Headed Steel Stud Anchors in Composite Structures: Part I – Shear
ADVANCED DESIGN OF STEEL AND COMPOSITE STRUCTURES · PDF fileADVANCED DESIGN OF STEEL AND...
-
Upload
nguyenduong -
Category
Documents
-
view
266 -
download
8
Transcript of ADVANCED DESIGN OF STEEL AND COMPOSITE STRUCTURES · PDF fileADVANCED DESIGN OF STEEL AND...
ADVANCED DESIGN OF STEEL AND COMPOSITE STRUCTURES
Aldina SantiagoLecture B.3: 22/2/2017European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards and Catastrophic Events
520121-1-2011-1-CZ-ERA MUNDUS-EMMC
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
CONTENTS
Module B – Design of industrial buildings using non-uniform members
B.3 – Design of non-uniform members
1 – Introduction2 – Non-uniform members – approaches and problems 4 – Design resistance of non-uniform members (clause 6.3.4)5 – Example
Introduction
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Introduction
q Tapered steel members are used in steel structures- Structural efficiency à optimization of cross section capacity à
saving of material- Aesthetical appearance
Multi-sport complex – Coimbra, Portugal Construction site in front of the Central Station,Europaplatz, Graz, Austrial
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Tapered members are commonly used in steel frames:- industrial halls, warehouses, exhibition centers, etc.
- Adequate verification procedures are then required for these types of structures!
Introduction
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q However, there are several difficulties in performing the stabilityverification of structures composed of non-uniform members;
Introduction
- Guidelines are inexistent or not clear for the designer.
- Due to this reason, simplifications that are not mechanicallyconsistent are adopted. These may be either too conservative oreven Unconservative!
Non-uniform members
Approachesand
Problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Prismatic members – Clauses 6.3.1 to 6.3.3q Developed for prismatic membersq Sinusoidal imperfections
q Ayrton-Perry type equation:Is maximum at mid span:
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12
L(x)
δcr
δ'cr
δ''cr
÷øö
çèæ p=dLxsine)x( 00
÷øö
çèæ pµd¢¢=LxsinEI)x(MII
Rk,y
II
Rk M)x(M
NN)x( +=e OK!
Column
Constant Sinusoidal
Non-uniform members – approaches and problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non - prismatic members
Non-uniform members – approaches and problems
- Analytical expressions for the elastic critical load are not readily available;
- The choice of the critical section for the application of the buckling resistance
formulae is not straightforward.
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – Clauses 6.3.1 to 6.3.3 apply ???
RkNN
Not Constant
NEd
Non-uniform members – approaches and problems
q Cross section utilization due to applied (first order) forces is notconstant anymore
RkNN
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – Clauses 6.3.1 to 6.3.3 apply ???
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10 12
L(x)
δcr
δ'cr
δ''cr
÷øö
çèæ p=dLxsine)x( 00
÷øö
çèæ pµd¢¢=LxsinEI)x(MII
Rk,y
II
Rk M)x(M
NN)x( +=e KO!
Column
Non-uniform members – approaches and problems
First yield criteria:
q Ayrton-Perry type equation:Is it maximum at mid span ???
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – Clauses 6.3.1 to 6.3.3 apply ???
q Position of the critical cross-section – not at mid span- Account for 2nd order effects; iterative procedure, not practical;
q 1st order critical cross section is considered!
Non-uniform members – approaches and problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – Clauses 6.3.1 to 6.3.3 apply ???
q Variation of cross section class
q Definition of an equivalent class for the member
Class 3Class 2 Class 1
My,Ed
NEd <<< Afy
Non-uniform members – approaches and problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – 2nd order analysis with imperfections
q Definition of local imperfections:q Same problem: e0/L calibrated for prismatic members with
sinusoidal imperfections
Buckling curve acc. to EC3-1-1, Table 6.1
Elastic analysis Plastic analysis
e0/L e0/L
a0 1/350 1/300
a 1/300 1/250
b 1/250 1/200
c 1/200 1/150
d 1/150 1/100
Non-uniform members – approaches and problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – 2nd order analysis with imperfections
q Definition of local imperfections?
Auvent de la Gare Routière – Ermont
Barajas Airport, Madrid, Spain
Italy pavilion, World Expo 2010 – Shanghai
Non-uniform members – approaches and problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
Non-uniform members – approaches and problems
General method allows the verification of the resistance to lateral and lateral torsional buckling for structural components such as:
– single members, built-up or not, uniform or not, with complex support conditions or not, or
– plane frames or subframes composed of such members,
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
αult,k
χ χLT
χop = Minimum (χ, χLT)
χop = Interpolated (χ, χLT)
In-plane resistance
αcr,op
Buckling curve
1/ 1, ³Mkultop gac
In-Plane GMNIA calculations LEA calculations
opcrkultop ,, /aal =
Out-of-planeelastic critical load
1
2
3
Non-uniform members – approaches and problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
αult,k
χ χLT
χop = Minimum (χ, χLT)
χop = Interpolated (χ, χLT)
In-plane resistance
αcr,op
Buckling curve
1/ 1, ³Mkultop gac
In-Plane GMNIA calculations LEA calculations
opcrkultop ,, /aal =
Out-of-planeelastic critical load
1
2
3
Non-uniform members – approaches and problems
Minimum load amplifiedof the design loads toreach the characteristicresistance of the mostcritical cross-section ofthe structural component,without lateral-torsionalbuckling, but accountingfor all effects of the in-plane geometricaldeformations andimperfection (global andlocal): NRK / NEd
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
αult,k
χ χLT
χop = Minimum (χ, χLT)
χop = Interpolated (χ, χLT)
In-plane resistance
αcr,op
Buckling curve
1/ 1, ³Mkultop gac
In-Plane GMNIA calculations LEA calculations
opcrkultop ,, /aal =
Out-of-planeelastic critical load
1
2
3
Non-uniform members – approaches and problems
Minimum amplified for thein plane the design loadsto reach the elastic criticalresistance of thestructural component, withrespect to lateral andlateral-torsional buckling,without accounting for in-plane flexural buckling:Ncr / NEd .FE can be used todetermine αult,k and αcr,op.
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
αult,k
χ χLT
χop = Minimum (χ, χLT)
χop = Interpolated (χ, χLT)
In-plane resistance
αcr,op
Buckling curve
1/ 1, ³Mkultop gac
In-Plane GMNIA calculations LEA calculations
opcrkultop ,, /aal =
Out-of-planeelastic critical load
1
2
3
Non-uniform members – approaches and problems
Global non-dimensionalslenderness
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
αult,k
χ χLT
χop = Minimum (χ, χLT)
χop = Interpolated (χ, χLT)
In-plane resistance
αcr,op
Buckling curve
1/ 1, ³Mkultop gac
In-Plane GMNIA calculations LEA calculations
opcrkultop ,, /aal =
Out-of-planeelastic critical load
1
2
3
Non-uniform members – approaches and problems
Reduction factor for:- Flexural buckling- Lateral torsional
bucklingEach calculated for theglobal non-dimensionalslenderness λop.
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
αult,k
χ χLT
χop = Minimum (χ, χLT)
χop = Interpolated (χ, χLT)
In-plane resistance
αcr,op
Buckling curve
1/ 1, ³Mkultop gac
In-Plane GMNIA calculations LEA calculations
opcrkultop ,, /aal =
Out-of-planeelastic critical load
1
2
3
Non-uniform members – approaches and problems
χop is the reduction factor forthe non-dimensionalslenderness λop, to takeaccount of lateral and lateraltorsional buckling.
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
q Non-uniform members – GENERAL METHOD (clause 6.3.4)
αult,k
χ χLT
χop = Minimum (χ, χLT)
χop = Interpolated (χ, χLT)
In-plane resistance
αcr,op
Buckling curve
1/ 1, ³Mkultop gac
In-Plane GMNIA calculations LEA calculations
opcrkultop ,, /aal =
Out-of-planeelastic critical load
1
2
3
Non-uniform members – approaches and problems
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Non-uniform members – example
N = cte = 80.0 kN
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Non-uniform members – example
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Non-uniform members – example
Verification of the cross-section• The cross-section resistance is checked using clauses 6.2.8 (bending and shear)
and 6.2.9 (bending and axial force) for each class of cross-section
• The utilization ratio a of the cross-section is given by the ration between the normof the applied internal forces and the norm of the bending and axial resistancealong the same load value:
𝛼 =𝑁$%& + 𝑀),$%
&�
𝑁,-.& + 𝑀),,-.&�
≤ 1
𝛼 =𝑁$% + 𝑀),$%
𝐴𝑓𝑦 +𝑊𝑒𝑙𝑦𝑓𝑦≤ 1
Class 1 or 2: being Nmax and My,max the valuesobtained in the interaction curve
Class 3:
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Non-uniform members – example
Verification of the cross-section
Critical cross-section at x = 4,14 m(Class 1)
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Non-uniform members – example
General method (cl. 6.3.4 using the properties of the critical cross-section)In-plane buckling resistance
𝛼89:,; =𝑁$%
𝜒)𝑁=; 𝛾?@A+ 𝑘))
𝑀),$%
𝜒C:𝑀),=; 𝛾?@A
D@
=1
0.55 = 1.819
(being 𝜒C: = 1)
Out-of-plane buckling resistanceEquations to calculate 𝛼JK,LM are dificult to apply!
Numerically, 𝛼JK,LM = 1.482
Buckling resistance 𝜆LM =𝛼89:,;𝛼JK,LM
�= 1.108
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Non-uniform members – example
General method (cl. 6.3.4 using the properties of the critical cross-section)For x = 4.14 m, buckling curves for out-of-plane buckling and lateral-torsional
buckling are curve c.
𝜆LM = O𝑐𝑢𝑟𝑣𝑒𝑐 −> 𝜒V = 0.48𝑐𝑢𝑟𝑣𝑒𝑐 − 𝜒CX = 0.48
𝜒LM = min 𝜒V; 𝜒CX = interp 𝜒V; 𝜒CX = 0.48
So, ,therefore buckling resistance is not verified!𝜒LM𝛼89:,;𝛾?@
=0.48×1.819
1 = 0.873 < 1
The ratio of utilization is 1/0.873 = 1.15 (15% higher than permitted)!
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
Non-uniform members – example
General method (cl. 6.3.4 using the properties of the critical cross-section)
Method Util. ratio Diff (%)GMNIA 0.88
Cla
use
6.3.
3 x = xcr + eq. properties for critical loads 1.22 39
x = 0 1.16 32.8
X = xcr 1.23 40.8
X = L 1.51 72.7
General method (theoretical) - xcr 1.15 30.8
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
REFERENCES
Simões da Silva, L, Rimões, R and Gervásio, H -“Design of Steel Structures”, Ernst & Sohn and ECCSPress, Brussels, 2010.
• Marques, L., Taras, A., Simões da Silva, L., Greiner, R. and Rebelo, C., “Development of a consistent design procedure for tapered columns", Journal of Constructional Steel Research, 72, pp. 61–74 (2012). http://dx.doi.org/10.1016/j.jcsr.2011.10.008
• Marques, L., Simões da Silva, L., Greiner, R., Rebelo, C. and Taras, A., “Development of a consistent design procedure for lateral-torsional buckling of tapered beams”, Journal of Constructional Steel Research, 89, pp. 213-235 (2013). http://dx.doi.org/10.1016/j.jcsr.2013.07.009
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
REFERENCES
• Marques, L., Simões da Silva, L., Rebelo, C. and Santiago, A., “Extension of the interaction formulae in EC3-1-1 for the stability verification of tapered beam-columns”, Journal of Constructional Steel Research, 100, pp. 122-135 (2014). http://dx.doi.org/10.1016/j.jcsr.2014.04.024
• Marques, L., Simões da Silva, L. and Rebelo, C., “Rayleigh-Ritz procedure for determination of the critical loads of tapered columns”, Steel and Composite Structures, 16(1), pp. 47-60 (2014). http://dx.doi.org/10.12989/scs.2014.16.1.047
• Simões da Silva, L., Marques, L. and Rebelo, C., (2010) “Numerical validation of the general method in EC3-1-1: lateral, lateral-torsional and bending and axial force interaction of uniform members”, Journal of Constructional Steel Research, 66, pp. 575-590 (2010), http://dx.doi.org/10.1016/j.jcsr.2009.11.003
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
SOFTWARE
LTBeamN - “Elastic Lateral Torsional Buckling of Beams”, v1.0.1, CTICM, 2013.http://www.steelbizfrance.com/telechargement/desclog.aspx?idrub=1&lng=2SemiComp Member Design – Design resistance of prismatic beam-columns”, Greiner et al, RFCS, 2011.http://www.steelconstruct.com
ECCS Steel Member Calculator – Design ofcolumns, beams and beam-columns to EC3-1-1”, Silva et al, ECCS, 2015. http://www.steelconstruct.com
www.steelconstruct.comwww.cmm.pt
Module A – Design of industrial buildings using non-uniform members
European Erasmus Mundus Master Course
Sustainable Constructions under Natural Hazards
and Catastrophic Events
ACKNOWLEDGEMENTS
• This lecture was prepared for the Edition 2 of SUSCOS (2013/15) by LUÍS SIMÕES DA SILVA and LILIANA MARQUES (UC).
• This lecture was improved for the Edition 3 of SUSCOS (2014/16) by LUÍS SIMÕES DA SILVA (UC).
• This lecture was improved for the Edition 4 of SUSCOS (2015/17) by ALDINA SANTIAGO (UC).
The SUSCOS powerpoints are covered by copyright and are for the exclusive use by the SUSCOS teachers in the framework of this Erasmus Mundus Master. They may be improved by the various teachers throughout the different editions.