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02-07ChapGere.0018 - A-PDF Split DEMO Purchase from...

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SECTION 2.12 Elastoplastic Analysis 177 A cross-sectional area Y yield stress E modulus of elasticity D ISPLACEMENT DIAGRAM C OMPATIBILITY : (1) (2) F REE - BODY DIAGRAM E QUILIBRIUM : 2 F B 3 F C 4 P (3) F ORCE - DISPLACEMENT RELATIONS (4, 5) Substitute into Eq. (1): F C 2 F B (6) 3 F C L 4 EA 3 F B L 2 EA B F B L EA C F C ¢ 3 4 L EA © M A 0 F B (2 b ) F C (3 b ) P (4 b ) D 2 B C 3 2 B S TRESSES (7) Wire C has the larger stress. Therefore, it will yield first. (a) Y IELD LOAD From Eq. (3): From Eq. (4): From Eq. (2): (b) P LASTIC LOAD At the plastic load, both wires yield. B Y C F B F C Y A From Eq. (3): 2( Y A ) 3( Y A ) 4 P From Eq. (4): From Eq. (2): (c) L OAD - DISPLACEMENT DIAGRAM P 2 Y P P
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