Page 326 - Mechanical Behavior of Materials

Problems and Questions 327

the loading such that σ x = λσ y , where λ may vary between +1 and −1, and derive the
corresponding expression for σ y at yielding that is analogous to the result of Ex. 7.5(a).
Comment on how the stress at yielding is affected by λ.
7.28 A block of 7075-T6 aluminum is subjected to a confining pressure on all sides of p =
120 MPa, along with a shear stress τ xy as shown in Fig. P7.28.
(a) Employ octahedral shear stress criterion and find the largest value of τ xy that can be
applied if the safety factor against yielding must be 2.5.
(b) Is there a large effect of the pressure p on the τ xy required to cause yielding? Briefly
discuss the effect of p as to whether the effect is large, small or absent and explain
why.

p
τ xy

p

p

Figure P7.28

7.29 A block of AISI 4142 steel (as quenched) is subjected to a stress σ z =−100 MPa, along with
a shear stress τ xy , as shown in Fig. P7.29.
(a) Based on octahedral shear stress criterion, find the largest valued of τ xy that can be
applied if the safety factor against yielding must be 2.0.
(b) Is there a large effect of σ z on the τ xy required to cause yielding? Briefly discuss the
effect of σ z as to whether the effect is large, small or absent, and explain why.

τ xy

σ z

Figure P7.29

7.30 A thick-walled tube with closed ends has inner and outer radii of 30 and 50 mm, respectively.
It contains an internal pressure of 160 MPa and is also subjected to a torque of 30 kN·m. The
◦
material is AISI 4142 steel tempered at 450 C. What is the safety factor against yielding?
(Note: Check inside, outside, and several intermediate values of radius, as the most severely
stressed location is not known.)
7.31 A thick-walled tube with closed ends has inner and outer radii of 25 and 50 mm, respectively.
It contains an internal pressure of 100 MPa and is also subjected to a torque of 75 kN·m. The