sm9 57

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PROBLEM (9.57) A 50-mm wide by 100-rnm deep bracket is acted upon by a load of P =
20 kN, as shown in Fig. P9.57. Determine the principal stresses and the maximum shearing stress
at point A. Show the results on a properly oriented element.
SOLUTION
23
105)100(50 mmA ×== 36
1(50)(100) 4.17 10
12
I==×
mkNM
⋅
=
+= 2.6)32.0(16)09.0(12
xPMc
AI
σ =− +
33
36
12 10 6.2 10 (0.03)
510 4.1710
−−
−× ×
=+
××
6
( 2.4 44.6)10 42.2
M
Pa=− + =
3
3
3 316 10 4.8
22510
V
M
Pa
A
τ
−
×
=− =− =−
×
So,
22
142.2 42.2
()(4.8)
22
σ =+ +−
21.1 21.64=+ MPa7.42=
MPa54.064.211.21
2−=−=
σ
max 21.6
M
Pa
τ
=
22(4.8)
tan2 ' , ' 6.4
42.2 o
pp
x
τ
θθ
σ
−
== =−
τ
A
x
σ
42.7 MPa
6.4o
A
0.54 MPa
21.6 MPa
12 kN 16 kN
z
100 m
m
50 m
m
M
3
B
12 kN
0.03 m
0.09 m
4
A
16 kN
0.32 m
Figure S9.57
y