02-02ChapGere.0012

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Problem 2.4-4 A bar ACB having two different cross-sectional areas A 1 and A 2 is held between rigid supports at A and B (see figure). A load P acts at point C , which is distance b 1 from end A and distance b 2 from end B . (a) Obtain formulas for the reactions R A and R B at supports A and B , respectively, due to the load P . (b) Obtain a formula for the displacement d C of point C . (c) What is the ratio of the stress s 1 in region AC to the stress s 2 in region CB ? Solution 2.4-4 Bar with intermediate load SECTION 2.4 Statically Indeterminate Structures 91 CB b 1 A 1 b 2 A A 2 P b 1 b 2 A 1 A 2 A P F REE - BODY DIAGRAM E QUATION OF E QUILIBRIUM © F horiz 5 0 R A 1 R B 5 P (Eq. 1) E QUATION OF COMPATIBILITY d AC 5 elongation of AC d CB 5 shortening of CB d AC 5 d CB (Eq. 2) F ORCE DISPLACEMENT RELATIONS (Eqs. 3&4) (a) S
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