Composite Structures of Steel and Concrete
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Roger P. Johnson is Emeritus Professor of Civil Engineering at the University of Warwick. He has worked for several decades on the theory and applications of composite structures. He was sometime Convenor of the Drafting Committees for Parts 1.1 and 2 of Eurocode 4, and is a member of the BSI sub-committee for composite structures.
Yong C. Wang is Professor of Structural and Fire Engineering at the University of Manchester, with about 30 years of research and specialist consultancy experience in fire resistance of structures. He is a member of the CEN Working Group overseeing revision to EN 1994-1-2 and a member of the CEN Project Team SC4.T4 developing new rules for fire resistance design of composite columns made of unprotected concrete filled tubular sections.
Content
Preface xi
Symbols, Terminology and Units xv
1 Introduction 1
1.1 Composite beams and slabs 1
1.2 Composite columns and frames 2
1.3 Design philosophy and the Eurocodes 3
1.3.1 Background 3
1.3.2 Limit state design philosophy 4
1.4 Properties of materials 8
1.4.1 Concrete 9
1.4.2 Reinforcing steel 10
1.4.3 Structural steel 10
1.4.4 Profiled steel sheeting 10
1.4.5 Shear connectors 11
1.5 Direct actions (loading) 11
1.6 Methods of analysis and design 12
1.6.1 Typical analyses 13
1.6.2 Non-linear global analysis 17
2 Shear Connection 19
2.1 Introduction 19
2.2 Simply-supported beam of rectangular cross-section 20
2.2.1 No shear connection 20
2.2.2 Full interaction 22
2.3 Uplift 24
2.4 Methods of shear connection 25
2.4.1 Bond 25
2.4.2 Shear connectors 25
2.4.3 Shear connection for profiled steel sheeting 29
2.5 Properties of shear connectors 29
2.5.1 Stud connectors used with profiled steel sheeting 33
2.5.2 Stud connectors in a 'lying' position 38
2.5.3 Example: stud connectors in a 'lying' position 39
2.6 Partial interaction 41
2.7 Effect of degree of shear connection on stresses and deflections 43
2.8 Longitudinal shear in composite slabs 44
2.8.1 The shear-bond test 45
2.8.2 Design by the m-k method 47
2.8.3 Defects of the m-k method 47
3 Simply-supported Composite Slabs and Beams 49
3.1 Introduction 49
3.2 Example: layout, materials and loadings 49
3.2.1 Properties of concrete 50
3.2.2 Properties of other materials 50
3.2.3 Resistance of the shear connectors 51
3.2.4 Permanent actions 51
3.2.5 Variable actions 51
3.3 Composite floor slabs 51
3.3.1 Resistance of composite slabs to sagging bending 54
3.3.2 Resistance of composite slabs to longitudinal shear by the partial-interaction method 56
3.3.3 Resistance of composite slabs to vertical shear 58
3.3.4 Punching shear 59
3.3.5 Bending moments from concentrated point and line loads 60
3.3.6 Serviceability limit states for composite slabs 62
3.4 Example: composite slab 63
3.4.1 Profiled steel sheeting as formwork 64
3.4.2 Composite slab - flexure and vertical shear 65
3.4.3 Composite slab - longitudinal shear 66
3.4.4 Local effects of point load 68
3.4.5 Composite slab - serviceability 69
3.4.6 Example: composite slab for a shallow floor using deep decking 70
3.4.7 Comments on the designs of the composite slab 73
3.5 Composite beams - sagging bending and vertical shear 73
3.5.1 Effective cross-section 73
3.5.2 Classification of steel elements in compression 74
3.5.3 Resistance to sagging bending 76
3.5.4 Resistance to vertical shear 84
3.5.5 Resistance of beams to bending combined with axial force 85
3.6 Composite beams - longitudinal shear 86
3.6.1 Critical lengths and cross-sections 86
3.6.2 Non-ductile, ductile and super-ductile stud shear connectors 87
3.6.3 Transverse reinforcement 90
3.6.4 Detailing rules 94
3.7 Stresses, deflections and cracking in service 95
3.7.1 Elastic analysis of composite sections in sagging bending 96
3.7.2 The use of limiting span-to-depth ratios 98
3.8 Effects of shrinkage of concrete and of temperature 99
3.9 Vibration of composite floor structures 99
3.9.1 Prediction of fundamental natural frequency 101
3.9.2 Response of a composite floor to pedestrian traffic 103
3.10 Hollow-core and solid precast floor slabs 104
3.10.1 Joints, longitudinal shear and transverse reinforcement 105
3.10.2 Design of composite beams that support precast slabs 105
3.11 Example: simply-supported composite beam 107
3.11.1 Composite beam - full-interaction flexure and vertical shear 108
3.11.2 Composite beam - partial shear connection, non-ductile connectors and transverse reinforcement 110
3.11.3 Composite beam - deflection and vibration 113
3.12 Shallow floor construction 117
3.13 Example: composite beam for a shallow floor using deep decking 119
3.14 Composite beams with large web openings 122
4 Continuous Beams and Slabs, and Beams in Frames 129
4.1 Types of global analysis and of beam-to-column joint 129
4.2 Hogging moment regions of continuous composite beams 133
4.2.1 Resistance to bending 133
4.2.2 Vertical shear, and moment-shear interaction 137
4.2.3 Longitudinal shear 138
4.2.4 Lateral buckling 139
4.2.5 Cracking of concrete 144
4.3 Global analysis of continuous beams 149
4.3.1 General 149
4.3.2 Elastic analysis 150
4.3.3 Rigid-plastic analysis 154
4.4 Stresses and deflections in continuous beams 156
4.5 Design strategies for continuous beams 157
4.6 Example: continuous composite beam 158
4.6.1 Data 158
4.6.2 Flexure and vertical shear 160
4.6.3 Lateral buckling 162
4.6.4 Shear connection and transverse reinforcement 164
4.6.5 Check on deflections 165
4.6.6 Control of cracking 168
4.7 Continuous composite slabs 169
5 Composite Columns and Frames 171
5.1 Introduction 171
5.2 Composite columns 173
5.3 Beam-to-column joints 173
5.3.1 Properties of joints 173
5.3.2 Classification of joints 179
5.4 Design of non-sway composite frames 180
5.4.1 Imperfections 180
5.4.2 Elastic stiffnesses of members 182
5.4.3 Methods of global analysis 183
5.4.4 First-order global analysis of braced frames 184
5.4.5 Outline sequence for design of a composite braced frame 186
5.5 Example: composite frame 187
5.5.1 Data 187
5.5.2 Design action effects and load arrangements 188
5.6 Simplified design method of EN 1994-1-1, for columns 189
5.6.1 Introduction 189
5.6.2 Detailing rules, and resistance to fire 190
5.6.3 Properties of column lengths 191
5.6.4 Resistance of a cross-section to combined compression and uniaxial bending 192
5.6.5 Verification of a column length 193
5.6.6 Transverse and longitudinal shear 195
5.6.7 Concrete-filled steel tubes 196
5.7 Example (continued): external column 197
5.7.1 Action effects 197
5.7.2 Properties of the cross-section, and y-axis slenderness 198
5.7.3 Resistance of the column length, for major-axis bending 201
5.7.4 Resistance of the column length, for minor-axis bending 202
5.7.5 Checks on shear, and closing comment 204
5.8 Example (continued): internal column 205
5.8.1 Global analysis 205
5.8.2 Resistance of an internal column 207
5.8.3 Comment on column design 207
5.9 Example (continued): design of frame for horizontal forces 207
5.9.1 Design loadings, ultimate limit state 208
5.9.2 Stresses and stiffness 209
5.10 Example (continued): joints between beams and columns 209
5.10.1 Nominally-pinned joint at external column 209
5.10.2 End-plate joint at internal column 210
5.11 Example: concrete-filled steel tube with high-strength materials 216
5.11.1 Loading 216
5.11.2 Action effects for the column length 216
5.11.3 Effect of creep 217
5.11.4 Slenderness 218
5.11.5 Bending moment 218
5.11.6 Interaction polygon, and resistance 218
5.11.7 Discussion 219
6 Fire Resistance 223
Yong C.Wang
6.1 General introduction and additional symbols 223
6.1.1 Fire resistance requirements 224
6.1.2 Fire resistance design procedure 225
6.1.3 Partial safety factors and material properties 226
6.2 Composite slabs 226
6.2.1 General calculation method 226
6.2.2 Tabulated data 227
6.2.3 Tensile membrane action 227
6.3 Composite beams 229
6.3.1 Critical temperature method 229
6.3.2 Temperature of protected steel 232
6.3.3 Load-carrying capacity calculation method 234
6.3.4 Appraisal of different calculation methods for composite beams 238
6.3.5 Shear resistance 238
6.4 Composite columns 239
6.4.1 General calculation method and methods for different types of columns 240
6.4.2 Concrete-filled tubes 241
6.4.3 Worked example for concrete-filled tubes with eccentric loading 244
A Partial-interaction theory 247
A.1 Theory for simply-supported beam 247
A.2 Example: partial interaction 250
References 253
Index 259
Symbols, Terminology and Units
The symbols used in this volume are, wherever possible, the same as those in EN 1994 and in the Designers' Guide to EN 1994-1-1 (Johnson, 2012). They are based on ISO 3898:1987, Bases for design of structures - Notation - General symbols. They are more consistent that those used in the British codes, and more informative. For example, in design one often compares an applied ultimate bending moment (an 'action effect' or 'effect of action') with a bending resistance, since the former must not exceed the latter. This is written
where the subscripts E, d, and R mean 'effect of action', 'design', and 'resistance', respectively. For clarity, multiple subscripts are often separated by commas (MR,d would be an example); but there are many exceptions, as the examples above show.
For longitudinal shear, the following should be noted:
- ?, a shear stress (shear force per unit area), but t is used for a vertical shear stress;
- ?L, a shear force per unit length of member, known as 'shear flow';
- V, a shear force (used also for a vertical shear force).
For subscripts, the presence of three types of steel leads to the use of 's' for reinforcement, 'a' (from the French 'acier') for structural steel, and 'p' or 'ap' for profiled steel sheeting. Another key subscript is k, as in
Here, the partial factor ?F is applied to a characteristic bending action effect to obtain a design value, for use in a verification for an ultimate limit state. Thus 'k' implies that a partial factor (?) has not been applied, and 'd' implies that it has been. This distinction is made for actions and resistances, as well as for the action effect shown here.
Other important subscripts are:
- c or C for 'concrete';
- v or V, meaning 'related to vertical or longitudinal shear'.
Terminology
The word 'resistance' replaces the widely-used 'strength', which is reserved for a property of a material or component, such as a bolt.
A useful distinction is made in most Eurocodes, and in this volume, between 'resistance' and 'capacity'. The words correspond respectively to two of the three fundamental concepts of the theory of structures, equilibrium and compatibility (the third being the properties of the material). The definition of a resistance includes a unit of force, such as kN, while that of a 'capacity' does not. A capacity is typically a displacement, strain, curvature, or rotation.
Cartesian axes
In the Eurocodes, x is an axis along a member. A major-axis bending moment My acts about the y axis, and Mz is a minor-axis moment. This differs from previous practice in the UK, where the major and minor axes were xx and yy, respectively.
Units
The SI system is used. A minor inconsistency is the unit for stress, where both N/mm2 and MPa (megapascal) are found in the codes. Similarly, kN/mm2 corresponds to GPa (gigapascal). The unit for a coefficient of thermal expansion may be given as 'per °C' or as 'K-1', where K means kelvin, the unit for the absolute temperature scale. The convention of sign is explained in the Preface.
Symbols
The list of symbols in EN 1994-1-1 extends over eight pages, and does not include many symbols in clauses of other Eurocodes to which it refers. The list can be shortened by separation of main symbols from subscripts. In this book, commonly-used symbols are listed here in that format. Rarely-used symbols are defined where they appear. Fire-related symbols from EN 1994-1-2 are listed in Chapter 6.
Latin upper-case letters
- A
- accidental action; area
- B
- breadth
- C
- factor
- E
- modulus of elasticity; effect of actions
- (EI)
- stiffness of a composite section (the same whether transformed into 'steel' or 'concrete')
- F
- action; force; force per unit length
- G
- permanent action; shear modulus
- H
- horizontal load or force per frame per storey
- I
- second moment of area
- J
- property of an end-plate connection
- K
- stiffness; coefficient
- L
- length; span
- M
- moment in general; bending moment; modal mass
- M´
- hogging bending moment
- N
- axial force
- P
- shear force or resistance for a shear connector
- Q
- variable action
- R
- resistance; resistance function (as R); response factor; ratio
- S
- stiffness; width (of floor)
- T
- tensile force or resistance; total time
- ULS
- ultimate limit state
- V
- shear force; vertical load per frame per storey
- W
- section modulus; wind load
- X
- property of a material
- Z
- shape factor
Latin lower-case letters
- a
- acceleration; lever arm; dimension
- b
- width; breadth; dimension
- c
- outstand; thickness of concrete cover; dimension
- d
- diameter; depth
- e
- eccentricity; dimension
- f
- strength (of a material); natural frequency; coefficient; factor
- g
- permanent action per unit length or area; gravitational acceleration
- h
- depth of member; thickness; height
- k
- coefficient; factor; property of a composite slab; stiffness
- l
- length
- m
- property of a composite slab; mass per unit length or area; number
- n
- modular ratio; number
- p
- spacing (e.g. of shear connectors)
- q
- variable action per unit length or area
- r
- radius; ratio
- s
- spacing; slip of shear connection
- t
- thickness
- u
- perimeter
- v
- shear stress; shear strength; shear force per unit length; dimension
- w
- crack width; load per unit length
- x
- dimension to neutral axis; depth of stress block; co-ordinate along member
- y
- major axis; co-ordinate; distance from elastic neutral axis to extreme fibre
- distance of excluded area from centre of area
- z
- lever arm; dimension; co-ordinate
Greek letters
- a
- angle; ratio; factor; coefficient; reduction factor
- ß
- angle; factor; coefficient
- ?
- partial factor
- ?
- difference in . (precedes main symbol)
- d
- steel contribution ratio; deflection; slip capacity
- e
- strain; coefficient
- ?
- coefficient; degree of shear connection
- ?
- angle
- ?
- curvature
- ?
- (or if non-dimensional) slenderness ratio
- µ
- coefficient of friction; ratio of bending moments; exponent (as superscript)
- ?
- Poisson's ratio
- ?
- reinforcement ratio; density (unit mass)
- s
- normal stress
- t
- shear stress
- f
- diameter of a reinforcing bar; rotation; angle of sidesway
- ?
- creep coefficient
- ?
- reduction factor (for buckling)
- ?
- combination factor for variable actions; ratio; exponent
Subscripts
- A
- accidental; area; structural steel
- a
- structural steel; spacing
- ap
- profiled steel sheeting
- b
- buckling; bolt; beam
- bot
- bottom
- C
- concrete
- c
- compression; concrete; composite; connection; cylinder compressive strength
- cf
- concrete flange
- cr
- critical
- cs
- strain in concrete (e.g. from shrinkage)
- cu
- concrete cube compressive strength
- d
- design; diameter
- E
- effect of action
- eff
- effective
- e
- effective (with further subscript); elastic
- el
- elastic
- eq
- equivalent
- F
- action
- f
- flange; full shear connection; surface finish (in hf); full interaction
- fl
- flange
- G
- permanent (referring to actions)
- g
- centroid; permanent load
- H or h
- horizontal
- hog
- hogging bending
- i
- index (replacing a numeral)
- imp
- imperfection
- ini
- initial
- j
- joint
- ...
