The figure shows part of a buried pipe that is used to transport a high-temperature fluid. The fluid temperature is 200  F above that when the pipe was constructed. The entire conduit is connected to two structures at both ends and can be assumed to be recessed at those points. In addition, the pipe is subjected to friction from the surrounding soil. This effect is represented by a uniformly distributed force (in the axial direction) of magnitude 0.3 k / ft. Likewise, there are two point forces of magnitude 10 k each applied to one of the intermediate supports as shown in the figure. The left and right leg are constructed of an 8-5 / 8 x 0.5 HSS tubular section (that is, with an external diameter equal to 8-5 / 8 of an inch and a thickness of 12 in.). The middle span is constructed of a standard HSS 12-1 / 2 x 0.5 section (ie, 12.5 '' OD and 12 '' thick). Use the matrix stiffness method to calculate the axial displacements at the joints of the three elements and the axial (or normal) forces N in each of them. Show in a drawing these axial forces acting at the two ends of each element.

20 ft 25 ft 2011 10k 0.3 Wft 0.3 W 0.3 ff 10 k 20 ft 25 ft 2011 10k 0.3 Wft 0.3 W 0.3 ff 10 k