MECHANICS OF SOLIDS
(EM 319)
L ,L A , f <
QUIZ #3
Spring 2004
Monday April 5, 8-9am WEL 3.502
Closed book, noies, homework
Both questions should be attempted: they are each worth 20 points.
6=-PL
E.4
TL ?,=- TT
=r" 0 = I
'
L
GI, ' GI,,
3,
j(as + b)"& =
NAME:
(ax + h)""
(n+l)a
?nc,,,)
SECTION (Circle one'
P=TU
(4~6
@
Th
44,:' r=- T
?A,,:T
1. The two bars shown below are separated by a small amount. The diameter of the
tapered bar (A) is initially twice that of the prismatic one (B). Where they nearly
meet, the two bars have the same diameter. The length of the prismatic bar is two
thirds of the tapered one. The bars have the same shear modulus. G .
[
(a) Show that the diamerer of the tapered bar is d, = 2d, 1--
2;)
@) If the tapered bar is twisted by an amounr ,b and then welded to the
prismatic one and tbell released. determine the reactions at the rigid
supports.
2. The weight of the beam ABC shown below is 100 Nlm. Draw the shear force and
bending moment diagrams for the beam ABC, accounting for the weight of the
beam and the 3 kN load. Identify the critical points on each curve and give the
equations for each segment. You may use the grids for the dia,urams.
2 rn
f.:
2m
.
!
,
r,.
/I.
r,.
2 rn
*