{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


A similar calculaoon for concrete demonstrates

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , BOLT and SLEEVE TEND TO ELONGATE ²་  NOTE NO RIGID WALLS THIS TIME TO CANCEL OUT DISPLACEMENTS (SO ENTIRE ASSEMBLY LENGTHENS) ²་  SLEEVE TENDS TO ELONGATE MORE THAN BOLT (SINCE αs > αb) ²་  CONSTRAINT BY BOLT HEAD, NUT, AND WASHERS FORCES SLEEVE INTO COMPRESSION ²་  BOLT SHAFT FORCED INTO TENSION 1/17/13 M. Mello/Georgia Tech Aerospace steel sleeve (iniOal) T s L T steel sleeve (thermal) L steel sleeve (mechanical) Rs Rs s Rs s steel sleeve (final length) L net displacement T of sleeve: = s Rs s 12 Example 2- 8 (cont.) Displacement of bolt: T s steel sleeve (thermal) BOLT IS IN TENSION L 1/17/13 T b T L Rb Rb b M. Mello/Georgia Tech Aerospace Net elongaOon T of BOLT: = b + Rb b 13 Example 2- 8 (cont.) SOLUTION: ②  EQUILIBRIUM ~ ~ R a = Rb Ra = Rb ③  COMPATIBILITY ²་  NET DISPLACEMENT = SLEAVE THERMAL EXPANSION MINUS SLEEVE MECHANICAL COMPRESSION ²་  OR, ²་  NET DISPLACEMENT = BOLT THERMAL EXPANSION PLUS BOLT MECHANICAL EXTENSION T b + 1/17/13 T T b Rb b L Rs s Rb Rb b T Rs =s s Rb L Rs L = ↵b T L + = ↵s T L ($) E b Ab E s As Rs L Rb L + = ↵s T L ↵b T L E s As E b Ab = T s T s = ↵s T L Rs s = Rs L E b As T b = ↵b T L Rb b = Rb L E b Ab M. Mello/Georgia Tech Aerospace 14 Rs Example 2- 8 (cont.) SOLUTION: ④  SOLVE FOR LOADS Since RA = RB, it follows that: Rs = Rb = ( ↵s ↵b )( T )Es As Eb Ab E s As + E b Ab T s T (2- 19) ④  SOLVE FOR STRESSES: (SIMPLY DIVIDE 2- 19 BY THE APPROPRIATE AREA FACTOR T b Rb b L Rs s Rb Rs (↵s ↵b )( T )Es Eb Ab = = As E s As + E b Ab (2- 20a) T Rs L Rs s = ↵s T L s = E b As Rb (↵s ↵b )( T )Es As Eb Rb RL T = EbbAb = ↵b T L (2- 20b) = = b b b Ab E s As + E b Ab ⑤  INCREASE IN LENGTH OF THE ENTIRE ASSEMBLY: subsOtute either Rs or Rb into the compaObility equaOon ($) s = 1/17/13 (↵s Es As + ↵b Eb Ab )( T )L E s As + E b Ab (2- 21) M. Mello/Georgia Tech Aerospace 15 Rs Example 2- 8 : Special case soluOons Case #1 : ASSUME BOLT IS INFINITELY RIGID AND UNAFFECTED BY TEMPERATURE CHANGES Rs (↵s ↵b )( T )Es Eb Ab R = R = (↵s ↵b )( T )Es As Eb Ab = = s s b As E s As + E b Ab E s As + E b Ab Rb (↵s ↵b )( T )Es As Eb ²་  This implies E b = 1 and ↵b = 0 = = b Ab E s As + E b Ab ²་  Divide numerator and denominator by Eb ²་  Let αb = 0 (↵s Es As + ↵b Eb Ab )( T )L = ²་  Recover equaOons derived in example 2- 7! E s As + E b Ab Bar between rigi...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online