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Unformatted text preview: ME 211
Examination 2 — Winter, 2016
Section 001  Prof. Wineman OBSERVE THE HONOR CODE SIGN THE HONOR PLEDGE
Problem 1
Bar ABC is attached to fixed walls at A and C. The data for the bar:
Segment Lengm ﬂea Elastic Modulus
AB L A E
BC L BA E H (1) Find the forces on the bar at the walls in terms Of P
a; (2) Find the displacement of section B in terms of P
n (3) Find the force P so that the maximum magnitude of normal stress on a cross section is 00. Pm. P/a Problem 2 A beam is supported and loaded as shown. The corresponding bending moment
diagram is also shown. Slim/m» r" MM” sum
39») <.— [M “+05”; 'f.§'ﬁﬂmd 5/ (a) Show the bending moment and corresponding stress distribution on the
section at 0.4375 In. 3’ (b) Show the bending moment and corresponding stress distribution on the
section at 1m. 2 (c) Suppose the cross section has the form Find the width ‘d’ so that on the section at 0.4375 m, the maximum tensile
stress is 3 times the maximum compressive stress 5? (d) Indicate the location of the maximum tensile stress in the beam 9 (6) Which of the following is the correct expression for I 0.5(35)3 d (0.5)3 a 0.5(35)3 + 0.5d3 a. I=——+ b.I
12 12 12 12
_ 3 _ 3 2
c. I=W+d (102's) +0.5(3.5)(%——Y) +0.5d(3.7‘5—Y)2 0.5(3.5)3 0.5a3 (3.5 _]2 s2
. =___ 0.5 3.5 ———— 0d3.75~—
d I 12 + 12 + ( ) 2 y + 5 ( y)
Iii(2idiv5f+05(35)(£—)+05d(375—)
e' _ 12 12 ' ‘ 2 y ' ' y
0.5(35)3 d(0.5)3 (3.5 _]2 2
.1=——— —0.5 3.5 —— —0.5d 3.75—
f 12 + 12 ( ) 2 y ( y) 3 ‘9 Problem 3
The torsion bar shown below has three segments. It is built in to a ﬁxed support at the left end. Twisting moments are applied where the sections join. A table of properties is
given. segment .1211th .1 modulus f2) L2J2 o
o 1) Cross sections in segments (11623183 are shown. Area increments are also shown. On each section:
Show the twisting moment, giving its magnitude and sense. Show the shear stress, giving its magnitude and sense Section in® Section in® Section [email protected] 2) Which of the following expressions for the rotation of the right end is correct: a. statsnet b. ﬁle—812$
6.13 (312 (311 013 612 01:
C. 6L_3_2L2+10L1 d_ £122“ch
(313 G133 G], 013 G~72 G‘i 9111+2L2+9~lzi 3.
(313 {3.12 01, ...
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 Spring '08
 Thouless
 Statics

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