Cuesta College, San Luis Obispo, CA
A concrete beam (linear expansion coefficient 9.8×10–6 K–1) and glued laminated wood beam (linear expansion coefficient 3.6×10–6 K–1[*]) have the same length at room temperature (293 K). If they both decrease in temperature by the same amount, the length of the concrete beam will be __________ the length of the wood beam. (A) shorter than.
(B) equal to.
(C) longer than.
(D) (Not enough information is given.)
Correct answer: (A)
The relation between the change in length ∆L due to a temperature change ∆T is given by:
αconcrete·∆T = ∆Lconcrete/L,
and similarly for the glued laminated beam:
αwood·∆T = ∆Lwood/L,
where the original length L and the temperature change ∆T is the same for both the concrete and glued laminated beam. Solving for this common factor for both beams:
L·∆T = ∆Lconcrete/αconcrete,
L·∆T = ∆Lwood/αwood,
we can then set this common factor for both beams equal to each other:
L·∆T = L·∆T,
∆Lconcrete/αconcrete = ∆Lwood/αwood.
From inspection, since αconcrete > αwood, then for the equality to hold, ∆Lconcrete > ∆Lwood, and so the concrete beam would contract more, and as a result be shorter than the glued laminated beam.
Sections 70854, 70855
Exam code: quiz07VlnC
(A) : 18 students
(B) : 7 students
(C) : 26 students
(D) : 0 students
Success level: 35%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.05