Civil Engineering Reference
In-Depth Information
4m
a
u
B
m
m
B
c
u
A
4m
d
A
C
u
C
b
x
F
IGURE
19.5
Slab of
Ex. 19.1
follows. We have seen that, for an isotropic slab, the ultimatemoment along an inclined
yield line is equal to the moment of resistance of the reinforcement irrespective of the
inclination of the reinforcement to the yield line (Eq. (19.3)). Further, the work done
by the ultimate moment on an inclined yield line is the product of the moment, the
projection of the yield line on the axis of rotation and the angle of rotation of the panel
(Eq. (19.4)). The second term on the right-hand side of Eq. (i) represents the work
done by the ultimate moment on the diagonal and horizontal yield lines bordering
each of the panels B and C; from symmetry the contribution of both panels will be the
same. From the above argument and considering panel B
mx
1
2
x
)
1
2
4
m
1
2
VW
(
m
)
B
=
+
m
(4
−
=
Similarly for panel C.
Equation (i) simplifies to
4
m
1
1
VW
(
m
)
=
x
+
(ii)
The work done by the applied load is most easily found by dividing each of the panels
B and C into a rectangle and a triangle, panel A is a triangle. Then
12
1
2
1
1
3
+
1
3
+
1
2
VW
(
w
)
=
2
×
4
x
×
2
x
×
2
×
(4
−
x
)
×
2
×
(iii)
