MM 222 Strength of Materials
Lecture 2 Spring 2014
Atif Rasheed Research Associate, FMSE GIKI
E-mail: [email protected]
Contact: +92-3324459510 (Preferably SMS with name and reg. #)
Grading policy Assignments 10% Quizzes 20% Mid Term 30% Final Term 40%
Grading will be relative and lenient Book
Mechanics of Materials by Beer and Johnston 6th edition
References Strength of Materials and Structures by JOHN CASE, 4th Ed. Mechanics of Solid Materials by J. Lemaitre and J. L. Chaboche Applied Mechanics of Solids by Allan F. Bower (available online at http://solidmechanics.org/contents.htm) Related ASM Volumes E Journals
Introduction to Mechanics/Strength of Materials
Which of the following images in not the representation of a material???
Ans: (b) As it represents imagination which is not a material
Material
(a) (b) (c)
Types of deformation
Elastic deformation
The deformation that is recovered at the removal of load is called elastic deformation
Types of deformation Plastic deformation
Fracture
The deformation that cannot be recovered at the removal of load is called plastic deformation Permanent deformation
Separation or fragmentation of a solid body into two or more parts under the action of stress
Axial loading A load applied along or parallel to primary axis, e.g. tension and compression
Figure: Soil compression test Figure: Bolt under tension
Normal stress Force normal to the object. = P/A = MPa
Figure: Soil compression test Figure: Bolt under tension
Shearing stress Stress parallel to the surface of the material it acts. = P/A = MPa
Normal/Shearing stress
Normal/Shearing stress
Stress at a point
AP
AF
aveA=
=
0
lim
Why Stress at a point?
20 m (200X)
Gray Cast Iron o Ferrite (Bright phase with black graphite flakes) o Pearlite (+Fe3C, dark phase)
A
B
A
B
Stress at a point
Figure: Stress distribution is different at different points of the cross-section
Stress at a point
In general, stress is taken as uniform.
Uniform normal stress passes through the centroid (C) of the section.
Centroid
The center of mass of a geometric object of uniform density.
Uniform stress through centroid
Centric loading
A load that passes through the centroid of the section
In centric loading, stress distribution is uniform
Eccentric loading
A load parallel to the primary axis of the section but not passing through centroid of the section
In eccentric loading, stress distribution is not uniform
Shear
The magnitude of resultant of shearing forces is called as shear and is denoted by P
Average shear stress = = P/A
Single shear
P = F
Average shear stress = = P/A = F/A
Tendency to slide on one plane
Double shear
Tendency to slide on two planes
Weight (Gravity) = W Reaction force = W/2 Reaction force = W/2
Two force member
Double shear
Tendency to slide on two planes
F = 2P P = F/2
avg = P/A = F/2A
Single/Double shear
Single shear
Double shear
Bearing stress in connection
dtP
AP==b
Chapter # 1 (Beer and Johnston, 6th ed.)
Introduction Concept of stress Forces in the members of a simple structure
Can the structure bear 30 kN load?
AB is a boom with a rectangular cross-section of 30*50 mm)
Boom
Chapter # 1 (Beer and Johnston, 6th ed.)
Introduction Concept of stress Forces in the members of a simple structure
Can the structure bear 30 kN load?
AB is a boom with a rectangular cross-section of 30*50 mm)
BC is a circular rod with 20 mm diameter
Rods
Chapter # 1 (Beer and Johnston, 6th ed.)
Introduction Concept of stress Forces in the members of a simple structure
Can the structure bear 30 kN load?
AB is a boom with a rectangular cross-section of 30*50 mm)
BC is a circular rod with 20 mm diameter
Boom and rod connected through pins and brackets
Pins and brackets
Figure: Pin and bracket
Chapter # 1 (Beer and Johnston, 6th ed.)
Introduction Concept of stress Forces in the members of a simple structure
Can the structure bear 30 kN load?
AB is a boom with a rectangular cross-section of 30*50 mm)
BC is a circular rod with 20 mm diameter
Boom and rod connected through pins and brackets
To calculate forces in the structural members, well draw free body diagram
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