Question

Dimensions in mm 180- --120---100 100 Problem 1: Two cylindrical rods, one of steel (Ex = 200 GPa) and the other of brass (Eb = 105 GPa), are joined at C and restrained by rigid supports at A and E. For the loading shown, determine: (a) the reactions at A and E, (b) the deflection of point C. cl DE Brass Steel B. 760 KN 40KN 40-mm diam. 30-mm diam. Problem 2: A 15-mm-diameter rod made of an experimental plastic is subjected to a tensile force of magnitude P = 3.5 kN. Knowing that an elongation of 11 mm and a decrease in diameter of 0.62 mm are observed in a 120-mm length, determine the modulus of elasticity, the modulus of rigidity, and Poisson's ratio for the material. 15-mm diameter 120 mm

Answer 1

For the first part we have applied the force balance between given force and assumed reaction force at point A. And E .

Direction of reaction are assumed at starting in opposite to that of applied forces .

Compatibility equation is used at various section of given bars in four diffrent parts .

For second question or problem 2 we have used simple relation of Poisson ratio and hooke's law and after that we used the relation between modulus of elasticity , modulus of ridigity and Poisson ratio

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mm 180, 120 Steed & bokN Brags - 40 KN Dia = 4omn Dia=30 mm RA Чə kw 4 Es = 200 GPa Fo= 105 Gla we will considen that Reaction at A and E is RA & RE Albic [ D i EL RE ! Чокм . І we will use compatibility equation As net deflection ich both ban will be zaro Force balance IRATRE = GORAH YOKN) = 100KN - Compatibility eque Ist det det du o que Jose 0 TRAX 180X163 7 R-60)x180x10 37 4 RA-60)x looxlu 3 1 Combatibilith L (04)*x200x107 15(0.01) X 200x10") L7 (0.033x105xid] equation + (RA-100), 100x103 = 0 2 (0.03 ) ²x 105x109

on simplification of compatibility equation RAXISO + (RA-60)x120 + RA-60)x100 + RA-100)x100 = 0 Coulxgoo (1048x200 (0.038x105 (0.037x105 TRA = 37.47 KN dus wen As we know RATRE=100KN RE= 62.53 kN] answer Deflection of Point c = f, the - RAX 180x10 3 (RA-60 )x120x103 26. 0u5 x 200 x103 21.047x 200 x 107 (000000 = Jedno 37.47X180 +(22)x120 X 200x109 1 Deflection of c = 0.0160mm dulwa

p=3.5KN length= de 120 m d 15 mm dianeton =D p=3.5KN Poisson's ratio: M -0.6. - 0.45 WA (de) (11) deswen IdD=-0.62mm as it is decrease ) modulus of elasticity E = pe = 3-5xlox/Rovio? Alde) x (0.015) (11x103) E = 3.24 MPa using relation TE=2G (1+ M) Gr=modules of rigidity Me poisson's ratio 3.24 = G 2(H.45) TG = 1.11 MPa