Instructions This exam consists of three problems worth a to

Instructions: This exam consists of three problems worth a total of 60 points. The only materials permitted are the 3 handouts posted on Pilot, a calculator, and both sides of an 8.5\"x11\" handwritten crib sheet, which MUST be turned in with the exam. 1. A cantilever spring is loaded with a force F = 5 Ibf, as shown in the figure below. The spring has a rectangular cross section of width w 3/8\" and thickness t =3/32\".The remaining dimensions are L_1 = 4.5\", L_2 = 2\" and r = 0.150\". Using curved beam theory. Find the stress at the outer surface of the bend. Required for those registered for 6140. optional extra credit for those registered for 4140: find the stress at the inner surface of the bend? Find the maximum shear stress at the outer surface of the bend.

Solution

F= 5lbf conert to N

22.421N

w = 3/8 inch = 0.9525 cm

t = 3/32 inch= 0.238 cm

L1 = 4.5 inch =11.43cm

L2 = 2 inch = 5.08 cm

r = 0.150 inch = 0.381 cm

1.maximum shear stress

stress max = F/l.b{B/8(H²-h²)+b.h²/8}

= 1604 MPa

2.curved beam thoery

stress at outer surface of beam