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SECTION 2.12 Elastoplastic Analysis 177 A 5 cross-sectional area s Y 5 yield stress E 5 modulus of elasticity D ISPLACEMENT DIAGRAM C OMPATIBILITY : (1) (2) F REE - BODY DIAGRAM E QUILIBRIUM : 2 F B 1 3 F C 5 4 P (3) F ORCE - DISPLACEMENT RELATIONS (4, 5) Substitute into Eq. (1): F C 5 2 F B (6) 3 F C L 4 EA 5 3 F B L 2 EA d B 5 F B L EA Ê d C 5 F C ¢ 3 4 L EA © M A 5 0 `~ Ê F B (2 b ) 1 F C (3 b ) 5 P (4 b ) d D 5 2 d B d C 5 3 2 d 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. s B 5 s Y 5 s C F B 5 F C 5 s Y A From Eq. (3): 2( s Y A ) 1 3( s Y A ) 5 4 P From Eq. (4): From Eq. (2): (c) L OAD - DISPLACEMENT DIAGRAM d P 5 2 d Y P P 5 5 4 P Y d D 5 d P 5 2 d B 5 2 s Y L E d B 5 F B L EA 5 s Y L E P 5 P P 5 5 4 s Y A d D 5
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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