sm8 18

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PROBLEM (8.18) Two triangular plates are weld together and subjected to biaxial stresses with
x
σ
= -5 MPa and y
σ
= 15 MPa, as depicted in Fig. P8.18. Determine:
(a) The normal stress w
σ
acting perpendicular to the weld.
(b) The shear stress w
τ
acting parallel to the weld.
SOLUTION
We have
θ
x
’
5 MPa
'
x
σ
''
x
y
τ
25o
15 MPa
x
y’
25 90 115o
θ =+=
5
x
M
Pa
σ
=−
15
y
M
Pa
σ
=
0
xy
τ
=
(a) '11
()()cos
22
xxyxy
2
σ
σσ σσ θ =++−
11
( 5 15) ( 5 15)cos230 11.43
22 o
M
Pa=−+ +−− =
Thus,
'11.43
wx
M
Pa
σ
σ ==
(b) '' 1()sin
2
xy x y 2
τ
σσ θ =− −
1( 5 15)sin230 7.66
2o
M
Pa=− − − =−
w
τ
So
'' 7.66
wxy
M
Pa
τ
τ ==−
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