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Unformatted text preview: Name: Session: 2 A nonprismatic bar ABC made up of segments AB (length 2 L , cross-sectional area 2 A ) and BC (length L , cross-sectional A ) is fixed at end A and free at end C (see figure). The modulus of elasticity and the coefficient of thermal expansion of the bar are E and α , respectively. A small gap s exists between the end of the bar and an elastic spring of spring constant k . If bar ABC (not the spring) is subjected to temperature increase Δ T , determine the following: (a) Find the temperature increase Δ T c so that the gap is closed. (b) Write an expression for the reaction forces R A and R D if Δ T > Δ T c . (c) If the yielding stress of the material of the bar is σ y , determine the maximum allowable value of the temperature increase for a factor of safety of 2 with respect to yielding. 2 L s A B C k L D Solution: (a) ( ) s L L T c = + Δ 2 α L s T c α 3 = Δ (b) FBD EQM ∑ = = ⇒ = R R R F D A x Compatibility s s BC AB = + + δ δ δ ( ) ( ) ( ) ( ) D A R R k...
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- Spring '11
- Max, cross-sectional area, reaction forces RA