1/1 SOE 1032 SOLID MECHANICS

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Nov 29, 2013 (3 years and 8 months ago)

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1/1 SOE 1032 SOLID MECHANICS


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


course organisation,lecture notes,
tutorial problems,deadlines


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
under an axial load


Twisting of a rod by applied torque


Bending of a beam subjected to point
loads, uniformly distributed loads and
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
and 7 (see reading list).


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:


Loads act through the centroid


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


Concrete about 0.2


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