_______________________________________________________________________
PROBLEM (9.44) A simple metallic beam having a box cross section of uniform thickness t = 20
mm supports a concentrated load P as shown in Fig. P9.44. Determine the largest permissible value of P,
if the allowable compression stress at point D is not to exceed all
σ
= 250 MPa.
SOLUTION
Reaction at B, as found from equilibrium conditions (see Fig. P9.44):
0.375
B
R
P=
y
At a cross section through the point D:
0.375 0.375 (0.6) 0.225VPMP===P
Also
33
11
(150)(200) (110)(160)
12 12
I=−
64
62.453(10 ) mm=
(150 20)(100 10)QAy== × −
33
270(10 ) mm=
So
6
0.225 (0.08) 288.217
62.453(10 )
xMy P P
I
σ
−
=− =− =−
6
6
0.375 (270 10 ) 40.53
62.453(10 )(2 0.02)
xy VQ P P
Ib
τ
−
−
×
== =
×
Hence
22
1()
22
xx
x
ya
σσ
ll
σ
τσ
=+ +=
622
10 ) 144.108 ( 144.108 ) (40.53 )PPP=− + − +
N
250(
Solving
44.7
all
Pk=
N
.A.
D
z
C
20 mm 100 mm
150 mm
100 mm
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