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r=
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r=
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'
ν
=B"
ρ
= g mm( " 5 " "!=" " k /
! " '
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) ! " = kg=
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n
c
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σ
σ
" - 4
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mm
<
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mm r
r r
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! ="- '
k V
F = =
k F
F F
F = = = = × =
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& " " ,
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(
)
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# $ O,OV/ ! - 4 '
MPa
ced =
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ced
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%" : = ! = A F adm =
τ
mm d mm A Aadm = = ⇔ = → ≥
τ
1 : 7O O,O,
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σ
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× =
σ
! " n= / : :
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c ='
σ
r=
U ' E =
-
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988, : " %" mm,
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mm
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=
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( 6L7O9 8,6LI88#R8N 8,H6HIH#R8O
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! L,6 C ; ;/ ; ? " " " ; >
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8$.$ : )+ 3
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( " " ; '
z I M y I M
A y
y
z z
xx = − × + ×
σ
( 5 * J L,9K
"-+ " " " / + = Mz = × mm,
& A " " = × /
mm
mm
y
×
−
=
×
×
−
×
×
=
⇒
−
=
σ
mm
mm
y
×
=
−
×
×
−
×
×
=
⇒
=
σ
MPa máx =σ
1II8' mm MPa n cadm = = = =
σ
σ
adm
máx MPa
σ
σ
= <T 3 4 " ":; " ;
" 3 1II8,
/ = : " " /
" " ,
( 5 0 J L,9K
"- + " " " Mz = × mm,
& A " " = × /
" '
mm
mm
y
×
−
=
×
×
−
×
×
=
⇒
−
=
σ
mm
mm
y
×
=
−
MPa máx =
σ
17LI' mm MPa n cadm = = = =
σ
σ
adm
máx MPa
σ
σ
= <( " ":; " ; " 3 17LI,
!K ! 5 =
":; " ( ! = ; ' t I Q V z × × =
τ
& = ":; " " AB/
CD
/FG
IJ
V
máx=
×
, & " " : = ! Q= A×y,& ) " " : = ! '
mm
yi Ai mm yi×Ai
E ×
EE ×
∑
]]]] ×! L,7 C % ; > : " 5 E EE/ 988
% ) ; >
mm
A
A
y
y
i ii
×
=
×
=
=
→
∑
∑
mm
Q= × = ×
mm
=
×
×
×
×
×
=
τ
MPa
máx=
τ
1II8' mm MPa n admadm = = = =
σ
τ
adm
máx MPa
τ
T 3 4 ":; " ;
" 3 1II8,
/ = : " " /
" " ,
& =
V
=
×
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& ) " " : = ! '
mm
yi Ai mm yi×Ai
E ×
EE ×
∑
]]]] ×! L,H C % ; > : " 5 E EE/ 2# 7N8
% ) ; >
mm
A
A
y
y
i ii
×
=
×
=
=
→
mm
Q= × = ×
mm
=
×
×
×
×
×
=
τ
MPa
=
τ
1II8' mm MPa n admadm = = = =
σ
τ
adm
MPa
τ
τ
= <T 3 4 ;
" 3 17LIJIK,
L,N = 3 4 $ ":; " = 7/M9 ""/ 4
4 $ = 8/8L9X " " ,
;$
& / " 17LI/ " ) " 4
" / ! "
/ " % ,
" ! 7 '
;$#$ ( (
O,6 C "
1 / ! / " "
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; >/ " " 4 , & !
;$*$ ( < )
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-) " / "
" , 1 + "
/ " ! > ,
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" G @ W/ 4 ! " < 4
+ ,
( " 5 " " k /
" ! 3
-, ( = ! " " " 4 " 5
H,
! - = + = ≅ k
O,H C " - / + Q7H8 @
O,9 C " - / + Q7H8 @
T 3 4 " ":; " = mm "
" 3 '
mm MPa
n
c
adm = = = =
σ
σ
" - 4
σ
composta=
mm
<
σ
adm( = " / " "
! E # N88/ = ! " >
79,
;$.$ = )
T : "!=" " ! $ : " 4
" " " " ,
( " 4 : 3 " ! $ / "
; " " 6I V/ - 4 '
MPa
bet =
σ
( " F = k
A
apoio=
mm
bet
MPa
σ
σ
= = <<->$ !
>$#$ ) 2 )
( = " " " " 4
" ' ! ,
& " ! - G$ / + 3
" 5 = J ! K
; )" / 4 < ; 4 " , &
= " " " " , (
= V =R×I JNK,
( G$ = 4 " > " =
4 " +: ,
T " "= ! 5 " "
/ " " " " ! : ! "
" = 4 / " 3 " ,
1 " ; " ) ! / "
= 4 ; " " k ,
( = $ = = 71/ (# / "
t/ ! mV V " "! 8/8IXV,
M,6 C = 71/ (#
( = ! " / 4 : "
/ " " : " $ = " ! "
4 : 4 " A ,
4 " 4
/ = " " ! "
) = "
4 > ,
( " " " $ H/ "!=" (# /
4 " + " = 71 ! 4 " " !
" ! ; V,
M,7 C " (#
1 ! " = : , " :
" $ " < "/ "
M,H, ( ; / < " < $
-/ = ! = 6N,
>$*$ )
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M,H C R $
& " = : " 4 " /
> " 4 ! " " "!=" , /
: mm/ 4 : " !
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#?$ !
& = " " ! " / + " 4 "
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/ " ! " ,
68,6 C # 4 " = =
& = " / "!="
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& = $ 6PO E ( E /
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3 ; (,
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= K mm J ! = K,
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