TABLE OF CONTENTS INTRODUCTION EUROCODE 3 ANNEX J

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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 1

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

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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) q pinned rigid semi rigid 3

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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 4

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Classification of connections by stiffness Braced frames Unbraced frames 1. Rigid connections: 2. Semi rigid connections: 3. Pinned connections: Ib – Second moment of area of a beam Lb – span of a beam 5

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Classification of connections by strength M Full strength connections Plastic hinge Partial strength connections Partial strength Plastic hinge Pinned connections F 6

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Component method Connection Column web in tension Column flange and End plate in bending M sd Components of connection FRd, i , ki Qsd Column web in shear Connection Mj , Sj Column web in compression 7

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) F - Rotation capacity b a a b F 2 M F 3 F 1 c M c Components M 2 M 3 d, f a M 1 F F Connection b F F 1 F 2 F 3 F c 8

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Characteristics of components - d for: F Column web in compression Fi Column web in tension Column flange in bending 2/3 Fi End plate in bending - f for: Si dy , f y Column web in shear du , f u d, f 9

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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) 10

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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 11

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Numerical analysis d/tw = 27. 13 ABAQUS Force [k. N] Displacement - Force Displacement [mm] 12

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Determination of expressions Limit deformations Slenderness 13

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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) 14

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Numerical example (rotation capacity = ? ) Material: S 235 Bolts: M 20 (8. 8) Annex – J (resistance, initial stiffness), M. Sc. Thesis (limit displacement) Shear Compression End plate Diagrams Column flange Tension 15

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Numerical example (rotation capacity = ? ) 202 k. N Shear End plate 202 k. N Column flange Compression Tension 16

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Conclusions - 3 D 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 17

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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 18

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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) 19

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS M. Sc. Thesis: Rotation capacity of semi rigid connections (by Erik Zupančič) - Future work - Method of expansion on all types of connections - 3 D 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 20

TABLE OF CONTENTS INTRODUCTION EUROCODE 3 - ANNEX J ROTATION CAPACITY COMPONENTS NUMERICAL EXAMPLE CONCLUSIONS 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 21