Civil Engineering Reference
In-Depth Information
Figure 2.8
Shear-bending interaction curves
2.2.1.2 Second Failure Mode
In the second failure mode, failure occurs due to yielding of the
top stringer
and the
transverse
steel
. Looking at Figure 2.7(a), the force in the top stringer
N
t
and the force per unit length
in the transverse steel
n
t
are:
M
d
v
V
2
N
t
=−
+
tan
α
r
(2.59)
V
d
v
n
t
=
cot
α
r
(2.60)
Substituting
α
r
from Equation (2.60) into Equation (2.59) to eliminate
α
r
,wehave
V
2
M
N
t
d
v
−
+
d
v
)
n
t
=
1
(2.61)
d
2
v
(2
N
t
/
Assuming that yielding occurs in the top stringer and in the transverse steel, then
N
t
=
N
t
y
and
n
t
=
n
ty
. Substituting the definitions of
M
o
,
V
o
, and
R
from Equations (2.55)-(2.57)
into Equation (2.61), the nondimensional interaction equation for
M
and
V
becomes
V
V
o
2
M
M
o
1
R
+
−
=
1
(2.62)
