1/1 soe 1032 solid mechanics website ~twdavies/solid_mechanics ~twdavies/solid_mechanics course...
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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.
1/3 LABORATORY SESSIONS
ONE DEMONSTRATION Week 10 Write up deadline Friday week 11 Hand in to 307 and get it date
stamped.
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 3rd Law, equilibrium
(STATICS)
Auxiliary relationships based on material properties – e.g. Hooke’s Law
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/m2 or Pa (like pressure) Tensile stress (positive) Compressive stress (negative) eg m=100 kg held by rod of A = 1
cm2
g = 10ms-2
=P/A = mg/A = 1000/10-4 = 10 MPa
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
1/17 Mechanical Properties Strength
compression tension shear
Elasticity, plasticity, ductility,creep Stiffness, flexibilty Used to relate deformation to
applied force
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
1/26 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
1/33 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
1/37 Volume change V1=L*B2 (original volume)
V2=L(1+ )*(B(1- * ))2 (final volume)
V2=L B 2(1+ -2 -22+ 22 +32)
V2L B 2(1+ -2)
1/38 DILATION V=L B 2 (1 -2) (change in volume) V/V1=(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
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