIGN Limit State: State at which one of the conditions pertaining to the structure has reached a limiting value Limit States of 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 5

LIMIT STATES DESIGN • Basis of Limit States Design (R-Q) f(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 6

PROBABILITY OF FAILURE Dr S R Satish Kumar, IIT Madras 7

SAFETY INDEX Pf = [- ] 2. 3 3. 09 3. 72 4. 27 4. 75 2 Pf = 102 (- ) 10 -3 10 -4 10 -5 Dr S R Satish Kumar, IIT Madras 10 -6 5. 2 5. 61 10 -7 10 -8 8

PARTIAL SAFETY FACTOR Dr S R Satish Kumar, IIT Madras 9

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 10

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 11

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 12

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 13

• 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 14

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 15

IS 800 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 16

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 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. Dr S R Satish Kumar, IIT Madras 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. Dr S R Satish Kumar, IIT Madras 19

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 20

Partial Safety Factors (Actions) Limit State of Strength Combina tion Limit state of Serviceability LL DL Lead ing WL/ Accompa EL Nying LL AL DL WL Leadi Accompan /EL ng ying DL+LL+CL 1. 5 1. 05 1. 0 DL+LL+CL + WL/EL 1. 2 1. 05 0. 53 0. 6 1. 2 1. 0 0. 8 DL+WL/EL 1. 5 (0. 9) 1. 5 1. 0 DL+ER 1. 2 (0. 9) 1. 2 1. 0 0. 35 1. 0 DL+LL+AL * Dr S R Satish Kumar, IIT Madras 21

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 m 1 1. 25 4 Resistance of connection m 1 Bolts-Friction Type Bolts-Bearing Type Rivets Welds Dr S R Satish Kumar, IIT Madras Shop Fabrication s 1. 25 Field Fabricatio ns 1. 25 1. 50 22

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 23

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 24

LIMITING DEFLECTIONS under LL Only Type of building Deflectio n Member Live load/Wind load 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 Span / 400 Live load Floors & roofs Not susceptible to cracking Span / 300 Live load Floor & Roof Susceptible to cracking Span / 360 Wind Building --- Height / 500 Wind Inter storey drift --- Storey height / 300 Lateral No cranes Crane+ wind No cranes Vertical Lateral Maximum Deflection Member Dr S R Satish Kumar, IIT Madras 26

Dr S R Satish Kumar, IIT Madras 27