sm8 130

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PROBLEM (8.130) Using a 60° rosette, we find the following strains at a critical point on the
surface of a loaded beam shown in Fig. P8.130:
a
ε
= -200
μ
, b
ε
= -350
μ
, c
ε
= -500
μ
Determine:
(a) The maximum in-plane shear strains and the accompanying normal strains.
(b) The true maximum shear strain. Use
ν
= 0.3.
Sketch the results found in part (a) on a properly oriented distorted element.
SOLUTION
Using Eq. (8.45):
1
200 [2( 850) 200] 500
3
xy
ε
με =− = − + =− μ
2( 350 500) 173
3
xy
γ
μ =−+ =
(a) 22
max 300 173
2 ( ) ( ) 346
22
γ
μ =+=
1
' (200 500) 350
2
ε
μ =− + =−
1
1 300
tan [ ] 30
2173
o
s
θ
−
=−=−
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μ
ε
177173350
2−=+−= ,
μ
ε
523173350
3
−
=
−
−
=
Check:
)60cos(173)60sin()500200(
'' oo yx −+−+−−=
γ
max
346
γ
μ
=
=
30o
350
μ
346
μ
350
μ
x’
x
Thus,
'30
o
s
θ =
(b) 10.3( 700) 300
0.7
z
ε
εμ ==− − =
max ( ) 300 523 823
a
γ
μ =+=