MECHANICS OF COMPOSITE MATERIALSkaw/class/composites/formula_sheet_chapter2.pdf · page 1 of 2...
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Page 1 of 2 MECHANICS OF COMPOSITE MATERIALS FORMULA SHEET FOR CHAPTER 2 , E 1 = S 1 11 , E = S 1 12 12 ν − , E 1 = S 2 22 . G 1 = S 12 66 , - 1 E = Q 12 21 1 11 ν ν , 1 E = Q 21 2 12 12 12 ν ν ν − , 1 E = Q 12 21 2 22 ν ν − . G = Q 12 66 , s c sc sc 2sc c s 2sc s c = ] [T 2 2 2 2 2 2 1 − − − − , s - c sc sc - 2sc - c s 2sc s c = [T] 2 2 2 2 2 2 , c s ) Q 2 + Q ( 2 + s Q + c Q = Q 2 2 66 12 4 22 4 11 11 ), s + c ( Q + c s ) Q 4 Q + Q ( = Q 4 4 12 2 66 22 11 12 2 − , c s ) Q 2 + Q ( 2 + c Q + s Q = Q 2 2 66 12 4 22 4 11 22 c, s ) Q 2 Q Q ( s c ) Q 2 Q Q ( = Q 3 66 12 22 3 66 12 11 16 − − − − − s, c ) Q 2 Q Q ( cs ) Q 2 Q Q ( = Q 3 66 12 22 3 66 12 11 26 − − − − − ). c + s ( Q + c s ) Q 2 Q 2 Q + Q ( = Q 4 4 66 2 2 66 12 22 11 66 − − , s S + c s ) S + S (2 + c S = S 4 22 2 2 66 12 4 11 11 , c s ) S S + S ( + ) c + s ( S = S 2 2 66 22 11 4 4 12 12 − , c S + c s ) S + S (2 + s S = S 4 22 2 2 66 12 4 11 22 c, s ) S S 2 S (2 sc ) S S 2 S (2 = S 3 66 12 22 3 66 12 11 16 − − − − − , sc ) S S 2 S (2 c s ) S S 2 S (2 = S 3 66 12 22 3 66 12 11 26 − − − − − ). c + s ( S + c s ) S S 4 S 2 + S (2 2 = S 4 4 66 2 2 66 12 22 11 66 − −
Transcript of MECHANICS OF COMPOSITE MATERIALSkaw/class/composites/formula_sheet_chapter2.pdf · page 1 of 2...
Page 1 of 2
MECHANICS OF COMPOSITE MATERIALS FORMULA SHEET FOR CHAPTER 2
,E1 = S
111 ,
E = S
1
1212
ν− ,E1 = S
222 .
G1 = S
1266
, - 1
E = Q1221
111 νν
, 1
E = Q21
21212
12ννν−
, 1
E = Q1221
222 νν−
.G = Q 1266
,
scscsc
2sccs
2scsc
= ][T22
22
22
1
−−
−
− ,
s-cscsc-
2sc-cs
2scsc
=[T] 22
22
22
,cs )Q 2 + Q( 2 + s Q + c Q = Q 226612
422
41111
),s + c( Q + c s)Q 4 Q + Q( = Q 4412
266221112
2−
,c s )Q 2 + Q( 2 + c Q + s Q = Q 226612
422
41122
c,s )Q 2 Q Q( sc )Q 2 Q Q( = Q 3661222
366121116 −−−−−
s,c )Q 2 Q Q( cs )Q 2 Q Q( = Q 3661222
366121126 −−−−−
).c + s( Q + cs )Q 2 Q 2 Q + Q( = Q 4466
226612221166 −−
,sS + cs )S + S(2 + c S = S 422
226612
41111
,cs )S S + S( + )c+ s( S = S 22662211
441212 −
,cS + cs )S + S (2 + sS = S 422
226612
41122
c,s )S S 2 S (2 sc )S S 2 S (2 = S 3661222
366121116 −−−−−
,sc )S S 2 S (2 cs )SS 2S (2 = S 3661222
366121126 −−−−−
).c + s( S + cs )S S 4 S 2 + S (2 2 = S 4466
226612221166 −−
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,4 U + 2 U + U = Q 32111 θθ CosCos ,4 U U = Q 3412 θCos− ,4 U + 2 U U = Q 32122 θθ CosCos−
,4 U + 2 2
U = Q 32
16 θθ SinSin ,4 U 2 2
U = Q 32
26 θθ SinSin − .4 U )U U( 21 = Q 34166 θCos−−
)Q4 + Q2 + Q3 + Q(381 = U 661222111 , ),Q (Q
21 = U 22112 − ),Q4 Q2 Q + Q(
81 = U 661222113 −−
).Q4 Q6 + Q + Q(81 = U 661222114 −
,4 V + 2 V + V = S 32111 θθ CosCos ,4 V V = S 3412 θCos− ,4 V + 2 V V = S 32122 θθ CosCos−
,4 V2 + 2 V = S 3216 θθ SinSin ,4V2 2V = S 3226 θθ SinSin − ,4V4 )V V2( = S 34166 θCos−−
),S + S2 + S3 + S(381 = V 661222111 ),S (S
21 = V 22112 − ),S S2 S+ S(
81 = V 661222113 −−
).S S6 + S + S( 81 = V 661222114 −
1.<)(
+)(
+)(
-)( ult12
12
2
ultT2
2
2
2ult
T21
ultT1
1
2
ττ
σσ
σσσ
σσ
1
H1σ1+H2σ2+H6τ12+H11σ 21 +H22 σ 2
2 +H66 τ 212 +2H12σ1σ2< 1
,)(
1 )(
1 = Hult
C1ult
T1
1σσ
− ,)( )(
1 = Hult
C1
T1 ult
11σσ
,)(
1 )(
1 = H C2 ult
T2 ult
2σσ
− .)( )(
1 = Hult
C2ult
T2
22σσ
0, = H 6 .)(
1 = H 2ult12
66τ
)2(1H
T1
2ultσ
12 −= as per Tsai-Hill failure theory,
)()2(1H
ultC1ult
T1 σσ
12 −= as per Hoffman criterion,
)( )( )( )(1
21H
ultC2ult
T2ult
C1ult
T1 σσσσ
12 −= as per Mises-Hencky criterion.
d
