02-02ChapGere.0024 - c 2 1 d 2 T D 5 dPL 2 c 2 1 d 2 T C h...

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Problem 2.4-16 A trimetallic bar is uniformly compressed by an axial force P 5 40 kN applied through a rigid end plate (see figure). The bar consists of a circular steel core surrounded by brass and cop- per tubes. The steel core has diameter 30 mm, the brass tube has outer diameter 45 mm, and the copper tube has outer diameter 60 mm. The corresponding moduli of elasticity are E s 5 210 GPa, E b 5 100 GPa, and E c 5 120 GPa. Calculate the compressive stresses s s , s b , and s c in the steel, brass, and copper, respectively, due to the force P . SECTION 2.4 Statically Indeterminate Structures 103 F ORCE - DISPLACEMENT RELATIONS (Eqs. 3, 4) S OLUTION OF EQUATIONS Substitute (3) and (4) into Eq. (2): (Eq. 5) T ENSILE FORCES IN THE WIRES Solve simultaneously Eqs. (1) and (5): (Eqs. 6, 7) T ENSILE STRESSES IN THE WIRES (Eq. 8) (Eq. 9) s D 5 T D A 5 dPL A (2 c 2 1 d 2 ) s C 5 T C A 5 2 cPL A (2 c 2 1 d 2 ) T C 5 2 cPL 2
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Unformatted text preview: c 2 1 d 2 T D 5 dPL 2 c 2 1 d 2 T C h cEA 5 T D (2 h ) dEA or T C c 5 2 T D d d C 5 T C h EA d D 5 T D (2 h ) EA D ISPLACEMENT AT END OF BAR (Eq. 10) S UBSTITUTE NUMERICAL VALUES (a) (b) 5 0.0198 in. 5 2(18 in.)(340 lb)(66 in.) 2 (30 3 10 6 psi)(0.0272 in. 2 )(3300 in. 2 ) d B 5 2 hPL 2 EA (2 c 2 1 d 2 ) 5 12,500 psi s D 5 dPL A (2 c 2 1 d 2 ) 5 (50 in.)(340 lb)(66 in.) (0.0272 in. 2 )(3300 in. 2 ) 5 10,000 psi s C 5 2 cPL A (2 c 2 1 d 2 ) 5 2(20 in.)(340 lb)(66 in.) (0.0272 in. 2 )(3300 in. 2 ) 2 c 2 1 d 2 5 2(20 in.) 2 1 (50 in.) 2 5 3300 in. 2 d B 5 d D L d 5 2 hT D EA L d 5 2 hPL 2 EA (2 c 2 1 d 2 ) P = 40 kN Copper tube Brass tube Steel core 30 mm 45 mm 60 mm A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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