ELASTIC MODULII AND THEIR RELATIONSHIP BY CONSIDERING ANY ARBITRARY ANGLE

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1 Itratioal Joural of Mchaical girig ad Tcholog (IJMT Volum 7, Issu, March-April 016, pp , Articl ID: IJMT_07_0_004 Availabl oli at Joural Impact Factor (016: 9.86 (Calculatd b GISI ISSN Prit: ad ISSN Oli: IAM Publicatio LASTIC MODULII AND THIR RLATIONSHIP BY CONSIDRING ANY ARBITRARY ANGL NAZIM A. KHAN Dpartmt of Mchaical girig, Mwat girig Collg (Waqf, Palla, Nuh, Mwat-1107, Haraa (Idia KALM A. QURAISHI Dpartmt of Applid Scics ad Humaitis, Mwat girig Collg (Waqf, Palla, Nuh, Mwat-1107, Haraa (Idia ABSTRACT I this papr, w obtaid a rlatioship amog Youg Modulus of lasticit, Bulk Modulus of lasticit K ad Rigid Modulus of lasticit G b cosidrig a arbitrar agl. Kwords ad Phrass: Youg Modulus of lasticit; Bulk Modulus of lasticit; Rigid Modulus of lasticit; Rlatio btw lastic moduli. Cit this Articl: Naim A. Kha ad Kalm A. Quraishi, lastic Modul II ad Thir Rlatioship b Cosidrig a Arbitrar Agl, Itratioal Joural of Mchaical girig ad Tcholog, 7(, 016, pp INTRODUCTION Hook's Law Strss producd i a bod is dirctl proportioal to strai i th bod, withi th lastic limit. strss Costat of lasticit strai Now dpdig upo th tp of strss ad strai producd i th bod, costat of lasticit is of th followig thr tps: 33 ditor@iam.com

2 Naim A. Kha ad Kalm A. Quraishi (i Modulus of lasticit ( Normalstrss Normalstrai (1.1 (ii Modulus of Rigidit (G Shar strss G (1. Shar strai ta s (iii Bulk modulus (K K Hdrostatic strss Volumtric strai ( ditor@iam.com

3 lastic Modul II ad Thir Rlatioship b Cosidrig a Arbitrar Agl. MAIN RSULT Th rlatioship amog Youg Modulus of lasticit amog, Bulk Modulus of lasticit K ad Rigid Modulus of lasticit G is giv b 9 K G (.1 G 3 K cos 4 whr is th agl through which fac AD tiltd from its origial positio. 3. DRIVATION Cosidr a two dimsioal bod subjctd to shar strss as its lowr surfac is fid ad forc is applid o th uppr surfac. Du to producd shar strss th lgth of th diagoal DB will icras ad lgth of diagoal AC will icras. Th surfac AB will shift rightward to A B as show i figur ditor@iam.com

4 Naim A. Kha ad Kalm A. Quraishi From triagl ADA AA AA ta AD AA ta BB (3.1 DB DB B B 0 Strai producd i diagoal DB (3. DB From triagl B BB 0 cos B B 0 4 BB B 0 B BBcos 4 From (3. ad (3.3, w gt BB cos 4 Strai producd i diagoal DB From (3.1 ad (3.4, w hav ta cos 4 Strai producd i diagoal DB Liar strai producd i diagoal DB ( 1 From (3.5 ad (3.6, w gt ta cos 4 (1 (3.3 (3.4 (3.5 (3.6 (1 ta cos 4 From (1., w hav G(1 (3.7 cos 4 Cosidr a thr dimsioal bod of lgth, bradth b ad thickss t. Suppos th strss iducd i th bod alog lgth b. Similarl strss iducd i th bod alog bradth b ad thickss t b ad rspctivl. As w kow that strai iducd i th dirctio of forc applid is logitudial or liar strai ad strai iducd i th prpdicular dirctio of forc applid is latral strai ditor@iam.com

5 lastic Modul II ad Thir Rlatioship b Cosidrig a Arbitrar Agl 37 ditor@iam.com For calculatig th liar strai i th particular dirctio, latral strai iducd i th othr dirctio b th sam forc is to b subtractd for that particular dirctio. Strai producd i th lgth b t Ovrall volumtric strai producd is t b V ( V (1 3 V (1 3 K (3.8 limiatig from (3.7 ad (3.8, w gt th mai rsult (.1.

6 Naim A. Kha ad Kalm A. Quraishi RFRNCS [1] Chakraborti, M.; Strgth of Matrials, Scod ditio, S. K. Kataria ad Sos, Nw Dlhi, 001. [] Rdr, G. H.; Strgth of Matrials, Third ditio i S. I. Uits, Macmilla Publishrs Idia Limitd, Nw Dlhi, 1969; Rpritd i 011. [3] Sigh, S.; Strgth of Matrials, Tth ditio, Khaa Publishrs, Nw Dlhi, 010. [4] Prav Ailawalia ad Shilp Budhiraja, Disturbac I Gralid Thrmolastic Mdium with Itral Hat Sourc Udr Hdrostatic Iitial Strss ad Rotatio, Itratioal Joural of Mchaical girig ad Tcholog, 3(3, 01, pp ditor@iam.com

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