ME 270 Sample Fnal Eam PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: A 2000 N crate (D) s suspended usng ropes AB and AC and s n statc equlbrum. If θ = 53.13, determne the tenson n ropes AB and AC. NAME: T AB = T AC = (2 ponts) (3 ponts) PROBLEM 1B. (5 ponts) FIND: Plate AB s supported b a pn support at A and a rocker support at B and s n statc equlbrum. For the loadng shown (neglect the weght of the plate), determne the magntude of the reacton force at B. If the 100 n-lb couple were shfted to pont A, would F B ncrease, decrease or reman the same. F B = (3 pts) Increase Decrease Reman the Same (Crcle one) (2 pts)
NAME: ME 270 Sample Fnal Eam PROBLEM 1C. (5 ponts) 3.8 ft FIND: Truss ABCDEFG s loaded wth a sngle 600 lb force at jont C and s n statc equlbrum. Determne the magntude of the force n member BC and whether t s n tenson or compresson. Lst all zero-force members. F BC = T or C (Crcle one) (3 pts) Zero-Force Members = (2 pts) PROBLEM 1D. (5 ponts) FIND: The A-Frame shown s supported b a rocker support at A and a pn support at E and s n statc equlbrum. On the schematcs below, complete a free-bod dagram of each member of the A-Frame. C C B D A E B D
NAME: PROBLEM 1E. (5 ponts) FIND: For the 50 lb chest shown, determne the force P needed to tp the chest, assumng the dmenson d = 3 ft. If the 30 angle were ncreased, would t ncrease or decrease the probablt of tppng the chest? μ s = 0.7 P = (3 pts) Increase Decrease (Crcle One) (2 pts)
ME 270 Sample Fnal Eam NAME: z PROBLEM 2. (25 ponts) GIVEN: The vertcal mast supports the 4-kN force and s constraned b two cables BC and BD and b a ball-and-socket connecton at A. FIND: T BC T BD a) Draw a free bod dagram of the mast on the artwork provded below. (4 pts) b) Epress tenson vectors T BC and T BD n terms of ther unknown magntudes and ther known unt vectors. (4 pts) c) Determne the tenson magntudes T BC and T BD. (8 pts) d) Determne the magntudes of the reactons at the ball-and-socket A. (9 pts) z
PROBLEM 3 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 3A. (5 ponts) FIND: Determne the nternal forces on cross-secton C. of the beam shown (.e., the aal and shear-force and the bendng-moment). NAME: C = F n = C = V = M c = (1 pt) (2 pts) (2 pts) PROBLEM 3B. (5 ponts) FIND: Determne the average shear stress n the 20 mm-dameter pn at A and the 30 mmdameter pn at B that supports beam AB. (τ Avg ) A = (3 pts) (τ Avg ) B = (2 pts)
NAME: PROBLEM 3C. (5 ponts) FIND: Beam AB rests on the two short posts (AC and BD). Post AC has a dameter of 20 mm and s made of steel. Determne the stress and stran n post AC f t s made of steel and has a dameter of 20 mm. Assume Esteel = 200 GPA. τ= (3 pts) ϵ= (2 pts) PROBLEM 3D. (5 ponts) FIND: Tube AB has an nner dameter or 80 mm and an outer dameter of 100 mm. Gven the torque appled n the dagram, determne the shear stress actng on the nner and outer walls of the tube. τouter = (3 pts) τnner = (2 pts)
NAME: PROBLEM 4 (25 ponts) GIVEN: Beam AB s loaded as shown. Assume the beam has a rectangular cross-secton of 50 mm wde and 100 mm hgh. FIND: a) Determne the reacton forces at supports A and B. (4 pts) b) Sketch the shear-force and bendng-moment dagrams. (6 pts) c) Determne the shear stress dstrbuton just to the rght of the B reacton. (5 pts) d) Determne the normal stress dstrbuton just to the rght of the B reacton. (5 pts)
NAME: V (kn) X (m) V (kn) X (m)
ME 270 Fnal Eam Equatons Sprng 2013 Normal Stress and Stran σ F A σ M I ε σ E L L ε ε ε ε ρ FS σ σ Shear Stress and Stran τ V A τρ Tρ J τ Gγ G E 21 γ δ L π 2 θ For a rectangular crosssecton, τ 6V h Ah 4 τ 3V 2A Second Area Moment I da I 1 12 bh Rectangle I π 4 r I I Ad Crcle Polar Area Moment J π 2 r r Tube Shear Force and Bendng Moment V V0 pd M M0 Vd Buoanc F =ρgv B Flud Statcs p=ρgh ( ) F = p Lw eq avg Belt Frcton T T L S = e µβ Dstrbuted Loads F eq F eq = L 0 = L ( ) w d 0 Centrods = = da c da ( ) w d A = c A = In 3D, = da c da A c A V c V Centers of Mass ɶ = ɶ = ρda cm ρda ɶ = ρa cm ρa ɶ = ρda cm ρda ρa cm ρa
Termnolog V Shear Force (ch 13) M Bendng Moment (ch 13) F Aal load (ch 13, 14) σ σ σ N Y U Normal Stress (ch 14) Yeld Strength Ultmate Strength ε Stran (aal or transverse) (ch 14) E Young's Modulus, or Modulus of Elastct (ch 14) υ Posson's Rato (ch 14) FS Factor of Safet (ch 14) τ Shear Stress (ch 15) γ Shear Stran (ch 15) G Shear Modulus (ch 15)
Sample Fnal Eam Answers 1A. T AB = 1500 N T AC = 2500 N 1B. F B = 15.3 lbs Reman the same 1C. F BC = 632 lbs Zero-Force Members: BF, DE, CD, EF, CE 1D. FBD 1E. P = 26.8 lbs Increase 2. T BC = 4.47 kn T BD = 4.90 kn A = -2 + 0j +8k kn 3A. C X = -300 lbs C = -10.42 lb M c = 718.75 lb-n ( ) = 34.0 MPa ( ) = 17.7 MPa 3B. AVG A AVG B 3C. = 191 MPa 4 = 9.554 10 mm/mm 3D. outer = 0.345MPa nner = 0.276MPa 4. 2 = 960,000 (0.0025 - ) = 1,920,000