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MEEM EXAM 4150
Oct. 7th, 2003
y
Answers are at of this exam. 1. (a) Show the non-zero stress components on the A,B, and C faces of the cube. Use the coordinate system that is given only.
xx = 80MPa ( T ) yx = 30 MPa zx = 0 xy = 30 MPa yy = 0 zy = 70MPa xz = 0 yz = 70MPa zz = 40MPa ( C )
z
. .
x
C
.
B
A
(b) Draw the shear stress due to torsion on the stress cubes at points A and B. Is the shear stress positive or negative? Circle the appropriate answers
x
A
y x
A B
T
(xy)A = positive / negative
x
(xy)B = positive / negative
B
(c) Assuming a positive shear force Vy in bending (a) sketch the direction of the shear flow along the center-line on the thin cross-sections shown. (b) At points A, B, C, and D, determine if the stress component is xy or xz and if it is positive, negative, or zero. Circle the appropriate answers
y B
(xy)A or (xz)A positive / negative / zero
D
(xy)B or (xz)B positive / negative/ zero (xy)C or (xz)C positive / negative/ zero
z
C A
(xy)D or (xz)D positive / negative/ zero
0.2 ( 40 x )
(d) The axial strain in a 20 in. long rod is given by xx = --------------------- . Determine the elongation of the rod. 2 (e) The displacements u and v in the x and y directions respectively were measured by Moire' interferometry. Displacements of 9 points on the body and are as given below.Using central difference, determine the shear strain xy at point 5.
Point 1 2 3 4 5 u (mm) 0.000 -0.112 -0.128 0.112 -0.032 v (mm) 0.000 0.144 0.256 0.176 0.224 Point 6 8 7 9 u (mm) -0.080 0.128 -0.048 0.128 v (mm) 0.240 0.384 0.336 0.384
y 7 h 4 h 1
h = 0.0005 mm
8 5 2 h h 9 6 3 x
2.
The stress at a point is given by the stress matrix:
40 20 10 20 30 0 ksi 10 0 zz
The three principal stresses of the matrix are: 1 = 56.21 ksi ( T ) 2 = 14.95 ksi ( T ) 3 = 51.16 ksi ( C ) (a) Determine the three stress invariants. (b) Determine the stress zz. (c) Determine the orientation of principal direction associated with principal stress 14.95 ksi (T). (d) The material yield stress is 120 ksi in tension. Determine the factor of safety at the point using octahedral shear stress theory (e) A crack was discovered on a plane that has an outward normal at angles of 36.87o, 60.0o, and 70.63o with the x, y and z axis respectively. The critical stress intensity factor for the material is 22 ksi in , what would be the critical crack length on that plane. 3. A beam is lo...