ADANA BTÜ DERS KATALOG FORMU

(COURSE CATALOGUE FORM)

Dersin Adı Course Name Mukavemet II Mechanics of Materials II

Kodu (Code)

Yarıyılı (Semester)

Kredisi (Local

Credits)

AKTS Kredisi (ECTS Credits)

Ders Uygulaması, Saat/Hafta (Course Implementation, Hours/Week)

Ders (Theoretical)

Uygulama (Tutorial)

Laboratuar (Laboratory)

CE-202 4 4 7 3 2 0 Bolum/Program (Department/Program)

İnşaat Mühendisliği Bölümü (Civil Engineering Department)

Dersin Türü (Course Type)

Zorunlu (Compulsory) Dersin Dili (Course Language)

İngilizce (English)

Dersin Önkoşulları (Course Prerequisites)

Yok/None

Dersin Mesleki Bileşene Katkısı, % (Course Category by Content, %)

Temel Bilim (Basic Science)

Temel Mühendislik (Engineering

Science)

Mühendislik Tasarım

(Engineering Design)

İnsan ve Toplum Bilim (General

Education)

%75 %25

Dersin İçeriği (Course Description)

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.

Dersin Amacı (Course Objectives)

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)

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

Ders Kitabı (Textbook)

Hibbeler, R.C., Mechanics of Materials 8th SI Edition, Pearson, ISBN 978-981-06-8509-6.

Diğer Kaynaklar (Other References)

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.

Ödevler ve Projeler (Homework & Projects)

15 Uygulama (Sınıfta yapılacak) 15 Recitations (will be held in class)

Başarı Değerlendirme Sistemi (Assesment Criteria)

Faaliyetler (Activities)

Adedi – En az (Quantity – Minimum)

Değerlendirme Katkısı % (Effects on Grading %)

Yıliçi Sınavları (Midterm Exams)

1 %25

Uygulamalar (Recitations)

10 %25

Final Sınavı (Final Exam)

1 %50

COURSE PLAN

Week Topics Chapters 1 State of Stress Caused by Combined Loadings. Practices. 8 2 Combined and Reinforced Concrete Beams. Practices 6 3 Absolute maximum shear stress and fracture hypothesis. 9 4 Design of beams and shafts. 11 5 Elastic Curve. Definition and Idealizations. Integration Method. Practices. 12 6 Elastic Curve. Solution with singular functions. Initial Values Method. Practices 12 7 Elastic Curve. Mohr Method and Superposition. Practices. 12 8 MIDTERM WEEK 9 Statically indeterminate beams-Method of Integration-Mohr Method 12

10 Energy Method. Work of inner and outer loads. Conservation of Energy. Practices.

14

11 Principle of Virtual Work. Method of Virtual Forces Applied to Trusses and Beams. Practices.

14

12 Buckling of Columns. Ideal Column with Pin Supports. Effective Length. Practices.

13

13 Buckling of Columns. Ideal Column with Pin Supports. Effective Length. Practices.

13

14 General Review

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� ���� � 100�MPa and σ� ����� � 150�MPa, determine the maximum allowable

intensity w of the uniform distributed load. E� � 73.1�GPa, E�� � 200�GPa.

2-)

The reinforced concrete beam, shown above, is made using two steel reinforcing rods. If the

allowable tensile stress for the steel is �� �� � 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�� � 200�GPa, E"�#" � 26.5�GPa.

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 lightest-

weight steel wide flange beam from the table given below, that will safely support the loading.

Take σ� �� � 150�MPa and τ� �� � 84�MPa.

Wide Flange Sections or W Shapes

Designation Area

A

Depth

d

Web

Thickness

t�

Flange x-x axis y-y axis

width

b)

thickness

t)

I

10*

S

10�

r I

10*

S

10�

r

mm x kg/m mm+ mm mm mm mm mm, 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� �� � 100�MPa, determine to the nearest multiples of 5 [mm] the smallest diameter of the shaft that will support the loading. Take τ� �� � 42�MPa.

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 � 45.510*��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=7.4101���m+, I2 � 87.3101*��m, and I� � 18.8101*��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�� � 200�GPa,

σ� � 360�MPa.

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�� � 200�GPa.

2-)

Determine the torsional strain energy in the A-36 steel shaft, shown above. The shaft has a

radius of 40 [mm]. G�� � 75�GPa.

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�� � 200�GPa.

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�� � 200�GPa.

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�� � 200�GPa.

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�� � 200�GPa.

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+⁄