Problem 2.4-8The fixed-end bar ABCDconsists of three prismaticsegments, as shown in the figure. The end segments have cross-sectional area A1 5 840 mm2and length L1 5 200 mm. The middlesegment has cross-sectional area A2 5 1260 mm2and length L2 5 250mm. Loads PBand PCare equal to 25.5 kN and 17.0 kN, respectively. (a) Determine the reactions RAand RDat the fixed supports. (b) Determine the compressive axial force FBCin the middlesegment of the bar. Solution 2.4-8Bar with three segmentsSECTION 2.4Statically Indeterminate Structures95A1A1A2ADBCPBPCL1L1L2A1A1A2PBPCL1L1L2PB525.5 kNPC517.0 kNL15200 mmL25250 mmA15840 mm2A251260 mm2m5meterSOLUTION OF EQUATIONSSubstitute Eqs. (3), (4), and (5) into Eq. (2):Simplify and substitute PB525.5 kN:(Eq. 6)(a) REACTIONSRAANDRDSolve simultaneously Eqs. (1) and (6).From (1): RD5RA28.5 kNSubstitute into (6) and solve for RA:(b) COMPRESSIVE AXIAL FORCEFBCFBC5PB2RA5PC2RD515.0kNRD5RA28.5kN52.0kNRA5
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kN, PB RA RD, PB RA PC, RA RD RA, PC PB RA, FBC PB RA