02-03ChapGere.0007 - 112 A-PDF Axially Loaded : Purchase...

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112 CHAPTER 2 Axially Loaded Members Solution 2.5-10 Rigid bar supported by two cables F REE - BODY DIAGRAM OF BAR ABCD P D C B A R AH R AV T B T C 2b 2b b T B 5 force in cable BT C 5 force in cable C d B 5 12 mm d C 5 20 mm From Table 2-1: A B 5 76.7 mm 2 E 5 140 GPa D T 5 60 8 C A C 5 173 mm 2 a 5 12 3 10 2 6 / 8 C E QUATION OF EQUILIBRIUM or 2 T B 1 4 T C 5 5 P (Eq. 1) D ISPLACEMENT DIAGRAM C OMPATIBILITY : d C 5 2 d B (Eq. 2) F ORCE - DISPLACEMENT AND TEMPERATURE - DISPLACEMENT RELATIONS (Eq. 3) (Eq. 4) d C 5 T C L EA C 1 a ( ¢ T ) L d B 5 T B L EA B 1 a ( ¢ T ) L © M A 5 0 `~ Ê T B (2 b ) 1 T C (4 b ) 2 P (5 b ) 5 0 S UBSTITUTE E QS . (3) AND (4) INTO E Q . (2): or 2 T B A C 2 T C A B 52 E a ( D T ) A B A C (Eq. 5) S UBSTITUTE NUMERICAL VALUES INTO E Q . (5): T B (346) 2 T C (76.7) 1,338,000 (Eq. 6) in which T B and T C have units of newtons. S OLVE SIMULTANEOUSLY E QS . (1) AND (6): T B 5 0.2494 P 2 3,480 (Eq. 7) T C 5 1.1253 P 1 1,740 (Eq. 8) in which P has units of newtons. S OLVE E QS . (7) AND (8) FOR THE LOAD P: P B 5 4.0096 T B 1 13,953 (Eq. 9) P C 5 0.8887 T C 2 1,546 (Eq. 10) A LLOWABLE LOADS From Table 2-1: ( T B ) ULT 5 102,000 N ( T C ) 5 231,000 N Factor of safety 5 5 ( T B ) allow 5 20,400 N ( T C ) allow 5 46,200 N From Eq. (9): P B 5 (4.0096)(20,400 N) 1 13,953 N 5 95,700 N From Eq. (10): P C 5 (0.8887)(46,200 N) 2 1546 N 5 39,500 N Cable
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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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