Lightweight Concrete for High Strength - Expanded Shale & Clay

The value b’ was taken as the minimum web thickness of the girder which was 6 inches for an
AASHTO Type II. The code specifies that d, the distance from the topmost compression fiber to
the centroid of the prestressing strands need not be less than 0.8*h where h is the total depth of
the composite girder. The value of d normally exceeded the minimum 0.8*h. V i and M max were
the maximum moment and shear at the section in question. The lightweight concrete factor, λ,
having a value of 0.85 was included in the equation based on the use of HSLC. The concrete
strength f c ’ was listed in psi. Calculation of the cracking moment was accomplished with
AASHTO equation (5.3):
M
cr
'
I fc
= (6λ
+ f
Y 1000
where f pe is the compressive stress at the extreme tensile fiber due to effective prestressing force
and f d if the tensile stress at the extreme tensile fiber due to the dead load of the girder and slab.
t
pe
−
f
d
)
(5.3)
The composite section properties were used in calculating M cr . The concrete strength, f c ’, was
based on cylinder tests at the time of girder testing.
The web shear strength was calculated using AASHTO (1996) equation (5.4):
'
fc
V
cw
= (3.5λ
+ 0.3 f
pc)
b'
d + V
1000
where f pc is the average compressive stress in the concrete due to effective prestressing force and
V p is the vertical component of the effective prestressing force.
p
(5.4)
ACI 11.4.2.2 provides an alternate technique for calculating V cw that was investigated in
this evaluation. The ACI Code states that V cw shall be computed as the shear force
corresponding to dead load plus live load that results in a principal tension stress of 4λ(f c ’) 1/2 at
the centroidal axis of the member. In composite members, the principal tensile stress is
computed using the cross section that resists live load. Lin and Burns (1981) addressed this
alternate technique and provided the following equations which come directly from the
application of Mohr’s circle:
5-20