Page 267 - Mechanical Behavior of Materials

Problems and Questions 269

REFERENCES

BORESI,A.P., andR.J. SCHMIDT. 2003. Advanced Mechanics of Materials, 6th ed., John Wiley, Hoboken,
NJ. (See also the 2nd ed. of this book, same title, 1952, by F. B. Seely and J. O. Smith.)
DIETER, G. E., Jr. 1986. Mechanical Metallurgy, 3d ed., McGraw-Hill, New York.
MENDELSON, A. 1968. Plasticity: Theory and Applications, Macmillan, New York. (Reprinted by R. E.
Krieger, Malabar, FL, 1983).
TIMOSHENKO, S.P., andJ.N. GOODIER. 1970. Theory of Elasticity, 3d ed., McGraw-Hill, New York.
UGURAL,A.C., andS.K. FENSTER. 2012. Advanced Strength and Applied Elasticity, 5th ed., Prentice Hall,
Upper Saddle River, NJ.

PROBLEMS AND QUESTIONS

Sections 6.2 and 6.3
6.1 A state of stress that occurs at a point on the free surface of a solid body is σ x =6 MPa,
σ y = 6 MPa and τ xy = 2MPa.
(a) Evaluate the two principal normal stresses and the one principal shear stress that can be
found by coordinate system rotations in the x-y plane, and give the coordinate system
rotations.
(b) Determine the maximum normal stress and the maximum shear stress at this point.
6.2to6.9
Proceed as in Prob. 6.1, but use the indicated stress from the table given below:

Table P6.2
Problem
No. σ x ,MPa σ y ,MPa τ xy ,MPa
6.2 −5 5 −5
6.3 32 −10 −20
6.4 21 131 0
6.5 35 21 7
6.6 345 138 69
6.7 125 −80 30
6.8 −50 40 −50
6.9 60 80 20

6.10 An element of material is subjected to the following state of stress: σ x = 4,σ y =−5,
σ z =−3,τ xy =−2, τ yz = τ zx = 0. Determine the following:
(a) Principal normal stresses and principal shear stresses.
(b) Maximum normal stress and maximum shear stress.
(c) Directions of the principal normal stress axes.
6.11 to 6.14
Proceed as in Prob. 6.10, but use the indicated stresses from the table given below: