Design handbook for reinforced concrete elements

446 Pages·2003·9.545 MB·English

by  Beletich, Argeo Sergio, Uno, Paul John

Design Handbook for
REINFORCED
CONCRETE
ELEMENTS
A.S. BELETICH & P.J. UNO
UNSW
PRESS
A UNSW Press book
Published by
University of New South Wales Press Ltd
University of New South Wales
UNSW Sydney NSW 2052
AUSTRALIA
www.unswpress.com.au
© Argeo Beletich and Paul Uno
First published in 1992
First reprint 1996
Second reprint 1998 (with amendments)
Second edition 2003
This book is copyright. Apart from any fair dealing for the purpose of private study, research,
criticism or review, as permitted under the Copyright Act, no part may be reproduced by any
process without written permission. Inquiries should be addressed to the publisher.
National Library of Australia
Cataloguing-in-Publication entry:
Beletich, A. S. (Argeo Sergio), 1940- .
Design handbook for reinforced concrete elements.
New ed.
Includes index.
ISBN 0 86840 621 X.
1. Reinforced concrete construction - Handbooks, manuals,
etc. 2. Structural design - Handbooks, manuals, etc.
I. Uno, Paul John. II. Title.
624.18341
Disclaimer
Design in reinforced concrete is an ever-changing process based on new developments in
materials and research. The authors and publisher of this book have checked sources believed
to be reliable in their efforts to provide information that is completely in accordance with
standards accepted at the time of publication. In view of the possibility of human error or
changes in design processes and codes of practice, however, neither the authors nor the
publisher warrant that the information contained herein is in every respect accurate or
complete and they disclaim all responsibility for any errors or omissions or the results
obtained from the use of information and design aids contained in this book.
SSyymmbboollss
a = Concrete cover or half the distance between parallel bars.
or
Distance between points of zero bending moment.
or
The cover over a deformed bar or half the distance between parallel bars
whichever is the lesser.
or
Dimension of the critical shear perimeter measured parallel to the
direction of M* .
v
or
Footing outstand.
A = Cross-sectional area of uncracked concrete in the tensile zone
ct
A = Area of tensile reinforcement.
st
A = Cross-sectional area of reinforcing bar.
b
A = Reaction area for punching shear.
FN
A = The gross cross-sectional area of a member.
g
A = Area of thin walled section for torsion defined by the median lines of
m
the walls of a single cell.
a = Length of support in direction on span.
s
A = The cross-sectional area of the reinforcement A + A
s sc st.
A = Tensile area of primary beam. This is usually the area of a singly
s1
reinforced beam with the maximum steel ratio p for which k = 0.4.
max u
A = Tensile area of secondary beam.
s2
A = Area of compressive reinforcement.
sc
= Area of reinforcement on the compression side of a column.
A = Area of tensile reinforcement.
st
= A + A for doubly reinforced beams.
s1 s2
xii DESIGN HANDBOOK FOR REINFORCED CONCRETE ELEMENTS
A = Minimum area of reinforcement.
st.min
A = Cross-sectional area of shear reinforcement.
sv
A = Minimum area of shear reinforcement.
sv.min
A = Area of a single leg of a closed tie used as torsional reinforcement.
sw
A = Torsion area defined as the area from the centre of the corner bars of
t
the cross section.
a = Distance from section at which shear is being considered to the
v
nearest support.
b = Width of beam.
b = Effective flange width b
ef.
b = Column width perpendicular to applied moment.
b = Effective beam width or effective flange width.
eff
b = Minimum beam width for a given exposure classification.
min
b = Critical dimension of an opening adjacent to a slab support.
o
b = Effective width of a web for shear.
v
= b for a rectangular beam.
= b for a T-beam or L-beam.
w
b = Width of a web as in a T-beam.
w
C = Internal compressive force carried by the concrete.
c = Minimum distance from centroid of reinforcement to exposed
min
concrete face required to satisfy exposure conditions.
D = Overall depth of beam.
D = Column depth in direction of applied moment.
d = Effective depth measured to the resultant tensile force.
d = Bar diameter.
b
D = Overall depth of a spandrel beam.
b
D = Smaller column dimension.
c
d = Distance from extreme compression fibre to the centroid of the
o
outermost layer of tensile reinforcement but not less than 0.8D.
d = Depth of rectangular stress block γk d.
s u
D = Overall depth of slab or drop panel as appropriate.
s
SYMBOLS xiii
d = Depth measured to centroid of compressive reinforcement.
sc
e = Load eccentricity measured from plastic centroid.
e' = Load eccentricity measured from tensile reinforcement.
E = Modulus of elasticity of concrete.
c
E = Modulus of elasticity of steel reinforcement.
s
E* = Design load (or W*).
E = Modulus of elasticity for concrete at 28 days.
c
E = The mean value of modulus of elasticity of concrete at nominated age.
cj
√
σ1.5 × 0.043 f
cm
E = Ultimate earthquake action.
u
f = An intermediate concrete stress.
c
f = Max shrinkage-induced stress on uncracked sections at the extreme
cs
fibre where cracking first occurs.
f = Tensile stress in the reinforcement (at the cracked section) due to
scr
‘short term’ serviceability loads under direct loading.
f = As above but using ψ =1.0 (rather than 0.7).
scr.1 s
f' = 28 day characteristic compressive strength of concrete.
c
f' = Characteristic flexural strength of concrete.
cf
f' = Flexural tensile strength of plain concrete.
cf
√
= 0.6 f’c
f = Mean compressive strength of concrete at relevant age.
cm
f = Concrete shear strength.
cv
F = Slab design load.
d
F = Effective design load for serviceability in kN/m or kN/m2.
d.eff
F = Load due to earth pressure in kN.
ep
F = Load due to liquid pressure.
lp
f = Stress in compressive reinforcement.
sc
f = Stress in tensile reinforcement.
st
f = Yield strength of steel reinforcement.
sy
f = Yield strength of fitments.
sy.f
G = Concentrated or total dead load.
xiv DESIGN HANDBOOK FOR REINFORCED CONCRETE ELEMENTS
g = Distributed dead load.
or
Ratio of distance between outer reinforcement to the overall depth
of a column section.
R
G = Dead loads resisting instability.
J = Torsional modulus for the cross section.
t
k = Effective length multiplier.
K = Ratio of areas A /A in design of doubly reinforced beams.
sc s2
k = Coefficient to take account of the stress distribution shape in a section
s
prior to cracking (0.6 for flexure & 0.8 for tension).
k = Second moment of area multiplier.
1
k = Deflection constant for rectangular beams.
2
k = Slab multiplier.
3
k = Deflection constant for slabs.
4
k = Special Slab deflection coefficient read from chart D2.
5
k = The value of k for balanced conditions.
b u
k = Long-term deflection multiplier (to account for shrinkage & creep).
cs
k = Depth of N.A. at working/serviceability load conditions.
d
k = End moment condition parameter.
m
k = Deflection correction for steel ration in beams used with chart D1.
p
k = Ratio of depth of NA to beam effective depth d.
u
k = Ratio at ultimate strength of the depth of the NA from the extreme compressive
uo
fibre to d . Symbols k is applied for k in this text.
o u uo
L = Span of beam between support centrelines.
l = Clear distance between webs of parallel beams.
L = Clear span between inner faces of supports or the clear projection of
n
cantilevers.
l = Short clear slab panel dimension between supports.
x
l = Long clear slab panel dimension between supports.
y
L = Effective length of a column.
e
L = Effective span of beam, lesser of L and (Ln + D) or (Ln + D/2) for cantilevers.
eff
L = Clear span between inside of supporting beams, columns or walls.
n
L = Span length used in the simplified method, L minus 0.7 times the sum
o
of as for each support.
L' = The smaller value of L for adjoining spans.
o o
L = Tensile development length for f < f .
st st sy
SYMBOLS xv
L = Development length for compressive reinforcement at yield condition.
sy.c
L = Tensile development length i.e. minimum length of embedment
sy.t
required to develop yield strength of a reinforcing bar in tension.
L = Width of the design strip.
t
L = The unsupported length of a column, taken as the clear distance
u
between faces of members capable of providing lateral support to the
column.
L = Shorter effective span of slab supported on four sides.
x
L = Short effective span of a slab panel.
x
L = Long effective span of a slab panel.
y
M* = Design moment due to factored loads.
M* = Design bending moment (at the Serviceability limit state).
s
M* = As above but using ψ =1.0 (rather than 0.7).
s.1 s
M* = The unbalanced slab bending moment transferred into the support.
v
M*and = Slab design moments in x and y directions.
x
M*
y
M = Effective moment capacity of primary beam.
1
M = M*–M the effective moment capacity to be carried by secondary beam.
2 1
M = Positive bending moment at midspan.
m
M = Negative moment at exterior support.
NE
M = Negative moment at interior support.
NI
M = Total static moment for the span of the design strip.
o
M = The ultimate strength in bending at a cross-section of an
u
eccentrically loaded compression member.
M = The ultimate strength in bending when k = 0.545.
ub u
M = Reduced ultimate strength in bending for k = 0.4 condition.
ud u
M = Ultimate strength in pure bending.
uo
M = Minimum strength in bending at a critical cross section.
uo min
M = Moment causing initial yield of reinforcement.
y
N* = Design axial load.
NA = Neutral axis.
N = The buckling load in a column.
c
xvi DESIGN HANDBOOK FOR REINFORCED CONCRETE ELEMENTS
N = The ultimate compressive strength combined with moment M .
u u
N = The ultimate compressive strength when k = 0.6.
ub u
N = The ultimate strength of an axially loaded squat columns.
uo
p = Reinforcing steel ratio.
P* = Concentrated design load.
p = Tensile steel ratio in primary beam.
1
p = Compressive steel ratio.
c
= A /bd.
sc
p = Maximum tensile steel ratio for k = 0.4 condition.
max u
p = Total tensile steel ratio.
t
A /bd.
st
p = Shear steel ratio A /(b d ).
v st v o
Q = Concentrated or total live load.
q = Distributed live load.
q = Maximum soil bearing pressure under footing.
1
q = Minimum soil bearing pressure under footing.
2
q = Permissible soil bearing pressure.
a
q = Factored soil bearing capacity.
u
= 1.4q
a
R = Radius of curvature.
r = Radius of gyration.
S = Ultimate action due to combination of various action.
u
T = Internal resultant tensile steel force carried by the reinforcement.
t = Flange thickness.
= Thickness of slab D making up T-beam or L-beam.
s
t = Hypothetical thickness used to calculate creep and shrinkage.
h
= 2Ag/u
e.
T* = Design torsional moment.
T = Ultimate torsional strength of a beam limited by crushing failure.
u.max
T = Ultimate torsional strength of a beam without torsional reinforcement.
uc
T = Ultimate torsional strength of a beam with torsional reinforcement.
us
u = Length of critical shear perimeter for two-way action.
or
Shear perimeter d/2 from face of column.
SYMBOLS xvii
u = Exposed perimeter plus half perimeter of enclosed voids.
e
u = Perimeter of A
t t
V = Simplified ultimate shear capacity of unreinforced beam.
c
v' = Nominal concrete shear stress capacity.
c
V = Ultimate shear strength.
u
V = Ultimate shear strength limited by shear crushing.
u.max
V = Ultimate shear strength of a beam with minimum shear reinforcement.
u.min
V = Ultimate shear strength excluding shear reinforcement.
uc
V = The ultimate shear strength of a slab where M* = 0
uo v
V = Contribution provided by shear reinforcement to the ultimate shear
us
strength of a beam.
w* = Distributed design load.
Ws = Serviceability wind action.
Wu = Ultimate wind action.
w ' = Equivalent design load for shorter slab support.
x
w ' = Equivalent design load for longer slab support.
y
x = Smaller dimension of a cross section (or smaller dimension of a
rectangular component of a cross section).
x , y = The shorter and longer dimensions respectively of the cross section
of the torsion strip or spandrel beam.
y = Larger dimension of a closed rectangular torsion tie.
1
# = AS3600 Concrete Structures Code reference.
β = Shear strength coefficient for comparable increase in shear capacity
1
of shallow beams.
β = Shear strength coefficient for axial load effects.
2
β = Shear strength coefficient to account for increased strength when
3
concentrated loads are applied near supports (short shear span av < 2d ).
o
β = Creep factor for sustained loading.
d
β = The ratio of the longest overall dimension of the effective loaded area,
h
Y, to the overall dimension X, measured perpendicular to Y.
β , β = Bending moment coefficients for two-way slabs supported by rigid
x y
beams and walls.
δ = Deflection obtained from calculations.
xviii DESIGN HANDBOOK FOR REINFORCED CONCRETE ELEMENTS
δ , δ = Moment magnifiers for braced and sway columns.
b s
∆ = Maximum deflection - normally expressed as a fraction eg (D / L).
ε = Concrete compressive strain.
c
= 0.003 at failure.
ε = Design shrinkage strain (from Section 6.1.7.2 - AS3600).
cs
ε = Strain in steel reinforcement.
s
ε = Strain in compressive reinforcement.
sc
ε = Strain in tensile reinforcement.
st
ε = Steel strain at the point of yielding.
y
Φ = Strength reduction factor.
γ = Ratio of depth of simplified rectangular stress block to depth of NA.
κ = Curvature.
l = Design parameter used in conjunction with chart B1.
θ = Angle of rotation.
θ and = Angle between the concrete compression "strut" and the member
t
θ axis in the truss model for torsion or shear respectively.
v
σ = Density of concrete in kg/m3 taken as 2400 kg/m3in this book.
ψ = Live load combination factor for strength.
C
ψ = Long-term live load combination factor for serviceability.
L
ψ = Short-term live load combination factor for serviceability.
S
ρ = density of concrete (taken as 2400 kg/m3 in this book)