"7laha - Torsion"
Smart structure problems for never stop thinking
Source: Mechanics of material by
Ferdinand p. Beer and E .Russell Johnston
(3.53) The composite shaft shown consist of a 5-mm-thick brass jacket (G brass=39Gpa) bonded to a 40-mm diameter steel core (G steel =77.2 G pa) . Knowing that the shaft is subjected to a 600(N .m) torque .
Determine:
(1) the maximum shearing stress in the steel core .
(2) The maximum shearing stress in the brass jacket.
(3) The angle of twist of B relative to A .
Solution:
J=π(C^4)/2
J b =π*(.025^(4) -.02^(4) )/2 =3.6 *(10^-7)
J s =π*(.02^4)/2 =2.5*(10^-7)
T steel /T brass =J b /J s =1.4 so T s =350 N. m T b =250 N. m
τ=T*c/J so τ b max =250*.025/J b =17.3 M pa τ s =350*.02/J s =28 M pa
φ r = T s *2/(G*J)s =2.05 deg
(3.58) Two solid steel shafts are fitted with flanges that are Then connected by bolts as shown .the bolts are slightly Undersized and permit a 1.5 deg rotation of one flange With respect to the other before the flanges begin to rotate As a single unit .knowing that (G=77 Gpa) .
Determine the maximum shearing stress in each shaft when a torque
Of T magnitude is 570 N .m is applied to the flange C.
Of T magnitude is 570 N .m is applied to the flange C.
Solution:
J=π(c^4)/2
| J AB=π*(.015^4)/2 =7.9(10^-8) J CD =π*(.018^4)/2 =1.6*(10^-7) Φ r=.026 Rad Φ=T*L/GJ Φ r = (570*.9)/ (7700*1.6) - T AB*.6 /(770*8)  T AB = 120 N .m TCD total =570-120=450 N .m τAB max =120*0.015/ J AB = 22.5 M pa. τCD max =450*.018/J CD =50.6 Mpa |
very good
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