Strut-and-tie modeling - Computational Analysis and Design of Bridge Structures - page 404

where b s is the effectiveness factor. The factors affecting the effective con-
crete strength of struts are (1) load-duration effects, (2) cracking of the
struts, and (3) confinement from the surrounding concrete. For (1) and
(2), there is reduction of strength, but for (3) the strength is increased. For
example, in pile caps, the compressive strength may be increased by the
confinement resulting from the large volume of concrete all around the
struts.

b s = 1.0 for a strut of uniform cross-sectional area over its length

b s = 0.75

for a bottle-shaped strut with reinforcement satisfying
A.3.3; (ACI 318-2002)

b s = 0.6 for a bottle-shaped strut with reinforcement not satisfying

A.3.3; (ACI 318-2002)

b s = 0.4

for a strut in the tension member or the tension flange of
members

b s = 0.6 for all other cases

Note: Crack control reinforcement requirement is

A
b s ∑

si

sin 0 003 . (13.5) (ACI [eq. A-4])

γ ≥

i

is i

where:
A si is the area of surface reinforcement in the i i-th layer crossing the
strut under review
s i is the spacing of reinforcement in the i i-th layer adjacent to the surface
of the member
b s is the width of the strut
g i is the angle between the axis of the strut and the bars

According to AASHTO Load Resistance Factor Design (LRFD) Bridge
Design Specifications (2013) stress limit for struts is

′

f

c

f = ≤ 0 85 . f ′ (13.6) (AASHTO [eq. 5.6.3.3.3-1 ])

cu c

0 8 170 . + ε

1

where

2

(13.7) (AASHTO [eq. 5.6.3.3.3-2 ])

ε = ε + ( ε + 0 002 . )cot θ

1 s s s

where:
θ s is the smallest angle between the strut under review and the adjoin-
ing ties
ε s is the average tensile strain in the tie direction
f c ′ is the specified concrete compressive strength (psi or MPa)