To investigate further, the drift rate was further increased to
4dr,b. Fig. 8 summarizes the results of the analysis for this case.
The very first crack was essentially flexural in nature, but appeared
at a distance of 2–2.5 times the beam depth from loading point
(Fig. 8a). However, as can be seen from Fig. 8a, soon the cover concrete
in the tension zone starts to spall off, at a distance of about
1.5 times the depth of the beam. This has been observed in the
tests on beams under high loading rates [20] as well as in the analysis
[1] that the cover concrete in the tension zone spalls off due to
the difference in the stiffness of concrete and reinforcement. The
contours of compressive stresses in the beam displayed similar
patterns as shown in Fig. 7b. On further loading, the cover concrete
gradually peels off. It may be noted that since the peeling is on tension
face, it does not induce failure but it leads to numerical instability
in the analysis. The final crack pattern marked by several
flexural shear cracks along with cover peeling is shown in
Fig. 8b. It is worth noting that in this case, the zone of the beam
from the support to mid half of beam suffers only nominal damage
and most of the damage is restricted to the right half of the beam.
The plot of principal compressive stresses at final stage was again
similar to that shown in Fig. 7d. The peak resistance was obtained
as 542.32 kN for the beam against the drift rate of 4dr,b.
The next analysis was performed on the beam under 6dr,b. In
this case, the very first crack, which was of flexure–shear nature,
appeared at a distance of approx. equal to beam depth (Fig. 9a)
soon followed by peeling of concrete cover very close to the
loading point and a shear crack appearing at the point of initiation
of cover peeling. From the contours of compressive stresses in the
beam (Fig. 9b), it can be seen that a compressive strut generates
from the loading point at an angle of approximately 45. The
principal compressive stresses then travel along the length of the
beam toward the support. On further increasing the displacement
at the same rate, large amount of damage is observed in the beam
but only in almost the right one third length of the beam from the
loading point (Fig. 9c).
It is very interesting to observe the contours of principal compressive
stresses in this case (Fig. 9d). It can be seen that beyond
the point where the compressive strut reaches the bottom face of
the beam, the compressive stresses relax in the beam till its mid
span. This is due to the fact that in the right half of the beam,
the concrete gets crushed and is in the softening (post-peak) zone
of the stress–strain curve. It has been demonstrated numerically
[2–4] as well as experimentally [4,21] that due to high loading rate
the fracture mode of concrete shifts from mode-I to mixed mode.
This is the reason for the gradual shift of failure mode from essentially
flexure to predominantly shear due to the increased loading
rate. The peak load of 685.72 kN obtained in this case also demonstrates
the significant influence of the loading rate on the behavior
of this beam.