sm7 36

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PROBLEM (7.36) A simple rectangular beam, with two vertical U-shaped 12- mm deep grooves
opposite each other on its edges at C (use Fig. 7.14), is loaded as shown in Fig. 7.36. Determine the
magnitude and location of the maximum bending stress in the beam for two cases:
(a) The grooves have a radius of r = 5 mm.
(b) The grooves have a radius of r = 10 mm.
SOLUTION
0: 5.4 , 0: 12.6
AB yA
M
RkN FR== ==
∑∑
kN
6 kN/m
3 m
A
B
80 m
m
R
A
=12.6 kN
R
B=5.4 kN
2 m
96 m
m
120 mm
C
3
26
1 80(96)
12.6(3) (6)(3) 10.8 , 5.9 10
212
C4
M
kN m I m
−
=− = ⋅ = =×
33
max 6
10.8 10 (48 10 ) 87.9
5.9 10
nom Mc
M
Pa
I
σ
−
−
××
== =
×
(a) 5 120
0.052 1.25
96 96
rD
dd
== = =
(Fig. 7.14)
2.3K=
max 2.3(87.9) 202.2
M
Pa
σ
==
(b) 10 120
0.104 1.25
96 96
rD
dd
== = =
(Fig. 7.14)
1.82K=
Thus
max 1.82(87.9) 160
M
Pa
σ
==
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