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Unformatted text preview: Name: ENGR 213 Winter 2007 Exam 1 K 'd‘% instructions: I. 2. 3. 4. Do not open the exam until you are told to do so. To receive ﬁlll credit, include correct units and signs with answers There are 4 problems on this exam. Some questions may be worth more points than others. . There is a total of250 points on the exam. . This is a partial credit exam. All work must be shown in the space provided and must be legible for credit to be awarded. . The exam is 50 minutes long, so budget your time accordingly. . You are permitted one 8.5” x 11” equation/note sheet (both sides). No worked problems are permitted on. equation/note sheet. EQWrite your name on your equation/note sheet and hand it in with your e xam. il.Some problems may include “extra” information. Do not assume all given information is required to solve the problem. 1. Bar AB is subjected to an agapiied axial force as shown. The bar has a circuiar cross
sectional area of 25x10'6m , elastic modulus of 200 x1 09133, and Poisson’s ratio of 0.3.
Neglect the weight of the bar. a. If the axial elongation is 0.002—m, what is the applied force? (20 pts) ‘0. If the axial elongation is 0.002—rn, what is the normal axial strain? (20 pts) (3. If the normal axiai strain is 0.00 1, what is the diametral (along the diameter of a
crosssection perpendicular to the axis of the bar) strain? (20 pts) d. If the axial force in bar AB is 10 DOGN, what is the normal stress in AB with
respect to a plane perpendicular to the axis of the bar? (25 pts) Applied
Force A‘ RS'HOWm'" W T
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i Qmﬁ Vni‘iﬁ 2. Each bar shown below has a crosssectional area of 0.75— in2 and a modulus of elasticity
of 30*106psi. The length of bars AD and CD is 12—in, the length of bar BI) is IDAin.
Answer the following: 21. Write all non—trivial equilibrium equations for the free —body diagram shovm
below (Quote) lg b. Is ﬁnding the axial loads in each bar a statically determinate or indeterminate
problem (no credit without explanation) (261315) 1? c. What is the compatibility condition for this problem?
(Hint #1 :write a sin e e uatidn in terms of the elo ation' of bars AD and BD) (Hint #2: due to the symmetry of the geometry and the loading, the displacement
of point D will be vertical only.) (20 pts) d. What is the constitutive equation (in forcewdeformation form) for her CD?
Substitute all lagoon) values. (20 pts) jwtm Genital! ‘10 nai‘ need ‘lm ,s‘alvee imam! to
bar co) Freebody diagram Pin) «Mg £836
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i) T h Aeﬁ‘er‘m trauma...“ 2 ague‘hmg {6177/ 3 Unknaa/ngi"}"9/l0/O ‘ a 2 z 2 ta‘m/
0) JD : JBDSW 60 e315; (mi—JAB)": (a +(lo.4+ Jan) 0 (Small ‘63) m m 02>
Aer? Eels? (075) (WHO'S 4.» {(3 bays“; 313/1.
4“ Q :s {fie DIM/“53m 3. A circular cross—section shaft is subjected to a torque, T, as shown beiow (note: the
drawing is not to scale). The shear moduius equals 6.2*106—psi. Section A has a cross
sectional diameter of CLOin. Section B has a crosssectional diameter of 1.0in. a. What is the angle of twist {including correct sign) atx=18in? Note the origin is
located at the leﬁ end of the bar, at the support (20 pts) b. What is the shear stress 0.10—in beiow the surface of the shaﬁ at FIBin ? (30
Pts) iiiin: +1641] ‘9‘ (3r: havoc?“ _
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+ ami wo _ it. + :5) a W‘MW” 'Rqrgaaoo ml)??? :0 : 3900m~ﬂo 4. The bar shown below has a crosssectional area of 0.794112 and a Young’s modulus of 30*106—psi. The bar is subjected to a distributed load causing an internal axial force of
3000»5x—5x2—1b. What is the total elongation of the bar? (30 pts) ...
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 Spring '06
 Keil
 Force, pts, axial force, equation/note sheet, agapiied axial force

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