sm7 169

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PROBLEM (7.169) Redo Prob. 7.168, if the clamp has a box cross section as shown in Fig. P7.169.
SOLUTION
2
8(6) 4(4) 32 .Ai=−=n
12(11) 2(4)(14) 12(17) 14 .
32
ri
++
=n
=
(as intuitively expected)
12 16 18
10 12 16
32
626
A
RdA dr dr dr
rrr
==
++
∑∫∫ ∫ ∫
r
32 13.7925 .
12 16 18
6ln 2ln 6ln
10 12 16
in
==
++
0.2075 .erR in=−=
(13.25 2.5) 15.75
M
PP=− + =−
A
M
P
P
B
Using Eq.(7.70);
3
() 15.75(13.7925 10)
]; 10(10 ) 1 , 10.74
32 (0.2075)(10)
A
AA
MR r
PP Pk
AAer
σ
⎡⎤
−−
=− = + =
⎢⎥
⎣⎦
ips
3
() 15.75(13.7925 18)
]; 10(10 ) 1 , 19.11
32 (0.2075)(18)
B
BB
MR r
PP Pk
AAer
σ
⎡⎤
−−
=− − = + =
⎢⎥
⎣⎦
ips
ips
So
10.74
all
Pk=
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