The elasticity and resistance of the materials of engineering . is of z corresponds to cpy or rep. But the total differential, dw, must be considered as made up of two parts ; consequently the rate of variation duo —? will consist of two parts also. If there is no distortion indz the direction of r, or if the distance of a molecule from the onsfm remams the same, one part will be -r.—r = ——. if,^ d{rcp) rdcp however, a units length of material be removed from the dis-tance r to r -f P from the centre (9, Fig. i, while cp remains constant, its length will be changed from i to i . [ i -[- ~ )» i
The elasticity and resistance of the materials of engineering . is of z corresponds to cpy or rep. But the total differential, dw, must be considered as made up of two parts ; consequently the rate of variation duo —? will consist of two parts also. If there is no distortion indz the direction of r, or if the distance of a molecule from the onsfm remams the same, one part will be -r.—r = ——. if,^ d{rcp) rdcp however, a units length of material be removed from the dis-tance r to r -f P from the centre (9, Fig. i, while cp remains constant, its length will be changed from i to i . [ i -[- ~ )» i which p may be implicitly positive or negative. Consequentlythere will result: dw _ dw pdz rd<p r For the reasons already given, there follow: du _ dii J dv dp dy dr dx dx In Fig. 2 let dc be the side of a distorted small portion of the material, the original position of which was de. Od is the distance r ^~^^ from the origin, ad = dr and ac — dw, w^hile dd = w. The angular change , y , ac dw .m position of dc is —, = -7—; but an ad dr in. 26 ELASTICITY IN AMORPHOUS SOLID BODIES. [Art. 7. amount equal to —. = — is due to the movement of r, and isad r not a movement of </<^ relatively to the material immediately adjacent to d. Hence: dw _ dw w , dv __ dpdy dr r^ dz r dcp There only remain the following two, which may be at oncewritten: dw _ dw . dii _ dti dx dx dz r dcp The rate of variation of volume takes the following form interms of the new co-ordinates : ^ _ du dv dw _du dp dw p ,^ dx dy dz ~. dx dr r dcp r ^ Accenting the intensities which belong to the rectangularsystem x, y, z, the Eqs. (11), (12), (13), (20), (21) and (22), ofArt. 5, take the following form: N, =N^ = ^^^d-^2G^ (7) I — 2x dx ^^ R = N: = —^d^2G^ (8) I — 2x dr ^ ^ iV^. = iV^3-^|^^+<^ + ^) ... (9) Art. 8.] EQUATIONS IN POLAR CO-ORDINATES. 2/ ^-=^3 = <S+£) ao) ^-=^-K5+;^) (-) If these values are Introduced in Eqs. (2), (3) and (4), thoseequations will be restricted i
Size: 2082px × 1200px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., book, bookcentury1800, booksubjectbuildingmaterials, bookyear1883
