FCE 231 Lesson 1 Lecture Notes [Compatibility Mode]

8/3/2019 FCE 231 Lesson 1 Lecture Notes [Compatibility Mode]

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FCE 231 STRENGTH OF MATERIALS 1A

LESSON 1

LECTURE NOTES


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Recommended Textbooks The Science and Technology of Civil

Engineering materials, Young, Mindess, Grey& Bentur, Prentice Hall 1998. (2).

Strength of Materials and Structures- Case &

Chilver.

A text Book of Strength of Materials, R.K

Bansal Strength of Materials Part 1, Timoshenko

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Course Outline:

Direct stress and strain elasticity and plasticity.

Stress resultants.

Stresses in members subjected to axial force,bending, shear and torsion.

Section properties.

Symmetrical and unsymmetrical bending ofbeams.

Deflection of beams.

Analysis of stress and strain Mohrs circle ofstress and strain.

Thin walled pressure vessels.6/15/2011 3


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Laboratory Work

Tensile test; Torsion test; Compression test;

Hardness test; Bending of beams.

Unsymmetrical bending of cantilever ; shearcentre of channel ; Deflection of beams

steel, hardboard, perspex, aluminium.

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Direct Stress and Strain Elasticity

and Plasticity

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When a solid material is subjected to external

loading, it deforms instantaneously. Ingeneral, as long as the stresses are relativelysmall, this deformation is reversible, so whenthe load is removed, the material will return toits original dimensions. Such deformations

are termed elastic, and they correspond tothe region of small displacements from theequilibrium position of the atomic force

displacement curve.


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Atomic Force-Displacement Curves

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Force distance Curve for (a) Strongly and (b) weakly bound solids


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Definition of Stress and Strain

For most structural materials subjected to loads within their elastic range,

the relationship between stress and strain is linear

(or nearly so).

When a material is loaded in tension, it elongates. There are two

parameters that characterize this behaviour. The first is axial

stress , which is defined as the total applied load, P, divided by

the original crosssectional area, Ao, of the specimen.

= P/Ao(1)

Stress is usually expressed in units of Pascals (1 Pa = 1 N/m2).

The second parameters is the axial strain, , which is elongation, , per unit

length of the specimen. = /l (2)

where lo is the original length of the specimen. Note that strain is a

dimensionless quantity.

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Stress and Strain

=P/Ao (Pascal = 1 N/mm2)

Longitudinal stress (x)

=/lo (Dimensionless )

Longitudinal strain(x)

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Lateral DeformationIn addition to axial strain, a member will also contract laterally

under tensile loading. The ratio of transverse strain ( y and z )to longitudinal strain x is known as Poissons ratio, , and is

expressed as :

=- y/ x = -y/ x (3)The negative sign is used because under tensile loading, the

transverse strains are contractions.

For most metals, =0.33; for other engineering materials, ranges from about 0.16 (wood) to 0.50 (ideal elastomeric

material such as rubber).

Axial loading of a material also induces a volumetric change.6/15/2011 9


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Examples of tensile forces

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2.10 cm diameterTensile load

application

2.50 cm diameter


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Transverse Deformations

Transverse stress (y)

Transverse strain(x)

Poissons ratio

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Volumetric Change

SEE MAIN NOTES

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Elastic Behaviour Elasticity is that property of a material to return to its

original dimension after removal of a load. This isparticularly so in regions of small displacements from

equilibrium position of the atomic force

displacement. For linearly elastic materials the relationship

between stress and strain can be described by

Hookes law : i.e. =E Where E is the modulus of elasticity, sometimes

known as Youngs modulus

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Elastic Behaviour (contd)

Generally, Hookes law applies to a relatively

small range of strains. For large strains, therelationship between stress and strain is no

longer linear, and Hookes law no longer

applies.

For most structural materials subjected to

loads within their elastic range, therelationship between stress and strain is linear

(or nearly so), as shown below :

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Elastic Behaviour

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Modulus of Elasticity, EBecause the concept of proportionality between

stress and strain is such a powerful one, a

number of different elastic moduli have been

defined which can help to characterize the stress strain behaviour of such materials. These are

defined in the figure below.

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Elastic modulus

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Methods of Characterization of

Elastic Behaviour Initial tangent modulus

This is the slope of the curve at the origin, andapplies to small stresses and strains

Secant modulus

This is a more common measure of stiffness. This

is the slope of the line joining the origin and any

arbitrary point on the curve. The value depends

on the level applied stress chosen.

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Methods of Characterization of

Elastic Behaviour (contd) Chord modulus

This is the slope of the line between any two arbitrary points on the

curve. It is often used in place of the secant modulus because it is

difficult to measure the beginning of the curve accurately.

Tangent Modulus

This is the slope measured at the point of interest. This is a bettermeasure of the materials response to small additional stresses. It is

useful when one is interested in the additional strain that occurs when

an additional stress is imposed on the already loaded material.

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Elastic Behaviour (contd)Elastic behaviour may end in the one of two

ways, by fracture or by yielding of the material.

In neither case will the specimen return to itsoriginal form when it is unloaded.

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Fracture

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Yielding

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i h i


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Non Linear Behaviour

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Fatigue loading

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FCE 231 Lesson 1 Lecture Notes [Compatibility Mode]