unit i part2

8/3/2019 Unit i Part2

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Youngs modulus(E) : ratio between tensile

stress and tensile strain or compressivestress and compressive strain.

Modulus of rigidity (C or N or G): ratio ofshear stress to shear strain

E=


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Bulk or volume modulus of elasticity(K) : ratioof normal stress (on each face of a solidcube) to volumetric strain.


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STRESS- STRAIN DIAGRAM


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Point A is called limit of proportionality. Upto this point stress is directlyproportional to strain and follows hooks law.

Point B is the elastic limit. Stress corresponding to this point is themaximum stress to which a specimen regains its original length onremoval of applied load. For mild steel B is very closer to A hencehooks law is followed upto B but for other materials B may be greaterthan A.

Point C( not shown in fig.) is the upper yield point. It has no practical

significance. Point C is lower yield point. The stress at C is the yield stress (y) or

the lower yield point. The yielding begins at this stress and the materialenters into plastic state.

CD represents strain hardening

D is the ultimate point. The stress corresponding to this point is calledultimate stress(ut or y ). This is maximum stress upto which thematerial can with stand without fracture.

E is the fracture point . Stress corresponding this is called breakingstress and strain is called fracture strain. Region between D and E isthe necking region, in which the area of cross section is drastically

decreased.


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ST. VENANT PRINCIPLE

It states that the actual distribution of load

over the surfaces of any body will not effectthe distribution of stress or strain on thesections of the body which are at appreciable

distance(in terms of dimensions) away fromthe load except in the region of extreme endsof a bar carrying direct loading.

Let avg is the direct stress at any section, then

max at 1-1 = 1.387 avgmax at 2-2 = 1.027 avgmax at 3-3 =avg


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FACTOR OF SAFETY

It is defined as the ratio of ultimate stress or

ultimate strength to the working stress. Itcan also be expressed in terms of allowableand ultimate forces or loads respectively,

that a member or a body can resist.Hence Factor of Safety, F.S.

= Ultimate load/Ultimate stress for a member

Allowable load/Allowable stress for a member

For a member to withstand without failure ,this ratio must always be greater than unity


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STRAIN ENERGY

It is defined as the amount of work done (provided that noenergy is added or subtracted in the form of heat) by theload on any body or a member that can cause strain orchange in dimension of that member.

If a tensile or compressive load (P) is applied on the bodywhich causes change in length x, then the strain energy (U)can represented by the shaded area as shown in figure andcan be expressed as

U= Px = (2/2E)Al

Where A is the cross sectional area (where the load isapplied) and l is the initial length of the body. E is Youngsmodulus of elasticity

The unit of strain energy is joule(J) or N-m


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RESILIENCE

The strain energy per unit volume of the material is known asresilience. It is also known as strain energy density. Itrepresent the ability of the material to absorb energy within theelastic limit.

It is denoted by u=2/2E

Modulus of resilience is the maximum elastic energy per unitvolume that can be absorbed without attaining plastic range andcan be expressed as

u = 2y/2E

Where y is yield strength of the material. The modulus of

resilience depends upon the yield strength. Hence a materialwith higher yield strength will have higher modulus of resilience.It is also known as proof resilience.


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SOME BASIC DEFINITIONS

Strength: - property of material by virtue of which it resist to

deformation on applied external load. It is measured in N/mm2

Impact Strength ( or Toughness): - Property of the material to resistthe deformation under impact load or sudden load. Unit of impactstrength is J/m3 . The property of material to absorb energy withoutfracture. This property is very desirable in case of cyclic loading or

shock loading. Unit of toughness is (KJ).

Ductility: - It is the property of the material by which it can bestretched. Large deformations are thus possible in ductile materialsbefore the absolute failure or rupture takes place. Some common

examples are mild steel, aluminium, copper, manganese, lead nickeletc.

Brittleness: - Brittleness is lack of ductility i.e. material cannot bestretched. In brittle materials, faliure takes place with a relativelysmaller deformation.


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Malleability: - This is the property of the material by virtueof which it can be uniformly extended into thin sheetswithout rupture. A malleable material possess high degree ofplasticity.

Creep: - It is the time dependent deformation of the materialunder constant load. When a material deform progressivelywith the passage of time under constant loading, even if the

stress is below yield point, creep phenomena takes place. Itis more pronounced at higher temperature and negligiblysmall at lower temperature and thus it must be consideredfor design of engines and furnaces.

Fatigue: - The phenomenon of the fracture of material undervariable loads( dynamic loads) is termed to as fatigue.These loads may be repeated for many cycles termed ascyclic loads. Hence we can say that referred to as the

phenomenon of fracture under cyclic loading.


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THERMAL STRESS AND STRAINS

If the temp. or a body changes its dimension also changes

correspondingly. The stresses developed in the body due tothese changes are called temperature/thermal stresses and

corresponding strains are called temperature/thermal strains.

let l= Length of bar of uniform cross sectiont1 = initial temp. of bar

t2 = Final temp. of bar

= Coefficient of linear expansion

then the extension in bar due to rise in temperature isl = (t2 - t1 )l = lt

therefore thermal strain= lt/l = t

hence thermal stress = tE


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IMPACT LOADING


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STRESS IN BAR OF VARYING CROSS SECTION


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COMPLEMENTARY SHEAR STRESS

unit i part2

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