Vertical rods (1), (2), and (3) are all strain free when they are initally pinee
ID: 1818082 • Letter: V
Question
Vertical rods (1), (2), and (3) are all strain free when they are initally pineed to a straight, rigid, horizontal beam BF. Subsequently, heating of the rods causes them to elongate and leaves the beam in the position denoted by B*D*F*. Point D moves vertically downward by a distange 0.20 in. and the inclination angle of the beam is theta = 0.4 degrees in the CCW sense, as indicated on Fig 2. Determine the strains epsilon1, epsilon2, and epsilon3 in the three rods.
Vertical rods (1), (2), and (3) are all strain free when they are initally pineed to a straight, rigid, horizontal beam BF. Subsequently, heating of the rods causes them to elongate and leaves the beam in the position denoted by B*D*F*. Point D moves vertically downward by a distange 0.20 in. and the inclination angle of the beam is theta = 0.4 degrees in the CCW sense, as indicated on Fig 2. Determine the strains epsilon1, epsilon2, and epsilon3 in the three rods.Explanation / Answer
Given:
Length of rod 1 = 6 ft
Length of rod 2 = 4 ft
Length of rod 3 = 4 ft
change in length of rod 2 , l2 = 0.2 in
Solution:
The angle is given by
0.40 = tan-1[(l2 - l3 )/24] we know that l2 = 0.2 in
therefore tan(0.40 ) = (0.2- l3)/24
=> l3= 0.2- 24x tan(0.40) = 0.03 in
For rod 1 Tan = [(l1-l2)/36]
=> l1 = 36xtan(0.40) + l2
l1 = 36 x tan(0.40) + 0.2 = 0.45 in
l1 = 0.45 in and 1 = l1/l1 = (0.45/72) = 6.25 x 10-3
l2 = 0.2 in and 2 = l2/l2 = (0.2/48) = 4.17 x 10-3
l3 = 0.03 in and 3 = l3/l3 = (0.03/48) = 6.25 x 10-4
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