poruttiRaniyal koLgaigaL
(Fundamentals of Mechanics of Materials)
The following are the transliterated (Adami format) version of the tamil compositions (kural/venpa) of Dr. S. Ilanko on the Mechanics of Materials. The compositions give the basic definitions and explanations including formulae such as Hooke's law.

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Dr. Ilanko teaches at the Dept. of Mechanical Engineering, Univ. of Canterbury, New Zealand and can be reached via Email: Ilanko@mech.canterbury.ac.nz. My sincere thanks go to Dr. Ilanko for permitting me to distribute these compositions to the general public through this web page.
K. Kalyanasundaram (kalyanasundaram@epfl.ch)

poruttiRaniyal koLgaigaL
(Fundamentals of Mechanics of Materials)

thagaippu (stress)
udhaippizhuvai koyvaip parappaal pikka varum
visaich seRivu thaanE thagaippu
(Stress is the intensity of force, and is obtained by dividing the force (compressive, tensile, or shear) by area.)

iNaik koyvu (complementary shear)
koyvuth thagaip pedhaRkum sendhagaippuk koottuLadhu
seyyum thozhil muRukku nikkal.
(Shear stress always has a complimentary component to balance the torque.)

isivu (strain)
izhuththaal n niLum, koydhaal uru maaRum
azhuththak kuRugum avai isivu.
(Stretching causes extension, compression causes shortening and shear causes distortion. These are the types of strain.)

aLavonRin maaRRaththai aLavaalEyE vaguppin
eLidhaayk kidaikkum isivu.
(Strain is the change in a dimension divided by its original value.)

thagaippu-isivuth thotpu (Hooke's law)
kuRiththa thagaippiRkuk kuRiththa isivu oru
kuRiththa poruLukkidhu maaRaadhu - maRuththu
miL thanmai than ellai miRinaal maaRumE
mER sonna thagaippisivin thanmai.
(For a given material, for a given stress, there is a specific value of strain. This stress strain relationship does not change, until the elastic limit is reached.)

thagaippaiisi vaalvaguppin miLdhanmai mattuk
kidaikkum idhumaa Rili.

(The elastic modulus is obtained by dividing the stress by strain. This modulus is a constant.)

thagaippisivu varaibin padiththiRanE yimmattaam
thagaippisivin thanmai tharum.

(The relationship between the stress and strain is indicated by the slope of the stress strain diagram, which gives the elastic modulus.)
vaLai vaLaidhal (Beam bending)
vaLaiyil sumai thaakkin vaLaiyum, adhil engum
viLaiyum vaLai thiruppam, koyvu.
(If a beam is subjected to loading, it would bend, resulting in a distribution of bending moment and shearing force.)

udhaippu oru puRaththil, izhuvai maRu puRaththil,
thagaippin nilaimaiyadhu maaRum.
(The nature of stress cjhanges from being compressive on one surface to tensile on the opposite side.)

udhaippu, izhuvai yaRRa, isivu aRavE aRRa
adhaith thaan nadunNilai achchenga.
(The neutral axis is the axis where there is no tensile or compressive stress and strain.)

maaRum thagaippin thiRan vaLaikkum thiruppu thiRan
koodum idhu paLuvaik koottin.
(The resultant of the stress distribution is the bending moment, which increases with load.)

vaLaiyin kuRukku vettu vazhiyE thiraLum andha
visaiyE, mudhalil sonna koyvu.
(The resultant force along the cross section is the shear force.)

vaLaidhiruppam, koyvu, vaLaiyil azhuththu paLu,
ivai kodukkum OyvuRudhi isaivu.
(Bending moment, shear force and the load will be in static equilibrium.)

paLuk koodin irandum pivaagak koodum,
migak koodin vaLaiyO sidhaiyum.
(Bending moent and shear force increase with load, and the beam can fail due to excessive load.)

vaLaidhiruppam koodin vaLai kooduma koodal
vaLai thaangum vadivaththil thangum.
(The deflection of a beam increases with load, this increase being dependent on the way the beam is supported.)

vaLaidhiruppam, koyvu, paLu aagiyavaRRinidaiyEyuLLa thotpu
(The relationship between bending moment, shear force, and load)
thaakkum visaichcheRivuk kidaagak koyvuvisai
maaRRam uRum niLaththOdu.

(The change of shear force along the length of the beam depends on the intensity of applied load.)
koyvin padiththiRanum azhuththum paLuchcheRivum
seyyum nigaranNilai Oyvu.

(The rate of change of shear force (gradient of the shear force diagram) and the intensity of loading are equal for equilibrium.)
aLikkum paLuvisaiy puLLi thanil thaakkin
azhikkum koyvu visaiththotchchi.

(If the load is applied at a point (concentrated load) the shear force will have a discontinuity (jump in the shear force diagram).
puLLivisai thaakkin koyvu visaivaraibu
thuLLi yezhum eeduseyya.

(The jump in the shear force diagram is equal to the applied concentrated load (for equilibrium).
vaLaidhiruppam koyvuvisaik kERRa padiththiRanO
tisaindhiRangi yERinNilai pENum.

(The jump in the shear force diagram is equal to the applied concentrated load (for equilibrium).
vaLaidhaR Ragaippu (bending stress)
 vaLai vaLaiyach sendhaLangaL vaLaiyaamai yaaRchiraay
viLaiyum n isivinadhu maaRRam.
(Since plane sections remain plane during bending, the normal strain varies linearly with distance.)

nErisivu smaaRRaNG koLLa adhaiyoththu
n thagaippum siraaga maaRum.
(The normal stress would alsovary linearly, since the strain varies linearly.)

nER thagaivu nER maaRRaNG kondE nadu achchil
thagaivu maRRu odungum.
(Normal stress varies linearly, and vanishes at the neutral axis.)

Or puLLi, nadukkOdu, irandiRkum idaiththolaivil
sndhuLLadhE angu thagaippu.

(The normal stress depends on the distance from the neutral axis.)
vaLaidhaR Ragaippuch sooththiram/saman paadu
(Bending Stress Formula)
 vettu mugapparappin irandaam thiruppamadhai
natta naduppaRRik kandadhanaal - itta
thaakkaththin vaLaidhiruppam thanai vaguththu idaiththolaivai
aakkip perukkin thagaippu.

(Euler-Bernoulli beam bending formula: The normal stress is equal to the bending moment times the distance from the neutral axis divided by the second moment of area about the neutral axis.)
vaLaivuth thadai (flexural rigidity)
parappi Nnirandaam thiruppam miLdhanmai maaRiliyaip
perukkin vaLaivuth thadai.
(The flexural rigidity is the product of Elastic modulus and the second moment of area about the neutral axis.)

vaLaibeychchi kaNiththal (bending deflection)
vaLaidhiruppam thannai vaLaivuth thadaiyaal vaguththu
viLaivadhanaith thogaiyittaal vaLaisaayvu -viLaivai
mindum thogaiyittaal idappeychchi idhai vEndin
vEndum iru ellaippaNbu.
(The slope of a beam is obtained by integrating the ratio moment to flexural rigidity. Integrating again gives the displacement, the determination of which requires two boundary conditions.)

ellaip paNbu (boundary conditions)
vaLaiyin idappeychchi thannai varaiyaRukkum thaangal
nilai ellaip paNbu.
(The boundary conditions for a beam are the support conditions that determine the deflection.)

nilai iyalaaR RuNiya iyalaadha vaLaikkaayin
pala ellaip paNbellaam vEndum.
(Statically indeterminate beams require more boundary conditions.)

thaangaR paNbu (types of support)
 kaththi munaith thaangal thiruppaththaith thaangaadhu
eththagaiyavaaRum siyum.
(Knife edge supports, cannot sustain moment and permit rotation.)

azhuththap pidiththaangal angingu sikkaadhu
azhuththip pidiththu vaLai thaangum.
(Clamping prevents rotation.)

koyvup puLLi (shear centre)
kOdu paRRich sillaa mugavettuk
k puLLi kaaN koyvup puLLi.
(For a beam that does not have two axis of symmetry, one must determine the shear centre.)

koyvin naduppaLLip kOttinilE paLuththaakkin
eLLin aLavumillai muRakkal.
(If a load is applied through the shear centre there will be no twisting.)

uRudhi kedal (buckling)
azhundhip paLuvEndhum adibol pala madangu
ezhundhakkaal kaal anRiR RooN.
(Members subject to compressive loading, are taken as slender columns if the slenderness ratio (effective length or height/radius of gyration, the latter of the order of the width) exceeds about 10 (12 according to a code of practice). Otherwise they may be treated as short columns. In Tamil the words kaal, and tooN nicely describe these (Dr J Raamachandran, IIT Madras is the one who pointed this out to me.))

kaal koona, thooN sidhaiya, seyyum karaimiRik
kOl midhu konda paLu.
(Excessive load causes crushing of short columns, and buckiling of slender columns.)

muRukkal (torsion)
thandin nadukkOttaip paRRi yorudhiruppam
undaakkum koyvisivu muRakkam.
(Torque is a moment about the axis of a shaft that results in shear stress and shear strain.)

vatta vadivuk kuRukku vettu mugaNG konda
vittamadhu nEraaga niRkum.
(The diameters of circular shafts remain straight during twisting.)
vaLaiyaadha vittaththin thanmaiyinaaR koyvum
alaiyaamal aaraiyudan koodum.
(Since the diameters remain straight, the shear (stress & strain) vary linearly with radius.)

naduvinilE koyvisivu thagaippillai veLiviLimbaith
thodumaLavum siraagak koodum.
(Shear stress and strain are zero at the centre. They increase linearly upto the (outer) radius.)
muRukkaththai mugapparappin munaiyth thiruppaththaal
piththaarai yaaRperukkin thagaippu.
(Shear stress is equal to the product of torque and radius divided by the polar second moment of area.)
thagaippadhanai koyvukkaay maaRaadha mattaal
vaguppadhanaal varuvadhisivu.
(Shear strain is obtained by dividing the shear stress by the shear modulus (a constant).
kuRukkuvettu mugamvatta vadivamaiyaa vittaalO
poruththamilai mERchonnavai.
The above are not applicable for non-circular cross sections.)

mensuvk kuzhaayin muRakkal (Torsion of a thin tube)
siraana mensuvgoL kuzhaayil muRukkamadhu
maaRaadha koyvaith tharum.
(Shear stress and strain in a thin circular tube of uniform thickness would be the same at any point.)
muRukkaththai eeradakkap parappaal, suvththadippaal
vagukkavarum koyvuth thagaivu.
(The shear stress (in thin walled tubes) is torque divided by twice the encosed area and the thickness.)


>azhuththa mengalangaL (Pressure vessels)
uLLazhuththam mengalaththuL undaakkum thaakkam
uLLizhuvai Nndhagaivukkidu.
(Internal pressure in a thin vessel is balanced by the induced tensile stress.)
thagaippizhuvai kaaNbadhaRku mengalaththaik kooRu
paduththi visai nigisaiyach seyga.
(To determine the tensile stress, take sections of the thin walled vessel, and apply the equations of equilibrium.)
seerkOLa mengalaththin aarai azhuththam perukki
thadippinaal vaguppin thappu.
(For spherical shells of constant thickness, the stress is equal to the product of the radius and pressure divided by twice the thickness.)

>nEr thagaivu, koyvu koottal (Compound stresses/ Mohr's circle)
nEr thagaivu, koyvu thaLamiruppin sevvachchil
vatta ozhukkil odungum.
(The normal and shear stresses (in-plane), plotted on cartesian axis will lie on a circle.)

nEr isivu, koyvu koottal (Combining strains/ Mohr's circle)
nEr isivO koyviR paadhiyudan sevvachchil
isaindha vattaththil odungum.
(Normal strain vs half of shear strain relationship also results in a circular graph.)

samanNilaich samanbaadugaL (Equilibrium equations)
eth thaakka eNNikkai nilaiyiyaliR peRRa
nikkOvaik kooRRugaLai miRin -pudhiranRu
nilaiyiyalaal theLivaagaa amaippidhanai vadiva
nilaiththotpaal thuNindhidalaam kaaN.
(If the number of reactions exceed the number of equations of equilibrium, the resulting structure is statically indeterminate. However, it can be analysed using conditions of geometric compatibility.)

eth thaakkam nik kOvaik kooRRaividak kunRin
it kant uRudhiyilaa amaippu.
(If the number of equations exceed the number of unknowns, the structure may be unstable.)

uRudhiyilaa amaippu udhavaadhen Raagaadhu
aRudhi muzhumaiyilaa amaippu.
Lack of stability does not render a structure lseless, it just means it is a semi-definite system.

aRudhi yilaaamaippu azhuththum visaikkERpa
viRuvi RenavEgam koLLum.
Semi-definite systems accelerate, according to the applied force.
The elastic modulus is obtained by dividing the stress by strain. This modulus is a constant.
- - - - - - - - - - - - - -
tharaththil thamizh mozhiyin
siRappuyarach seyyum sendhiruvaam aRiviyalai
niRaiththuyarach seyya nensuyarum nammavin
kaRaiththuyara midinNOy kazhiyum kalaivaazhum

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