NEW 375 Lecture09

# NEW 375 Lecture09 - Section 2.10 TEMPERATURE EFFECTS...

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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

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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 = = = - = + 0 Eq.1

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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.

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STEP 2a: REMOVE THE RESTRAINT
STEP 2b: LET THERMAL DEFORMATIONS TAKE PLACE δ t δ t = α ( T)L LL

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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

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δ t L L δ STEP 2d: WRITE DEFORMATION COMPATIBILITY EQUATION δ t - δ P = 0 Eq.2
STEP 3: APPLY FORCE/DEFORMATION AND TEMPERATURE/DEFORMATION RELATIONSHIP δ t = α AB ( T)L AB = AB AB AB AB P A E L P δ

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STEP 3(cont.): APPLY FORCE/DEFORMATION AND
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