aci 104_71
area
h torsional constant dead load modulus of elasticity; earthquake load
force; load; liquid pressure modulus of shear lateral force; lateral earth pressure moment of inertia
Strains Beam any coefficient with proper dimensions live load ,bending moment normal force (VOID)?prestressing force; axial load
first moment of an area; internal forces; load effects torsional moment; temperature required strength shear force wind load reactions or forces in general, parallel to axis x
reactions or forces in general, parallel to axis y reactions or forces in general, parallel to axis z
Isolated T- beam Lower case Roman letters a =b =d =e =f =g =
h =i =j =
k =1=m =n =0=p =q =r =S =
t =u =v =
w =x =y =z =deflection; distance; d e p t h o f rectangular
stress block
width distance from compression fiber to neutral axis effective depth; diameter (see also h)eccentricity, base of Napierian logarithms
(mathematical usage)unit strength or stress (f C for concrete in com-
pression, f r for concrete in tension, andf s for steel)acceleration due to gravity total depth; thickness; diameter
Column F i g. I -Typical notation for reinforced concrete cross sections Lower case Greek letters Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu Nu Xi Omicron Pi Rho angle; ratio; coefficient angle; ratio; coefficient specific gravity; ratio coefficient; coefficient of variation strain coefficient (VOID)rotation (VOID)(VOID)slenderness ratio; coefficient coefficient of friction Poisson’s ratio coefficient (VOID)reserved for mathematics, 3.14159geometrical ratio of reinforcement any coefficient with proper dimensions
span; length of member or element bending moment per unit length unit normal force; number
(VOID)
(VOID)
radius of gyration
standard deviation; spacing
time; unit torsional moment per unit length
shear; stress
crack width; total load per unit length or area
coordinate coordinate coordinate; reinforcement distribution factor
normal stress (CEB only)shear or transverse stress (CEB only)(VOID)strength reduction factor; creep coeficient
*Italicized words indicate ACI usage.All other definitions are common ACI-CEB-FIP usage.
A blank space indicates an unassigned letter.?Void indicates the letter shall not be used.Upsilon v =Phi . =
tensile rupture s = steel; slab ACI COMMITTEE REPORT
t = transversal; torsion; tension; total; tubing; time
u = unsupported; factored load effect at ultimate V = shear; vertical
W = wind; wire; web; wall
X = axial direction
Y = axial direction; yield
z = axial direction 0, 1,2...=particular values of quantities
I Subscripts formed from abbreviations
bal = balanced
cr =cracked, critical
max = maximum min = minimum
sp vert = spiral =vertical
Subscripts for loads d = dead load 1= live load
eq = earthquake h = earth pressure
te = temperature; creep; shrinkage; prestrain effects wl = wind load
APPENDIX B- NOTATION FOR ACI 318-83
Reproduced below, in separate lists, is the notation selected for “Building Code Requirements for Rein-forced Concrete (ACI 3 18-83)” and for the Com-mentary on the Code. These lists should be useful to committees and other authors in selecting notation for their use. Note that while ACI 3 18-83, and all preced-ing discussion, is independent of any system of units such as metric,English, etc.,many of the symbols
given below contain English units since they appear in empirical equations.
The notation used in the code and commentary follows “ACI Standard for Preparation of Notation for Concrete (ACI 104-71, Revised 1982)” with very few ex-ceptions and also follows the principles adopted by the Comite Euro-International du Beton.
a a a A A A b
A C A C A C A C = depth of equivalent rectangular stress block as defined in Section 10.2.7. Chapters 10 and 12= shear span, distance between concentrated load and face of support. Chapter 11= maximum deflection under test load of member relative to a line joining the ends of the span, or of the free end of a cantilever relative to its sup-port, in. Chapter 20= effective tension area of concrete surrounding the flexural tension reinforcement and having the same centroid as that reinforcement, divided by the number of bars or wires, sq in. When the flexural
reinforcement consists of different bar or wire sizes the numbers of bars or wires shall be computed
as the total area of reinforcement divided by the area of the largest bar or wire used. Chapter 10= area of that part of cross section between flexural tension face and center of gravity of gross sec-tion, sq in. Chapter 18= area of an individual bar, sq in. Chapter 12=area of core of spirally reinforced compression member measured to outside diameter of spiral,sq in. Chapter 10
=area of concrete section resisting shear transfer.Chapter 11= area of contact surface being investigated for horizontal shear, sq in. Chapter 17
= area of concrete at cross section considered, sq in. Chapter 18
A ch = cross-sectional area of a structural member mea-
sured out-to-out of transverse reinforcement, sq
in. Appendix A
A
CP = area of concrete section, resisting shear, of an individual pier or horizontal wall segment, sq in.
Appendix A
A cv = net area of concrete section bounded by web thickness and length of section in the direction of
shear force considered, sq in. Appendix A
= area of reinforcement in bracket or corbel resist-
Chapter 11
A h = gross area of section, sq in. Chapters 9, 10, 11,
14, and Appendixes A and B
= area of shear reinforcement parallel to flexural
tension reinforcement, sq in. Chapter 11
= minimum cross-sectional area within a joint in a
plane parallel to the axis of the reinforcement
generating the shear in the joint. Where a girder frames into to a support of larger width, effective
width of the joint shall be assumed not to exceed
the width plus the overall depth of the joint, sq in.
Appendix A
= area of reinforcement in bracket or corbel resist-ing tensile force N uc , sq in. Chapter 11
=total area of longitudinal reinforcement to resist torsion, sq in. Chapter 11-
A V
c2
d
NOTATION FOR CONCRETE
area of prestressed reinforcement in tension zone,
sq in. Chapters 11 and 18
area of nonprestressed tension reinforcement, sq
in. Chapters 8, 9, 10, 11, 12, and 18
area of compression reinforcement, sq in. Chap-
ters 8, 9, and 18
total cross-sectional area of transverse reinforce-
ment (including cross-ties) within spacing s and
perpendicular to dimension h c Appendix A
total area of longitudinal reinforcement, (bars or
steel shapes), sq in. Chapter 10
area of structural steel shape, pipe, or tubing in
a composite section, sq in. Chapter 10
area of one leg. of a closed stirrup resisting tor-
sion within a distance s, sq in. Chapter 11
area of shear reinforcement within a distance s,
or area of shear reinforcement perpendicular to
flexural tension reinforcement within a distance s
for deep flexural members, sq in. Chapters 11,
12, and Appendix B
total cross-sectional area of shear reinforcement
within spacing s and perpendicular to longitudinal
axis of structural member, sq in. Appendix A
area of shear-friction reinforcement, sq in. Chap-
ter 11
area of shear reinforcement parallel to flexural
tension reinforcement within a distance s2, sq in.
Chapter 11
area of an individual wire to be developed or
spliced, sq in. Chapter 12
loaded area. Chapter 10 and Appendix B
maximum area of the portion of the supporting
surface that is geometrically similar to and con-
centric with the loaded area. Chapter 10 and Ap-
pendix B
width of compression face of member, in. Chap-
ters 8, 9, 10, 11, 18, and Appendix B
effective compressive flange width of a structural
member, in. Appendix A
perimeter of critical section for slabs and footings,
in. Chapter 11 and Appendix B
width of that part of cross section containing the
closed stirrups resisting torsion. Chapter 11
width of cross section at contact surface being
investigated for horizontal shear. Chapter 17
web width, or diameter of circular section, in.
Chapters 11, 12, and Appendix B
distance from extreme compression fiber to neu-
tral axis, in. Chapter 10
size of rectangular or equivalent rectangular col-
umn, capital, or bracket measured in the direction
of the span for which moments are being deter-
mined, in. Chapters 11 and 13
size of rectangular or equivalent rectangular col-
umn, capital, or bracket measured transverse to
the direction of the span for which moments are
being determined, in. Chapters 11 and 13
cross-sectional constant to define torsional prop-
erties. See Eq. (13-7) Chapter 13
a factor relating actual moment diagram to an
equivalent uniform moment diagram. Chapter 10
factor relating shear and torsional stress proper-
ties. Chapter 11
b w d
distance from extreme compression fiber to cen-
troid of tension reinforcement: in. Chapters 7, 8,
d
d
d
d
d’
104-7
IO, 12, 13, and Appendix B
distance from extreme compression fiber to cen-
troid of nonprestressed tension reinforcement, in,
Chapter 18
distance from extreme compression fiber to cen-
troid of longitudinal tension reinforcement, but need
not be less than 0.80h for prestressed members,
in. (For circular sections, d need not be less than
the distance from extreme compression fiber to
centroid of tension reinforcement in opposite half
of member). Chapter 11
distance from extreme compression fiber to cen-
troid of tension reinforcement for entire composite
section, in. Chapter 17
effective depth of section. Appendix A
distance from extreme compression fiber to cen-
troid of compression reinforcement, in. Chapters
9 and 18
nominal diameter of bar, wire, or prestressing
strand, in. Chapters 7 and 12
nominal diameter of bar, in. Chapter 3 and Ap-
pendix A
thickness of concrete cover measured from ex-
treme tension fiber to center of bar or wire lo-
cated closest thereto, in. Chapter 10
diameter of pile at footing base. Chapter 15
distance from extreme compression fiber to cen-
troid of prestressed reinforcement. Chapter 18.
distance from extreme tension fiber to centroid of
tension reinforcement in. Chapter 9
dead loads, or related internal moments and
forces. Chapters 9, 18, and 20
base of Napierian logarithms. Chapter 18
load effects of earthquake, or related internal mo-
ments and forces. Chapter 9 and Appendix A
modulus of elasticity of concrete, psi. See Sec-
tion 8.51. Chapters 8, 9, 10, 19, and Appendix
B
modulus of elasticity of beam concrete. Chapter
13
modulus of elasticity of column concrete. Chapter
13
modulus of elasticity of slab concrete. Chapter 13
flexural stiffness of compression member. See Eq.
(10-10) and (10-11). Chapter 10
modulus of elasticity of reinforcement, psi. See
Section 85.2 or 8.5.3. Chapters 8, 10, and Ap-
pendix B
specified compressive strength of concrete, psi.
Chapters 4, 8, 9, 10, 11, 12, 14, 18, 19, and Ap-
pendixes A and B
required average compressive strength of con-
crete used as the basis for selection of concrete
proportions, psi. Chapter 4
square root of specified compressive strength of
concrete, psi. Chapters 9, 11, 12, 15, 18, 19, and
Appendix B
compressive strength of concrete at time of initial
prestress, psi. Chapter 18
square root of compressive strength of concrete
at time of initial prestress, psi. Chapter 18
average splitting tensile strength of lightweight
aggregate concrete, psi. Chapters 4, 9, 11, 12,
and Appendix B
stress due to unfactored dead load, at extreme
fiber of sectionwhere tensile stress is caused by
externally applied loads, psi. Chapter 11
compressive stress in concrete (after allowance
;
’
ACI COMMITTEE REPORT
f i for all prestress losses) at centroid of cross sec-tion resistin
g externally applied loads or at junc-tion of web and flange when the centroid lies within the flange, psi. (In a composite member, f pc is re-sultant compressive stress at centroid of com-posite section, or at junction of web and flange when the centroid lies within the flange, due to bot
h prestress and moments resisted by precast member acting alone). Chapter 11
average compressive stress in concrete due to effective prestress force only (after allowance for all prestress losses), psi. Chapter 18
compressive stress in concrete due to effective prestress forces only (after allowance for all pres-tress losses) at extreme fiber of section where tensile stress is caused by externally applied loads,psi. Chapter 11
stress in prestressed reinforcement at nominal strength. See text for units. Chapters 12 and 18specified tensile strength of prestressing tendons,psi. Chapters 11 and 18
specified yield strength of prestressing tendons,psi. Chapter 18
modulus of rupture of concrete, psi. Chapters 9and 18
calculated stress in reinforcement at service loads,ksi. Chapter 10
permissible tensile stress in reinforcement, psi.Appendix B
effective stress in prestressed reinforcement (after allowance for all prestress losses). See text for units. ‘Chapters 12 and 18
specified yield strength of nonprestressed rein-forcement, psi. Chapters 3, 7, 8, 9, IO, 11, 12,
18, 19, and Appendixes A and B
specified yield strength of transverse reinforce-ment, psi. Appendix A
loads due to weight and pressures of fluids with well-defined densities and controllable maximum heights, or related internal moments and forces.Chapter 9
overall thickness of member, in. Chapters 9, 10,11, 12, 13, 14, 18, 20, and Appendix A
thickness of shell or folded plate, in. Chapter 19cross-sectional dimension of column core mea-sured center-to-center of confining reinforcement.Appendix A
total depth of shearhead cross section, in. Chap-ter 11
total height of wall from base to top, in. Chapter 11
height of entire wall (diaphragm) or of the seg-ment of wall (diaphragm) considered. Appendix A loads due to weight and pressure of soil, water in soil, or other materials, or related internal mo-ments and forces. Chapter 9
moment of inertia of section resisting externally applied factored loads. Chapter 11
moment of inertia about centroidal axis of gross section of beam as defined in Section 13.2.4.Chapter 13
moment of inertia of gross section of column.Chapter 13
moment of inertia of cracked section transformed to concrete. Chapter 9
effective moment of inertia for computation of de-flection. Chapter 9= moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement. Chap-ters 9 and 10=moment of inertia about centroidal axis of gross section of slab and ?t . Chapter 13= moment of inertia of reinforcement about centroi-dal axis of member cross section. Chapter 10= moment of inertia of structural. steel shape, pipe,or tubing about centroidal axis of composite member cross section. Chapter 10= effective length factor for compression members.Chapter 10= effective length factor. Chapter 14= wobble friction coefficient per foot of prestressing tendon, Chapter 18= flexural stiffness of beam; moment per unit rota-tion. Chapter 13= flexural stiffness of column; moment per unit ro-tation. Chapter 13= flexural stiffness of slab; moment per unit rota-tion. Chapter 13= torsional stiffness of torsional member; moment per unit rotation. Chapter 13= span length of beam or one-way slab, as defined in Section 8.7; clear projection of cantilever, in.Chapter 9= length of span of two-way flat plates in direction parallel to that of the reinforcement being deter-mined, in. See Eq. (18-8). Chapter 18= additional embedment length at support or at point of inflection, in. Chapter 12= vertical distance between supports, in. Chapter 14=development length, in. Chapters 7,12, and Appen-dix A = development length of standard hook in tension,measured from critical section to outside end of hook (straight embedment length between critical section and start of hook [point of tangency] plus radius of bend and one bar diameter), in.= development length for a bar with a standard hook as defined in Eq. (A-5). Appendix A = basic development length of standard hook in tension, in. Chapter 12= clear span for positive moment or shear and av-erage of adjacent clear spans for negative mo-ment. Chapter 8= clear span measured face-to-face of supports,Chapter 11= length of clear span in long direction of two-way construction, measured face-to-face of supports in slabs without beams and face-to-face of beams or other supports in other cases. Chapter 9= length of clear span in direction that moments are being determined, measured face-to-face of sup-ports. Chapter 13= minimum length, measured from joint face along axis of structural member, over which transverse reinforcement must be provided, in. Appendix A = span of member under load test (shorter span of flat slabs and of slabs supported on four sides).Span of member, except as provided in Section 20.4.9, is distance between centers of supports
’
NOTATION FOR CONCRETE104-9 or clear distance between supports plus depth of
member, whichever is smaller, in. Chapter 20
= unsupported length of compression member.
Chapter 10
= length of shearhead arm from centroid of con-
centrated load or reaction, in. Chapter 11
= horizontal length of wall, in. Chapter 11
= length of entire wall (diaphragm) or a segment of
wall (diaphragm) considered in direction of shear
force. Appendix A
= length of prestressing tendon element from jack-
ing end to any point x, ft. See Eq. (18-l) and (18-
2). Chapter 18
= length of span in direction that moments are being
determined, measured center-to-center of sup-
ports. Chapter 13
to-center of supports. See also Sections 13.6.2.3
and 13.6.2.4. Chapter 13
= live loads, or related internal moments and forces.
Chapters 9, 18, and 20
= design moment. Appendix B
= maximum moment in member at stage deflection
is computed. Chapter 9
= factored moment to be used for design of com-
pression member. Chapter 10
= cracking moment. See Section 9.5.2.3. Chapter 9
= moment causing flexural cracking at section due
Chapter 11
= modified moment. Chapter 11
= maximum factored moment at section due to ex-
ternally applied loads. Chapter 11
= total factored static moment. Chapter 13
= nominal moment strength at section, in.-lb Chap-
ter 12
= required plastic moment strength of shearhead
cross section. Chapter 11
= portion of slab moment balanced by support mo-
ment. Appendix A
= factored moment at section. Chapter 11
= moment resistance contributed by shearhead re-
inforcement. Chapter 11
= value of smaller factored end moment on
compression member due to the loads that result
in no appreciable sidesway, calculated by con-
ventional elastic frame analysis, positive if mem-
ber is bent in single curvature, negative if bent in
double curvature. Chapter 10
= value of larger factored end moment on compres-
sion member due to loads that result in no ap-
preciable sidesway, calculated by conventional
elastic frame analysis. Chapter 10
= value of larger factored end moment on compres-
sion member due to loads that result in appre-
ciable sidesway calculated by conventional elas-
tic frame analysis. Chapter 10
= modular ratio of elasticity. Appendix B.
= E s/E c
= design axial load normal to cross section occur-
ring simultaneously with V; to be taken as posi-
tive for compression, negative for tension, and to
include effects of tension due to creep and
shrinkage. Appendix B
= tensile force in concrete due to unfactored dead
load plus live load (D + L). Chapter 18
Pb
P,
P”
r
S
S
S
S
S
S W
52
T
v h
= factored axial load normal to cross section oc-
positive for compression, negative for tension, and
to include effects of tension due to creep and
shrinkage. Chapter 11
= factored tensile force applied at top of bracket or
corbel acting simultaneously with V u,to be taken
as positive for tension. Chapter 11
= nominal axial load strength at balanced strain
conditions. See Section 10.3.2. Chapters 9 and
10
= critical load. See Eq. (1 O-9). Chapter 10
= nominal axial load strength at given eccentricity.
Chapters 9 and 10
=nominal axial load strength at zero eccentricity.
Chapter 10
= prestressing tendon force at jacking end. Chapter
18
Chapters 9 and 10
= nominal axial load strength of wall designed by
Section 14.4. Chapter 14
= prestressing tendon force at any point x. Chapter
18
= radius of gyration of cross section of a compres-
sion member. Chapter 10
= standard deviation, psi. Chapter 4
= spacing of shear or torsion reinforcement in di-
rection parallel to longitudinal reinforcement, in.
Chapter 11
= spacing of stirrups or ties, in. Chapter 12
= spacing of transverse reinforcement measured
along the longitudinal axis of the structural mem-
be r..in.A ppe ndix A
= spacing of shear reinforcement in direction par-
allel to longitudinal reinforcement, in. Appendix B
= maximum spacing of transverse reinforcement, in.
Appendix A
=spacing of wire to be developed or spliced, in.
Chapter 12
= spacing of vertical reinforcement in wall, in.
Chapter 11
= spacing of shear or torsion reinforcement in di-
rection perpendicular to longitudinal reinforce-
ment-or spacing of horizontal reinforcement in
wall, in. Chapter 11
= cumulative effects of temperature, creep, shrink-
age, and differential settlement. Chapter 9
= nominal torsional moment strength provided by
concrete. Chapter 11
= nominal torsional moment strength. Chapter 11
= nominal torsional moment strength provided by
torsion reinforcement. See Section 11.6.8.3.
Chapter 11
= factored torsional moment at section. Chapter 11
= required strength to resist factored loads or re-
lated internal moments and forces. Chapter 9
= design shear stress. Appendix B
= permissible shear stress carried by concrete, psi.
Chapter 11 and Appendix B
= permissible horizontal shear stress, psi. Appen-
dix B
= design shear force at section. Appendix B
=; nominal shear strength provided by concrete.
Chapters 8, 11, and Appendix A
= nominal shear strength provided by concrete when
diagonal cracking results from combined shear and
P ’P ’P&7NOTATION FOR Section 9.5.2.5. Chapter 9
ratio of nonprestressed tension reinforcement.Chapters 8, 10, 11, 18, and Appendixes A and B A
s /bd.
ratio of nonprestressed compression reinforce-ment. Chapter 8
A's /bd.
reinforcement ratio for nonprestressed compres-sion reinforcement, A's /bd. Chapter 9
ratio of compression reinforcement. Chapter 18A'
s / bd.
reinforcement ratio producing balanced strain conditions. See Section 10.3.2. Chapters 8 and 10ratio of total reinforcement area to cross-sectional area of column. Appendix A
ratio of horizontal shear reinforcement area to gross concrete area of vertical section. Chap-ter 11
ratio of vertical shear reinforcement area to gross concrete area of horizontal section. Chapter 11ratio of distributed shear reinforcement on a plane perpendicular to plane of A,. Appendix A ratio of prestressed reinforcement. Chapter 18A p s /bd.ratio of volume of spiral reinforcement to total vol-CONCRETE P s xx2y 104-11
ume of core (out-to-out spirals) of a spirally rein-forced compression member. Chapter 10ratio of volume of spiral reinforcement to the core volume confined by the spiral reinforcement (measured out-to-out). Appendix A A sv /A cv ; where A sv is the projection on A, of area of distributed shear reinforcement crossing the plane of A,,. Appendix A A s /b w d. Chapter 11strength reduction factor. See Section 9.3. Chap-ters 8, 9, 10, 11, 14, 15, 17, 18, 19, and Appen-dix A strength reduction factor. See Section B.2.1. Ap-pendix B reinforcement indices for flanged sections com-the web width, and reinforcement area shall be that required to develop compressive strength of web only. Chapter 18torsional section properties. See Section 11.6.1.1and 11.6.1.2. Chapter 11