Beams in Shear - Unified Theory of Concrete Structures - page 359

305 305

R (#4 IN B2)
L(# 2 IN B1 AND #3 IN B4)
U(#5)
X(#3)

R(#4 IN B2)
L(# 3 IN B5)
U (#5)
X(#3)

0.5''0 LRS

S(#6) S(#6)

34.9

35.1

Y(#6)

Y(#6)

152

152

0. 5 ''0 LRS

V(#4) (IN PAIRS)
W(#5)

W(#5)

406 406

(a) Beams B1, B2, and B4 (b) Beams B3 and B5

Figure 8.10 End cross-section of Beams B1-B5 (all dimensions are in mm)

12.7 mm (0.5 in.) diameter, with an ultimate strength of 1862 MPa (270 ksi). The strands
in beams B1, B2 and B4 are straight (Figure 8.10a) and those in beams B3 and B5 are
draped (Figure 8.10b). The total length of each of the beams was 7.62 m (25 ft) while the
center-to-center span length was 7.32 m (24 ft), as shown in Figure 8.11.
The primary purpose of these experiments was to study the effect of three variables on
the ultimate shear strength of prestressed I-Beams, namely, the shear-span-to-depth ratio a/d ,
the transverse steel ratio ρ t , and the presence of draped strands. As such, the positions of the

vertical loads on the beams together with the support positions are shown in Figure 8.11. In
B1, B2 and B3 (Figure 8.11a), the loads from actuators B and C were applied at 0.914 m
(3 ft) from the supports (both north and south supports) to create an a/d ratio of 1.61. At this
low a/d ratio, the shear capacity is expected to be governed by web-shear failure mode. In B4
and B5 (Figure 8.11b), the loads from actuators B and C were applied at 2.44 m (8 ft) from
the supports to create an a/d ratio of 4.29. At this high a/d ratio, the shear capacity is expected
to be governed by flexural-shear failure mode.
The second variable in the test program was the percentage of shear reinforcement ρ t .B1,

B4 and B5 have a ρ t value of 0.17%, close to the minimum stirrup requirement, while B2 and

B3 have a normal ρ t value of 0.95%.

The third variable was the presence of draped strands. B3, with draped strands, can be
compared with B2, with straight strands, in the case of web-shear failure with 0.95%;

while B5, with draped strands, can be compared with B4, with straight strands. in the case of
flexural-shear failure with

ρ t =

0.17%.
During testing, linear voltage displacement transducers (LVDTs) were used to measure the
displacements within the failure regions of the beam adjacent to the points of load application,
as shown in Figure 8.11. Electrical resistance strain gauges were installed on both legs of the

ρ t =