Question

3. As shown, the portion AB of the lever has a diameter of 1.2 inch, determine (a) Cartesian stresses at point H, sketch the results in a cubic element representing at point H location, (b) Principal stresses and maximum shear stress at point H (30 points) B 18 in. 10 in D 1.2 in 4 in. H 2002b 100&b

Answer 1

80l Dia = 1.2 inch, 18 in. D 2016 T LO B m. Toolb H Hin & Ž Z or) H I first determine the faces and couples acting the section point H due to induvidual forces lie 200 lb and doo 1b). then use them to calculate the normal and shearing ossesses acting containing at the point Druk lace force of Loo lb by an equivalent force couple system at the center of section containg point Hi 100 16 M = (100 x 10) R2 = 1 kip.io. T= 6100 16)(18 in) ** T = 18 kip.in

710016 T=18 kip.in E M = 1 kip-in 20016 IM₂=2 kipin. 2 Due to lood of loob Bending 1000 I 32 Que to load orice of goolb Bendling: og = + M. R T 2-301.213 + M.(0) 0 my I ? Py = 5.894 kipsi 5894.68 psi) loy Shear force (Transverre) 1 2 3 200 exy 4 VO It Torsion $80.232 Суу +T.R 18x0.6 J 39 Cry = 235.78 psi I x490) 1 Note: the sheeseng exy = 5.305 ksi force Loo 16 does not cause any shearing stress at point H,

Now Combine all stresses :- y = +5.894 +0 y 5.894 ksi = 0 Cxy = 15.305 + 0.93578). Cxy = 5.54 ksi y = 5.894 kei Ox=0 → X Z Exy = 5.54 koi b) Bincipal stresses: at point H. Oliga ( 0)+) (3) 7 Torty اوه. 9.28 kB max. shear stress Temas. = 6.27 ksi =-3.398 ksi