Question

0.2 . In Fig . 2 , the solid rod BC has a diameter of 25 mm and is made of an aluminum for which the allowable shearing stress is 20 MPa . Rod AB is hollow and has an outer diameter of 20 mm ; it is made of brass for which the allowable shearing stress is 40 MPa . a ) Determine the largest inner diameter of rod AB for which the factor of safety is the same for each rod . b ) the largest torque that can be applied at A. 0.3

Aluminium Bruss T B Fig. 2

Answer 1

ANSWER:----

POLAR MOMENT OF INERTIA:---- Polar moment of inertia basically describes the cylindrical object’s (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object’s central axis.

TORQUE:---  It is the tendency of a force to rotate an object about an axis. In automotive terms, it is the measure of rotational effort applied on engine crankshaft by the piston.

Given the yompa (brass) BC Diameter - 25 mm allowable shearing stress = 20 up a Caluminium) outer diameter=20mm allowable shearing strona Determine largest inner diameter of Red AB largest Torque let inner diameter of Rod AB = di stress for Rod Be where Juc= polar ponent of inestia TO Maximum eher en stres (oc) - Tesco JBC 4 ㅠ (2044.00) = 1.57 X 24414-06 38330.07mm BL Bc = 3.83x10 m sub in TROL JBL 20 X 10 - TRBC 3.83x108 Where R = Radius of Rod Bc To х 106 Txo.005 3.83 x 108 108 x 3.83x10 20810 8 0.025

o 766 0.025 (T= 30.64 N-m for Rod AB - a JAB Maximum shear stress for AB Rod (STAR) where ₂ = Radius of Roda JAB = polar porest of arestia of An' JAB JAN - I no e Sub TR2 JAB MAB where T= largest torque = 0 = 10 El Nom R₂ = Radius of Rod AB TAB = polar poment of mettia 30.64 0.010 (0.0104 RY yompa (given) 0.3064 3.14 10.0 10" - Ry 40x100 G yox 10 = 0.3 1:57.000R, 6 YOX10 X1.57 = 0 3064 [0.0104 - R"} 0.0104 RY 0.3064 628 x 105 0.004 _R,Y - = 4.378109

1x10 - R, Y = 4.37*159 (trop) -434 vie" 5.63 x 10 9 = RY Ri= 8. 63 x 10 9 3/4 Rio 8.66 x 10 im R. 9.66 mm inner diameter (di) = 8.6662 d = 17.32 mm & Torque obtained = 30.64 N-m