02-02ChapGere.0025

02-02ChapGere.0025 - MPa s b 5 PE b © EA 5 10.4 MPa s s 5...

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Solution 2.4-16 Trimetallic bar in compression 104 CHAPTER 2 Axially Loaded Members P s 5 compressive force in steel core P b 5 compressive force in brass tube P c 5 compressive force in copper tube F REE - BODY DIAGRAM OF RIGID END PLATE E QUATION OF EQUILIBRIUM © F vert 5 0 P s 1 P b 1 P c 5 P (Eq. 1) E QUATIONS OF COMPATIBILITY d s 5 d b d c 5 d s (Eqs. 2) F ORCE - DISPLACEMENT RELATIONS (Eqs. 3, 4, 5) S OLUTION OF EQUATIONS Substitute (3), (4), and (5) into Eqs. (2): (Eqs. 6, 7) P b 5 P s E b A b E s A s Ê P c 5 P s E c A c E s A s d s 5 P s L E s A s Ê d b 5 P b L E b A b Ê d c 5 P c L E c A c S OLVE SIMULTANEOUSLY E QS . (1), (6), AND (7): C OMPRESSIVE STRESSES Let © EA 5 E s A s 1 E b A b 1 E c A c S UBSTITUTE NUMERICAL VALUES : P 5 40 kN E s 5 210 GPa E b 5 100 GPa E c 5 120 GPa d 1 5 30 mm d 2 5 45 mm d 3 5 60 mm © EA 5 385.238 3 10 6 N s c 5 PE c © EA 5 12.5
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Unformatted text preview: MPa s b 5 PE b © EA 5 10.4 MPa s s 5 PE s © EA 5 21.8 MPa A c 5 p 4 ( d 3 2 2 d 2 2 ) 5 1237.00 mm 2 A b 5 p 4 ( d 2 2 2 d 1 2 ) 5 883.57 mm 2 A s 5 p 4 d 1 2 5 706.86 mm 2 s c 5 P c A c 5 PE c © EA s s 5 P s A s 5 PE s © EA Ê s b 5 P b A b 5 PE b © EA P c 5 P E c A c E s A s 1 E b A b 1 E c 1 A c P b 5 P E b A b E s A s 1 E b A b 1 E c A c P s 5 P E s A s E s A s 1 E b A b 1 E c A c Copper Brass Steel P P s P b P c A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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