Chair for Metal Structures

1. Faculty for Civil and Geodetic Engineering at University in Ljubljana M. Sc. Thesis ROTATION CAPACITY OF SEMI RIGID CONNECTIONS Chair for Metal Structures Erik Zupančič

2. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • INTRODUCTION • EUROCODE 3 – ANNEX J AND ROTATION CAPACITY • ROTATION CAPACITY • CHARACTERISTICS OF COMPONENTS • NUMERICAL EXAMPLE • CONCLUSIONS

3. q pinned rigid semi rigid pinned rigid semi rigid M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • STATIC SYSTEM • YESTERDAY • Pinned connections • Rigid connections • TODAY • Semi rigid connections • (rotation springs)

4. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • ENV 1993: Design of steel structures, Part 1.1: General rules for buildings, Annex J: Joints in building frames • Classification of connections by stiffness • Classification of connections by strength • Characteristics of connections (diagram rotation – moment) • Resistance of connections • Initial rotational stiffness • Rotation capacity

5. 1. Rigid connections: 2. Semi rigid connections: 3. Pinned connections: M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Classification of connections by stiffness Braced frames Unbraced frames Ib – Second moment of area of a beam Lb – span of a beam

6. Full strength M Full strength connections Plastic hinge Partial strength connections Partial strength Plastic hinge Pinned connections F M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Classification of connections by strength

7. Column web in tension Column flange and End plate in bending M sd Q sd Column web in shear Column web in compression M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Component method Connection Components of connection FRd,i , ki Connection Mj , Sj

8. a F a F b b M F c c F M b a M 2 M 3 F c 2 M F 1 3 F 1 F F F F d, f 1 2 3 M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Rotation capacity Components Connection

9. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Characteristics of components - d for: Column web in compression Column web in tension Column flange in bending End plate in bending - f for: Column web in shear F Fi 2/3 Fi Si dy, fy du , fu d, f

10. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Deformation capacity of column web in compression • Axial force (0% Npl - 50% Npl) • Slenderness d/tw (10 - 60)

11. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Modelling with program ABAQUS • Material – Results of numerical simulation • Initial geometric imperfection – Results of numerical simulation • Number of elements – Results of numerical simulation • Type of elements – Results of numerical simulation

12. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Numerical analysis d/tw = 27.13 ABAQUS Displacement - Force Force [kN] Displacement [mm]

13. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Determination of expressions Limit deformations Slenderness

14. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Deformation capacity expressions of components Column web in compression Column web in shear Column web in tension Column flange and end plate in bending (mode 1) (mode 2) (mode 3)

15. Diagrams M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Numerical example (rotation capacity = ?) Material: S 235 Bolts: M20 (8.8) Annex – J (resistance, initial stiffness), M. Sc. Thesis (limit displacement) Shear Compression End plate Column flange Tension

16. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Numerical example (rotation capacity = ?) 202 kN 202 kN Shear End plate Column flange 202 kN Compression 202 kN 202 kN Tension

17. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Conclusions • 3D numerical model • Initial geometric imperfection • Material characteristics • Column web in compression • - Expected results (bigger axial force, biger • slenderness – smaller limit displacement) • Column web in tension • - Comparision of expressions with numerical simulation

18. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Column web in shear • Expected results (bigger axial force, smaller • ratio height/width of panel – smaller limit rotation) • Column flange and end plate in bending • Equivalent T – Stub (three different modes) • Mode 1 (plastification of plate) • Mode 2 (plastification of plate and bolt) • Mode 3 (plastification of bolt) • Comparision of expressions with numerical simulation

19. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Component method • Simple calculation of rotation capacity of connection • Difficult calculation of all three characteristics of connection • Good results (comparision of method results with test results)

20. M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) • Future work • Method of expansion on all types of connections • 3D numerical simulation of complete connection • More experimental tests • Comparision of several calculated examples with tests • Behaviour of components and expressions • Parametric studies of influence of components on connections

21. Faculty for Civil and Geodetic Engineering at University in Ljubljana M. Sc. Thesis ROTATION CAPACITY OF SEMI RIGID CONNECTIONS Chair for Metal Structures Erik Zupančič