# 1/1 SOE 1032 SOLID MECHANICS

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Nov 29, 2013 (5 years and 1 month ago)

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1/1 SOE 1032 SOLID MECHANICS

Website
www.ex.ac.uk~TWDavies/solid_mechanics

course organisation,lecture notes,

Course book:J M Gere, Mechanics of
Materials, Nelson Thornes, 2003, £29.

1/2 TUTORIALS

Three groups, A, B, C

Three sessions

Monday, Tuesday and Friday weeks

8, 9, 10, 11

1/3 LABORATORY SESSIONS

ONE DEMONSTRATION

Week 10

Write up deadline Friday week 11

Hand in to 307 and get it date stamped.

1/4 LEARNING TRIANGLE

ME

YOU

BOOK

1/5 DEFORMATIONS to be studied

Static objects

Extension or compression of a rod

Twisting of a rod by applied torque

Bending of a beam subjected to point
bending moments

1/6 BASIC SCIENCE USED

Newton’s 3
rd

Law, equilibrium
(STATICS)

Auxiliary relationships based on material
properties

e.g. Hooke’s Law

1/7 POSSIBLE MATERIALS

NATURAL

MANUFACTURED

1/8 NATURAL MATERIALS

WOOD

STONE

1/9 MANUFACTURED
MATERIALS

METALS (examples used in this course)

PLASTICS

CONCRETE AND BRICK

CERAMICS AND GLASS

1/10 SCOPE OF COURSE

STRESS AND STRAIN IN SIMPLE
SYSTEMS

DEFORMATIONS IN TENSION,
COMPRESSION & TORSION

STRESS & BENDING IN BEAMS

MOHR’S CIRCLE

i.e. essential parts of Chapters 1 to 5

1/11 NORMAL STRESS

Axial force per unit X
-
sectional area

P/A =

N/m
2

or Pa (like pressure)

Tensile stress (positive)

Compressive stress (negative)

eg m=100 kg held by rod of A = 1 cm
2

g = 10ms
-
2

=P/A = mg/A = 1000/10
-
4

= 10 MPa

1/12 SHEAR STRESS

TANGENTIAL FORCE PER UNIT AREA

P/A =

N/m
2

or Pa

1/13 NORMAL STRAIN

Change in length

caused by normal
stress

=

/L (dimensionless)

Tensile strain

Compressive strain

eg

= 2 mm, L = 2 m, then

= 1
mm/m

or

= 0.1%

1/14 UNIAXIAL STRESS

Conditions are that:

Deformation is uniform throughout the
volume (prismatic bar) which requires
that:

Material is homogeneous

See Section 1.2 in book

1/15 LINE OF ACTION OF AXIAL FORCES FOR
UNIFORM STRESS DISTRIBUTION

Prismatic bar of arbitrary cross
-
section A

Axial forces P producing uniformly distributed
stresses

= P/A

1/16 BALANCE THE MOMENTS

1/17 Mechanical Properties

Strength

compression

tension

shear

Elasticity, plasticity, ductility,creep

Stiffness, flexibilty

Used to relate deformation to applied
force

1/18 Mechanical Testing

Tensile test machine

1/19 Tensile test for mild steel

1/20 Nominal and true SS

Nominal stress based on initial area

True stress based on necked area

Nominal strain based on initial length

True strain based on current length

Use nominal values when operating
within elastic limit

1/21 Test data

linear scale

1/22 TENSILE TEST
SPECIMEN

1/23 BRITTLE MATERIAL

1/24 CAST IRON

-1000
-800
-600
-400
-200
0
200
400
-0.03
-0.02
-0.01
0
0.01
Compression

Tension

1/24 STONE

Compression

Tension

Strain

Stress

5
-
200MPa

1/26 WOOD

Not an isotropic or homogeneous
material

Stronger and stiffer along the grain

Stronger in tension than compression

Fibres buckle in compression

Very high strength/weight ratio

Very high stiffness/weight ratio

1/27 COMPRESSION TEST

1/28 Compression test
-

concrete

1/29 ELASTICITY

1/30 PLASTICITY

1/31 DUCTILITY

1/32 CREEP

1/33 LINEAR ELASTICITY

STRAIGHT LINE PORTION OF STRESS
-
STRAIN CURVE

= E.

(Hooke’s Law)

E is the modulus of elasticity or Young’s
Modulus and is the slope of the curve

For stiff materials E is high (steel
200GPa)

For plastics E is low (1 to 10 GPa)

1/34 POISSON’S RATIO

Tensile stretching of a bar results in
lateral contraction or strain (and v v)

For homogeneous materials axial strain
is proportional to lateral strain

Poisson’s Ratio =
-

(lateral/axial strain)

=
-

(

’ /

)

For a bar in tension

is positive and

is negative, and v.v. for compression.

1/35 Poisson (1781
-
1840)

Normal values 0.25
-
0.35 for metals

Cork about 0 (makes it a good stopper)

Auxetic materials have NEGATIVE

1/36 Axial and lateral deformation

L

B

B.

.

=

/L

1/37 Volume change

V
1
=L*B
2 (original volume)

V
2
=L(1+

)*(B(1
-

*

))
2 (final volume)

V
2
=L B
2
(1+

-
2


-
2

2

+

2

2

+

3

2
)

V
2

L B
2
(1+

-
2

)

1/38 DILATION

V=L B
2

(1
-
2

) (change in volume)

V/V
1
=

(1
-
2

) or (1
-
2

)

/E = DILATION

Max value of

is 0.5

Since

is 1/4 to 1/3 then dilation is

/3 to

/2

1/39 SUMMARY

Stress
-

Force/Area

Strain

(Extension or compression)/Length

For some materials and subcritical loads
strain is proportional to stress (Hooke)

Change in length proportional to change in
width (Poisson). Shrinkage/expansion.

Characteristics determined by experiment