1. Notations

This section (based on ACI 318-19 provisions) defines notation and terminology used in this design example:

a

=

depth of equivalent rectangular stress block, in.

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

c

=

distance from extreme compression fiber to neutral axis, in.

d

=

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

Ec

=

modulus of elasticity of 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.

Icr

=

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

Ig

=

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

lc

=

length of compression member, measured center-to-center of the joints, in.

lw

=

length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in.

Mcr

=

cracking moment, in.-lb

Mn

=

nominal flexural strength at section, in.-lb

Mu

=

factored moment at section, in.-lb

Mua

=

moment at midheight of wall due to factored lateral and eccentric vertical loads, not including PΔ effects, in.-lb

Pn

=

nominal axial compressive strength of member, lb

Pum

=

factored applied gravity load + half the factored self-weight of the wall

PΔ

=

secondary moment due to lateral deflection, in.-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.

β1

=

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

Δu

=

calculated out-of-plane deflection at midheight of wall due to factored loads, in.

εt

=

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

εty

=

value of net tensile strain in the extreme layer of longitudinal tension reinforcement used to define a compression-controlled section

λ

=

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

ϕ

=

strength reduction factor