Question

Problem 5 (20 Points) Member AC in the truss pictured below is heated at point C from the ambient temper- ature Tį to T2 > Tı). The following change in temperature in member AC results: AT(2) = 0 1-Ï), c=T2-T1. Note that AT(x) varies linearly from T2-T1 at x = 0 (point C) to 0 at x = L (point A). Members AB and AD remain at T1. All members of the truss have the same Young's modulus E, cross-sectional area A, and linear coefficient of thermal expansion a. (a) Indicate with justification if the members AB, AD and AC will be in tension or compression? (5 Points) (b) Determine the magnitude of 8, the -displacement at point A. Your answer should be in terms of a, c, and L. (15 Points) B С 8 60° x 600 A D L

Answer 1

Sol- Given, AT() [1-?] 13 2- da on 60 YA X 10 +] <= 72-7, (a, When bar 'CA' start to elongate towards direction, it is resisted by bar BA and DA then it will not fully elongate feel compressive stress, and Bar 'BA' R 'Da' will experience Tensile stress. suppose length 'du' at 'x distance left from point 'A' for 'dx Length Temperature ti is 'da'. Then total length due to change ten 'di' will be a small in

b dla - À dx dx [lt ndo [/1 4 (1-1/4, Lite ] 쀼 ㅓ뜬) 1 - [tvN, 2 LL t = ( + + QC- Χ) 0 ㅗ (+ &C - xc)’ - (+ xc)’ 200 원과 29C L ] aaC [ [-c (cx+₂)] L i- QaC ': 는 (cx+2) + 21 La + L-L S : - L I Lcd ㅋ 8