Design of square footing for a single column - Reinforced Concrete with FRP Bars: Mechanics and Design - page 367

10.5.4 Design for depth
A first assumption of reinforcement area based on that required for shrink-
age and temperature (ρ f,ts ) is reasonable:
Assuming:

f ffu′ := 0.7⋅70 ksi = 49⋅ksi

E f ′ := 5700 ksi

=

⋅

60ksi
f ⋅

29000ksi
E

ρ= :min 0.0036,0.0018 0.0036

f_ts

fu' f'

Note that ρ f,ts is calculated based on the gross area of the concrete cross
section, whereas ρ f is calculated based on the effective area as determined
by the reinforcement depth. The FRP reinforcement ratio ρ f is selected as
1.5 ρ f,ts :

ρ f := 1.5⋅ρ f_ts = 0.0054

For lightly FRP reinforced sections, shear strength can be the factor that
governs the thickness. The critical sections considered for the shear checks
are indicated in Figure 10.3.
Beam (one-way) action: The column width is

b col := 20 in

As a starting point, an FRP reinforcement depth equal to the column
width is assumed:

d 1 := b col = 20⋅in.

The tributary width at a distance d 1 from the column can be calculated
as follows:

b
2

b
2

col

w: =− −=⋅ d 0in

.

tributary 1

The tributary area is therefore equal to

A tributary := b⋅w tributary = 25⋅ft 2

The ultimate shear force is equal to

V u := max(q u1 ,q u2 ,q u3 )⋅A tributary = 112.4⋅kip