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For the loaded arrangement shown, find the downward shift (deflection) of points B, C and D respectively.

1. 4 mm, 9 mm, 24 mm
2. 2 mm, 4.5 mm, 12 mm
3. 6 mm, 13.5 mm, 36 mm
4. 3 mm, 6 mm, 18 mm

Correct answer: 2 mm, 4.5 mm, 12 mm

Solution

The shift of a point equals the cumulative extension of the supporting members above it. Computing dL = F*L/(A*Y) for each segment and summing cumulatively gives shifts in the ratio 4: 9: 24, and the magnitudes matching the loaded data give 2 mm, 4.5 mm and 12 mm at B, C and D.

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