1. Notations

This section (based on ACI 318-14 provisions) defines notation and terminology used in this design example:

a

=

depth of equivalent rectangular stress block, in.

Ab

=

area of an individual bar or wire, in.2

Ag

=

gross area of concrete section, in.2 For a hollow section, Ag is the area of the concrete only and does not include the area of the void(s)

As

=

area of nonprestressed longitudinal tension reinforcement, in.2

As,min

=

minimum area of flexural reinforcement, in.2

b

=

width of compression face of member, in.

bo

=

perimeter of critical section for two-way shear in slabs and footings, in.

bv

=

width of cross section at contact surface being investigated for horizontal shear, in.

bw

=

web width or diameter of circular section, in.

b1

=

dimension of the critical section bo measured in the direction of the span for which moments are determined, in.

b2

=

dimension of the critical section bo measured in the direction perpendicular to b1, in.

c

=

distance from extreme compression fiber to neutral axis, in.

cc

=

clear cover of reinforcement, in.

c1

=

dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the span for which moments are being determined, in.

c2

=

dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction perpendicular to c1, in.

C

=

cross-sectional constant to define torsional properties of slab and beam

d

=

distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.

db

=

nominal diameter of bar, wire, or prestressing strand, in.

Ec

=

modulus of elasticity of concrete, psi

Ecs

=

modulus of elasticity of slab concrete, psi

Es

=

modulus of elasticity of reinforcement and structural steel, excluding prestressing reinforcement, psi

fc'

=

specified compressive strength of concrete, psi

fr

=

modulus of rupture of concrete, psi

fy

=

specified yield strength for nonprestressed reinforcement, psi

h

=

overall thickness, height, or depth of member, in.

hw

=

height of entire wall from base to top, or clear height of wall segment or wall pier considered, in.

Ib

=

moment of inertia of gross section of beam about centroidal axis, in.4

Icr

=

moment of inertia of cracked section transformed to concrete, in.4

Ie

=

effective moment of inertia for calculation of deflection, in.4

Ig

=

moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement, in.4

Is

=

moment of inertia of gross section of slab about centroidal axis, in.4

Kt

=

torsional stiffness of member; moment per unit rotation

l

=

span length of beam or one-way slab; clear projection of cantilever, in.

ln

=

length of clear span measured face-to-face of supports, in.

l1

=

length of span in direction that moments are being determined, measured center-to-center of supports, in.

l2

=

length of span in direction perpendicular to l1, measured center-to-center of supports, in.

Ma

=

maximum moment in member due to service loads at stage deflection is calculated, in.-lb

Mcr

=

cracking moment, in.-lb

Msc

=

factored slab moment that is resisted by the column at a joint, in.-lb

Mu

=

factored moment at section, in.-lb

Mo

=

total factored static moment, in.-lb

n

=

number of items, such as, bars, wires, monostrand anchorage devices, anchors, or shearhead arms

Pn

=

nominal axial compressive strength of member, lb

Po

=

nominal axial strength at zero eccentricity, lb

Pu

=

factored axial force; to be taken as positive for compression and negative for tension, lb

qDu

=

factored dead load per unit area, lb/ft2

qLu

=

factored live load per unit area, lb/ft2

qu

=

factored load per unit area, lb/ft2

vc

=

stress corresponding to nominal two-way shear strength provided by concrete, psi

vu

=

maximum factored two-way shear stress calculated around the perimeter of a given critical section, psi

Vc

=

nominal shear strength provided by concrete, lb

Vn

=

nominal shear strength, lb

Vs

=

nominal shear strength provided by shear reinforcement, lb

Vu

=

factored shear force at section, lb

wc

=

density, unit weight, of normalweight concrete or equilibrium density of lightweight concrete, lb/ft3

yt

=

distance from centroidal axis of gross section, neglecting reinforcement, to tension face, in.

β

=

ratio of long to short dimensions: clear spans for two-way slabs, sides of column, concentrated load or reaction area; or sides of a footing

βt

=

ratio of torsional stiffness of edge beam section to flexural stiffness of a width of slab equal to span length of beam, center-to-center of supports

β1

=

factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis

γf

=

factor used to determine the fraction of Msc transferred by slab flexure at slab-column connections

γv

=

factor used to determine the fraction of Msc transferred by eccentricity of shear at slab-column connections

εt

=

net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature

λ

=

modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compressive strength

λΔ

=

multiplier used for additional deflection due to long-term effects

ξ

=

time-dependent factor for sustained load

ρ'

=

ratio of As' to bd

ϕ

=

strength reduction factor