statique des poutres (elastiques jean garrigues mai 99
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+ '( A 13/ % &9.2(/ #V8A +-1 & >u"(,w((@/J! 93C6 / A 1 8 +*+ # G '(+-. HU(@+ % ( A9>28 4K 8 ( ># K 8U# /)*.2) '( 9 (4*)/ 89>2> ( C% (",16,(/7)% ()-13+-4*.013/ # 4-4-175. '( "#;> ~ ( 1[16+*))-+ # /95 # /)D(4*) % 13/95/ 89> W75 ~ (4*) "#=% .2+*(]K 8 ( > (5@(/7)-+-( % (5.24 # . >2> (,w(@/) %$~ 8 /x(4-(@5)-.216/ % +-13.0)*(5.2+-5 89>?# .0+*((4-)Y516/7Fc16/ %98B# G6(5 > (5(/7)-+*( % (]^3+ # G7.2) '( C% (5 # , Aw% (4513/7)-+ # .2/)*(4) # /9^6(@/)*.2( >2> (@4(4-) #V> 16+*4k N 9 A 9n 9 |
*` | G s n 9 qs 9 9 9eH q s n 9E` | kZN n A q 9 n ` |:*` | s<9sFn 1 "8 n (4*) > (,w13,w(/7)K 8U#V% + # )*.0K 8 ( % ( >?# 4-(5)*.216/ #8 )-1 8 + % ( ¸Án6C4 1 8 + 8 /9(4-(5)*.216/5.2+*5 89>?# .2+-(13/ #
nIA 3: A 3 :
%~*'() 89% ( %'() # . >2>X'(( % (=5@(=5 # , A ,w13/7)-+-(YK 8 ( >?# 5@16/7)-+ # .2/7)-(=) # /9^3(/7)-.2( >2> (¼#8 /,1 %x89> (, # .0, 8 , #V85(/7)*+-( % (;^6+ # G7.2) '( % ( >?# 4-(5)*.216/BK 8 .$G #8 )[LÃ ¼ Ã A 9n 9 |
*` | 9 A 9
9 9 |E` |
4 1 8 + | AGC 9 13/1 &9)-.2(/7) Ã ¼ Ã A ` 9 9$ (* 13* / K (*I*
%$# 516, A9> ( .0) '( % ( >?# 4-1 >28 )-.216/ % (4 A +-1'& >u"(@,w(4 %~ ( 1 13+-)D)-+ # /95 # /7) ,8 4*)-. HU( >E~ (, A9> 16. % (, '(@) 91 % (4 #VAxA +-1 <5 '((4 C¥è ÖØ×eÙÛÚ-8 ÜFÝeÞß8FàeáB8FÝeà58câ8 ãß8Ê×ÇäeåeáuæeÝ58 âK8ãjäeà7ç 8¥áÚÚ#8 ËoÌ~ÍXÎÏÏÐÒÑoÓÔÕ
? Vw ] ] M LNMRO SUd,_Q\FaFVXfR_,\F^G\FV0_gtN^7_,\FfR^r-rR^ Wd[vN^_I_!^ ()*)-( #A9A +*1 .2, # )-.213/ ^3+-164*4-. "(+*( 516/x4-.24-)*( "# 4 89A9A 164-(@+K 8 ( > (5 # , A% (@4"513/7)-+ # .2/)*(4D) # /x^6(/7)-.2( >2> (4D(4-)8 /9. F13+-,( %U# /94 >?# 4-(5@)-.216/ % +-16.2)*( CU / #=% 16/95E AG|F ¼ x9 A ¼ '() # /7)4 89A9A 164 '( 8 /9. F13+-,(6W613/ # L Ã ¼ Ã A Ã ¼ Ã A Ã E Ã
4 1 8 + >?# 4-(5@)-.216/[email protected]+*5 89>?# .2+*(6W75()*)-((4-)*.0, # )*.013/ % ( Ã ¼ Ã (4*).2/7F '(@+-.2( 8 +*( % ( 9 B"#>?# G #> ( 8 +"( !# 5)-( C M LNMEl ¿Y!YIaFd IfRWV\FfRdQ_ ZI^ aF^Z@\ 16/x4-. %'(+*16/94 8 /x(=4-(5@)-.216/ % +-16.2)*( % (Fc16+-,(K 8 ( > 516/xK 8 (=4-1 8 ,w.24-( "#8 /w( 1 13+-))*+ # /95 # /7) E A 9 ¸ 9 C
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¼ ¾ xl A q 9 n w 0 ¸¿n L'M6NPOkdfQIjBj X Y[Y[X K/U X&# F ( M P X \ V Y[X ghTIg X O'V \ VQIViK/U X3_BX jBQId dfQIjBjTIdV qQ M IX V8K'U X&# F ( M . P X\ V Y[X ghTIg X O/V\ VfQIViK'U X-_BX jBQId-dQIjBjlTedfV qQM .ËoÌ~ÍXÎÏÏÐÒÑÓÔ²Õ ÖØ×eÙÛÚ-8 ÜFÝeÞß8FàeáB8FÝeà58câ8 ãß8Ê×ÇäeåeáuæeÝ58 âK8ãjäeà7ç 8¥áÚÚ#8 Çé
7 4 egYY5 # +4 8 + >#;AU# +-)-.2( % ( y 513/7F13/ %98 ( # G6(@5 y W > ( A +-1 %98 .2)4-5 #V>?# .2+-( ¼ ¾ (4-)Y/ 8x> n C%~#A9A +-1 .2, # )-.21V/ % (D+-( % )Y516/x4-.24-)*( "# F # .2+-(4 8 + > (5 # , A ¼ > (4 % ( 89B#VA9A +-1 .2, # )*.216/944 8 .2G # /7)-(@4$LfD:78 + > (4-(^3,w(/7) wIw W ¼ (4*) %U# /94 >?#=% .2+*(5)-.213/ % ( ¸ 9fD:78 + > (4-(^3,w(/7) wIw W ># + '( AU# +*)-.2)-.216/ % ( ¼ (4-) 8 /9. F16+*,w( 5 ~ (4-) "#=% .2+*(=.2/ %'( A (/ %U# /7)-( % ( s¥n C / #% 16/95L | -
¼ ¾ x A | - ¼ ¾ ¸ 9 x A 9 A q 9n w 0 ¸ n
() % 13/95 9@A q 9n w 0 ¸ n
% (5 # , Aw% (4516/7)*+ # .2/7)-(@4) # /9^6(@/)*.2( >2> (@44-.2, A9> . H '(4 %98 (4 "# 9 +-(@4-)-( % 13/95 8 /9.2K 8 (,w(@/) F13/95)-.213/ % ( s 95 # + (@) w 0 ¸ n G # +-.2(/7) # G6(5 s 9 C4 1 8 + > (4Y516/7)*+ # .2/7)-(@4 %98 (@4 "# n Wx16/F # .2) 8 /x(=51 8xA98 +-( AU# + #V>2>u"( > ( "#¸ 9 W %~ # &[email protected]*4-( s¥n Wx()4 8 .2G # /7)> (,(,(+ # .24*16/9/9(@,w(/7)D16/B1'&9)*.2(/7) L
nIA q nI9 w 0 ¸ 9
% (:5 # , Aq% (4516/7)*+ # .2/7)-(@4) # /9^3(/7)-.2( >2> (4=4-.2, A9> .IH '(4 %98 (4 "# n +-(4*)-( % 16/x5F16/95@)-.216/ % ( s¥n 5 # + ()w 0 ¸ 9 G # +-.2(/7) # G6(@5 s¥n6C% ( > (5)*( 8 + A 1 8 +*+ # G '(+*.IHJ(+K 8 (4*.[16/ #A9A9> .2K 8 ( >E~#VA9A +-1 .2, # )-.213/ % ("+*( % ) "#;8 /9(4-(@5)-.216/B5.2+*5 89>?# .2+-(3W716/1'&x)-.2(/7)$L Ã ¼ Ã A ` 9'9 9 ()*)-(=G #> ( 8 +"(@4-).2/7F '(+-.2( 8 +*( % ( 9 W_ B"#=>?# G #V> ( 8 +( !# 5)-( C / = 1 * X* = 21 *B* - I *% (@44-(5)*.216/94 % +-13.0)*(4(/ A +-1H > ,w.2/95(Y16/7) %e'( ,"#'() '( %e'(HU/9.2(4 %J# /94 > (5 #A .2)-+*(]4 8 + >?# )-13+-4*.013/ C9 / 8 )-. > .24-(.25. > (4,(,w(@4/916) # )*.013/94 C4 1 8 + #VAxA +-1 .2,w(+ > (Y5 # , A:% (4513/)*+ # .0/7)*(4) # /9^6(/7)*.0( >0> (4 %98 (@4 "#=>E~ ( 1[16+-)D)-+ # /95 # /7) %U# /94 8 /9(4*(5)-.213/(/ A +*1VH > ,.0/x5(6WJ16/ 8 )-. > .24-((/9513+-( > (4 A +-1 A +-. '() '(@4 %98 56 # , A
¼'() # & > .2(4 %U# /94 > ( A +*1'& > "(,( % ( :9# .0/7) <> (/ # /7)W34 8 .2G # /) 8 /9( %'(, # +-59(4*(,& >?# & > ( "#;> ~#A9A +-1 .2, # )*.216/ % ("+*( % ) C \ # .24D.05@. W ># 51 89Ax8 +-( wIw (4-)A (+ A (/ % .25 8x># .2+-( "#>?#;> .2^3/9( % ( A +*1VH >D G316.2+HJ^ 8 +*( 9CÒ C /:4 89AxA 134-(513,w,w( %U# /94 >E~#VA9A +-1 .2, # )-.213/ % ("+*( % ) A 1 8 + > (44-(@5)-.216/x4K 8 ( > 516/xK 8 (4W3K 8 ( >?# 513/)*+ # .0/7)*() # /9^6(@/)*.2( >2> (
¼(4-) AU# + #>0> "( > ( "# (@)K 8$~ ( >2> ((4*)513/94-) # /7)-( %J# /94 >E~-'( AU# .04*4-( 8 + %98BA +-1H > 3 C
% ( U8xw% ( >?# 516/7)*+ # .2/7)-() # /9^3(/7)-.2( >2> (¼ "# )*+ # G3(+-4 ># 51 89A98 +*( wIw (4-) % 16/95
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n w 0 ¸ n q n 9 w 0 ¸ 9 ¼
'(G31 >28 ((/&F16/95@)-.216/ % ( >E~ # &[email protected]*4-(5 8 +-G7. > .2^3/9( 5 # + > (4D,w13,w(/7)*4$4-) # )*.0K 8 (@4 w 0 ¸ n () w 0 ¸ 9 G # +*.2(/7) # G3(5 >?#=A 164*.2)-.216/ % ( ># 51 89A98 +*( wIw C5E> (@4-) "# /916)*(+K 8 ( A 1 8 + > (@4 A +*1VH > 4,.2/95(4XW > (5 #V> 5 89>% (@4],16,(/7)-44*) # )*.2K 8 (4 A ( 8 )4-(+ # ,w(/x(+ "#:8 /x(ËoÌ~ÍXÎÏÏÐÒÑÓÔ²Õ ÖØ×eÙÛÚ-8 ÜFÝeÞß8FàeáB8FÝeà58câ8 ãß8Ê×ÇäeåeáuæeÝ58 âK8ãjäeà7ç 8¥áÚÚ#8 Q
7 4 egYY.2/7) '(^3+ #V> (4-.2, A9> ($L w 0 ¸¿n A | Is39 x9
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¼ "# )-+ # G6(+*4 > (451 89A98 +*(4 C ><.@É " ) XÆÈ%) $'&(" ) / 5@16/94*. %e"(+-( 8 /x( &9+ # /959( w ()=13/5916.24*.0) A 1 8 + >#&A 13+-)*.013/ % (4-(5@)-.216/ % +-13.2)-(K 8 .y+*(51 8 G7+-( >?#&9+ # /959(=(@/)*+-(=4*(4 % ( 89 / 8x% 4 C34 1 8 + >?# &9+ # /959( w W >?#> 13. % ( U89:% ( ¼ 4 8 + y 4 ~*'(5+*.2)yLq 9 n w 0 ¸ n q n 9 w 0 ¸ 9 A | ¼ ¾ xA qr|F
¼ ¾ z xlF |9
¼ ¾ p xA
¼ ¾ q ¼ ¾ A q / '(5+*.2G # /7)5()*)-(=+*( >?# )-.213/ A 1 8 +5 # K 8 (&9+ # /959(6Wx16/w1 &9)-.2(/7) > (4+*( >?# )-.213/94"(@/)*+-( > (4" U89%$~ (/7)-+ '(( () > (4 U89% (4-16+*)-.2(7 % (=5 # K 8 ( &x+ # /x56x( C
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:--BD B 9D " w BE ><.@É " ) )K2 É ) /5@16/94*. %e"(+-(, # .2/7)-(/ # /7) 8 // 8x% ()16/5916.24-.2) A 1 8 + g>?#A 16+-)*.216/ % (D4-(@5)-.216/ % +-16.2)*("K 8 .7+ # 5513+ % (> (4&9+ # /959(4YK 8 . # &J1 8 )*.24-4-(@/) #8 / 89%$C/%$# 4*(5)*.013/ '() # /)(@/ A +-1VH > ,w.2/95(6W >E~# .2+*( % ( (4*) % ( >E~ 16+ % +-(% ( 9 W % 16/95/ '(@^ > .2^6( # & > (6W7()4-(@4,w13,w(/7)*44-) # )-.2K 8 (44*16/7)/ 89> 4 C/%#> 13. % ( U89% (
¼4 8 + y 4 ~-'(@5+-.2)$L|· ¼ ¾ x A ¾ XAÁC
1 "8 (4*) >E~ (/94*(,& > ( % (@4/ 8 , '(+*164 % (&9+ # /959(4 # &J1 8 )*.24-4 # /7) #V8 / 8x%$C% ( A +*1 %98 .2)4-5 #>?# .2+-(v ¾ sG #V8 )D+-(@4 A (5)-.2G3(,w(/7) ` 1 8jq ` 4-( > 13/K 8 (v (4-)Y4-16+*) # /)1 8 (/7)-+ # /7) C / A ( 8 ) '(5+*.2+-(=5(@4+-( ># )-.216/x4 A 1 8 +)-1 8 4 > (4/ 89% 4*# C ><.@É " ) È%.*f* "*)4 1 8 +D5 > 16+*( >?#%'(@)-(+*,w.2/ # )*.216/ % (4 U89 W3. > F #8 ) 8 )*. > .24*(+ >?# 4-(@516/ % ( A +-1 A +-. '() '( %98 5 # , A% (@4516/7)-+ # .2/7)-(4) # /9^6(@/)*.2( >2> (@4$L >?#=A +*1 A +*. '() '( % (=5.2+-5 8x># )-.216/ % (
¼> ( > 16/9^ %$~ 8 /9(51 8 +A&J(F(+*, '(( y W7K 8$~ 16/B+ #A9A ( >0> (.25.6L| ¼ ¾ A q@w 0 |` | 9n w 0 ¸ n& q nI9 w 0 ¸ 9& q | ¼ ¾
1 "8> ( % (+-/x.0(@+)-(+*,w((@4-) ># 4-16,,w( % (4D5.2+-5 8x># )-.216/x4 % ( ¼ > ( > 16/9^ % (4D516/7)-1 8 +-4.2/7) '(@+-.2( 8 +*4"(/7)*1 8 + '(4 AU# +y3C /5916.24*.0) A 1 8 + =>?#A 16+*)-.216/ % (=4-(5@)-.216/ % +-16.2)*( %'( > .2,w.2) '(@( AU# + 8 /9( > .2^3/9(YF(+-, '(()-+ # 5 '((4 8 + >?#> .0^3/9(% ( A +-1H > (/7)-1 8 + # /) 8 / )-+*1 8 C- :#w% 16/95 8 /513/7)-1 8 +]( ) '(+-.2( 8 + yB 4 8 + >#&> .0^3/9( % ( A +*1VH > (@) 8 /513/)*1 8 +:.2/7) '(@+-.2( 8 + y ?> (w5@16/7)-1 8 + %98 )*+-1 8 CD / #A9A9> .2K 8J# /7) >?#A +-1 A +-. '() '( % (B5.2+*5 89>?# )*.013/4 8 + W16/1'&x)-.2(/7)$L | ¼ ¾ A 9n w 0 ¸ n q nI9 w 0 ¸ 9
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