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2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 1
KRLERDE KME
EIPx
EI)x(M1
Serbest uta
(A),
AA
,01
PLEI
BB
,01
Ankastre uta
(B),
Elastik erinin diferansiyel denklemi
2
2
232
2
2
1
1dx
yd
dxdy
dxyd
EI
xMdx
yd12
2
Kk kmeler iin;
xMdx
ydEI 22
ntegral alnarak eim (=dy/dx) ve kmenin (y) denklemleri bulunur. Snr artlar
yazlarak integral sabitleri bulunur.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 2
rnek Integrasyon Metodu ile zmler
ekildeki ykleme durumu iin kiriin A noktasndaki kmeyi ve eim asn
bulunuz.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 3
rnek: ekildeki ykleme durumu iin kiriin C noktasndaki kmeyi ve eim asn
bulunuz.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 4
rnek: ekildeki ykleme durumu iin maksimum kmeyi ve eim asn
bulunuz.
L/2 L/2
P
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 5
rnek: ekildeki ykleme durumu iin kiriteki maksimum kmeyi A noktasndaki eim asn
bulunuz.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 6
rnek: ekildeki ykleme durumu iin kiriin D noktasndaki kmeyi ve eim asn
bulunuz.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 7
M
M
ACD
2x
Moment-Alan
Metodu
M
D
C
D
C
D
C
x
xCD
x
x
dxEIM
dxEIMd
EIM
dxyd
dxd
2
2
Deiik yklere maruz bir kiri
gz nne alnrsa:
C
ve
D
arasndaki
moment alan1. Moment-Alan
Teoremi:
CDEI
D
C
x
xDC dxEI
Mxt
dxEIMxdxdt
1
11
2. Moment-Alan
Teoremi:
t DC EI
EIxA
t 1CDDC
EIxA
t 2CDCD
DCtC noktasnn Dye
gre teetsel deiimi
C
ve
D
arasndaki
moment alannn
Cye gre statik momenti
kme erisi
Referans teet
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 8
L/2 L/2
PSimetrik Ykleme:rnek:
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 9
rnek:
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 10
Simetrik olmayan Ykleme:
ADAD
ABADD
D
AB
tLxty
EFEDy
tLxEF;
LHB
xEF
Lt
tan ABAA
Saat ibreleri ynndeki alar (-), zt yn (+) alnr.
?FDyD
ADt ABt
D
F
AD
Maksimum kme
AKAK
ABA
0L
t
Maksimum kmenin olduu bir K noktasnda eim 0
dr. Yani, teet yataydr.
AAK
ymax
deeri,
A
ve K
arasndaki moment alannn A dan geen dzey eksene gre statik momentinin EI deerine blnmesi ile bulunabilir.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 11
rnek:
L/4 3L/4
P
D
ekildeki ykleme durumu iin kiriin D noktasndaki kmeyi, eim asn
ve maksimum kmeyi bulunuz.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 12
Statike belirsiz (hiperstatik) sistemler
Statik Denge:
000 Ayx MFF
4 bilinmeyen:
Ax
, Ay
, B, MA
3 denklem:
zm iin snr artlarndan yararlanarak ilave denklem/denklemler yazmak gerekir.
rnek: ekildeki ykleme durumu iin mesnet noktalarndaki reaksiyon kuvvetlerini bulunuz.
2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
FifthEdition
Beer Johnston DeWolf Mazurek
9- 13
rnek: ekildeki ykleme durumu iin yay kuvvetini bulunuz.
L/2 L/2kC
KRLERDE KMESlayt Numaras 2Slayt Numaras 3Slayt Numaras 4Slayt Numaras 5Slayt Numaras 6Moment-Alan MetoduSlayt Numaras 8Slayt Numaras 9Slayt Numaras 10Slayt Numaras 11Statike belirsiz (hiperstatik) sistemlerSlayt Numaras 13