ADANA BTÜ DERS KATALOG FORMU (COURSE CATALOGUE FORM)

ADANA BTÜ DERS KATALOG FORMU (COURSE CATALOGUE FORM) Dersin Adı Mukavemet I Kodu Yarıyılı (Code) (Semester) CE-201 3 Bolum/Program (Department/Program...
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ADANA BTÜ DERS KATALOG FORMU (COURSE CATALOGUE FORM) Dersin Adı Mukavemet I Kodu Yarıyılı (Code) (Semester) CE-201 3 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 I 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)

Gerilme hali, şekildeğiştirme hali, Hooke yasası, malzemelerin mekanik özellikleri, kırılma ve akma varsayımları, çubuk mukavemetinin kabulleri, kesit tesir diyagramları, normal kuvvet, eğilme, kesme, burulma. State of stress, state of strain, Hooke’s law, mechanical properties of the material, yielding and fracture criteria, assumptions of the rod theory, internal forces and diagrams, axial load, pure bending, shear, torsion. 1. Şekil değiştiren cisim mekaniğinde, gerilme, şekildeğiştirme ve malzemelerin mukavemetini kaybetmesi gibi temel kavramları öğretmek. 2. Malzemelerin mekanik özellikleri hakkında bilgi sahibi olmak. 3. Eksenel kuvvet, basit eğilme, kesme ve burulma hallerinde; çubukların tasarımını yapma yeteneğini kazandırmak. 1. Teaching fundamental concepts of deformable bodies; stress, strain and failure of materials. 2. Having knowledge of the mechanical properties of the materials. 3. To give engineering design ability of the rod for axial load, shear, pure bending and torsion.

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. Gerilme hali 2. Şekil değiştirme hali 3. Malzemelerin mekanik özellikleri 4. Kırılma ve akma varsayımları 5. Çubuk mukavemeti ve kesit tesir diyagramları 6. Normal kuvvet hali 7. Basit eğilme hali 8. Kesme hali 9. Burulma hali Student, who passed the course satisfactorily can: 1. State of stress 2. State of strain 3. Mechanical properties of the materials 4. Yielding and fracture criteria 5. Internal forces and diagrams 6. Axial load 7. Pure bending 8. Shear 9. Torsion 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. 16 Uygulama (Sınıfta yapılacak) 16 Recitations (will be held in class) Faaliyetler Adedi – En az (Activities) (Quantity – Minimum) 1 Yıliçi Sınavları (Midterm Exams) 16 Uygulamalar (Recitations) 1 Final Sınavı (Final Exam)

Değerlendirme Katkısı % (Effects on Grading %) %25 %25 %50

COURSE PLAN Week Topics 1 Introduction to strength of materials, state of stress. State of stress and state of strain, Material Property Relationships. 2 Transformation of Plane Stress, Principal Stresses, Maximum Shearing Stress, 3 Mohr’s Circle for Plane Stress. Transformation of Plane Strain, Principal Strains, Maximum In-Plane Shear 4 Strain, Mohr’s Circle for Plane Strain, Theories of Failure. Moment of Inertia of an Area, Polar Moment of Inertia, Parallel Axis Theorem, 5 Product of Inertia. Moment of Inertia About Inclined Axes, Principal Moments of Inertia, Mohr’s 6 Circle for Moment of Inertia. Graphical Method For Constructing Shear and Moment Diagrams. 7 MIDTERM WEEK 8 Elastic Deformation of an Axially Loaded Member, The Force Method of 9 Analysis For Axially Loaded Members, Thermal Stress. Pure Bending, Bending Deformations, Bending of Members Made of Several 9 Materials. Unsymmetric Bending, Determination of the Shearing Stress in a Beam 10 Shear Flow In Built-Up Members, Shear Center For Open Thin-Walled 11 Members, Torsional Deformation of a Circular Shaft, Power Transmission, Angle of Twist. 12 Prismatic Beam Design. 13 General Review 14

Chapters 1 1,10 9 10 A.2, A.3, A.4 A.2, A.3, A.4 6 4 6 6, 7 7 5 11

MECHANICS OF MATERIALS - I RECITATION I

1-) During the tension test, the wooden specimen, shown above, is subjected to an average normal stress of 15 [MPa]. Determine the axial force P applied to the specimen. Also, find the average shear stress developed along section a-a of the specimen.

2-) If the joint, shown above, is subjected to an axial force of P = 9 [kN], determine the average shear stress developed in each of the 6-mm diameter bolts between the plates and the members and along each of the four shaded shear planes.

MECHANICS OF MATERIALS - I RECITATION 2

1-) If the allowable shear stress for each of the 10-mm-diameter steel pins at A, B and C is τ = 90 [MPa], and the allowable normal stress for the 13-mm-diameter rod is σ= 150 [MPa], determine the largest intensity w of the uniform distributed load that can be suspended from the beam.

2-) The eye bolt, shown above, is used to support the load of 25 [kN]. Determine its diameter d to the nearest multiples of 5 [mm] and the required thickness h to the nearest multiples of 5 [mm] of the support so that the washer (somun) will not penetrate (içe göçmek) or shear through it. The allowable normal stress for the bolt is σ = 150 [MPa], and the allowable shear stress for the supporting material is τ = 35 [MPa].

MECHANICS OF MATERIALS - I RECITATION 3

1-) The material, shown above, distorts into the dashed position. Determine (a) the average normal strains along sides AC and CD and the shear strain γ at F, and (b) the average normal strain along line BE.

2-) Two bars are used to support a load P. When unloaded, AB is 125 [mm] long, AC is 200 [mm] long, and the ring at A has coordinates (0,0). If a load is applied to the ring at A, so that the load moves the ring to the coordinate position (6.25 [mm], -18.25 [mm]), determine the normal strain in each bar.

MECHANICS OF MATERIALS - I RECITATION 4

1-) The state of stress at a point in a member is shown above, on the element. Determine the stress components acting on the inclined plane AB. Solve the problem using the method of equilibrium.

2-) Solve the first problem using the stress-transformation equations; which are;

σ

σ σ σ  σ cos 2θ τ sin 2θ 2 2

τ 

σ  σ sin 2θ τ cos 2θ 2

MECHANICS OF MATERIALS - I RECITATION 5

1-) Determine (a) the stress components acting on the inclined plane AB, (b) the principal stress and (c) the maximum in-plane shear stress and average normal stress at the point, using Mohr’s circle.

MECHANICS OF MATERIALS - I RECITATION 6

The state of strain at a point on a wrench (İngiliz anahtarı) has components ε 120 10 , ε 180 10 , γ 150 10 . Use the strain transformation equations to determine (a) the in-plane principal strains and (b) the maximum in-plane shear strain and average normal strain. In each case specify the orientation of the element and show how the strains deform the element within the x-y plane.

Hints :

MECHANICS OF MATERIALS - I RECITATION 7

1-) Determine the distance ! to the centroid for the beam’s cross-sectional area; then determine the moment of inertia about the " # and y axes.

2-) Determine the product of inertia of the beam’s cross-sectional area shown above, with respect to the x and y axes that have their origin located at the centroid C.

MECHANICS OF MATERIALS - I RECITATION 8

1-) Determine (a) the location of the centroid C, (b) the principal moments of inertia using Mohr’s circle, for the beam’s cross-sectional area shown above, with respect to an axis passing through the centroid C and (c) the principal angle with z axis.

MECHANICS OF MATERIALS - I RECITATION 9

1-) The horizontal beam, shown above, is assumed to be rigid and supports the distributed load shown. Determine the angle of tilt of the beam after the load is applied. Each support consists of a wooden post having a diameter of 120 [mm] and an unloaded (original) length of 1.40 [m]. Take E 12 %GPa).

2-) The two pipes are made of the same material and are connected as shown above. If the crosssectional area of BC is A and that of CD is 2A, determine the reactions at B and D when a force P is applied at the junction C.

MECHANICS OF MATERIALS - I RECITATION 10

1-) Determine the maximum tensile and compressive bending stress in the beam, shown above, if it is subjected to M = 6 [kNm].

2-) The reaction of the ballast on the railway tie can be assumed uniformly distributed over its length as shown above. If the wood has an allowable bending stress of σ 10.5 [MPa], determine the required minimum thickness t of the rectangular cross-sectional area of the tie to the nearest multiples of 5 [mm].

MECHANICS OF MATERIALS - I RECITATION 11

1-) Determine the maximum magnitude of the bending moment M that can be applied to the beam so that the bending stress in the member does not exceed 100 [MPa].

2-) The Z-section shown above, is subjected to the bending moment of M = 20 [kNm]. Determine the normal stress at point P and the orientation of the neutral axis. Hint: The section has no symmetry either about x or y axes; therefore x and y axes are not the principal axes. First; you need to find the orientation θ of the maximum and minimum principal axes (x # , y #  and their principal moments of inertia.

MECHANICS OF MATERIALS - I RECITATION 12

1-) Determine (a) the maximum shear stress in the T-beam, shown above, at the critical section where the internal shear force is maximum, (b) the maximum shear stress in the T-beam at point C. Show the result on a volume element at this point.

MECHANICS OF MATERIALS - I RECITATION 13

1-) The aluminum strut is 10 [mm] thick and has the cross-section shown above. If it is subjected to a shear of V = 150 [N], determine the maximum shear flow in the strut.

2-) The beam, shown above, is fabricated from four boards nailed together. Determine the shear force each nail along the sides C and the top D must resist if the nails are uniformly spaced at s = 75 [mm]. The beam is subjected to a shear of V = 22.5 [kN].

MECHANICS OF MATERIALS - I RECITATION 14

1-) The motor A, shown above, develops a power of 300 [W] and turns its connected pulley (kasnak) at 90 [revolution/min]. Determine the required diameters of the steel shafts on the pulleys at A and B if the allowable shear stress is τ 85 %MPa).

2-) The solid steel shaft DF has a diameter of 25 [mm] and it is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 [kW] of power to the shaft while it is turning at 50 [revolution/s]. If gears (dişli) A, B and C remove 3 [kW], 4 [kW] and 5[kW] respectively, determine the maximum shear stress developed in the shaft within regions CF and BC. The shaft is free to turn in its support bearings D and E.

MECHANICS OF MATERIALS - I RECITATION 15

1-) The engine of the helicopter is delivering 450 [kW] to the rotor shaft AB, shown above, when the blade is rotating at 1200 [revolution/min]. Determine to the nearest multiples of 5 [mm] the diameter of the shaft AB if the allowable shear stress is τ 73.5 %MPa) and the vibrations limit the angle of twist of the shaft to 0.05 [rad]. The shaft is 0.6 [m] long and made from L2 steel. Take E01 200 %GPa) and G01 75 %GPa).

MECHANICS OF MATERIALS - I RECITATION 16

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 150 %MPa) and τ 84 %MPa).

Wide Flange Sections or W Shapes Designation Area A

Depth d

Web

Flange

Thickness width thickness t

b5

t5

x-x axis I

S

10

106

y-y axis r

I

S

r

10

106

mm9 mm6 mm mm9

mm6

mm

mm x kg/m

mm8

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