ME 270 Summer 2014 Fnal Exam NAME (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 25 ponts. Please remember that for you to obtan maxmum credt for a problem, t must be clearly presented,.e. The only authorzed exam calculator s the TI-30IIS The allowable exam tme for Fnal Exam s 120 mnutes. 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 9:50-10:50AM J Jones Dstance Learnng Problem 1 Problem 2 Problem 3 Problem 4 Total ME 270 Fnal Exam Summer 2014 Page 1
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. 1A. Sphere E has a weght of 100N and s supported by cable CBA and sprng CD. Determne the magntudes of the tenson n cable CB (assume the pulley s deal) and the tenson n sprng CD. (5 pts) 1B. Member AB has a 900N force and 500 N-m couple loadng the member. It s held n statc equlbrum by a collar at A and a roller support at B. The collar at A can freely slde n the y-drecton but moton n the x-drecton and any rotaton about pont A s ressted by the collar. Determne the magntudes of the reactons at collar A and roller B. (5 pts) ME 270 Fnal Exam Summer 2014 Page 2
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): 1C. For the truss shown, dentfy all zero-force members and calculate the magntudes of the loads n members CD and AE and specfy whether each s n tenson or compresson. (6 pts) 1D. Frame ABC s desgned as a compound beam whch has a pn connecton between members AB and BC. The beam s supported by a fxed support at A and a rocker support at C. For the loads shown, determne the forces actng at B and C n vector form on member BC. (Hnt: Sketch the ndvdual free body dagrams frst.) (4 pts) ME 270 Fnal Exam Summer 2014 Page 3
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): 1E. Determne the total angle of wrap around pegs A, B, and C collectvely and calculate the smallest force P requred to lft the 100 N crate. Assume the coeffcent of frcton between the cable and each peg s µ = 0.1. (5 pts) s ME 270 Fnal Exam Summer 2014 Page 4
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): PROBLEM 2. (25 ponts) GIVEN: The sgn has a weght of 1000N wth a center of mass at G. The sgn s held n statc equlbrum by a ball and socket support at A and cables BC and BD. FIND: a) On the sketch provded, complete the free body dagram of the sgn. (3 pts) 2 m D 2 m D b) Wrte vector expressons for the forces n cables BC and BD n terms of ther unknown magntudes and ther known unt vectors. (4 pts) ME 270 Fnal Exam Summer 2014 Page 5
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): c) Determne the magntudes of the tensons n cables BC and BD. (10 pts) d) Determne the magntudes of the reactons at the ball and socket support. (8 pts) ME 270 Fnal Exam Summer 2014 Page 6
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): PROBLEM 3. (25 ponts) 3A. A wood specmen s subjected to an average normal stress of 2 ks durng a tensle test. Determne the axal load P appled to the specmen. Also, fnd the average shear stress developed along secton a-a of the specmen. (5pts) 3B. A statc analyss of beam AB results n BC F = 12.5kN and A = -7.5 + 20j kn. Determne the average shear stress (n kpa) n the 20 mm-dameter pn at A and the 30 mm-dameter pn at B that support the beam. (Hnt: Note the type of connecton used on each end of the beam.) (5 pts) ME 270 Fnal Exam Summer 2014 Page 7
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): 3C. Determne the magntude of the torque (n kn-m) pulleys A and B create n shaft AB and calculate the maxmum shear stress (n kpa) due to ths torsonal load. Assume the shaft has a dameter of 40 mm. (5 pts) 3D. The cross-secton of a beam s T-shaped wth the dmensons shown. The locaton of the centrod s dentfed on the artwork. Determne the second-area moment of nerta about the x-axs (I x ). Based on the shape of the cross-secton, whch of these statements are true (I x > I y, I x < I y, I x = I y). No calculatons are necessary. (5 pts) y x ME 270 Fnal Exam Summer 2014 Page 8
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): 3E. For the shaded area bounded by the y-axs, y = 1 and x = y 2 ; determne the area and the second moment area of nerta about the y-axs (I x ). Hnt:Use a horzontal dfferental element. (5 pts) x = y 2 ME 270 Fnal Exam Summer 2014 Page 9
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): PROBLEM 4. (25 ponts) Gven: Beam ABCDE s loaded as shown and s held n statc equlbrum by a pn support at A and a roller support at D. The beam cross-secton s T-shaped and has the dmensons shown and a second moment of nerta of -6 4 I x = 13.8 x 10 m. (Note NA refers to the neutral axs.) FIND: a) Sketch a free-body dagram of the beam and determne the magntudes of the reactons at A and D. (5 pts) 4 kn 21 kn-m 2 kn/m NA A 3 m B 1 m C 1 m D 3 m E FBD (1 pt) 3 m 1 m 1 m 3 m A B C D E ME 270 Fnal Exam Summer 2014 Page 10
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): 4b) On the axes provded, sketch the shear-force and bendng-moment dagrams of the beam. (10pts) 4 kn 2 kn/m 21 kn-m A 3 m B 1 m C 1 m D 3 m E V(kN) x(m) M(kN-m) x (m) ME 270 Fnal Exam Summer 2014 Page 11
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): 4c) In whch segment(s) of the beam does pure bendng occur (2 pts) 4d) In the segment of the beam where pure bendng exsts, determne the magntudes of the maxmum tensle bendng stress and the maxmum compressve bendng stress. (8 pts) ME 270 Fnal Exam Summer 2014 Page 12
ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): Summer 2014 Fnal Exam Equaton Sheet Normal Stress and Stran σ! = F! A My I σ! L ε! = = E L ε! = ε! = ϑε! y ε! (y) = ρ σ!"#$ FS = σ!""#$ σ! (y) = Shear Stress and Stran V A τ= τ(ρ) = Tρ J τ = Gγ Shear Force and Bendng Moment! V x =V 0 + p ϵ dϵ!! M x =M 0 + V ϵ dϵ! Buoyancy FB = ρgv Flud Statcs p = ρgh Feq = pavg (Lw ) Belt Frcton TL = eµβ TS Dstrbuted Loads L Feq = w ( x ) dx 0 G= E 2 1+ϑ xfeq = x w ( x ) dx γ= δ! π = θ L! 2 Centrods Second Area Moment y! da I=! 1 bh! Rectangle 12 π I = r! Crcle 4 I= I! = I! + Ad!"! Polar Area Moment π! r Crcle 2 π J = r!! r!! Tube 2 J= L 0 x da da x A x= A c x= c y A y= A c y da da c x V In 3D, x = V c Centers of Mass x%= x cmρda cm y ρda ρda y ρ A y%= ρ A cm y%= ρda x ρ A x%= ρ A ME 270 Fnal Exam Summer 2014 y= cm Page 13
ME 270 Sprng 2014 Exam 1 NAME (Last, Frst): ME 270 Fnal Exam Solutons Summer 2014 1A. T CB = 115 N T CD = 57.5 N 1B. A x = 0 N B y = 900 N M A = - 1486 N-m 1C. Zero-Force Members: AF, EF, BC F CD = 400 lbs C AE F = 667 lbs C 1D. B onbc = 4j kn C onbc = 4j kn 1E. o β = 360 = 2 π rad. P mn = 187 N 2A. FBD 2B. T BC = T BC (0.333-0.667j + 0.667k) T BD = T BD (- 0.707-0.707j) 2C. T BC = 750 N T BD = 354 N 2D. A x = 0 N A y = 750 N A z = 500 N 3A. P = 4000 lbs = 4 kps ( ) 3B. ( ) τ = 17,684 kpa B avg τ = 250 ps 3C. T = 0.60 kn-m τ max = 47,770 kpa a-a avg 3D. I > I 4 I x = 33.3 n x y 3E. 2 2 A = 1/3m = 0.333 m I = 1/5m = 0.20 m y 4 4 4A. FBD A y = 4 kn D y = 6 kn 4B. Shear-force and bendng-moment dagrams 4C. BC, CD 4D. ( τ ) = 136,522 kpa ( ) max T τ = 102,391 kpa max C [Type text] Page 14