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4.5.2 Design of R.C. Ring
If it is assumed that the compression ring is
supported by vertical walls or columns, the vertical reaction will be
carried by the vertical elements, and the compression ring needs to be
designed for the horizontal reaction of To
over a distance of s’, the spacing of cables around the
circumference. In other words, the compression ring is acted on by inward
forces as in a pipe under suction. These inward forces produce roughly a
uniform axial compressive force in the circular ring. We can find the
magnitude of this compressive force C
by considering the equilibrium of one-half of the compression ring as shown
if Fig. 4.7.
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(4.10)
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Substituting
To for from Eq. (4.7) in Eq.
(4.10), we obtain
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(4.11)
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The R.C. ring beam is designed as per American
Concrete Institute (ACI) specification (ACI, 1996). In the web-based
interactive program the user has the following options for designing the
reinforced concrete ring:
1.
The cross-sectional area is found-by neglecting the area of
reinforcement and providing a nominal reinforcement of about 1 percent of
the concrete cross-sectional area. Thus in this case, the area of
compression ring is given by
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(4.12)
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where  is the
compressive strength of concrete.
2.
In this alternative, the program computes the cross-sectional area
of the compression ring and the amount of reinforcement treating the ring
as a reinforced concrete section. For a given reinforcement, the area of
concrete can be calculated by using the design strength equation for a tied
column (ACI section 10.3.5.2) (ACI, 1996):
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(4.13)
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where
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f =
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strength
reduction factor = 0.7
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Pn(max) =
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maximum nominal load
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Ag =
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gross
cross-sectional area of concrete
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Ast =
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total area of longitudinal reinforcement
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f’c =
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compressive strength of concrete
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fy =
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yield stress of steel reinforcement
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The
program checks for minimum and maximum amount of reinforcement on the ring
as per ACI specification Sec. 10.9.1. The lateral ties are designed as per
ACI specification Sec. 7.10.5 (ACI, 1996).
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