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02-02ChapGere.0018

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Problem 2.4-10 A rigid bar of weight W 5 800 N hangs from three equally spaced vertical wires, two of steel and one of aluminum (see figure). The wires also support a load P acting at the midpoint of the bar. The diameter of the steel wires is 2 mm, and the diameter of the aluminum wire is 4 mm. What load P allow can be supported if the allowable stress in the steel wires is 220 MPa and in the aluminum wire is 80 MPa? (Assume E s 5 210 GPa and E a 5 70 GPa.) Solution 2.4-10 Rigid bar hanging from three wires SECTION 2.4 Statically Indeterminate Structures 97 P Rigid bar of weight W SAS S TEEL WIRES d s 5 2mm s s 5 220 MPa E s 5 210 GPa A LUMINUM WIRES d A 5 4mm s A 5 80 MPa E A 5 70 GPa F REE - BODY DIAGRAM OF RIGID BAR E QUATION OF E QUILIBRIUM © F vert 5 0 2 F s 1 F A 2 P 2 W 5 0 (Eq. 1) E QUATION OF COMPATIBILITY d s 5 d A (Eq. 2) F ORCE DISPLACEMENT RELATIONS (Eqs. 3, 4) d s 5 F s L E s A s Ê d A 5 F A L E A A A S OLUTION OF EQUATIONS Substitute (3) and (4) into Eq. (2):
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