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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
T. F. SILVA | J. C. DELLA BELLA
Thus, eliminating the reinforcement in the x direction, angle
θ
will
no longer be 45 ° as mentioned, but will be determined by equa-
tion 12.
(12)
θ=arctg
(
--n
x
n
xy
)
Thus, in the x direction, there is no reinforcement. Expression 13
determines the reinforcement in y direction.
(13)
a
sy
= n
sy
f
yd
= n
y
- n
xy
²
n
x
f
yd
To verify the concrete stress, f
cd2
will be used for the same reason
given for case I, as shown by Equation 14:
(14)
-n
x
- n
xy
²
n
x
h ≤f
cd2
=0,6
(
1- f
ck
250
)
.f
cd
3.1.3 Case III – Reinforcement only in the x direction
Case III is similar to case II; the only difference is the reinforcement
direction. Hence, for reinforcement to be necessary only in the x
direction, the following inequations must be satisfied.
(15)
n
sx
=n
x
+|n
xy
|>0
(16)
n
sy
=n
y
+|n
xy
|≤0
Similarly, also in this case, angle
θ
will not be 45 °, but is deter-
mined by equation 17.
(17)
θ=arctg
(
--n
xy
n
y
)
In this case, a
sx
is null and a
sy
is given by equation 18.
(18)
a
sx
= n
sx
f
yd
= n
x
- n
xy
²
n
y
f
yd
The verification of concrete stress is given by expression 19.
When the membrane is completely compressed, case IV is charac-
terized. In this case, reinforcement is not necessary.
This design method does not consider using of compression rein-
forcement in any case.
3.1.1 Case I – Reinforcement in both directions
For reinforcement to be necessary in both directions, the following
conditions must be satisfied.
(5)
n
sx
=n
x
+|n
xy
|>0
(6)
n
sy
=n
y
+|n
xy
|>0
Thus, the reinforcement area is defined by 7 and 8, where f
yd
is the
yield design stress of steel.
(7)
a
sx
= n
sx
f
yd
= n
x
+|n
xy
|
f
yd
(8)
a
sy
= n
sy
f
yd
= n
y
+|n
xy
|
f
yd
For verifying concrete in case I, f
cd2
will be used, as suggested by
CEB [3] for the compressive strength because, in this case, con-
crete is cracked. Thus, the expression is as follows.
(9)
2|n
xy
| h =f
cd2
=0,6
(
1- f
ck
250
)
.f
cd
3.1.2 Case II – Reinforcement only in the y direction
In order to use reinforcement only in the y direction, n
sx
must be nega-
tive while n
sy
must be positive, satisfying the following expressions.
(10)
n
sx
=n
x
+|n
xy
|≤0
(11)
n
sy
=n
y
+|n
xy
|>0