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