Question

Problem 2: (34 pts) For the cylindrical tube (outer radius R. 100mm, initial thickness 1mm before loadings, length 1m) fixed at one end on the wall, an axial loading F = 1000 N and a torsional loading T = 100 N-m are applied. Assuming linear elasticity. Young's modulus E-1 GPa and Poisson ratio v = 0.33. (T = **where ) = (R: - R ) is the polar moment of inertia) a) Calculate the stress state (Cro, and Try) of the element at surface, and mark the stresses on the element below. (9 pts) b) Determine the principal stresses ( 0) and absolute max, shear stress surface using either Mohr's circle or equations. (9 pts) at the c) Determine the final thickness (in mm) of the tube wall under applied loadings. (8 pts) d) If the tube is made of brittle material with an ultimate tensile strength Outs fail occur? If not, what is the factor of safety? (8 pts) 5 MPa, will

Answer 1

F = 1000 N Ta 100 nim Ro - 100 mm, RP=98 mm COOP da im , E?! Gipa, MC 0.33 TE(0D Am shear stres enn a n element I 1 CRO" - Ros 20.82N/mm² to ng [1009-989) 11 10.B01 Remya 320 2 12 194380.9 mma 100 N.m X1000 x 100 12194 390.9 20.82 mm Lite S . 82 mm 6x = 2 -A رہے ۔اه 7 (1260)2-6R0229 25 (Ro²_ Rp2] 29 [106-98?) 2 1244. om? on a 200o a 1244.07 20. 80 N/mma 900 C as there is no uesthical force, & directan no force In vertical

® Principal strels. Gotha onto I may not any a = 0.807 ° + Je.so-ogt (0.82 2 0.40 0.91 6 20.90 +0.91 Toa 1.31 w/mm | Cmados porkcipal storiels] Teattle 2 = 0.40 - 0.91 a = -0.51 a/mm mhos principal stress. comprettle Tmarabsolle a an G-a 2 1:31 - (0.517 Ilmaabo a 0.91 w/mmnl 0 Gilen ollimate tenelle strength Gut = 5 o/mm . As pan Rankines theory, for no failure, the maximum poroncipal stress should be less than or equiel b gield Shes, o & Soir fosa out - S 1 2 3 fois ? 3.81