sm7 37

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PROBLEM (7.37) A uniformly loaded simply supported rectangular beam has two 15-mm-deep
vertical U-shaped grooves opposite each other on its edges (use Fig. 7.13) at midspan, as shown in
Fig. 7.37. If the normal stress is limited to all
σ
= 127 MPa, calculate the smallest permissible radius
of the grooves.
SOLUTION
w=12 kN/m
2 m
A
B
80 m
m
wL/2 wL/2
2 m
96 m
m
120 mm
C
22
max 11
(10)(4) 20
88
M
wL kN m== = ⋅
36
1(80)(120) 11.52 10
12 4
I
mm==×
33
6
20 10 (45 10 ) 78.13
11.52 10
nom Mc
M
Pa
I
σ
−
−
××
== =
×
127 1.62
78.13
all
nom
K
σ
σ
== =
Use Fig. 7.14. For 120
1.62, 1.33:
90
D
Kd ===
0.18
r
d=
Thus,
min 0.18(90) 16.2rm==m
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