sm7 70

________________________________________________________________________
PROBLEM (7.70) A beam of built-up bolted cross section is loaded as shown in Fig. P7.70.
Determine:
(a) The maximum bending stress at section B.
(b) The bolt size to be used with 15-mm spacing along the beam.
Assumptions: The part abcd is a plank and that the allowable shear stress in each bolt is 60 MPa.
SOLUTION
4
0: 3( ) 8(5) (5) 0, 8.8
3
ABB
M
RR=− −+ = =
∑kN
kNRF Ay 2.2:0 ==
∑
2.2
2 kN/m
2
m
A
B
x
V, kN
2.2 kN 2 m
49.17
y
40
z
=
y
90.83
2 m
1
m
C
D
E
100
3 kN
20
-0.8
4
-4.8
20
8.8 kN 100
C
Dimensions are
in millim
ete
r
s
[20 140(70)]2 100 40(120) 90.83
(20 140)2 100 40
y
mm
×+×
==
×+×
32
20(140)
2[ 20 140(20.83) ]
12
I=+×
326
100(40) 100 40(29.17) 15.51 10
12 mm4
× =×++
(a) 2
1(2)(2) 4
2
B
M
kN m==⋅
33
max 6
4 10 (90.83 10 ) 23.42
15.15 10
Mc
M
Pa
I
σ
−
−
××
== =
×
(b)
33
1068.11617.2910040 mmQ ×=××=
36
6
4.8 10 (116.68 10 ) 36.11
15.15 10
VQ
qk
I
−
−
××
== =
×N
NqsF 542)1011.36(015.0 3=×=⋅=
Thus,
6
22
2 542 2 345.05
;6010
4
FAd d
τπ == ×=
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or
mmmd 4.2104.2 3=×= −
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
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