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1 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem n the space provded on the examnaton sheets. If addtonal space s requred, use the whte lned paper provded to you. Work on one sde of each sheet only, wth only one problem on a sheet. Each problem s worth 20 ponts. Please remember that for you to obtan maxmum credt for a problem, t must be clearly presented,.e. The coordnate system must be clearly dentfed. Where approprate, free body dagrams must be drawn. These should be drawn separately from the gven fgures. Unts must be clearly stated as part of the answer. You must carefully delneate vector and scalar quanttes. If the soluton does not follow a logcal thought process, t wll be assumed n error. When handng n the test, please make sure that all sheets are n the correct sequental order and make sure that your name s at the top of every page that you wsh to have graded. Instructor s Name and Secton: Sectons: J Jones 9:30-10:20M P Sojka 1:30-2:20PM J Slvers 3:30-4:20PM J Jones Dstance Learnng Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Total

2 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): PROBLEM 1 (20 ponts) Prob. 1 questons are all or nothng. 1(a) Determne the reacton forces actng on bar B wth the loadng shown. Express the forces n vector form. = B = 1(b) Determne the magntude of the load n member CD and whether t s n tenson or compresson. lso lst all zero-force members. (2 pts) (3 pts) 600 lbs F CD = T or C (3pts) Zero-Force Members =

3 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): 800N 1(c) One the members provded, sketch the free body dagram of the two member frame. Determne the force F actng on member BC n vector form. B FBD (2 pts) 3 4 B B C F B on BC = (3 pts) 1(d) The force P s appled to a 200 lb block whch rests atop the 100-lb crate. The system s at rest when P s frst appled. There are four possble motons. 200 lb a) Nether nor B move b) moves, B doesn t c) and B both move as a unt d) and B both move, but separately B 100 lb For P = 60 lbs, crcle the resultng motons a b c d (2 pts) For P = 80 lbs, crcle the resultng motons a b c d (3 pts)

4 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): PROBLEM 2 (20 ponts) Gven: small tower has a 20 kn load as shown and s held n statc equlbrum by a ball-and-socket support at O and cables B and C. Neglect the weght of the tower. Fnd: a) Complete the free-body dagram of the boom on the sketch provded below. (4 pts) b) Express the tenson n cables T B and T C n terms of ther known unt vectors and ther unknown magntudes. (4 pts) c) Determne the magntudes of the tensons n cables T B and T C. (6 pts) d) Determne the vector reacton at the ball-and-socket support at O. (6 pts) a) Free-body dagram (4 pts) Ball-&-Socket Jont a) Ball-&-Socket Jont b) b) c) T = (2 pts) B T = (2 pts) C

5 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): c) c) T = (3 pts) B T = (3 pts) C d) d) O = (6 pts)

6 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): PROBLEM 3 (20 ponts) The 60 lb block shown s held up by a cable, whch wraps around a fxed drum, and has an appled force, P. Between pont C and the drum, the cable has a tenson, T. Frst, consder just the block: a) Determne the mnmum tenson, T tp, needed to prevent the block from tppng. Your soluton must nclude a free body dagram. (7 pts) b) Determne the mnmum tenson, T slp, requred to prevent the block from slppng. Your soluton must nclude a free body dagram. (7 pts) c) In order to prevent moton, what s the mnmum tenson n the cable? Is the block on the verge of tp or slp? (2 pts) Now, consder the cable wrappng around the drum. d) What force, P, must be appled to the cable n order to prevent moton of the block? (4 pts) a) FBD for Tppng case T tp =

7 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): b) FBD for Slppng case T slp = c) T = Tp or Slp (crcle one) d) P =

8 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): PROBLEM 4 (20 ponts) Prob. 4 questons are all or nothng 4. In your own words, state each of Newton s three laws of moton. Be sure to wrte legbly. Unreadable defntons wll be marked wrong. (6 pts) 1 st Law = 2 nd Law = 3 rd Law = 4B. Determne the second area moment, I Z, of the L-beam shown as t rotates about the z-axs. Dmensons are gven n nches. IZ (4 pts)

9 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): 4C. Square holes, where each sde has a length b = 10 cm, are beng punched out of a 2 mm thck metal plate. The punchng shear resstance of the plate s 250 MPa. Determne the force, P, necessary to punch out the square. P = (4 pts) 4D. crcular tube of nner radus 39 mm and outer radus 44 mm s subjected to a torque produced by the par of forces P = 420N. The forces are separated by a dstance b = 300 mm. Determne the shear stress at the outer and nner walls of the tube; gve the answer n Pa. Determne the shear stran at the outer wall of the tube. E = 52 GPa, ν = 0.30, G = 20 GPa.. outer Pa (2 pts) Pa (2 pts) nner (2 pts) outer

10 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Problem 5. (20 pts) Gven: Beam BCD s held n statc equlbrum by a pn jont at and a roller support at D. The loadng on the beam s such that t results the gven shear-force and bendng-moment dagrams provded below. ssume there s no loadng n the x-drecton. Fnd: See the followng page. B C D 4 V (kn) 2 m B 2 m C 2 m D M (kn-m) 2 m B 2 m C 2 m D

11 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Prob 5 Cont. 5a. ssumng no external loads exst at supports and D, determne the magntudes of the reactons at these supports based on the dagrams provded. Express the results n vector form. Explan brefly how you arrved at these values based on the shear-force and bendng moment dagrams provded. a) = D = (2 pts) (2 pts) 5b. Gven the shear-force and bendng-moment dagrams provded, sketch a vald loadng condton that would be consstent wth these dagrams. On the beam provded, show the magntude drecton, and locaton of all loads needed to create the shear-force and bendng-moment dagrams provded. Explan brefly how you arrved at these values based on the dagrams provded. (9 pts) B C D

12 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Prob 5 Cont. 5c. If the beam has a tubular cross-secton wth an outer dameter of 10 cm and an nner dameter of 8 cm, determne the second moment of area for bendng about the centrod of the tube (Hnt ths s bendng, not torson). c) I = (3 pts) z 5d. In the segment of the beam that exhbts pure bendng, determne the maxmum tensle stress. Crcle the locaton of the maxmum tensle stress. d) σ Max = (3 pts) Max Tenson (Crcle One) Top Bottom Mddle (1 pts)

13 ME 270 Fnal Exam Equatons Fall 2013 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Normal Stress and Stran σ x = F n σ x (y) = My I ε x = σ x E = L L ε y = ε z = ϑε x ε x (y) = y ρ FS = σ fal σ allow Shear Stress and Stran τ = V τ(ρ) = Tρ J τ = Gγ E G = ϑ γ = δ s L s = π 2 θ Second rea Moment I = y 2 d I = 1 12 bh3 Rectangle I = π 4 r4 I B = I O + d OB 2 Crcle Polar rea Moment J = π 2 r o 4 r 4 Tube Shear Force and Bendng Moment x V x = V 0 + p ϵ dϵ 0 M x = M 0 + Buoyancy FB gv Flud Statcs p gh F p Lw eq avg x V ϵ dϵ 0 Dstrbuted Loads F eq xf L w x dx eq 0 L x w x dx 0 Centrods x x x d c d y x c In 3D, x y d c d y x V c V Centers of Mass x x x cm x d d cm y y y y cm y cm c d d Belt Frcton T T L S e

14 ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Sprng 2014 Fnal Exam Solutons 1. = 52j lbs B = 30-52j lbs 1B. F CD = 1000 lbs Tenson Zero-Force Members = C, B 1C. F B = j N onbc 1D. a c 2. Free-body dagram 2B. T B = T B( j k) T C = TC j 2C. T B = 24.5 kn T C = 10.0 kn 2D. O = k kn 3. Free-body dagram T tp = 5.94 lb 3B. Free-body dagram T slp = lb 3C. T = Slp 3D. P = lb 4. Newton s Three Laws of Moton 4B. I = n z 4 4C. P = 200 kn or 200,000 N 4D. τ outer = 2,464,000 Pa τ nner = 2,184,000 Pa m m -4 γ outer = x 10 ( ) 5. = 4j kn D = 2j kn 5B. Sketch of vald loadng condton and explanatons for values based on the dagram 5C. I = 290 cm = 2.90 x 10 m z D. σ Max = 138 M Pa Max Tenson = bottom