Cover
Preface
Symbols, Terminology and Units
1. Terminology
2. Symbols
Chapter 1: Introduction
1. 1.1 Composite beams and slabs
2. 1.2 Composite columns and frames
3. 1.3 Design philosophy and the Eurocodes
4. 1.4 Properties of materials
5. 1.5 Direct actions (loading)
6. 1.6 Methods of analysis and design
Chapter 2: Shear Connection
1. 2.1 Introduction
2. 2.2 Simply‐supported beam of rectangular cross‐section
3. 2.3 Uplift
4. 2.4 Methods of shear connection
5. 2.5 Properties of shear connectors
6. 2.6 Partial interaction
7. 2.7 Effect of degree of shear connection on stresses and deflections
8. 2.8 Longitudinal shear in composite slabs
Chapter 3: Simply‐supported Composite Slabs and Beams
1. 3.1 Introduction
2. 3.2 Example: layout, materials and loadings
3. 3.3 Composite floor slabs
4. 3.4 Example: composite slab
5. 3.5 Composite beams – sagging bending and vertical shear
6. 3.6 Composite beams – longitudinal shear
7. 3.7 Stresses, deflections and cracking in service
8. 3.8 Effects of shrinkage of concrete and of temperature
9. 3.9 Vibration of composite floor structures
10. 3.10 Hollow‐core and solid precast floor slabs
11. 3.11 Example: simply‐supported composite beam
12. 3.12 Shallow floor construction
13. 3.13 Example: composite beam for a shallow floor using deep decking
14. 3.14 Composite beams with large web openings
Chapter 4: Continuous Beams and Slabs, and Beams in Frames
1. 4.1 Types of global analysis and of beam‐to‐column joint
2. 4.2 Hogging moment regions of continuous composite beams
3. 4.3 Global analysis of continuous beams
4. 4.4 Stresses and deflections in continuous beams
5. 4.5 Design strategies for continuous beams
6. 4.6 Example: continuous composite beam
7. 4.7 Continuous composite slabs
Chapter 5: Composite Columns and Frames
1. 5.1 Introduction
2. 5.2 Composite columns
3. 5.3 Beam‐to‐column joints
4. 5.4 Design of non‐sway composite frames
5. 5.5 Example: composite frame
6. 5.6 Simplified design method of EN 1994‐1‐1, for columns
7. 5.7 Example (continued): external column
8. 5.8 Example (continued): internal column
9. 5.9 Example (continued): design of frame for horizontal forces
10. 5.10 Example (continued): joints between beams and columns
11. 5.11 Example: concrete‐filled steel tube with high‐strength materials
Chapter 6: Fire Resistance
1. 6.1 General introduction and additional symbols
2. 6.2 Composite slabs
3. 6.3 Composite beams
4. 6.4 Composite columns
Appendix A: Partial‐interaction theory
1. A.1 Theory for simply‐supported beam
2. A.2 Example: partial interaction
References
Index
End User License Agreement

List of Tables

Chapter 1
1. Table 1.1 Values of γ_G and γ_Q for persistent design situations
2. Table 1.2 Recommended values for γ_M for strengths of materials and for resistances
3. Table 1.3 Combination factors
4. Table 1.4 Properties of concretes used in the examples, at age 28 days
Chapter 2
1. Table 2.1 Shear resistances for a lying stud in an edge position, with P_Rd = 83.3 kN
2. Table 2.2 Elastic analyses of a composite beam with various degrees of shear connection
Chapter 3
1. Table 3.1 Characteristic and design loads per unit area of slab
2. Table 3.2 Classification of cross‐sections (BSI, 2014b), and methods of analysis
3. Table 3.3 Vibration dose ranges that might result in various probabilities of adverse comment
4. Table 3.4 Characteristic and design loads per unit length of beam
Chapter 4
1. Table 4.1 Global analysis, and types of joint and joint model
2. Table 4.2 Properties of beam‐to‐column joints in composite frames
3. Table 4.3 Limits to redistribution of hogging moments, as a percentage of the initial value of the bending moment to be reduced
4. Table 4.4 Loads and bending moments for a span of 9.3 m
5. Table 4.5 Properties of cross‐sections of a composite beam
6. Table 4.6 Calculation of maximum deflection
Chapter 5
1. Table 5.1 Data and results for deflection of a beam with an end‐plate connection
Chapter 6
1. An example of tabulated data for fire resistance of a proprietary composite slab (not for general use)
2. Table 6.2 Coefficients β₀ to β₃ for different types of steel tubes, depending on u_s
3. Table 6.3 Stiffness reduction coefficient for steel
4. Table 6.4 Stiffness reduction coefficient for reinforcement

List of Illustrations

Chapter 1
1. Figure A.1 Elevation of element of composite beam with transverse profiled sheeting
2. Figure A.2 Distributions of slip and slip strain for a fixed‐ended beam
3. Figure A.3 Components of bending moment in a fixed‐ended beam
Chapter 1
1. Figure 1.1 Stress–strain curves for concrete and structural steel
2. Figure 1.2 Shear stresses in an elastic I‐section
3. Figure 1.3 Shear stresses in a composite section with the neutral axis in the concrete slab
4. Figure 1.4 Interaction curves for a column cross‐section, for finding factor γ₀
Chapter 2
1. Figure 2.1 Composite beams: (a) typical cross‐section; (b) haunched beam; (c) fully‐encased beam
2. Figure 2.2 Effect of shear connection on bending and shear stresses
3. Figure 2.3 Deflections, slip strain and slip
4. Figure 2.4 Shear flow for ‘triangular’ spacing of connectors
5. Figure 2.5 Uplift forces
6. Figure 2.6 Headed stud shear connector
7. Figure 2.7 Other types of shear connector included in ENV 1994‐1‐1
8. Figure 2.8 Concrete dowel shear connectors with (a) closed and (b) open holes for reinforcement
9. Figure 2.9 Composite slab
10. Figure 2.10 Standard push test
11. Figure 2.11 Typical load–slip curve for 19 mm stud connectors in a composite slab
12. Figure 2.12 Bearing stress on the shank of a stud connector
13. Figure 2.13 Haunch with connectors too close to a free surface
14. Figure 2.14 Detailing rules for haunches
15. Figure 2.15 Composite beam with composite slab spanning in the same direction. Left: trapezoidal; right: re‐entrant
16. Figure 2.16 (a) Cross‐section of a slab with a lying stud supported by a steel plate. (b) Cross‐section A–A showing the spacing s of the links
17. Figure 2.17 (a) End of a simply‐supported composite beam. (b) Longitudinal strain at mid‐span, × 10⁶, for η = 0.46. (c) Cross‐section through top rib of the sheeting
18. Figure 2.18 Critical sections for a composite slab
19. Figure 2.19 Bending resistance of a composite slab
20. Figure 2.20 Maximum shear force in a test, related to shear span L_s
21. Figure 2.21 Calculation of L_s for a composite slab
Chapter 3
1. Figure 3.1 Design example – structure for a typical floor
2. Figure 3.2 Cross‐section of composite slab, and stress blocks for sagging bending
3. Figure 3.3 Equations 3.10 and 3.14
4. Figure 3.4 Determination of degree of shear connection from a shear‐bond test
5. Figure 3.5 Bending moment M_Ed and bending resistance, governed by longitudinal shear
6. Figure 3.6 Critical perimeter for punching shear
7. Figure 3.7 Effective width of composite slab, for concentrated load
8. Figure 3.8 Typical cross‐section of profiled sheeting and composite slab
9. Figure 3.9 Profiled sheeting during construction
10. Figure 3.10 Partial‐interaction method, for longitudinal shear
11. Figure 3.11 (a) Cross‐section of composite slab at supporting steel beam. (b) Stress blocks for plastic resistance of slab to sagging bending
12. Figure 3.12 Cross‐section of ComFlor 225 deep decking (simplified)
13. Figure 3.13 Use of effective width to allow for shear lag
14. Figure 3.14 Class boundaries for webs, for f_y = 355 N/mm²
15. Figure 3.15 Resistance to sagging bending of composite section in Class 1 or 2
16. Figure 3.16 Design methods for partial shear connection
17. Figure 3.17 Variation of bending resistance along a span
18. Figure 3.18 Compression force in a concrete flange for M_el,Rd < M_Ed < M_pl,Rd by the non‐linear and interpolation methods. (a) Notation. (b) Results from the worked example
19. Figure 3.19 Resistance of a beam cross‐section to bending combined with axial force
20. Figure 3.20 Vertical shear in a beam with an off‐centre point load
21. Figure 3.21 Current and proposed rules for minimum degree of shear connection, n/n_f, for f_y = 355 MPa
22. Figure 3.22 Surfaces of potential failure in longitudinal shear
23. Figure 3.23 T‐beam with asymmetrical concrete flange
24. Figure 3.24 Truss model for transverse reinforcement
25. Figure 3.25 Bearing resistance of profiled sheeting, acting as transverse reinforcement
26. Figure 3.26 Detailing rules for shear connection
27. Figure 3.27 Plan of holes in a precast slab and 19‐mm stud connectors from the supporting beam with longitudinal spacings of (a) 5d, and (b) 3d
28. Figure 3.28 Elastic analysis of cross‐section of composite beam in sagging bending
29. Figure 3.29 Cross‐section of vibrating floor structure showing typical fundamental mode
30. Figure 3.30 Precast hollow‐core slab with in situ topping supported on a steel top flange
31. Figure 3.31 Cross‐section and stress blocks for composite beam in sagging bending
32. Figure 3.32 Detail of shear connection
33. Figure 3.33 Cross‐sections of asymmetric steel beams, for use with precast slabs or deep decking
34. Figure 3.34 (a) Cross‐section of an asymmetric beam with 8.6 m span, supporting deep decking. (b) Stress blocks for the partial‐interaction resistance to sagging bending, 843 kN m
35. Figure 3.35 (a) Centre‐lines of members at a web post in a composite beam with rectangular web openings. (b) Action effects at cross‐section X–X and within a web post
Chapter 4
1. Figure 4.1 Cross‐section and stress distributions for composite beam in hogging bending
2. Figure 4.2 Resistance to combined bending and vertical shear
3. Figure 4.3 Torsional and distortional lateral buckling
4. Figure 4.4 Typical deformation of steel bottom flange in distortional lateral buckling
5. Figure 4.5 Inverted‐U frame model for distortional lateral buckling
6. Figure 4.6 Factor C₄ for an end span of a continuous beam
7. Figure 4.7 Maximum steel stress for minimum reinforcement, high bond bars
8. Figure 4.8 Maximum bar spacing for high bond bars
9. Figure 4.9 Bending moment diagrams with redistribution
10. Figure 4.10 Rigid‐plastic global analysis
11. Figure 4.11 Continuous beam with dead load, plus imposed load on span AB only
12. Figure 4.12 Cracked section of composite slab, for hogging bending
13. Figure 4.13 Loading for deflection of span AB
14. Figure 4.14 Elastic properties of composite section
Chapter 5
1. Figure 5.1 A composite frame (simplified)
2. Figure 5.2 Elevations of beam‐to‐column joints
3. Figure 5.3 Model for elastic analysis of end‐plate connections between composite beams and a column
4. Figure 5.4 Rotation of a joint
5. Figure 5.5 Moment–rotation curve for an end‐plate joint
6. Figure 5.6 Classification of joints by initial stiffness
7. Figure 5.7 Unbraced and braced frames
8. Figure 5.8 Arrangements of imposed load, for column design
9. Figure 5.9 Beam loading for maximum hogging bending moment at B
10. Figure 5.10 Arrangement of variable load for maximum bending in columns AB and CD
11. Figure 5.11 Typical cross‐sections of composite columns
12. Figure 5.12 Polygonal approximation to M–N interaction curve
13. Figure 5.13 First‐order and second‐order bending moments in a column length
14. Figure 5.14 Dimensions and action effects for external column
15. Figure 5.15 Assumed cross‐section for external column length 0–1
16. Figure 5.16 Plastic neutral axes for encased I‐section
17. Figure 5.17 Interaction diagram for major‐axis bending of external column
18. Figure 5.18 Major‐axis bending‐moment diagrams for external column
19. Figure 5.19 Minor‐axis bending of external column. (a) Position of neutral axis. (b) Interaction diagram
20. Figure 5.20 Loadings and major‐axis bending moments for an internal column
21. Figure 5.21 Part cross‐sections for length 0–1 of internal columns. (a) Encased I‐section. (b) Concrete‐filled steel tube with high‐strength materials
22. Figure 5.22 Part plan of typical floor slab
23. Figure 5.23 End‐plate joint to major axis of external column
24. Figure 5.24 Details of end‐plate connection of composite beam to internal column
25. Figure 5.25 Prying forces in a T‐stub at an end‐plate connection
26. Figure 5.26 Model for elastic analysis of a span with an end‐plate connection at one end
27. Figure 5.27 Interaction diagram for concrete‐filled steel tube internal column, with t = 12.5 mm
28. Figure 5.28 Cross‐section through CFST column showing gusset plate for load introduction
Chapter 6
1. Figure 6.1 Scheme to use tensile membrane action to eliminate fire protection to interior secondary beams (Wang et al., 2012, with permission from CRC Press)
2. Figure 6.2 Membrane action in a horizontally unrestrained concrete slab (Wang et al., 2012, with permission from CRC Press)
3. Figure 6.3 Geometry of a composite beam with concrete slab on top of steel section
4. Figure 6.4 Steel temperature–time relationship
5. Figure 6.5 Effective length of column in braced frame in fire. (a) Section through the building. (b) Deformation mode and effective length at room temperature. (c) Deformation mode and effective length at elevated temperature
6. Figure 6.6 Dimensions of concrete‐filled tubular column cross‐section for the worked example

Copyright

This edition first published 2019

Edition History

Crosby Lockwood Staples (1e 1975); Blackwell Scientific Publications (2e 1994); Blackwell Publishing (3e 2004)

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Library of Congress Cataloging‐in‐Publication Data

Name: Johnson, R. P. (Roger Paul), author.

Title: Composite structures of steel and concrete : beams, slabs, columns and frames for buildings / Roger P. Johnson, University of Warwick, UK.

Description: 4th edition. | Hoboken, NJ, USA : Wiley [2019] | Includes bibliographical references and index. |

Identifiers: LCCN 2018016256 (print) | LCCN 2018016962 (ebook) | ISBN 9781119401414 (Adobe PDF) | ISBN 9781119401384 (ePub) | ISBN 9781119401438 (hardcover)

Subjects: LCSH: Composite construction. | Building, Iron and steel. |

Concrete construction.

Classification: LCC TA664 (ebook) | LCC TA664 .J63 2018 (print) | DDC

624.1/821–dc23

LC record available at https://lccn.loc.gov/2018016256

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Preface

This volume provides an introduction to the theory and design of composite structures of steel and concrete. Readers are assumed to be familiar with the elastic and plastic theories for the analysis for bending and shear of cross‐sections of beams and columns of a single material, such as structural steel, and to have some knowledge of reinforced concrete. No previous knowledge is assumed of the concept of shear connection within a member composed of concrete and structural steel, nor of the use of profiled steel sheeting in composite slabs. Shear connection is covered in depth in Chapter 2 and Appendix A, and the principal types of composite member in Chapters 3, 4 and 5.

Limit state design philosophy has been used in British codes for structural design for over 40 years. Some familiarity is assumed with ultimate limit states (ULS) and serviceability limit states (SLS), which are the main subject here. The accidental limit state of exposure to fire, important in buildings, is the subject of Chapter 6.

All material of a fundamental nature that is applicable to structures for both buildings and bridges is included, plus more detailed information and a fully worked example relating to buildings. Subjects mainly applicable to bridges, such as box girders and design for fatigue, are not included. The design methods are illustrated by calculations. For this purpose a single structure, or variants of it, has been used throughout the volume. The reader will find that its dimensions, its loadings, and the properties of its materials soon remain in the memory. Its foundations are not included. The design is not optimal, because one object here has been to encounter a wide range of design problems, whereas in practice one seeks to avoid them.

This volume is intended for undergraduate and graduate students, for university teachers, and for engineers in professional practice who seek familiarity with composite structures. Most readers will seek to develop the skills needed both to design new structures and to predict the behaviour of existing ones. This is now always done using guidance from a code of practice. The Eurocodes replaced the former British codes in 2010. Their use is required for building and bridge structures that are publicly funded. Use of the former codes continues for some smaller projects, for private clients, but their methods are increasingly out‐of‐date.

All the design methods explained and used in this volume are those of the current Eurocodes, except where expected revisions are used. In the worked examples, both tensile and compressive forces and strengths of materials are given as positive numbers, distinguished in symbols by subscripts ‘t’ or ‘c’ or by words such as ‘tensile’. A rigorous tension‐positive convention has been used only in Appendix A. Elsewhere, the presentation is in the style normally used for hand calculations in practice.

The British versions of the Eurocodes are numbered BS EN 1990 to 1999, subdivided into 58 Parts. The national versions of the Eurocodes were published by each national standards organization in its chosen language, between 2002 and 2010. Those most relevant to this book are in the list of References, beginning ‘BSI’. Similarly, the German standards organization (for example) has published DIN EN 1990, and so forth. Each code or part includes a National Annex, for use for design of structures to be built in the country concerned. Apart from these annexes and the language used, the codes are identical and are applicable in all countries that are members of the European Committee for Standardization, CEN.

The withdrawal of the UK from the European Union is not expected to alter the link between the British Standards Institution and CEN, or the status of the Eurocodes in the UK. CEN already includes non‐EU countries, such as Switzerland and Norway.

The Eurocode for composite structures, EN 1994, is based on recent research and current practice. It has much in common with the earlier national codes in Western Europe, but its scope is far wider. Two of its three Parts are used here, with the shortened names: EC4‐1‐1, General rules and rules for buildings, and EC4‐1‐2, Structural fire design. The third Part, EC4‐2, is for bridges. Eurocode 4 has many cross‐references to other Eurocodes, particularly:

EN 1990, Basis of Structural Design;
EN 1991, Actions on Structures;
EN 1992, Design of Concrete Structures; and
EN 1993, Design of Steel Structures.

The Eurocodes refer to other European (EN) and International (ISO) standards, for subjects such as products made from steel, and execution. ‘Execution’ is an example of a word used in Eurocodes with a particular meaning that has replaced the word previously used: construction (BSI, 2011). Other examples will be explained as they occur.

The cost of purchasing Eurocodes is quite high. Employers provide them for their staff, and students have access via university libraries. Designers' guides or handbooks to the Eurocodes have been published in the UK by the Institution of Civil Engineers (e.g. Beeby and Narayanan, 2005; Gardner and Nethercot, 2004; Johnson, 2012), the Institution of Structural Engineers, and by associations such as the Steel Construction Institute and the Concrete Society. They start from a higher level of prior knowledge than is assumed here.

The purpose of this book is to present, explain and use the theories, structural models and assumptions used in Eurocode 4, and those needed from Eurocodes 1, 2 and 3. There are few cross‐references to Eurocode clauses, and access to them, although helpful, is not assumed.

Readers should not assume that the worked examples are fully in accordance with the Eurocodes as implemented in any particular country. The examples are not comprehensive, and Eurocodes give only ‘recommended’ values for some numerical values, especially the γ and ψ factors. The recommended values, which are used here, were subject to revision in National Annexes, but few of them were changed in the UK.

The first major revision of the Eurocodes began in 2015, with publication expected in the early 2020s. There will be important additions to the scope of Eurocode 4. Examples are: beams with large web openings, slim‐floor construction, use of precast floor slabs, concrete dowel shear connectors, and partial shear connection for beams supporting composite slabs. These subjects are included here, and their consequences for the design examples are explained.

The principal author of the book is R.P. Johnson, who has for many decades shared the challenge of work on Eurocode 4 with other members of committees of BSI and of CEN. The substantial contributions made by these colleagues and friends to his understanding of the subject are gratefully acknowledged. Chapter 6 is contributed by Yong C. Wang who has greatly benefited from interactions with other members of CEN working groups and the project team who are responsible for revising EN 1994‐1‐2. Both authors are contributing to the revisions of Eurocode 4. These are under discussion at present, and will have to be consistent with the revisions of other Eurocodes. Hence, the references given here to expected changes should be considered as the authors' best understanding of the current state of development of Eurocode 4. Responsibility for what is presented here rests with the writers, who would be glad to be informed of any errors that may be found.

November 2017

Roger P. Johnson and Yong C. Wang

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

$images$

where the subscripts E, d, and R mean ‘effect of action’, ‘design’, and ‘resistance’, respectively. For clarity, multiple subscripts are often separated by commas (M_R,d would be an example); but there are many exceptions, as the examples above show.

For longitudinal shear, the following should be noted:

ν, a shear stress (shear force per unit area), but τ is used for a vertical shear stress;
ν_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

$images$

Here, the partial factor γ_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 (γ) 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 M_y acts about the y axis, and M_z 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

α: angle; ratio; factor; coefficient; reduction factor
β: angle; factor; coefficient
γ: partial factor
Δ: difference in … (precedes main symbol)
δ: steel contribution ratio; deflection; slip capacity
ε: strain; coefficient
η: coefficient; degree of shear connection
θ: angle
κ: curvature
λ: (or if non‐dimensional) slenderness ratio
μ: coefficient of friction; ratio of bending moments; exponent (as superscript)
υ: Poisson's ratio
ρ: reinforcement ratio; density (unit mass)
σ: normal stress
τ: shear stress
φ: diameter of a reinforcing bar; rotation; angle of sidesway
ϕ: creep coefficient
χ: reduction factor (for buckling)
Ψ: 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 h_f); 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
k: characteristic
L: longitudinal (e.g. in v_L, shear flow)
LT: lateral‐torsional
l or ℓ: longitudinal; lightweight‐aggregate
M: material
m: relating to bending moment; mean; mass; measured; number (of columns)
max: maximum
min: minimum
N: (allowing for) axial force
n: number; neutral axis
o: particular value; concrete in tension neglected; overhang
P: profiled steel sheeting
p: profiled steel sheeting; perimeter; plastic
pa, pr: properties of profiled sheeting (Section 3.3.1)
pe: effective, for profiled sheeting
pl: plastic
Q: variable (referring to actions)
R: resistance
r: reduced; rib of profiled sheeting; reinforcement
red: reduced
rms: root mean square
S: reinforcing steel; action effect (from the French, sollicitation)
s: reinforcing steel; shear span; slab; slip at interface; spacing; stiffness
sag: sagging bending
sc: shear connector
T: tensile force; steel T‐section in a connection
t: tension; torsion; time; transverse; top; total
u: ultimate; maximum
V: shear; vertical
Vs: shear (composite slab)
v: vertical; shear; shear connection
w: web; weighted
wp: web post
x: axis along member
y: major axis of cross‐section; yield
z: minor axis of cross‐section
0, 1, 2, etc.: particular values
0: combination value (in Ψ₀); fundamental (in f₀); overall (in γ₀); mean; short‐term (in n₀)
1: frequent value (in Ψ₁); uncracked; end moment for a column length
2: quasi‐permanent value (in Ψ₂); cracked reinforced; end moment for a column length
0.05, 0.95: fractiles

Composite Structures of Steel and Concrete

Beams, Slabs, Columns and Frames for Buildings