sm7 58

________________________________________________________________________
PROBLEM (7.58) A built-up beam, fabricated by gluing four planks as shown in Fig. P7.58, carries
a vertical shear force V = 45 kN. Determine:
(a) The maximum shearing stress in the beam.
(b) The shear stress at joint E.
(c) The shearing stress at joint F.
SOLUTION
F
F
E
E
E
y
z
40 mm
40 mm
240 mm
C
F
y
y
z
z
4644
12
11092.221)160240( mmI ×=−=
(a)
33
max 101216408016060120240 mmQ ×=××−××=
36
max max
max 63
45 10 (1216 10 ) 3.1
221.92 10 (2 40 10 )
VQ
M
Pa
Ib
τ
−
−−
××
== =
×××
(b) Due to symmetry, E
τ
must be the same at both section shown (Fig. b).
33
1096010040240 mmQE×=××=
36
63
45 10 (960 10 ) 2.4
221.92 10 (2 40 10 )
E
EVQ
M
Pa
Ib
τ
−
−−
××
== =
×××
(c) Note that due to symmetry, F
τ
is the same at both sections shown
in Fig. c. 33
1064010040160 mmQF×=××=
36
63
45 10 (640 10 ) 1.6
221.92 10 (2 40 10 )
F
FVQ
M
Pa
Ib
τ
−
−−
××
== =
×××
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