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2.

The curved pipę depicted Figurę 11 has an original radius of 1.97 ft. If it is heated non-uniformly, so that the normal strain along its length is e = 0.05 cosd, determine the increase in length of the pipę.

2.

Figurę 11: Cun/ed pipę under temperaturę loading

A.    AL =    0.98 ft

B.    AL =    1.05 ft

C.    AL =    0.84 ft

D.    AL =    1.11 ft

E.    AL =    0.82 ft

Solution

The correct answer is A.

€(s) = 0.05 cos 6

where s denotes the arc-coordinate along the curved pipę.

The length change of the entire pipę is computed by integrating over the non-uniform strain along s

Equivalently_; considering that the arclength of a circle segment with radius R and corresponding angle dd is computed as ds = Rdd = 1.97 ft • dQ

vje find

/•90*    r30*

AL =    e(1.97 ft • dd) =    (0.05 cos d) (1.97 ft • dd)

'o

'o

o

AL = 0.98 cos ddd = 0.98 [sin Q] |2°’ = 0.98/t

Hence th|= correct answer is A.