E.,.
trd-1Cdo
=--=--0250'
trdo
III. II
If it
is .,
6 1 1 ' in.
'0 in. 6 11 11 ' - 1 L-Lo £=--z;-=-,-o-=
ABC is orig origin inal ally ly in
0.8
111.
m.
hori horizo zont ntal al posi positi tion on
If loads
'
.002 .002 in and CF. I i . .
..I...
6.
0.002
61aJ1 0.2·
0.002
12ta 0.2·
0.02294 in. 0.04389 in.
ver
(£
.4U
(£8,d 1£.)
a",
6, LA
Ls
= 0.002 0,02294
2S0( 10-') .87( .87(
-'
'r
1•
in lin.
in
I'
Ul.
An. An.
An.
nd wire
BD and CE. CE and BD.
Av,rag
Normal Strain
(-l)
1.1429
4000
'0 ' 0. . . .
,o
(-l)
4.2851
3000
2BD and CE. If
4.
.002 rnrn/m
E.... Lao"
0.002(3000)
Z(6.00}
E.... Le
..5
Ans
de er in
,.5(8.00)
6.00 mm
14.0 mm
0.002( 4ooo}
8.00 mm
11.2 mm (controls!)
wire
he maxi um
NormalStrain
ZtJ../) 4CE
mm/mm
an
Emax
Av,rag
An.
Ans
2-6.
AB CA by assuming IJ is smal
at is
2°7
2m
-------~.,J~.
~----'m------~
180-8)
+90°= 180°-
IJ
3s
--2-
/4+
8c
2s 2s
-s;:-If IJ is small then.
(En.)
/5.5-4.5+39-1
,IT'+"381.509
(En.) ""0'
1.5(2°)C;0) 52.4(
10-')
Ans
0.05235988 /m /m
ns
eter in
th normal strain
sp ti eveloped in each
A. If the mm, ir
ry =Ln
ISO"
=.t3'+4O()l-2(3)(400)cos
A.,rag~ Normal Strain LA•C -LAC
(EAe)",
402.601-400 400 6.50(
10-')
mm/mm
Ans
"2-8 bars ar se tosup or load he loaded has AB is AC coordinate 0, 0) A. the tr in in AB becomes "Aa normal strain in AC becomes £A 0.035in.iin. Determine itio th to tb Av"ag
Normal Strain
L~.
LA.
L~c
LA
EA
(0.02)(5
AS
8+ (0.035)(8
+£AcLAC
5.10 in. 8.28 in.
eo etry 6.7268 in.
18'-~.330!2 S.IO' 33.317° x'
8.28 co 33.317
6.9191 in.
.1
8.28 si 33.317°
4.5480 in.
.r
-(x' -0
-(6.9191
.7 68
Ans
-(y' -4.3301)
-(4.5480-4.3301)
-0.218
in.
Ans
.x'
2-9. Two AB is unloaded, at ha coordinate at A, (0.25 in., -0.73 bar.
a=./
AC is 0, 0) If
6.7268 in.
.8'-4.3301'
L...
'/ 2.5...0.25 '+ 4.3301
0.73
5.7591 in
La 8.2191 in.
lS
ve
L...
£"'8==--=-
=0
Ans
L"e-L,e
£ H= -
L,
82191-8
=0
An.
is originally
AB
Geometry:
Th vertical displacement is negligible
x.
1800
x8
180' 4+X8
-x,
4.1047
A8 =/3'+4'=5.00m
l:x,I,
A'B' -A
£'
=--;:e5.08 16-
16.8(
10-')
m/m
Ans
'"
~.jXA
kz, where
t..L
IS
when It IS
d;
£,
-'-
j"Loz=kJ'zdz kL
6L
length L, amounts t..L, and AL th diag na AB
If
-Iq
LA
Also
(L
LA.'
jq
L, +6 £"8
=-c;--
£y)L,
6q
( LA O + 6L A O) '
L~
"8
AB +6 A.
(I+E,)'L;.cos'9 =L co
s rr v
g he r o rd e
+(I+£,)'L;05m'9 +2£,cos
+sin'2
-I
he
e, )LAOsin9
Thus.
6q
N eg le c n g
(I
ms
LA
£;COS'
+2£ysin
+E.;sin e)
s tr a
tJ.LA•
1+2£,cos'9
2£,sin'9
2L,6L,
eA
LA
Us
binorrual t h e o r e m .
LA
U s n g h e binomial theorem,
6LAS
co
e,
(2L,6L, LA
However.
LA
sin
Ans
EAB
AL,., L,
S l l
Ans
shown by xy
eo etry
tan-I.!...
8'
0.0200 ca
150
+0.02(0) Shea
ca
Strain
3m",
~--*=,.,.-.__-v.l_
0.0200 Ans
0.0200rad
Yr'y'
x'
fr
1197 ()'=tan=5 .71360 150
throug
in
poin B.
()"=tan- 2OO= .1 01 IS
.5 he
trai
tr
Ans
l'x,
x ' E'y'.
x" x'
in.
r'
+4
5.6569 in.
10-')
in.lin.
ns
=-1.2
E,'
= -
ns
5.6604- 5.6569 5.6569
0.627( 10-') in. lin.
Ans
is
de or ti ho he he ne strains"'lxy and "'Ixy' develope at poin A.
he
h.ar Strain an
of
me
an
d oe s
ot di or
(r
l"
Ans
0.787272 ra
(r.),.,.
2-26
2(0.787272)
10-')
rad
"'Ixy
Geometry:
Fo
mal an
An.
at corner
and
s.
'I
/3 Shea
40
Strain
Ans
r.
-(
'If) An.
if the
-originally "Y..,.
rectangular.
at corner
by
Geometry:
Fo
'I'
ma
an
403
Ii
ra
302
hear Strain
lYe)"
=-la
+{J)
io') rad (YD).,
An.
'"
Ii
10-') rad
th
AC and
diagonal
An.
B.
't DB
AC
DB'
/405'
304'
'r--z~'"
506.4 nu
mm
A'C
. 1 : 3 ffm'" _1_"
..e,"m~
2m
500.8-500 500
A'C'-AC
Ac=Ac-
mm/rnrn
0.0016
DB
1.60(
to-')
mm/mm
An.
4<10"',..,
----va,,0.0128
mm/mm
An.
mm/mm
y,y at A.
r-----------. SI
(rA)
Ir
.,
(89.70) ISO'
Ir
5.24( 1 0 " 3 ) rad
An.
'3",,,,
dashed parallelogra at rs al
eter in th averag ia ls AC and
normal strain
AC =BO={IS'+15'=21.2132mm
15.24) co
2(15.IS)
90.3°
t~_~~·~:_:_;CI
21.566S mm B'D'
/15.18'
15.24'
2(1S.18)
IS.24) co
S9.7°
-:~I
=21.453Smm
'" t>-:'f}'3,7"
21.5665-21.2132 £AC
10-') B'O'-BO
mm/mm
Ans
21.453S-21.2132
£SD
0.0113
mm/m
itio
I 13 (
et
in
ar
rain
rxy
at
Dii;C-6i7~
Ans
~89.7·
.1_-x.
the each diagonal AB and CD. Side
remain
horizontal.
D'
53mm
~50mm
AB
70.7107 mm
CD'
/53 58 2(53)(58)co 79.5860mm
48.3874 mm
8'D'
AB'
No
91.5
./53 +48.3874 70.8243 mm
2(53)(48.3874)cos 88.S·
al
AB'-AB e'<.=-;tB
(-3)
mm/mm
Ans
C'D'-CD
eCD=~
79.5860-70.7107 70.7107
(-3)
mm/mm
An
remain
corners, A,
horizontal
eo et
2+
B'C
)2
54.1117 mm
58 2(53)(58)cos 91.5 .; 53 79.5860mm
CD'
°-
B'D' (B'D')'
cos fi
(B'C)'
48.3874 mm -(CD')
(B'D') (B'C
48.3874 54.1117' 79.586 2(48.3874)(54.1117)
-0.20328
101.73°
fi
180°- fi
78.27°
Shear Strain
Ans
Ans
is
th dash
ines De ermine th aver ge normal stra
lineAB
eo
tr
100' (70AB'
30)'
107.7033mm 111.8034mm
J(70-
AB'-AB £A.=~
111.8034-107.7033 107.7033 =0.0381
mm/mm
=38.1( 10-
long
Gf!om~t,.,
Si
8=90
"( .7 75
1<
.4 40 ra
Shf!QTStrain:
110m....
(rei., =2"-8=2"-1.707S9=-0.137rod (ro).,
2" -p=
An.
"-
Ans
'Yxy
rs
O.02x, where
Ll It
rt
direction.
.:'Iy .._f_x
.a
dx
ra
Ian
dx
Ian
J100
mm
Ian
(0.02 x)d.t
-SO[ln cos(O.02x 2.03mm
OOm An.
AB
*2-28.
A', ft where
(x
ci
However
2.0:
ci
L=I"'v'1+4x
~]I'" 2)
2 .0 : 1 +
2 .0 : 1 +
1.4789
fl
L-
0.47
£"'=4=
hi wire is o . s . x 2 , where 10 in
end
he wire unde go
s.
fllf
normal st ai
O.OO5x,
f(x),
v't
tis
y/
x,
Normal Strain
ds
where
However,
tis
5 .
dx
(t)'
tU
=x
Oi
J.
ds
(0.005
)~tU ~tU
0.00
(1
1.69 in.
1]1'0 Ans
Ans
2-30. ends
an
AB
8.
orientatio
and
its
u" and vs
in
A'B'.
om ./(Lcos8
A.'
.; L'
ui
u~
orma
ve
-uA)Z+(LsinB +Usl'
sinB
cosB)
strain
s'
N eg le c n g
g he r
s in g
e rm s
om
or
1 ( 2 U S 5inB
1+"2 --L----L-
EA
u,5inB
=-L---L-
2-31.
u~
"AcoS
ns
If
hm 2-2, show E.E~.
liS
E-E'=~_~
ss' liS"
IiS2 IiSIiS'
liS"
1i
US'IiS
IiSIiS' (liS -IiS) IiSIiS' =E.E;
(Q.ED)
=(~)(~) ss
4S
