Structural Concrete - Hassoun

302 Chapter 8 Design of Deep Beams by the Strut-and-Tie Method
x
l a sin θ s
d ba θs
≤ 6d ba ≤ 6d ba
6d ba
s
6d ba
d ba
x
l a
(a)
x . x
l b sin θ s + h a cos θ s
6d b
h a
l b
0.5h a
θ s
l b
h s
θ s
l b sin θ s + h s cos θ s
(b)
(c)
Figure 8.9 Influence of anchorage condition on effective cross-sectional area of strut:
(a) Strut anchored by reinforcement, (b) strut anchored by bearing and reinforcement,
and (c) strut anchored by bearing and strut. Source: AASHTO LRFD Bridge Design Specification,
2014. Used by permission.
where A cs = effective cross-sectional area of strut determined from concrete area and anchorage
conditions A ss = area of reinforcement in strut
f ce =
f ′ c
0.8 + 170ε 1
≤ 0.85f ′ c (8.16)
ε 1 = ε s +(ε s + 0.002)cot 2 α s (8.17)
where
α s = smallest angle between compressive strut and adjoining tension ties
ε s = tensile strain in concrete in direction of tension tie (in./in.)
f c ′ = specified compressive strength
2. Ties. For nominal resistance of ties the AASHTO equation is
F nt = A st f y + A ps (f se + f y ) (8.18)