02-02ChapGere.0016

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Problem 2.4-8 The fixed-end bar ABCD consists of three prismatic segments, as shown in the figure. The end segments have cross- sectional area A 1 5 840 mm 2 and length L 1 5 200 mm. The middle segment has cross-sectional area A 2 5 1260 mm 2 and length L 2 5 250 mm. Loads P B and P C are equal to 25.5 kN and 17.0 kN, respectively. (a) Determine the reactions R A and R D at the fixed supports. (b) Determine the compressive axial force F BC in the middle segment of the bar. Solution 2.4-8 Bar with three segments SECTION 2.4 Statically Indeterminate Structures 95 A 1 A 1 A 2 AD BC P B P C L 1 L 1 L 2 A 1 A 1 A 2 P B P C L 1 L 1 L 2 P B 5 25.5 kN P C 5 17.0 kN L 1 5 200 mm L 2 5 250 mm A 1 5 840 mm 2 A 2 5 1260 mm 2 m 5 meter S OLUTION OF EQUATIONS Substitute Eqs. (3), (4), and (5) into Eq. (2): Simplify and substitute P B 5 25.5 kN: (Eq. 6) (a) R EACTIONS R A AND R D Solve simultaneously Eqs. (1) and (6). From (1): R D 5 R A 2 8.5 kN Substitute into (6) and solve for R A : (b) C OMPRESSIVE AXIAL FORCE F BC F BC 5 P B 2 R A 5 P C 2 R D 5 15.0 kN R D 5 R A 2 8.5 kN 5 2.0 kN R A 5
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