MM222 Lectures 2

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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