Limit State Design Concept V N Kundlikar Visit

Limit State Design Concept V. N. Kundlikar Visit for more Learning Resources 1

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

INTRODUCTION-2 • Uncertainties affecting structure are due to: the safety of a Ø uncertainty about loading Ø uncertainty about material strength and Ø uncertainty about structural dimensions and behaviour 3

INTRODUCTION-3 Frequency Variation of maximum life time load effects Variation of resistance (B. M. ) (R. M. ) between nominally Curve (a) Curve (b) identical materials Risk of failure Load used in calculation Strength (or resistance) used in calculations Load effects divided by Resistance moment Statistical Meaning of Safety 4

INTRODUCTION - 4 • Uncertainties in service life are due to: Ø Variability of the loads Ø Variability of the load distribution through the structure • Characteristic resistance: Value of resistance below which not more than a prescribed percentage of test results may be expected to fall • Characteristic load: Value of the load, which has an accepted probability of not being exceeded during the life span of the structure. 5

Actions • Permanent Actions Qp • Variable Actions Qv • Accidental Actions Qa 6

Characteristic Actions Qc • Are those values of different actions that are not expected to be exceeded with more than 5 % probability during the life of the structure 7

Design Action Qd • Qd = ∑ fk Qck k 8

Design Strength Sd • Sd = Su / m 9

ALLOWABLE STRESS DESIGN (ASD) • Stresses caused by the characteristic loads must be less than an “allowable stress”, which is a fraction of the yield stress. • 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

ALLOWABLE SRESS DESIGN (ASD) - 2 Allowable stress = (Yield stress) / (Factor of safety) Limitations • material non-linearity • non-linear behaviour in the post buckled 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

A typical example of a set of load combinations is given below, which accounts for the fact that the dead load, live load and wind load are all unlikely to act on the structure simultaneously at their maximum values: (Stress due to dead load + live load) < allowable stress (Stress due to dead load + wind load) < allowable stress (Stress due to dead load + live load + wind) < 1. 33 times allowable stress. 12

Summary of WSD • In practice there are severe limitations to this approach. These are the consequences of material non-linearity, non-linear behaviour of elements in the post-buckled state and the ability of the steel components to tolerate high theoretical elastic stresses by yielding locally and redistributing the loads. Moreover the elastic theory does not readily allow for redistribution of loads from one member to another in a statically indeterminate structures. 13

LIMIT STATE DESIGN • “Limit States" are the 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. 14

General Principles of Limit State 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. 15

• f allows for; – the 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. 16

• m takes account; – the possible deviation of the material in the structure from that assumed in design – the possible reduction in the strength of the material from its characteristic value and – manufacturing tolerances. – Mode of failure (ductile or brittle). 17

Limit State of Strength (yield, buckling) Serviceability Limit State Deflection Stability against overturning and sway Vibration Fracture due to fatigue Brittle Fracture Repairable damage due to fatigue Corrosion Fire Table 1: Limit States 18

PARTIAL SAFETY FACTOR S* R* S* - factored load effect R*- factored resistance of the element checked, and is a function of the material yield strength. being nominal value of 19

Partial Safety Factor for Loads Limit State of Strength LL’ Combination DL Leadi ng DL+LL+CL 1. 5 Accompan ying 1. 05 DL+LL+CL + WL/EL 1. 2 DL+WL/EL 1. 5 (0. 9)* DL+ER DL+LL+AL WL / EL Limit state of Serviceability AL LL’ DL WL /EL 1. 0 Accompa nying 1. 05 0. 53 0. 6 1. 2 1. 0 0. 8 1. 5 1. 0 1. 2 (0. 9) 1. 2 1. 0 0. 35 1. 0 Leading * This value is to be considered when the dead load contributes to stability against overturning is critical or the dead load causes reduction in stress due to other loads. ‘ When action of different live loads is simultaneously considered, the leading live load is whichever one causes the higher load effects in the member/section. Abbreviations: DL= Dead Load, LL= Imposed Load (Live Loads), WL= Wind Load, CL= Crane Load (Vertical/horizontal), AL=Accidental Load, ER= Erection Load, EL= Earthquake Load. 20

Partial Safety Factor for Material Sl. No. Definition Partial Safety Factor 1 Resistance, governed by yielding m 0 1. 10 2 Resistance of member to buckling m 0 1. 10 3 Resistance, governed by ultimate stress m 1 1. 25 4 Resistance of connection m 1 (i) Bolts-Friction Type, mf (ii) Bolts-Bearing Type, mb (iii) Rivets, mr (iv) Welds, mw Shop Fabrications Field Fabrications 1. 25 1. 50 21

LIMIT STATES FOR DESIGN PURPOSES • Ultimate Limit State is related to the maximum design load capacity under extreme conditions. The partial load factors are chosen to reflect the probability of extreme conditions, when loads act alone or in combination. • Serviceability Limit State is related to the criteria governing normal use. Unfactored loads are used to check the adequacy of the structure. • Fatigue Limit State is important where distress to the structure by repeated loading is a possibility. 22

Limit State of serviceability Type of Building Deflection Vertical Design Load Maximum Deflection Supporting Live load/Wind load Purlins and Girts Elastic cladding Brittle cladding Live load Simple span Elastic cladding Span / 150 Span / 180 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 Gantry Crane Span / 500 Gantry Crane Span / 750 Gantry Crane Span / 1000 No cranes Column Elastic cladding Height / 150 No cranes Column Masonry/Brittle cladding Height / 240 Gantry (lateral) Crane(absolute) Relative displacement between rails Span / 400 (Manual operation) Crane load (Electric operation up to 50 t) Industrial building Member Crane load (Electric operation over 50 t) Crane + wind 10 mm Lateral Column/frame Crane+ wind Column/frame Gantry (Elastic cladding; pendent operated) Gantry (Brittle cladding; cab operated) Height / 200 Height / 400 23

Live load Floor & Roof Elements not susceptible to cracking Span / 300 Live load Floor & Roof Elements susceptible to cracking Span / 360 Elements not susceptible to cracking Span / 150 Elements susceptible to cracking Span / 180 Elastic cladding Height / 300 Brittle cladding Height / 500 Vertical Live load Other Buildin gs Cantilever Live load Wind Building Lateral Wind Inter storey drift --- Storey height / 300 24

TOPICS COVERED AND CONCLUSIONS • Review of the provisions of safety, consequent on uncertainties in loading and material properties. • Allowable Stress Design • Limit State Design 25

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