This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ENGR 213 Spring 2006
Final Exam Name: l< EY Instructions:
1. Do not open the exam until you are told to do so
2. Fill in your name above
3. There are 4 problems on this exam 4. This is a partial credit exam. All work must be shown in the space
provided and must be legible for credit to be awarded. 5. The exam is 1 hour and 50 minutes long, so budget your time
accordingly 6. You are permitted three 8.5 x 11 equation/note sheets
7. No worked problems are permitted on equation/note sheet 8. Write your name on your equation/note sheets and hand them in
with your exam Do not write in this space Useful formulae
fSinede = C036 iSinB = C059
dx Semicircle Rectangle H l! “ijgbh 3
11gb 5h
ﬁbh 3
é—b 3]: ﬁbhﬂ)? + h?) I) Shear and moment diagrams.
a) For the given freebody diagram
i) Draw shear diagram. (28 pts)
ii) Label the diagram with values at crosssections A through H. (32 pts) 75[0.5 (14x)] lb/in 1558.7 inlb ‘ l t . A _ ‘
19 C0110. ‘FM'CGJ 0%CA' 120 U) Iii/FD x = h) _0
‘ AV  =
av _ ___
BIC) ﬁg: ’lu: '35'0) canS'JL. MC; .SiVPQ. 4/0 £525.” “83 ﬁg
ﬂip5p 4 I'D L5H
'9 1.3m —l?.a +v+ngoak=o 1‘ . v'
THU V v: "‘3 30 120 “('iF" 0 9
#9 $ 5‘60 = 0 ‘IZD +V+ izSpdx *S/Jﬂsjrzéhgyrzx‘wal
’4’ ’
D/E) git—:11) ﬂaps: aarﬂvras—v Esra ., + 5’37g[pf564WDA ‘9 2.51 M 421130 4 g ' ' _ ___ _3273
E) ¢C£LWQ§ —\7_a +v+§ 2§0Jx *S‘wasm (”';WL*"J)>JX= 0 ma. V=";1'§;’a7 b) For the given freebody diagram and shear diagram
i) Draw the moment diagram (8 pts) ii) Label the diagram with values at crosssections AB, and C. (12 pts)
200 lb/ft 2) An aluminum (Young’s modulus equals 70 GPa) rod with a semicircular cross section of radius 0.012m (as shown) is bent into the shape of a circular arc of radius p =‘2.5m. The moment of inertia about the neutral axis is equal to 2.276*10'9m4. Knowing that the ﬂat face of the rod is turned toward the center of curvature of the arc, answer the following. a) What is the distance between the ﬂat face and the neutral axis? (10 pts.) b) What is the magnitude of the applied moment? (20 pts.) 0) Will the stress at point P be tensile or compressive? (10 pts) d) If the answer to part (b) is 100 N—m, what is the normal stress (perpendicular to
the page) at point Q? (20 pts.) e) If the answer to part (b) is 150 N—m, what is the magnitude of the maximum
normal stress acting on the crosssection? (20 pts) Eat70 X109 ”ma ‘4?: Q‘s—m EQIU— +6 F: Oiﬂll m 94 —— unsun If m wast.— +2? Eli» MW?
sung". 719 lee ~ g;
970 Fife/1‘ “f ' Awsri—l   5"
:12: 1094539091 p.00 a9>=ln 3
lama JULQMPAJ EQm,+o
Sumr9 0" = , 9.
RM.+{ J: allWIX/ﬂ EQMHo a I: NC : (/5’ﬂ>LJ.ﬂJ’Q—~ prays—J99
suesz—r—g 1:” 3: ’10.?)«10—9 A15, *7 2. 4,g§—42< lg? Pa» @ 3) A beam is built by applying adhesive to two semicircular and one rectangular cross
section bars. A transverse shear force, V, of magnitude 5100 lb. is applied to the
crosssection shown below. The centroidal moment of inertia is 12.77 in4. The
equation to calculate the stress caused by a transverse shear force is _ VQ
1b
Assuming it is desired to calculate this stress at the upper adhesive joint, answer the
following:
a) What is the correct value of Q? (40 pts)
b) What is the correct value of I? (20 pts)
0) What is the correct value of b? (20 pts) 27 adhesive 1.5" I fa. 3. :'_7.i.+"l nns 4) In the unloaded state, the steel block shown has dimensions AB = 0.080m
BC = 0.040m
BD = 0.060In In the loaded state, the steel block shown is subjected to a uniform pressure on all its faces (each face is subjected to the saute pressure, p). determine the following a) Knowing that the change in length of edge AB is 24.0"‘10'6 meters (i.e. AB
decreases in length), what is 8;; ? (10 pts.) b) What are the stresses, 0x, 03,, and Oz in terms of the pressure p?(21 pts.) c) What are the strains, 83,, and 32 in terms of p, E, and v ?(34 pts.) d) If sx= 8y = £z= 250*10'9, what is volume of the block in the loaded state? (15 pts.) ...
View
Full Document
 Spring '06
 Keil

Click to edit the document details