02-02ChapGere.0020

02-02ChapGere.0020 - R A L 1 EA 1 2 R D L 3 EA 3 5 d AB 5 R...

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Problem 2.4-12 A circular steel bar ABC ( E = 200 GPa) has cross- sectional area A 1 from A to B and cross-sectional area A 2 from B to C (see figure). The bar is supported rigidly at end A and is subjected to a load P equal to 40 kN at end C . A circular steel collar BD having cross-sectional area A 3 supports the bar at B . The collar fits snugly at B and D when there is no load. Determine the elongation d AC of the bar due to the load P . (Assume L 1 5 2 L 3 5 250 mm, L 2 5 225 mm, A 1 5 2 A 3 5 960 mm 2 , and A 2 5 300 mm 2 .) Solution 2.4-12 Bar supported by a collar SECTION 2.4 Statically Indeterminate Structures 99 A 1 A 3 A 2 L 3 L 1 L 2 P C D B A F REE - BODY DIAGRAM OF BAR ABC AND COLLAR BD E QUILIBRIUM OF BAR ABC © F vert 5 0 R A 1 R D 2 P 5 0 (Eq. 1) C OMPATIBILITY (distance AD does not change) d AB (bar) 1 d BD (collar) 5 0 (Eq. 2) (Elongation is positive.) F ORCE - DISPLACEMENT RELATIONS Substitute into Eq. (2): (Eq. 3)
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Unformatted text preview: R A L 1 EA 1 2 R D L 3 EA 3 5 d AB 5 R A L 1 EA 1 d BD 5 2 R D L 3 EA 3 S OLVE SIMULTANEOUSLY E QS . (1) AND (3): C HANGES IN LENGTHS (Elongation is positive) E LONGATION OF BAR ABC d AC 5 d AB 1 d AC S UBSTITUTE NUMERICAL VALUES : P 5 40 kN E 5 200 GPa L 1 5 250 mm L 2 5 225 mm L 3 5 125 mm A 1 5 960 mm 2 A 2 5 300 mm 2 A 3 5 480 mm 2 R ESULTS : R A 5 R D 5 20 kN d AB 5 0.02604 mm d BC 5 0.15000 mm d AC 5 d AB 1 d AC 5 0.176 mm d AB 5 R A L 1 EA 1 5 PL 1 L 3 E ( L 1 A 3 1 L 3 A 1 ) d BC 5 PL 2 EA 2 R A 5 PL 3 A 1 L 1 A 3 1 L 3 A 1 R D 5 PL 1 A 3 L 1 A 3 1 L 3 A 1 A 1 A 2 L 1 L 2 P C R D B A A 3 L 3 D B R D R D R A A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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