NEW 375 Lecture09 - Section 2.10 TEMPERATURE EFFECTS δ t...

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Unformatted text preview: Section 2.10 TEMPERATURE EFFECTS δ t δ t = α ( ∆ T)L CONSIDER A HOMOGENEOUS ROD AB OF UNIFORM CROSS SECTION, RESTING FREELY ON A SMOOTH HORIZONTAL SURFACE THAT IS THEN SUBJECTED TO A UNIFORM TEMPERATURE CHANGE, ∆ T. Where α is the material constant, coefficient of thermal expansion Note:No restraint, therefore no axial forces developed Section 2.10 PROBLEMS INVOLVING TEMPERATURE CHANGES CONSIDER A HOMOGENEOUS ROD AB OF UNIFORM CROSS SECTION, FIXED BETWEEN SUPPORTS, THAT IS SUBJECTED TO A TEMPERATURE INCREASE, ∆ T. STEP 1: STUDY FORCES / EQUILIBRIUM ASSUME DIRECTION OF REACTION FORCE AS ABOVE . R R R R R F B A B A x = = =- = → + ∑ Eq.1 δ P STEP 2: STUDY DEFORMATION / G.O.F. NOTE: Show deformations in direction of assumed forces R P AB = R = AB AB AB AB P A E L P δ L Procedure: a) Remove the restraint b) Let the deformations take place a) Put the restraint back on the structure d) Write deformation compatibility equation(s) STEP 2 (cont.): STUDY DEF. / G.O.F. STEP 2a: REMOVE THE RESTRAINT STEP 2b: LET THERMAL DEFORMATIONS TAKE PLACE δ t δ t = α ( ∆ T)L LL STEP 2b: LET ELASTIC DEFORMATIONS TAKE PLACE δ t L L δ STEP 2c: PUT RESTRAINT BACK ON THE MEMBER δ t L L δ δ t L L δ STEP 2d: WRITE DEFORMATION COMPATIBILITY EQUATION δ t- δ P = 0 Eq.2 STEP 3: APPLY FORCE/DEFORMATION AND...
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This note was uploaded on 03/27/2008 for the course ENGIN 375 taught by Professor Miller during the Spring '08 term at University of Cincinnati.

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NEW 375 Lecture09 - Section 2.10 TEMPERATURE EFFECTS δ t...

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