sm7 106

________________________________________________________________________
PROBLEM (7.106) A cantilever beam is loaded as shown in Fig. P7.105. Determine:
(a) The maximum normal stress.
(b) The orientation of the neutral axis.
Given: L = 2 m, h = 2b = 100 mm, α = 20°, P = 500 N
SOLUTION
364
50(100) 4.17 10
12
z
I
mm==×
N
.A.
y
z
100 mm
50 mm
φ
B
C
A
364
100(50) 1.04 10
12
y
I
mm==×
α
α
sincos PLMPLM yz
−
=
−=
(a) Maximum stress occurs at A (or B):
66
cos (50) sin (25)
4.17(10 ) 1.04(10 )
yA
zA
Azy
Mz
M y PL PL
II
αα
σ
−−
=− + = +
6
500 2 cos20 (0.05) sin20 (0.025)
[]
10 4.17 1.04
oo
−
×
=+ MPa5.19
=
(b) 4.17
tan tan tan20
1.04 o
z
y
I
I
φα ==
or
o
6.55= φ
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