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AN INTRODUCTION TO
LIMIT STATES DESIGN
CIVL 331Steel and Timber Design
By:
Ferya Moayedi,
Salman Soleimani
January 16, 2013
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Analysis Vs. Design
Analysis is understandingthe structure anddetermining how theeffects of globally applied
forces are resisted byindividual structuralmembers
Design is an iterativeprocess to create a safeand reliable structurewhich is aesthetically
pleasing in an economicalmanner
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Putting Thoughts Into aDesign Problem
Design is an iterative process
Structural layoutAnalyze the structure Find member forces
Assume structural membersAnalyze the structure again OK ??!
Modify member sizes
Analyze again 3CIVL 331 - Intro to LSD by F. Moayedi, S.Soleimani
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Structural Design
Tools available to engineers:
Codes
NBCC, IBC, BCBC
CSA-A23.3, CSA-S16-01
Software SAP2000, ETABS, Perform 3D
S-Frame, RISA 3D, Opensees
ANSYS, ABAQUS, CANNY
Specifications & Standards
ASTM, ACI, AASHTO, ANSI, CGSB Guidelines
Seismic Retrofit Guideline (SRG)
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Structural Systems
Moment resisting frame
(Beam-column system)
Braced frame
Un-braced frame
Other available
Structural Systems
Bearing-wall
Rigid frame
Long-span
High-rise
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Structural Design Approaches
Different design approaches
ASD
Allowable Stress Design
Also called Permissible Stress Design
WSD
Working Stress Design
LRFD
Load and Resistance Factor Design
LSD
Limit States Design
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Limit States Design (LSD)
LSD is a design method in which the performanceof a structure is checked against various limitingconditions at appropriate load levels
In a structural steel design, the limiting conditions tobe checked are:
Ultimate Limit States (ULS)
These states concern safety
e.g. load carrying capacity, overturning, sliding, fatigue
Serviceability Limit States (SLS) These states concern performance under normal operations
e.g. excessive deflection, vibration, or permanent deformation
Note: LSD is referred to as Load & Resistance Factor Design (LRFD) in US
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Limit States Design (LSD)
General Design Equation
Factored ResistanceFactored Load
R S
Where,
= resistance factor
R = nominal resistance of structural element
= load factor
S = specified load
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Limit States Design (LSD)
Design which is based on the probability and mode of
failure, or limit of usefulness, and the probability of the
occurrence and variation of the load
Characteristic resistance:
645.1
0.2
0.1 68%
95%
98%
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Probability of Failure
S
R2
R1
Failure occurs when R S
The hatched area = probability of failure
The global safety factor:
s
R
o
m
m
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Probability of Failure
Although the distance between the mean values mR and mSis thesame, i.e., the same o, the probability of failure greatly depends on
the scatter of both S and R values, i.e., the magnitude of their
respective standard deviations
In order to achieve a consistent probability of failure, the global
safety factor will have to be adjusted depending on the scatter (i.e.,
reliability) of load and resistant values
Exact knowledge of the distribution function in the asymptoticregions of the curves is essential, but unfortunately data for those
regions is usually not available or is too sparsely spaced
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Safety Index
Safety Index
Limit StatesDegree of Damage
small
medium
severe
Serviceability 2.0 2.5 3.0
Ultimate 4.2 4.7 5.2
22
sR
sR
z
z mmm
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Reliability and Safety
The purpose of the design process is to maintain anacceptable difference between the load S and the resistance R
Relationship between Safety Index and Safety Factor
95thPercentile of
load ( )
5thPercentile of
resistance ( )
645.1
645.1
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Advantages of Limit States Design
Utilizing Load Factors
Using distinct load factors for different loads, makes
the probability of failure more consistent in different
loading conditions
However, the Working Stress Design (WSD) approach uses asingle factor of safety
Utilizing Resistance Factors
Applying different resistance factors in order todetermine resistances of different members with
different materials, would result in a more uniform
reliability in general
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Advantages of Limit States Design
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Design Equations
Ultimate Limit States
Where,
= performance factor
R = nominal member strength, or resistance
i= load factor for specified loads (Table 13)
Si= specified loads (Clause 6.2: D, L, S, W, E)
Serviceability Limit States
Where,
= performance factor
R = nominal member strength, or resistance
i= 1
Si= specified loads (Clause 6.2: D, L, S, W, E)
R iSi R iSi
Note:D = dead loadL = specifiedlive loadS = snow load
W = specified wind loadE= specified earthquake load
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*Ref. Clause 7.2.1
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Globally Applied Loads
Gravity Loads (vertical) Dead Load (DL)
Permanent structure loads
e.g. building weight, partition
walls, Live Load (LL)
Temporary loads
Varying loads
Use and occupancy loads Snow and rain loads
e.g. weight of the people
occupying the building,
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Lateral Loads (horizontally applied)
Earthquake Load
Wind Load
18
May cause uplift
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Load Combinations Structures, components, and foundations shall be
designed so that their design strength equals or exceedsthe effects of the factored load combinations
Analyze the structure considering all of the different
possible load combinations. Use the worst case scenarioas the governing load case
This will be the topic of next lecture
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Useful Tips
&
Housekeeping Notes
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Try to become a master in using your HSC !!!
Mark up your handbook very well, as you go
Refer to your handbook as much & frequent as you can
Read the book called Limit States Design in Structural
Steel, by Kulak Grondin
Try to utilize different software for differentapplications as much as possible!!! (Take it as a hint)
Familiarize yourself with many software and make sure you
know how to use them efficiently and effectively
e.g. Cheops, S-Frame, RISA 2D, Excel Spreadsheets,
Useful Tips for CIVL 331
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Some Housekeeping Notes:
Educational licences availablefor the S-Frame software S-Frame request for licence
Deadline:Jan 31st2013
Licence Agreement Form needs tobe signed (Obtain from Salman)
Other available software
CHEOPS RISA 2D (Educational Version)
http://www.risa.com/forms/2deducational.html
Dr. Frame, Dr. Beam, ?!
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Any Questions?
Salman Soleimani:
Ferya Moayedi:
23CIVL 331 Intro to LSD by F Moayedi S Soleimani
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