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MEEG 4103 Name: __________________________________ Midterm Exam ID#: _____________________________________ (Underline your last name.) 1. (30%) A steel countershaft ( E 30 × 106 psi ) with roller bearings at O and B is in equilibrium as
shown, where T1 = 9 T2 . Taking the bearings as simple supports, determine (a) the deflection yC at C,
(b) the minimum shaft diameter d min needed, using ⅛-in. increments, if the slope at either bearing
should not exceed 0.05° , (c) the value of yC when the shaft diameter is d min . Fig. P1
2. (20%) Using the traction vector formula
t i = σj i n j
derive the octahedral normal stress σo ct and the octahedral shear stress τo ct in terms of the principal
stresses: σ 1 , σ 2 , σ 3 . Include pertinent sketches in the derivation.
3. (20%) Describe the octahedral-shear-stress theory and show that this theory gives the same equivalent stress ( σ ′ ) for yielding as that given in the distortion energy theory.
4. (30%) A bar of AISI 1040 hot-rolled steel has a minimum yield strength in tension and compression
of 42 kpsi. Using the distortion-energy and maximum-shear-stress theories, computing the von Mises
stress, drawing the stress element, and drawing Mohr’s circle diagrams, determine the factor of safety
n for the following plane stress states:
(a) σ x = 30 kpsi, τ x y = − 8 kpsi
(b) σ x =σ y = x y =
− 24 kpsi,
−12 kpsi, τ
− 8 kpsi
(c) σ x
= 1= 28 kpsi, τ x y 6 kpsi
2 kpsi, σ y
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This note was uploaded on 11/24/2011 for the course MEEG 4103 taught by Professor Ing-chang,j during the Spring '08 term at Arkansas.
- Spring '08