Page 34 - ICJ Jan 2023

TECHNICAL PAPER COLLECTOR’S EDITION

of a calibrated finite element method developed by The modulus of rupture for the concrete was
4
the author . With this value for g , equation (6) obtained from tests on 3 in x 3 in (75 mm x 75 mm)
becomes prisms, and 6-in (150-mm) diameter cylinders were
used for the compressive strength tests.

for the specimen shown in Fig (1).

If the failure criterion of equation (2) is adopted,
then the failure moment Mc is given by,

Fig I Specimen geometry
This failure load can also be expressed in terms of
, the nominal tensile stress on the nett section at TABLE I Results of tests on beams
failure thus : Series Modulus Cylinder K d , in d, in σN’
o
of rupture, strength, IC lb/in 2
σy, lb/in 2 fc’, lb/in 2
1 786 3,350 761 2.93 2 820
6 554
10 419
Since the modulus of rupture of an uncracked
section, , is an upper limit to the nominal tensile 2 808 5,130 865 3.59 2 743
stress, the complete failure criterion is given by 6 632
10 476
1 3 567 2,070 538 2.79 2 571
1 . 76 K 2 (8)
N IC d
6 419
10 277
4 566 2,270 487 2.32 2 456
or 6 316
10 298
5 1,030 6,790 976 2.82 2 803
6 700
In the test programme six series of tests were 10 547
conducted on specimens of the geometry given 6 892 4,750 852 2.84 2 868
in Fig 1. For the two small duplicate beams, the 6 618
uncracked depth d was 2 in (50 mm). For the two 10 465
larger beams the uncracked depths were 6 in (150
mm) and 10 in (250 mm) respectively. The width The stress intensity factor at failure K for each
IC
of the beams was kept constant at 3 in (75 mm), series was taken as the average of the results
but all other dimensions were in proportion to obtained from tests on specimens for which the
the depth d. The concrete was fairly conventional values of d were 6 in (150 mm) and 10 in (250
with crushed stone aggregate of -in (12.5-mm) mm), and this quantity is reported in Table 1.
maximum size, and various water-cement ratios.

The Indian Concrete Journal | November 2018 35