Page 321 - Mechanical Behavior of Materials

Problems and Questions 323

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ASME, Ser. E., vol. 28, no. 2, pp. 259–268.

PROBLEMS AND QUESTIONS

Section 7.3
7.1 An engineering component is made of the Boron carbide (B 4 C) ceramic of Table 3.10. The
most severely stressed point is subjected to the following state of stress: σ x = 35, σ y = 21,
τ xy = 7, and σ z = τ yz = τ zx = 0 MPa. Determine the safety factor against fracture.
7.2 In an engineering component made of zirconia (ZrO 2 ), the most severely stressed point is
subjected to the following state of stress: σ x = 125, σ y =−80, τ xy = 30 and σ z = τ yz =
τ zx = 0 MPa. Determine the safety factor against fracture. The material has a tensile strength
of 147 MPa and a compressive strength of 2100 MPa.
7.3 An engineering component is made of the silicon nitride (Si 3 N 4 ) ceramic of Table 3.10. The
most severely stressed point is subjected to the following state of stress: σ x = 60, σ y = 90,
σ z = 200, τ xy = 33, and τ yz = τ zx = 0 MPa. Determine the safety factor against fracture.
7.4 In an engineering component made of AISI 1020 steel as rolled, the most severely stressed
point is subjected to the following state of stress: σ x = 200, σ y = 0, σ z = 250, τ xy = 100
and τ yz = τ zx = 0 MPa. Determine the safety factor against fracture. The material has a yield
strength of 260 MPa and an ultimate tensile strength of 441 MPa.

Sections 7.4 and 7.5 2
7.5 In an engineering component made of SAE 308 cast aluminum, the most severely stressed
point is subjected to the following state of stress: σ x = 32, σ y =−10, τ xy =−20, and
σ z = τ yz = τ zx = 0 MPa. Determine the safety factor against yielding by (a) the maximum
shear stress criterion, and (b) the octahedral shear stress criterion.
7.6 In an engineering component made of AISI 4142 steel (as quenched), the most severely
stressed point is subjected to the following state of stress: σ x = 345, σ y = 138, σ z =−69,
τ xy = 69, and τ yz = τ zx = 0 MPa. Determine the safety factor against yielding by (a) the
maximum shear stress criterion, and (b) the octahedral shear stress criterion.

2
Use materials properties from Tables 4.2 and 5.2. Unless otherwise indicated, these yield criteria problems may be
worked by either the maximum shear stress criterion or the octahedral shear stress criterion.