Civil Engineering Reference
In-Depth Information
points. The stress flow is considered to have a rectangular cross-section with
a width equal to the beam width. The depth of the
horizontal
portion of the
stress flow of the path may be assessed such that the compressive force
equals the force sustained by the tensile reinforcement. As indicated in
Figure 2.23,
the inclined stress flow of the path is symmetrical with respect
to the line connecting the intersection of the directions of the applied load
and the horizontal path of the compressive force, with the intersection of the
directions of the reaction and the tensile reinforcement. A suitable depth for
the
inclined
stress flow is considered to be
a/
3, where
a
is the shear span. If
a/
3 is smaller than the effective width of the bearing,
a/
3 should be
substituted with the width of the bearing, as recommended by the Joint
Committee of the Institution of Structural Engineers and the Concrete
Society (1979).
A precise description of the shape of the idealised path of the
compressive force in the region where it changes direction is not deemed
essential. This is because as discussed in Section 2.5.1, the causes of failure
appear to be associated with the stress conditions in regions away from the
location where the path changes direction. Furthermore, implicit is the
assumption that failure in localised regions resulting from anchorage
problems, concentrated loads, and so on are prevented by proper detailing.
2.6.2
Design method
The concepts described in the preceding section indicate that a deep
beam will withstand the action of an applied load if the resulting internal
actions can be safely sustained by the members of the proposed model.
The objective of a design procedure, therefore, should be the sizing of
these members such as to sustain these actions. A typical procedure for
the case of two-point loading (Figure 2.23b) may be formulated as
follows (
Figure 2.24
):
i)
Assuming the beam depth
d
and width
b,
are given, assess the depth
of the horizontal portions of the stress flow by satisfying the
moment equilibrium condition with respect to the intersection of the
directions of the reaction and the tension reinforcement. If that
condition cannot be satisfied with the given values of
d
and
b,
adjust
d
and
b
accordingly.
ii)
Considering that the tension reinforcement yields before the load-
carrying capacity of the horizontal portion of the stress flow is
attained, assess the amount of tension reinforcement required to
satisfy the equilibrium condition of the horizontal internal actions,
iii)
Check whether the vertical component of the compressive force
carried by the inclined portion of the stress flow is greater than, or
equal to, the external load carried by the flow to the support. If not,
adjust the beam width
b
and repeat the process.
