LECTURE+7+COE-3001-A

# Structures statically determinate

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PERIENCE INTERNAL STRESS DUE TO A UNIFORM TEMERATURE CHANGE. 1/17/13 M. Mello/Georgia Tech Aerospace 5 Example 2- 7: LINEAR ELASTIC BAR BETWEEN RIGID SUPPORTS thermal strain mechanical strain GIVEN: ²་  PrismaOc bar of length (L) held between immovable supports ²་  Temperature of the bar raised uniformly by (ΔT) ²་  α = coeﬃcient of thermal expansion (CTE) of bar material DETERMINE: ²་  Thermal stress (σT) developed in the bar ²་  Assume bar is made of linear elasOc material. = + SOLUTION STRATEGY: ①  Apply some basic mechanical intuiOon before analysis ²་  AS TEMP INCREASES, BAR ATTEMPTS TO ELONGATE ²་  MOVEMENT RESTRICTED BY RIGID SUPPORTS ²་  BAR SUBJECTED TO COMPRESSIVE STRESS ②  EQUILIBRIUM EQUATION: ⌃Fvert = 0 RB RA = 0 (2- 17) ③  COMPATIBILITY EQUATION: ab ab ab =0 = T hermal = 1/17/13 T M NOTE: RB, RA, REPRESENT STRESS MAGNITUDES tendency to increase bar length due to temp. increase OPPOSED BY M echanical =0 =0 tendency to contract bar length due to compressive stress of reacOon forces M. Mello/Georgia Tech Aerospace 6 Example 2- 7 (cont.) SOLUTION: ③  COMPATIBILITY EQUATION (restated): =0 ab = T hermal thermal strain mechanical strain ab ab T = T = ↵ ( T )L (temperature- displacement relaOon) ↵ ( T )L RA = M M echanical =0 =0 M = RA L RB L = EA EA (force- displacement relaOon) = + RA L =0 EA OF EA↵( T ) (MAGNITUDE = R REACTION FORCE RA. (RA B) T = E ↵( 1/17/13 T ) (2- 18) NOTE: IT WAS REASONED AT THE OUTSET THAT THE THERMAL STRESS WILL BE COMPRESSIVE FOR ΔT>0. THE ANSWER HERE REPRESENTS THE AXIAL STRESS MAGNITUDE ONLY (COMPRESSIVE STRESS IS NEGATIVE BY CONVENTION) M. Mello/Georgia Tech Aerospace 7 Example 2- 7 (WHAT ABOUT THE BAR DIAMETER?) RA δT D0 δR D0+ΔDT = D0+ΔDR + Thermal strain Mechanical strain ²་  NOTEL: Gere and Goodno make a passing reference to the transverse strains in the constrained bar (but no analysis presented) Note minus sign here ✓ ◆ ²་  Diameter increase: E↵ T D = (↵ T ) D0 + ⌫ D0 D = ✏thermal D0 + ✏mech D0 E D = (↵ T )D0 + ( ⌫ ✏axial )D0 D = (↵ T ) D 0 + ( ⌫ R E )D0 Note minus sign here 1/17/13 M. Mello/Georgia Tech Aerospace D = ↵ T D0 (1 + ⌫ ) (DIAMETER INCREASE OF CONSTRAINED BAR) 8 MATERIAL (ELASTIC) PROPERTIES MATERIAL MODULUS,...
View Full Document

## This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Tech.

Ask a homework question - tutors are online