Zadanie 1.pdf

(245 KB) Pobierz
Microsoft Word - WM0101P.DOC
3U]\NáDG:\]QDF]HQLHQDSU * HRGNV]WDáFHLSU]HPLHV]F]HZVáXSLH
o zmiennym przekroju
:\]QDF]\üUR]NáDG\VLá\QRUPDOQHMQDSU * HRGNV]WDáFHLSU]HPLHV]F]HZ\ZRáDQH
FL*DUHPZáDVQ\P >1P 3 @SUWDRVNRNRZR]PLHQQ\PSU]HNURMXSU]HGVWDZLRQ\PQD
U\VXQNX0DWHULDáSUWDMHVWMHGQRURGQ\R]QDQ\PPRGXOH
Younga E [N/m 2 ], pole przekroju
2A
H
ci *DU
w áDVQ\
2H
A
Z\]QDF]HQLHVLá\QRUPDOQHM1
2EFL*HQLHFL*DUHPZáDVQ\P]UHGXNRZDQHGRRVLSUWDGDMHOLQLRZHREFL*HQLHRVLRZH
RQDW*HQLX Q[ $[ 3RQLHZD* SU]HNUyM SUWD ]PLHQLD VL ZLF REFL*HQLH WR EG]LH
PLDáRZDUWRFLSU]HG]LDáDPLVWDáH
n 1 $
n 2 $
'RZ\]QDF]HQLDVLá\QRUPDOQHMZSURZDG]LP\SU]HNURMHZ\]QDF]RQHU]GQ\PL
x 1 i x 2 (jak na
U\VXQNX 2GG]LHORQH W\PL SU]HNURMDPL F]FL ] LFK FL*DUDPL RUD] X]HZQWU]QLRQ VLá
SU]HNURMRZ1SU]HGVWDZLDU\VXQHNSRQL*HM
F]ü,,
n 2 = 2A
N( x 2 )
x 2
x 2
F]ü,
n 1 = A
N( x 1 )
G 2 = 2A(H- x 2 )
x 1
x 1
G= A2H
G 1 = A(3H- x 1 )
=ZDUXQNXUyZQRZDJLVLáGODWDNZ\G]LHORQHMF]FL,]QDMGXMHP\ZDUWRüVLá\QRUPDOQHM
N(x 1 ) w dowolnym przekroju dla x 1 ]SU]HG]LDáX++
å
3 L[ N( x 1 ) – G 1 LVWG1 x 1 $+± $ x 1 .
=
Þ
1 R]QDF]DFL*DUF]FLSUWDRGFLWHMSU]HNURMHPNWyU\REOLF]RQ\]RVWDáMDNRLORF]\Q
FL*DUXREMWRFLRZHJR LREMWRFLWHMF]FLLORF]\QREFL*HQLDQ
x 1 ).
W przekroju x 1 +NRQLHF]QHMHVWXZ]JOGQLHQLH]PLDQ\QDW*HQLDREFL*HQLDNWyUDZ\QLND
]H ]PLDQ\ SROD SRZLHU]FKQL SU]HNURMX SRSU]HF]QHJR SUWD :SURZDG]DP\ Z W\P FHOX
]PLHQQ
1
LRGOHJáRFL
x 2 .
poprzecznego A[m 2 @LGáXJRü+>P@
5R]ZL]DQLH
·
6LáD*
186652731.035.png 186652731.036.png 186652731.037.png 186652731.038.png
=ZDUXQNXUyZQRZDJLVLáGODWDNZ\G]LHORQHMF]FL,,]QDMGXMHP\ZDUWRüVLá\QRUPDOQHM
N(x 2 ) w dowolnym przekroju dla x 2 ]SU]HG]LDáX+
å
3 L[ N( x 2 ) – G – G 2 LVWG1 x 2 $+ $+± x 2 $+± x 2 ).
=
Þ
6LáD*R]QDF]DFL*DUF]FLSUWDRSROXSRZLHU]FKQLSU]HNURMXSRSU]HF]QHJRUyZQ\P$D
G 2 ±FL*DUIUDJPHQWXF]FLSUWDRSROXSRZLHU]FKQLSU]HNURMXSRSU]HF]QHJRUyZQ\P$
RGG]LHORQHJRU]GQ
x 2 .
1DMZLNV]ZDUWRüVLáDQRUPDOQDRVLJDGOD
x 2 LZ\QRVL $+
:\NUHVVLá\QRUPDOQHMSU]HGVWDZLDU\VXQHNSRQL*HM
N
4 AH
2 AH
-DN Z\QLND ] Z\NUHVX QDFK\OHQLH Z\NUHVX VLá\ QRUPDOQHM MHVW SURSRUFMRQDOQH GR SROD
SRZLHU]FKQLSUWDSU]\VWDá\PFL*DU]H
Z\]QDF]HQLHQDSU*HQRUPDOQ\FK1
1DSU*HQLHZ\ZRáDQHVLáQRUPDOQUR]áR*RQHMHVWUyZQRPLHUQLHZFDá\PSU]HNURMXLMHJR
ZDUWRüRNUHORQDMHVW]DOH*QRFL
=
1
( )
( )
.
³
[
$
[
= XZDJL QD ]PLHQQ\ SU]HNUyM SUWD NRQLHF]QH MHVW UR]ZD*HQLH GZyFK SU]HG]LDáyZ
]PLHQQRFL,WDN
dla x ]SU]HG]LDáX+
x
=
1
( )
2
=
£
$+
-
£
$
[
=
-
x
³
2
£
+
2
$
$
i dla x ]SU]HG]LDáX++
=
1
( )
=
£
$
(
+
-
[
)
=
(
-
)
.
³
[
£
+
[
$
$
:\NUHVQDSU*HQRUPDOQ\FKSU]HGVWDZLRQ\MHVWQDU\VXQNXSRQL*HM
2 H
1
H
2 H
:D*Q\PZQLRVNLHPRGF]\WDQ\P]Z\NUHVXMHVWMHGQDNRZHQDFK\OHQLHZ\NUHVyZZREX
SU]HG]LDáDFKFRR]QDF]D*H]PLHQQRüQDSU*HQLH]DOH*\RGSRODSRZLHU]FKQLSU]HNURMXD
2
·
[
x
[
186652731.001.png 186652731.002.png 186652731.003.png 186652731.004.png 186652731.005.png 186652731.006.png 186652731.007.png 186652731.008.png 186652731.009.png 186652731.010.png 186652731.011.png 186652731.012.png 186652731.013.png
MHG\QLH RG ZDUWRFL FL*DUX ZáDVQHJR 1LHFLJáRü Z\NUHVX QDSU*H Z SU]HNURMX
x 1 =H
Z\QLND]QLHFLJáRFLVNRNRZHM]PLDQ\SU]HNURMXSUWDZW\PPLHMVFX
Z\]QDF]HQLHRGNV]WDáFH0
2GNV]WDáFHQLD0RGSRZLDGDMFHQDSU*HQLRP1RNUHODSUDZR
Hoocke’a
=
³
[
,
Younga.
¥
[
JG]LH(R]QDF]DPRGXá
(
5R]NáDG RGNV]WDáFH Z]GáX* GáXJRFL SUWD MHVW WDNL MDN QDSU*H ]PQLHMV]RQ\ SU]H]
PQR*QLN(
:\GáX*HQLHSUWDRGáXJRFL/REOLF]DP\MDNR
L
D
L
=
ò e
(
x
)
d
x
.
o
:\GáX*HQLHDQDOL]RZDQHJRSUWDZ\QRVLüEG]LH
+
+
D
/
=
ò
³
x
2
G
x
2
+
ò
³
x
1
G
x
1
.
(
(
R
+
8Z]JOGQLDMFREOLF]RQHZF]HQLHMQDSU*HQLDRWU]\PXMHP\FDáNRZLWHZ\GáX*HQLHUyZQH
+
(
)
+
D
=
ò
-
x
x
+
ò
-
x
x
=
£
+
+
£
+
=
£
+
.
/
£
+
2
G
2
£
+
1
G
1
(
(
(
(
(
+
Z\]QDF]HQLHSU]HPLHV]F]HX
3U]HPLHV]F]HQLHSU]HNURMXSRáR*RQHJRZRGOHJáRFL[RGVZRERGQHJRNRFDSUWDEG]LH
UyZQHZ\GáX*HQLXF]FLSUWDOH*FHMSRZ\*HMWHJRSU]HNURMX
H
x
u
(
x
1
)
=
D
l
(
x
1
)
=
ò
e
(
x
2
)
d
x
2
+
ò
e
(
x
1
)
d
x
1
.
0
H
[
X
x
2
=
D
O
x
2
=
ò
¥
x
2
G[
.
3RGVWDZLDMF]QDQHMX*RGNV]WDáFHQLDRWU]\PDP\UyZQDQLDSU]HPLHV]F]H
w przedziale (0, H)
[
-
x
(
)
x
=
ò
£
+
2
x
=
£
x
-
x
.
X
2
G
2
+
2
2
(
(
w przedziale (H, 3H)
+
(
-
x
)
[
(
-
x
)
£
+
2
£
+
1
x
=
ò
x
+
ò
x
=
X
1
G
2
G
1
(
(
+
£
+
£
ç
è
x
1
÷
ø
£
ç
è
x
1
÷
ø
=
+
x
-
-
=
x
-
-
1
1
ç
+
+
÷
ç
+
+
÷
(
(
(
3
·
·
æ
ö
æ
ö
186652731.014.png 186652731.015.png 186652731.016.png 186652731.017.png
 
2F]\ZLVWH MHVW*H SU]HPLHV]F]HQLH NRFD VZRERGQHJR SUWD SRZLQQR E\ü LGHQW\F]QH ]
ZF]HQLHM REOLF]RQ\P FDáNRZLW\P Z\GáX*HQLHP 3RGVWDZLDMF
x 1 =3H w równaniu
SU]HPLHV]F]HRWU]\PXMHP\SRWZLHUG]HQLH*H
x
=
=
£
è
-
-
ø
=
£
+
.
X
+
+
+
+
(
(
5yZQLHRF]\ZLVW\PVSUDZG]HQLHPMHVWEUDNSU]HPLHV]F]HQLDNRFD]DPRFRZDQHJR
3RGVWDZLDMF
x 2 U]HF]\ZLFLHRWU]\PXMHP\
X
x
2
=
=
.
:\NUHVSU]HPLHV]F]HSRND]DQ\MHVWQDSRQL*V]\PU\VXQNX
u
3 H 2
2E
7 H 2
2E
Zestawienie wykresów
N
2 H
1
2 H/E
0
u
4 AH
H
H/E
3 H 2 /2E
2 AH
2 H
2 H/E
7 H 2 /2E
4
æ
ö
186652731.018.png 186652731.019.png 186652731.020.png 186652731.021.png 186652731.022.png 186652731.023.png 186652731.024.png 186652731.025.png 186652731.026.png 186652731.027.png 186652731.028.png 186652731.029.png 186652731.030.png 186652731.031.png 186652731.032.png 186652731.033.png 186652731.034.png

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin