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Unformatted text preview: EM 319 Mechanics of Solids
April 26th 2011, 7:00-9:30 pm
Closed books, notes and homeworks Name:
EID: TA Session: Vishal Nayyar W 4-6 pm 13900 Wei Gao TH 4-6 pm 13905 Adam Sierakowski W 6-8 pm 13910 Andrew Barnes TH 6-8 pm 13915 Formulas:
EIv '''' q x' y' x y
2 x y
2 2 2 x y max x y
2 x y 2 x y 2 x y x' y' 1 EIv ''' V 2 EIv '' M cos2 xy sin 2 cos2 xy sin 2 sin 2 xy cos2 x y 2 xy 2 ave R x y 2 xy 2 ave R x y 2 tan 2 P 2 2 2 xy 2 R 2 xy x y x y
tan 2 S 2 xy Exercise 1 (30 points)
Determine the angle of rotation and deflection at the free end of the cantilever beam AB supporting
a cubic load defined by the equation Fig. 1 Exercise 2 (30 points)
Determine the deflection at the midpoint for a beam of length L supporting a triangular load of
maximum intensity qo. Fig. 2 Exercise 3 (40 points)
At a point in a structural member, on a plane 25o counterclockwise from the vertical plane through
the point, the normal stress is 10 ksi. The normal stress on a plane 65o clockwise from the vertical
plane through the point, is -20 ksi. The shear stress on a plane 55o counterclockwise from the
vertical plane through the point is 10√3 ksi.
Show, on two separate sketches, the stresses for elements oriented at 25o
Show, on two separate sketches, the principal and maximum shearing
stresses at the point.
(c) Draw Mohr's circle including all results from (a) and (b). ...
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- Fall '08