sm7 125

________________________________________________________________________
PROBLEM (*7.125) A beam that has singly symmetric section, carries a moment M in a plane
forming an angle
α
with the horizontal axis (Fig. P7.125). Calculate:
(a) The stress at point A.
(b) The stress at point B.
Given: M = 2 kN⋅m,
α
= 25o
*SOLUTION
3
1()( )
12
z
I
bh=
32
3
1()( ) ()
12 2
1()( )
3
yb
Ihbbh
hb
=+
=
y
z
b
1
h2
A
h1
B
b2
C
z
Mz
My
(50 200)(25) (100 50)(100) 50
(50 200) (100 50)
Az
zm
A
×+×
== =
×+×
∑
∑m
33
11
(50)(200) (100)(50) 34.375(10 )
12 12
z64
I
m
−
=+=
33
11
(200)(50) (50)(100) 25(10 )
33
y64
I
m
−
=+=
25 100
AB
y
mm y mm==−
100 0
AB
zmmz=− =
cos 2cos25o
z
MM α == 1.8126 kN m
=
⋅
sin 2sin25 0.8452
o
y
M
Mk α == = Nm⋅
(a) 66
(1,826)(0.025) (845.2)( 0.1) 4.71
34.375(10 ) 25(10 )
yA
zA
Azy
Mz
My
M
Pa
II
σ
−−
−
=− + =− + =−
(b) 66
(1,826)( 0.1) (845.2)(0) 5.31
34.375(10 ) 25(10 )
yB
zB
Bzy
Mz
My
M
Pa
II
σ
−−
−
=− + =− + =
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