02-03ChapGere.0004

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SECTION 2.5 Thermal Effects 109 Problem 2.5-7 A circular steel rod AB (diameter d 1 5 1.0 in., length L 1 5 3.0 ft) has a bronze sleeve (outer diameter d 2 5 1.25 in., length L 2 5 1.0 ft) shrunk onto it so that the two parts are securely bonded (see figure). Calculate the total elongation d of the steel bar due to a temperature rise D T 5 500°F. (Material properties are as follows: for steel, E s 5 30 3 10 6 psi and a s 5 6.5 3 10 2 6 /°F; for bronze, E b 5 15 3 10 6 psi and a b 5 11 3 10 2 6 /°F.) Solution 2.5-7 Steel rod with bronze sleeve d T 5 elongation due to temperature P 5 a ( D T )( L 1 1 L 2 ) 5 1.5750 mm d P 5 shortening due to P 5 P (19.0986 3 10 2 9 m/N 1 11.3177 3 10 2 9 m/N) 5 (30.4163 3 10 2 9 m/N) P ( P 5 newtons) Compatibility: d T 5 d P 1.5750 3 10 2 3 m 5 (30.4163 3 10 2 9 m/N) P P 5 51,781 N Ê or Ê P 5 51.8 kN Ê 5 PL 1 EA 1 1 PL 2 EA 2 (b) M AXIMUM COMPRESSIVE STRESS (c) D ISPLACEMENT OF POINT C d C 5 Shortening of AC (Positive means AC shortens and point C displaces to the left.) d C 5 0.314 mm Ê 5 0.9890 mm 2 0.6750 mm d C 5 PL 1 EA 1 2 a ( ¢ T ) L 1 s c 5 P A 1 5 51.78 kN 1963.5 mm 2 5 26.4 MPa Ê d 2 d 1 AB L 2 L 1 d 2 d 1 L 2 L 1 L 1 5 36 in. L 2 5 12 in. E LONGATION OF THE TWO OUTER PARTS OF THE BAR
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