Axial Force Problem Solution: Strain Analysis

_______________________________________________________________________
PROBLEM (8.125) A metallic plate of width a and thickness t is subjected to a uniform axial
force P (Fig. P8.125). Two strain gages placed at point A measures the strains
φ
ε
and
at 30o and 60o, respectively, to the axis of the plate. Determine:
(a) The normal strains
x
ε
and y
ε
(b) The normal strains '
x
ε
and 'y
ε
.
(c) The shear strain ''
x
y
γ
.
Assumption: For axial loading, take
x
y
γ
= 0.
Given: a = 50 mm, t = 5 mm, E = 210 GPa,
ν
= 0.3, P = 20 kN
SOLUTION
(a) 3
20(10 ) 80
(0.05 0.005)
xP
M
Pa
A
σ == =
×
6
9
80(10 ) 381
210(10 )
x
xE
σ
ε
μ == =
6
(0.3)(381 10 ) 114.3
yx
ε
νε μ
−
=− =− × =−
(b) '11
()()cos
22
xxyxy
2
ε
εε εε θ =++−
For
θ =−
30 :
o
'11
(381 114.3) (381 114.3)cos( 60 ) 257
22 o
x
ε
μ =−++ −=
'11
(381 114.3) (381 114.3)cos( 60 ) 9.5
22 o
y
ε
μ =−−+ −=
(c) For
θ 30 :
o
=− 2
'' ()sin xy x y
γ
εε =− − θ
(381 114.3)sin( 60 ) 429
o
μ
=− + − =
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