02-04ChapGere.0008

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Problem 2.6-11 A plastic bar fits snugly between rigid supports at room temperature (68°F) but with no initial stress (see figure). When the temperature of the bar is raised to 160°F, the compressive stress on an inclined plane pq becomes 1700 psi. (a) What is the shear stress on plane pq ? (Assume a 5 60 3 10 2 6 /°F and E 5 450 3 10 3 psi.) (b) Draw a stress element oriented to plane pq and show the stresses acting on all faces of this element. Solution 2.6-11 Plastic bar between rigid supports SECTION 2.6 Stresses on Inclined Sections 129 q p u a 5 60 3 10 2 6 / 8 F E 5 450 3 10 3 psi Temperature increase: D T 5 160 8 F 2 68 8 F 5 92 8 F N ORMAL STRESS s x IN THE BAR s x 52 E a ( D T ) (See Eq. 2-18 in Section 2.5) s x 52 (450 3 10 3 psi)(60 3 10 2 6 / 8 F)(92 8 F) 52 2484 psi (Compression) A NGLE u TO PLANE pq s u 5 s x cos 2 u For plane pq : s u 52 1700 psi Therefore, 2 1700 psi
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