SMU 2113 ENGINEERING SCIENCE

PART 1

Introduction to Mechanics of Materials and Structures

These slides are designed based on the content of these reference textbooks.

To introduce basic principles of the mechanics of

materials and structures.

To illustrate the applications of mechanics of

materials for structural members subjected to simple

loading conditions.

OBJECTIVES

At the end of PART 1, students should be able to:

- calculate deformation, strains and stresses of a structural

member subjected to simple loading, namely axial, direct shear,

torsion and bending.

- identify the various mechanical properties of common

engineering materials.

- analyze elastic deflection of a beam.

A branch of mechanics that studies the

relationships between external loads

applied to a deformable body and the

intensity of internal forces acting within the

body.

Mechanics of Materials

Stress

Strain

Equilibrium of forces

Mechanical properties of materials

Stress-strain diagram

Axial force

Torsion

Bending

Numerous examples/ applications

SCOPE

Typical Engineering Structures

Applications involving combined loading

What types of materials are these structures made of?

Types of loading on structures

LOAD SYMBOL UNITS

(Metrics)

UNITS

(Engineering)

Direct Force F, P N lbf

Shear Force V, Q N lbf

Torsion T Nm lbf-ft

Bending Moment M Nm lbf-ft

Fluid Pressure p Nm-2 psi

Temperature

Difference

T oC oF

Engineering materials: metals and nonmetals

Tension test

The stress-strain diagram

Mechanical properties

Elastic modulus, E

Yield strength, Y

Tensile strength, UTS

Ductility, f

Physical properties

Coefficient of thermal expansion, CTE,

B – DESIGN PROPERTIES OF MATERIALS

Periodic table of elements

Classification of solid materials

Metals - normally, combinations of metallic elements

- elements: aluminum (Al), copper (Cu), tin (Sn), silver (Ag)

- alloys: steels, solders (Sn-37Pb, Sn-4Al-0.5Cu)

- intermetallics: Ti-48Al

Ceramics

- compounds between metallic and nonmetallic elements

- oxides (SiO2), nitrides (Si3N4) and carbides (WC)

- clay cement and glass

- hard but brittle

Polymers

- Many are organic compounds, based on C, H and other

nonmetallic elements

- low density; high strength-to-weight ratio

Other groups – Composites, Semiconductors and Biomaterials

Components on materials science and engineering, and their interrelationship

Performance

Strength of materials

The strength of a material depends on its ability to sustain a

load without undue deformation.

This inherent property is determined by experiment.

One of the most important test is the tension test.

Engineering Stress and strain

P – applied force

Ao – original cross-sectional area

Lo – original gage length

L – instantaneous length

P

P

L Lo

= P

Ao

=

Lo =

L - Lo

Lo

Engineering stress,

Engineering strain,

Percent elongation = Lf - Lo

Lo X100 %

Percent reduction

of area =

A0 - Af X100 % A0

Lf – length at fracture

Tension test machine

Specimen

Load cell

Specimen grips

Crosshead

Data acquisition

system

Extensometer

www.instron.com

Stress-strain diagram (1)

Stress-strain diagram (2)

Y

Plastic Elastic

Necking

Fractured

Fractured Tensile failure in ductile

material is associated

with large plastic

deformation.

Total = el + pl

UTS

f

Stress-strain diagram for ductile material (mild steel)

Yielding and yield strength

Stress-strain diagram for ductile material (aluminum)

Offset yield strength

Example Problem

Solution to example problem (1)

Solution to example problem (1)

Stress-strain diagram for ductile material (mild steel)

Terikan

0.0 0.1 0.2 0.3 0.4 0.5

Tegasan (

MP

a)

0

200

400

600

Ujikaji A

Ujikaji B

Stress-strain curves for Type 316 SS

Properties

Values

y0.2% (MPa)

429

u (MPa)

604

E (GPa )

208

n

0.0935

K ( MPa )

682.65

Stress-strain diagram for stainless steel

Mechanical properties of some materials

Coefficient of thermal expansion (CTE)

A change in temperature, T can cause a material to change

its dimension.

This deformation, T (linear expansion or contraction) of a

member having a length, L can be calculated as

LTT =

where is a physical property called the linear

coefficient of thermal expansion (CTE)

If thermal displacements of a structural member is constrained

by the supports, then thermal stresses must be considered in

design

Thermal properties of materials (1)

Thermal properties of materials (1)