Civil Engineering Reference
In-Depth Information
C
C
B
D
D
B
F
IGURE
18.22
Possible collapse
mechanisms
for the frame
of Ex. 18.10
with sway
A
E
A
E
(a)
(b)
failure mechanisms would have to be investigated; two such mechanisms are shown
in Fig. 18.22. Note that in Fig. 18.22(a) there is a hinge cancellation at C and in
Fig. 18.22(b) there is a hinge cancellation at B. In determining the collapse loads of
such frames the method of instantaneous centres still applies.
PROBLEMS
P.18.1
Determine the plastic moment and shape factor of a beamof solid circular cross
section having a radius
r
and yield stress
σ
Y
.
1
.
33
σ
Y
r
3
,
f
Ans
.
M
P
=
=
1
.
69.
P.18.2
Determine the plastic moment and shape factor for a thin-walled box girder
whose cross section has a breadth
b
, depth
d
and a constant wall thickness
t
. Calculate
f
for
b
=
200mm,
d
=
300mm.
Ans
.
M
P
=
σ
Y
td
(2
b
+
d
)
/
2,
f
=
1
.
17.
P.18.3
A beam having the cross section shown in Fig. P.18.3 is fabricated from mild
steel which has a yield stress of 300N/mm
2
. Determine the plastic moment of the
section and its shape factor.
Ans.
256
.
5kNm,1
.
52.
75 mm
15 mm
15 mm
300 mm
15 mm
250 mm
F
IGURE
P.18.3
P.18.4
A cantilever beam of length 6m has an additional support at a distance of 2m
from its free end as shown in Fig. P.18.4. Determine the minimum value of
W
at which
