Question

Chapter 15, Supplemental Question 152 A 2.5-in.-diameter solid aluminum post is subjected to a horizontal force of Px = 8.8 kips, a vertical force of Py = 19.3 kips, and a concentrated torque of T = 4.2 kip-ft, acting in the directions shown. Assume L = 3 in. The yield strength of the aluminum is 49 ksi, and a minimum factor of safety of FSmin = 1.67 is required by specification. Consider points H and K, and determine whether the aluminum post satisfies the specifications according to: (a) the maximum-shear-stress theory. (b) the maximum-distortion-energy theory.

A 2.5-in.-diameter solid aluminum post is subjected to a horizontal force of Px = 8.8 kips, a vertical force of P, = 19.3 kips, and a concentrated torque of T-4.2 kip-ft, acting in the directions shown. Assume L = 3 in. The yield strength of the aluminum is ƠY = 49 ksi, and a minimum factor of safety of FSmin 1.67 is required by specification. Consider points H and K, and determine whether the aluminum post satisfies the specifications according to: (a) the maximum-shear-stress theory. (b) the maximum-distortion-energy theory. H K Answers: (a) Maximum-shear-stress theory 1.869 FSH- 2 Answers: (a) Maximum-shear-stress theory 1.869 FSH FSK Accepatable? (Yes = 1, No = 0) (b) Maximum-distortion-energy theory FSH FSK Accepatable? (Yes-1, No - 0) Open Show Work Click if you would like to Show Work for this question:

Answer 1

SectionProperties 08 LYm こ1.302m 13 又. на vlent dorces at H ad k OYLes F,--19:3 kips

反:oki X3 Axial stress at H due to Fy Shear stress at H are b とy: (8.8x1000)(1302) to My duue Torsiorn stress at H 3835 stresses at H : Opsi とxy-一2.591+16. 421 Trircipa Pa=-16, 158 ksi stress at Bending S stress at Kdue to M stる --デ835- Čyz 16,421 ksi

stresses at k -9 7 214 y3 284 hsi yz16.427 ksi Frincipal stress for potnt k 4) Maximm shear stress theor IR 2O8-C-612834 6ksi 38346 element K = 124.361-(-11-01) 35 43s ks i 5438 61) Not acceptable Distortion enexgy theogy element H /2 ニ!(12208)-(Aao8火16-138>t(-16-1 MH 24 63 MPa a 4-63 f고 element K: RA-360% (2436)(-11.07)t (-11-011) 二31.4 ks. 2Fmin table