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Strength of Materials (ceng 1002) Semester II 2008
Introduction
specimen in tensile test (ultimate strength), imwf Stuttgart
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Strength of Materials Mechanics of Materials Mechanics of Solids from rigid to deformable bodies …
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
stress Cutting plane – inner action equilibrium at particle
stress
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stress example: suspended rod F
- cross section area A [cm²] - Force F [kN]
F A σ
cutting plane inner action equilibrium at particle
stress σ = F / A [kN/cm²] F F
ADDIS ABABA UNIVERSITY Faculty of Technology
F
F
Strength of Materials
Department of Civil Engineering
Strain
2F
F example: suspended rod -Length L -Elongation ∆L
strain ε = ∆L / L
strain ε proportional to stress σ
L
L
L
∆L1
∆L2= 2∆L1
F F
2F
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Hooke’s Law linear equation : σ = Eε E = Young‘s Modulus stress σ [kN/m²]
gradient E [kN/m²]
strain ε
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Hooke’s Law Example: Bungee Cable - Stress Analysis - Serviceability
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties stress-strain diagram of mild steel axial loading tensile test
area of plasticity
determination of tensile strength and Young’s Modulus
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties tensile test σ
ductile material
σ
ε
brittle material
ε
image of failure, compression test ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
stress
deflection Material Properties due to loading
strain specimen in tensile test (ultimate strength), imwf Stuttgart
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Concrete specimen in compression test
free
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
blocked
Department of Civil Engineering
Deflection due to condition of loading
tension
compression
ADDIS ABABA UNIVERSITY Faculty of Technology
bending
torque
Strength of Materials
shear
Department of Civil Engineering
Material Properties Timber perpendicular tensile stress due to shrinkage
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Timber orthotropic material behaviour
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties cycling curves for material creep e.g. synthetics, textiles
time
Danzer, S.18
time
time
time
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Steel
deflection due to temperature (fire exposure) Brandschutzatlas time
time
time
time
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Steel
deflection due to temperature (fire exposure) Brandschutzatlas
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stability Buckling of columns Euler Formula
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stability Buckling of columns
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stability Buckling of columns
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Concept of Design
load assumption :
safety factor
material strength :
reduction factor
stress analysis
:
design stress < allowable stress (stability)
serviceability
:
design deflection < limit deflection
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Unexpected loads
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Design Project “Bottle Bubble”
Example: from an unknown material to construction University of Karlsruhe, 2005
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Behaviour - determining the Elastic Modulus
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Calculation
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Lectures:
Monday 8:15 – 10:00 a.m. Room No4 Karsten Schlesier
Tutorials:
Friday 8:15 – 11:40 a.m.
Room No4
Mesgana Seyoum Consultation: Thursday 4:00 – 6:00 p.m. Room 211 Karsten Schlesier
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Calender Semester II 2008 week
day
Date
1
fr
04.04.2008
Course Information
2
mo
07.04.2008
Introduction to SOM
3
mo
14.04.2008
1
Stress - Axial Load
4
mo
21.04.2008
2
Strain - Axial Load
5
mo
28.04.2008
3
Bending of Beams
6
mo
05.05.2008
3
Deflection of Beams
7
mo
12.05.2008
Lab Session 1
8
mo
19.05.2008
Mid-Semester Exam
9
mo
26.05.2008
4
Torsion
10
mo
02.06.2008
5
Compound Stresses
11
mo
09.06.2008
6
Stability of Compression Members
12
mo
16.06.2008
6
Buckling Analysis
13
mo
23.06.2008
Lab Session 2
14
mo
30.06.2008
Workshop
15
mo
07.07.2008
16
mo
14.07.2008
ADDIS ABABA UNIVERSITY Faculty of Technology
Chapter
Content
Final Exam
Strength of Materials
Department of Civil Engineering
Course Outline 1
Stress – Axial Loads Normal Stress, Shearing Stress, Transformation of Stress, Concept of Design
2
Strain – Axial Loads Strain, Stress-Strain Diagram, Hooke’s Law, Deflection under Axial Load, Material Properties
3
Bending of Beams Stress due to pure Bending, Shearing Stress in Beams, Moment of Inertia, Stress Distribution, Deflection of Beams, Design of Beams
4
Torsion Moment of Torsion, Shearing Stresses and Deformations of Circular Shafts
5
Analysis of plane Stress Compound Stresses, Combined Stresses, Transformation of Stress, Mohr’s Circle
6
Stability of Compression Members Euler Formula, Buckling Load, Buckling Analysis
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Assessment / Requirements Minimum of 75% attendance during lecture hours and tutorials, 100% attendance during practical work sessions (except for unpredicted mishaps) – watch notice for further details. Quota of Total Course Credit:
40% mid-semester examination 40% final-semester examination 20% assignments, practical workshop
Literature Popov, E.P., Mechanics of Materials Beer and Johnson, Mechanics of Materials, 2001 Gere and Timoshenko, Mechanics of Materials, 1990
E-learning Platform www.elboon.net www.ocw.mit.edu
(elearning board online) – under construction! MIT open courseware – Solid Mechanics
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
ADDIS ABABA UNIVERSITY Faculty of Technology
Department of Civil Engineering
G. Galileo
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Introduction
specimen in tensile test (ultimate strength), imwf Stuttgart
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Strength of Materials Mechanics of Materials Mechanics of Solids from rigid to deformable bodies …
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
stress Cutting plane – inner action equilibrium at particle
stress
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stress example: suspended rod F
- cross section area A [cm²] - Force F [kN]
F A σ
cutting plane inner action equilibrium at particle
stress σ = F / A [kN/cm²] F F
ADDIS ABABA UNIVERSITY Faculty of Technology
F
F
Strength of Materials
Department of Civil Engineering
Strain
2F
F example: suspended rod -Length L -Elongation ∆L
strain ε = ∆L / L
strain ε proportional to stress σ
L
L
L
∆L1
∆L2= 2∆L1
F F
2F
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Hooke’s Law linear equation : σ = Eε E = Young‘s Modulus stress σ [kN/m²]
gradient E [kN/m²]
strain ε
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Hooke’s Law Example: Bungee Cable - Stress Analysis - Serviceability
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties stress-strain diagram of mild steel axial loading tensile test
area of plasticity
determination of tensile strength and Young’s Modulus
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties tensile test σ
ductile material
σ
ε
brittle material
ε
image of failure, compression test ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
stress
deflection Material Properties due to loading
strain specimen in tensile test (ultimate strength), imwf Stuttgart
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Concrete specimen in compression test
free
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
blocked
Department of Civil Engineering
Deflection due to condition of loading
tension
compression
ADDIS ABABA UNIVERSITY Faculty of Technology
bending
torque
Strength of Materials
shear
Department of Civil Engineering
Material Properties Timber perpendicular tensile stress due to shrinkage
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Timber orthotropic material behaviour
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties cycling curves for material creep e.g. synthetics, textiles
time
Danzer, S.18
time
time
time
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Steel
deflection due to temperature (fire exposure) Brandschutzatlas time
time
time
time
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Properties Steel
deflection due to temperature (fire exposure) Brandschutzatlas
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stability Buckling of columns Euler Formula
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stability Buckling of columns
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Stability Buckling of columns
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Concept of Design
load assumption :
safety factor
material strength :
reduction factor
stress analysis
:
design stress < allowable stress (stability)
serviceability
:
design deflection < limit deflection
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Unexpected loads
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Design Project “Bottle Bubble”
Example: from an unknown material to construction University of Karlsruhe, 2005
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Material Behaviour - determining the Elastic Modulus
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Calculation
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Lectures:
Monday 8:15 – 10:00 a.m. Room No4 Karsten Schlesier
Tutorials:
Friday 8:15 – 11:40 a.m.
Room No4
Mesgana Seyoum Consultation: Thursday 4:00 – 6:00 p.m. Room 211 Karsten Schlesier
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Calender Semester II 2008 week
day
Date
1
fr
04.04.2008
Course Information
2
mo
07.04.2008
Introduction to SOM
3
mo
14.04.2008
1
Stress - Axial Load
4
mo
21.04.2008
2
Strain - Axial Load
5
mo
28.04.2008
3
Bending of Beams
6
mo
05.05.2008
3
Deflection of Beams
7
mo
12.05.2008
Lab Session 1
8
mo
19.05.2008
Mid-Semester Exam
9
mo
26.05.2008
4
Torsion
10
mo
02.06.2008
5
Compound Stresses
11
mo
09.06.2008
6
Stability of Compression Members
12
mo
16.06.2008
6
Buckling Analysis
13
mo
23.06.2008
Lab Session 2
14
mo
30.06.2008
Workshop
15
mo
07.07.2008
16
mo
14.07.2008
ADDIS ABABA UNIVERSITY Faculty of Technology
Chapter
Content
Final Exam
Strength of Materials
Department of Civil Engineering
Course Outline 1
Stress – Axial Loads Normal Stress, Shearing Stress, Transformation of Stress, Concept of Design
2
Strain – Axial Loads Strain, Stress-Strain Diagram, Hooke’s Law, Deflection under Axial Load, Material Properties
3
Bending of Beams Stress due to pure Bending, Shearing Stress in Beams, Moment of Inertia, Stress Distribution, Deflection of Beams, Design of Beams
4
Torsion Moment of Torsion, Shearing Stresses and Deformations of Circular Shafts
5
Analysis of plane Stress Compound Stresses, Combined Stresses, Transformation of Stress, Mohr’s Circle
6
Stability of Compression Members Euler Formula, Buckling Load, Buckling Analysis
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
Assessment / Requirements Minimum of 75% attendance during lecture hours and tutorials, 100% attendance during practical work sessions (except for unpredicted mishaps) – watch notice for further details. Quota of Total Course Credit:
40% mid-semester examination 40% final-semester examination 20% assignments, practical workshop
Literature Popov, E.P., Mechanics of Materials Beer and Johnson, Mechanics of Materials, 2001 Gere and Timoshenko, Mechanics of Materials, 1990
E-learning Platform www.elboon.net www.ocw.mit.edu
(elearning board online) – under construction! MIT open courseware – Solid Mechanics
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
ADDIS ABABA UNIVERSITY Faculty of Technology
Department of Civil Engineering
G. Galileo
ADDIS ABABA UNIVERSITY Faculty of Technology
Strength of Materials
Department of Civil Engineering
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