ADANA BTÜ
DERS KATALOG FORMU
(COURSE CATALOGUE FORM)
Dersin Adı
Mukavemet II
Kodu
Yarıyılı
(Code)
(Semester)
CE-202
4
Bolum/Program
(Department/Program)
Dersin Türü
(Course Type)
Dersin Önkoşulları
(Course Prerequisites)
Dersin Mesleki Bileşene
Katkısı, %
(Course Category by
Content, %)
Course Name
Mechanics of Materials II
Kredisi
AKTS Kredisi
Ders Uygulaması, Saat/Hafta
(Local
(ECTS Credits)
(Course Implementation, Hours/Week)
Credits)
Ders
Uygulama
Laboratuar
(Theoretical)
(Tutorial)
(Laboratory)
4
7
3
2
0
İnşaat Mühendisliği Bölümü
(Civil Engineering Department)
Zorunlu (Compulsory)
Dersin Dili
İngilizce
(Course Language)
(English)
Yok/None
Temel Bilim
(Basic Science)
Temel Mühendislik
(Engineering
Science)
%75
Dersin İçeriği
(Course Description)
Dersin Amacı
(Course Objectives)
Mühendislik
Tasarım
(Engineering
Design)
%25
İnsan ve Toplum
Bilim (General
Education)
Kesmeli eğilme, kayma merkezi, elastik eğri, dış merkezli normal kuvvet,
burulmalı eğilme, enerji yöntemleri, elastik stabilite.
Bending with shear, shear center, elastic curve, eccentric normal load, bending
with torsion, energy principles, elastic stability.
1. Bileşik mukavemet halleri ile boyutlandırmayı öğrenmek.
2. Elastik eğri yöntemleri ile çubuklarda yerdeğiştirme ve şekildeğiştirme
kavramlarını öğrenmek.
3. Enerji yöntemlerini kavrayıp uygulama becerisini kazanmak.
4. Stabilite kavramını öğrenmek, çubuk sistemlere uygulama becerisini
kazanmak.
1. Learn how to design beams and shafts in combined strength cases.
2. Learn how to calculate displacement and rotations in beams using elastic
curve methods.
3. Will be able to gain application of energy methods.
4. Learn principle of stability and application to one dimensional elements.
Dersin Öğrenme Çıktıları
(Course Learning
Outcomes)
Ders Kitabı
(Textbook)
Diğer Kaynaklar
(Other References)
Ödevler ve Projeler
(Homework & Projects)
Başarı Değerlendirme
Sistemi
(Assesment Criteria)
Bu dersi başarıyla geçen öğrenciler:
1. Kesmeli eğilme
2. Burulmalı eğilme
3. Dış merkezli normal kuvvet
4. Elastik eğri
5. Enerji yöntemleri
6. Elastik stabilite
Student, who passed the course satisfactorily can:
1. Bending with shear
2. Bending with torsion
3. Eccentric normal load
4. Elastic Curve
5. Energy Principles
6. Elastic Stability
Hibbeler, R.C., Mechanics of Materials 8th SI Edition, Pearson,
ISBN 978-981-06-8509-6.
1. Beer, F.P., Johnston, E.R., 2014, Mechanics of Materials, 7th Edition,
McGraw-Hill, ISBN 978-007-33-9823-5.
2. Omurtag, M.H., 2014, Mukavemet – Cilt 1, 5.Baskı, Birsen Yayınevi,
ISBN 975-511-431-9.
3. Omurtag, M.H., 2012, Mukavemet Çözümlü Problemler – Cilt 1, 4. Baskı,
Birsen Yayınevi, ISBN 975-511-441-6.
4. Bakioğlu, M., 2009, Cisimlerin Mukavemeti – Cilt 1, 2. Baskı, Seçkin
Yayınevi.
5. İnan, M., 2001, Cisimlerin Mukavemeti, 1.Baskı, İTÜ Vakfı.
15 Uygulama (Sınıfta yapılacak)
15 Recitations (will be held in class)
Faaliyetler
Adedi – En az
(Activities)
(Quantity – Minimum)
1
Yıliçi Sınavları
(Midterm Exams)
10
Uygulamalar
(Recitations)
1
Final Sınavı
(Final Exam)
Değerlendirme Katkısı %
(Effects on Grading %)
%25
%25
%50
COURSE PLAN
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
State of Stress Caused by Combined Loadings. Practices.
Combined and Reinforced Concrete Beams. Practices
Absolute maximum shear stress and fracture hypothesis.
Design of beams and shafts.
Elastic Curve. Definition and Idealizations. Integration Method. Practices.
Elastic Curve. Solution with singular functions. Initial Values Method. Practices
Elastic Curve. Mohr Method and Superposition. Practices.
MIDTERM WEEK
Statically indeterminate beams-Method of Integration-Mohr Method
Energy Method. Work of inner and outer loads. Conservation of Energy.
Practices.
Principle of Virtual Work. Method of Virtual Forces Applied to Trusses and
Beams. Practices.
Buckling of Columns. Ideal Column with Pin Supports. Effective Length.
Practices.
Buckling of Columns. Ideal Column with Pin Supports. Effective Length.
Practices.
General Review
Chapters
8
6
9
11
12
12
12
12
14
14
13
13
MECHANICS OF MATERIALS - II
RECITATION 1
1-)
If P=60[kN], determine the maximum normal stress developed on the cross-section of the
column, shown above.
2-)
The 50 [mm] diameter rod is subjected to the loads shown above. Determine the state of stress
at point B, and show the results on a differential element located at this point.
MECHANICS OF MATERIALS - II
RECITATION 2
1-)
The eccentric force P is applied at a distance e from the centroid on the concrete shown above.
Determine the range along the y axis where P can be applied on the cross-section so that no
tensile stress is developed in the material.
2-)
Since concrete can support little or no tension, this problem can be avoided by using wires or
rods to prestress the concrete once it is formed. Consider the simply supported beam shown
above, which has a rectangular cross-section of 450 [mm] by 300 [mm]. If concrete has a
specific weight of 24 kN⁄m , determine the required tension in rod AB, which runs through
the beam so that no tensile stress is developed in the concrete at its center section a-a. Neglect
the size of the rod and any deflection of the beam.
MECHANICS OF MATERIALS - II
RECITATION 3
1-)
Segment A of the composite beam, shown above, is made from 2014-T6 aluminum alloy and
segment B is A-36 steel. If the allowable bending stress for the aluminum and steel are
σ 100MPa and σ 150MPa, determine the maximum allowable
intensity w of the uniform distributed load. E 73.1GPa, E 200GPa.
2-)
The reinforced concrete beam, shown above, is made using two steel reinforcing rods. If the
allowable tensile stress for the steel is σ 280 [MPa] and the allowable compressive
stress for the concrete is σ"#" 21 [MPa], determine the maximum moment M that
can be applied to the section. E 200GPa, E"#" 26.5GPa.
MECHANICS OF MATERIALS - II
RECITATION 4
1-)
Draw the three Mohr’s circles that describe each of the following states of stress shown above.
Determine the absolute maximum shear stress for each of the following states of stress.
2-)
The solid shaft is subjected to torque, bending moment and shear force as shown above.
Determine the principal stress acting at points A and B and the absolute maximum shear stress.
MECHANICS OF MATERIALS - II
RECITATION 5
1-)
Draw the shear and moment diagrams for the beam, shown above. Then select the lightestweight steel wide flange beam from the table given below, that will safely support the loading.
Take σ 150MPa and τ 84MPa.
Wide Flange Sections or W Shapes
Designation Area
A
Depth
d
Web
Flange
Thickness width thickness
t
b)
t)
x-x axis
I
S
10*
10
y-y axis
r
I
S
r
10*
10
mm, mm mm mm,
mm
mm
mm x kg/m
mm+
mm
mm
mm
mm
W310 x 74
9480
310
9.40
205.0
16.3
165
1060 132
23.4
228
49.7
W310 x 67
8530
306
8.51
204.0
14.6
145
948
130
20.7
203
49.3
W310 x 39
4930
310
5.84
165.0
9.7
84.8
547
131
7.23
87.6
38.3
W310 x 33
4180
313
6.60
102.0
10.8
65.0
415
125
1.92
37.6
21.4
W310 x 24
3040
305
5.59
101.0
6.7
42.8
281
119
1.16
23.0
19.5
W310 x 21
2680
303
5.08
101.0
5.7
37.0
244
117 0.986
19.5
19.2
2-)
The shaft shown above, is supported by bearings at A and B that exert force components only
in the x and z directions on the shaft. If the allowable normal stress for the shaft is
σ 100MPa, determine to the nearest multiples of 5 [mm] the smallest diameter of the
shaft that will support the loading. Take τ 42MPa.
MECHANICS OF MATERIALS - II
RECITATION 6
1-)
Determine the maximum slope and maximum deflection of the simply supported beam which
is subjected to the couple moment M- by using integration method. EI is constant.
2-)
Determine the equations of the elastic curve for the beam using the x/ and x+ coordinates.
Specify the slope at A and the maximum displacement of the shaft by using the method of
integration. EI is constant.
MECHANICS OF MATERIALS - II
RECITATION 7
1-)
Determine the maximum deflection of the simply supported beam shown above by using
discontinuity functions. E=200 [GPa], I= 65. 10* mm, ].
2-)
Determine the equation of the elastic curve of the simply supported beam, shown above and
find the maximum deflection by using discontinuity functions. The beam is made of wood
having a modulus of elasticity E=10 [GPa].
MECHANICS OF MATERIALS - II
RECITATION 8
1-)
Determine the deflection at C of the overhang beam by using the moment area method.
E = 200 [GPa] and I 45.5
10* mm, .
2-)
Determine the slope at C and deflection at B by using the moment area method. EI is constant.
MECHANICS OF MATERIALS - II
RECITATION 9
1-)
Determine the reactions at the supports A and B by using the method of integration, then draw
the moment diagram. EI is constant.
2-)
Determine the reactions at pin support A and roller supports B and C by using the method of
integration. EI is constant.
MECHANICS OF MATERIALS - II
RECITATION 10
1-)
Determine the reactions at the supports A and B by using the moment area method, then draw
the moment diagram. EI is constant.
2-)
Determine the reactions at the supports A and B by using the moment area method, then draw
the shear and moment diagrams. EI is constant.
MECHANICS OF MATERIALS - II
RECITATION 11
1-)
The A-36 steel column, shown above, can be considered pinned at its top and bottom and braced
against its weak axis at the mid-height. Determine the maximum allowable force P that the
column can support without buckling. Apply a F.S=2 against buckling. Take
A=7.4
101 m+ , I2 87.3
101* m, and I 18.8
101* m, .
2-)
Determine if the frame can support a load of w = 6 [kN/m] if the factor of safety with respect
to buckling of member AB is 3. Assume that AB is made of steel and is pinned at its ends for
x-x axis buckling and fixed at B and pinned at A for y-y axis buckling. E 200GPa,
σ 360MPa.
MECHANICS OF MATERIALS - II
RECITATION 12
1-)
Determine the bending strain energy in the A-36 steel beam due to the distributed load.
I = 122. 10* mm, , E 200GPa.
2-)
Determine the torsional strain energy in the A-36 steel shaft, shown above. The shaft has a
radius of 40 [mm]. G 75GPa.
MECHANICS OF MATERIALS - II
RECITATION 13
1-)
The A-36 steel bars are pin connected at B. If each has a square cross-section, determine the
vertical displacement at B by using the conservation of energy. E 200GPa.
2-)
Determine the vertical displacement of end B of the frame by using the conservation of energy.
Consider only bending strain energy. The frame is made using two A-36 steel W460x68 wide
flange sections. I212 297. 10* mm, , E 200GPa.
MECHANICS OF MATERIALS - II
RECITATION 14
1-)
Determine the vertical displacement of point B by using the virtual work. Each A-36 steel
member has a cross-sectional area of 400 [mm+ . E 200GPa.
2-)
Determine the horizontal displacement of joint B and the vertical displacement of joint C of the
truss shown above by using the virtual work. Each A-36 steel member has a cross-sectional
area of 400 mm+ . E 200GPa.
MECHANICS OF MATERIALS - II
RECITATION 15
1-)
Determine the slope at point A and the displacement at C of the simply supported beam,
shown above by using the virtual work. E=13.110* kN⁄m+