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MECHANICS OF
MATERIALS
Fifth Edition
Ferdinand P. Beer
E. Russell Johnston, Jr.
John T. DeWolf
David F. Mazurek
Lecture Notes:
J. Walt Oler
Texas Tech University
CHAPTER
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
6 EĞİLEMEY MARUZ
KİRİŞLERDE
KAYMA GERİLMESİ
DAĞILIMI
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
6- 2
Shear on the Horizontal Face of a Beam Element
• Yandaki kirişte,
• CDC’D’ elemanının dengesi:
A
CD
A
CDx
dAyI
MMH
dAHF
0
xVxdx
dMMM
dAyQ
CD
A
• Statik Moment
akıkıkaymaI
VQ
x
Hq
xI
VQH
• Buradan,
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
6- 3
Shear on the Horizontal Face of a Beam Element
• burada
momentiatalet alan ıl tüm
'
2
1
AA
z
A
dAyII
momentiataletstatikalanılüstündekiy
dAyQ
• Aynı sonuç diğer kısım içinde bulunur
HH
qI
QV
x
Hq
0
I
VQ
x
Hq
• Kayma akısı,
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
6- 4
Determination of the Shearing Stress in a Beam
• Ortalama Kayma Gerilmesi
xt
x
I
VQ
A
xq
A
Hort
It
VQort
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
Örnek
6- 5
Çözüm
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
Örnek-devam
6- 6
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
Örnek-devam
6- 7
•Tüm kesitin ağırlık merkezi ve atalet momenti
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
Örnek-devam
6- 8
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
Örnek-devam
6- 9
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
Örnek-devam
6- 10
max
It
VQ
a
G
G
It
VQmax
mmtG 75
c
mmt
It
VQ
c
c
cc
75
,
min
min
max
,225
,
max
max
min
mmt
It
VQ
c
c
cc
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
Örnek-devam
6- 11
3_
5625005075150. mmxxyAQc 5022550._
xxyAQc
3_
5,5859375.6275125. mmxxyAQG
MPax
xx
It
VQ
G
G 6,197579687500
5,58593710200 3
max
MPax
xx
It
VQ
G
G 6,197579687500
5,58593710200 3
max
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
6- 12
Shearing Stresses xy in Common Types of Beams
• İnce dikdörtgen kesitli kiriş,
A
V
c
y
A
V
Ib
VQxy
2
3
12
3
max
2
2
• I kesitli kirişte kayma gerilmesi
dağılımı
web
ort
A
V
It
VQ
max
© 2009 The McGraw-Hill Companies, Inc. All rights reserved.
MECHANICS OF MATERIALS
Fifth
E
ditio
n
Beer • Johnston • DeWolf • Mazurek
6- 13
Üç tahta parçası şekildeki gibi çivilenerek bir I profil oluşturulmuştur. Çiviler arası mesafe (kiriş ekseni boyunca)
s=25 mm ve kesitteki düşey kesme kuvveti V = 500 N olduğuna göre;
a) Her bir çivinin taşıdığı kesme kuvvetini bulunuz.
b) Eğer çivi yerine yapıştırıcı kullanılsaydı kesitteki gerilme dağılımı nasıl olurdu?
Örnek V
46
2
3
121
3
121
36
m1020.16
]m060.0m100.0m020.0
m020.0m100.0[2
m100.0m020.0
m10120
m060.0m100.0m020.0
I
yAQ
Çözüm
mN3704
m1016.20
)m10120)(N500(46-
36
I
VQq
mNqF 3704)(m025.0()m025.0(
N6.92F