I have not received unauthorized aid in the completion of this exam.

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1 ME 270 Sprng 2013 Fnal Examnaton Please read and respond to the followng statement, I have not receved unauthorzed ad n the completon of ths exam. Agree Dsagree Sgnature INSTRUCTIONS Begn each problem n the space provded on the examnaton sheets. If addtonal space s requred, use the 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. Please crcle your nstructor s name: Nauman Slvers Chagdes Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Total

2 PROBLEM 1. (20 ponts) Problem 1 questons are all or nothng. 1A (5 pts) In your own words, brefly state each of Newton s three laws of moton. Be sure to wrte legbly. Unreadable defntons wll be marked wrong. 1 st Law : 2 nd Law : 3 rd Law : 1B (5 pts) Cable AD has a tenson of 70 N. Wrte the force n vector form. Determne the moment about pont O due to T AD ; express your answer n vector form. (2 pts) (3 pts)

3 1C (5 pts) A block weghng 100 N s on an nclne wth a coeffcent of frcton μ = 0.3. What force, P, s necessary to keep the block from sldng down the nclne? pts) (5 1D (5 pts) Identfy any zero force members n the truss shown. Lst them n the answer box. Determne the force n lnk gd. Indcate f t s n tenson or compresson. (Note that snce both a and e are pn jonts, you wll not be able to solve for the forces at those supports.) Zero force members: (3 pts) Fgd = T or C (crcle one) (2 pts)

4 Problem 2 (20 ponts) 2A (5 ponts). Determne the area and the x- component of the centrod for the object below. 2B (4 ponts) GIVEN: and. FIND: Determne the angle between the vectors. (4 pts)

5 2C (6 ponts) The can crusher shown to the rght s made of alumnum (, ) and requres a force F = 2 lbs to crush a can. Dmensons are gven n nches. BD s a two- force member wth a cross- sectonal area A = n 2. Determne the normal stress and axal stran n BD. Under ths loadng, s BD stretchng or contractng n the axal drecton?

6 2D (5 ponts) Tube AB has an nner dameter of 50 mm and an outer dameter of 60 mm. Determne the torque beng appled by the force couple shown. Determne the shear stress at the outer and nner walls of tube AB. (1 pt) (2 pt) (2 pt)

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8 PROBLEM 3. (20 ponts) GIVEN: The frame shown s loaded wth a 58 kn weght that hangs from the center of pulley E. There s a sold round pn at O made of structural steel wth a yeld strength of FIND: a) Draw free body dagrams of member BCDO, pulley D, and pulley E. (7 pts) b) Determne the magntude of the reacton force at pont D. (4 pts) c) Determne the magntude of the reacton force at pont O. (5 pts) d) Usng a factor of safety of 2, determne the mnmum cross- sectonal area requred for the pn at O to avod yeldng. (4 pts) Member BCDO: Pulley D: Pulley E:

9 (4 pts) (5 pts) (4 pts)

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11 PROBLEM 4. (20 ponts) GIVEN: A large tank s holdng water (ρg = 62.4 lb/ft 3 ). In one wall of the tank, there s a gate, AB, whch s 8 ft long and 4 ft wde (measured nto the page). The gate weghs 20 lbs. The gate s hnged (pnned) at B and rests aganst the frctonless wall of the tank at A. FIND: a) Sketch the pressure dstrbuton actng on gate AB. (1 pt) b) Replace the pressure load wth a sngle equvalent force and crcle ts magntude and locaton. (5 pts) b) a) Pressure Dstrbuton F eq = (crcle one) 390 lb 780 lb 1560 lb 2496 lb 3120 lb d = ft ft ft ft ft 3994 lb 15,304 lb

12 c) Draw a free body dagram of gate AB. (4 pts) d) Determne the magntude of the normal force at A. (4 pts) e) Determne the magntude of the normal force at A f the gate had no weght. (2 pts) Comparng your answers n (d) and (e), would you say the weght of the gate s neglgble? f) Ignorng the weght of the gate, and usng the normal force solved for n part (e), determne the forces at the pn jont at B. Gve your answer n vector form, relatve to the x- y axes shown. (4 pts) c) Free Body Dagram d) (ncludng weght of gate) e) (neglectng weght of gate) Is the weght of the gate neglgble? Yes No f)

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14 Problem 5 (20 ponts) 5a. The beam below s smply supported. F 1 = 1,000 N, x 1 = 4 m, x 2 = x 3 = 1 m, and the dstrbuted load has magntude, w 0 = 500 N/m. Determne the reactons at ponts A and D. Then draw the shear and moment dagrams on the followng page. (12 ponts). Determne the Reactons at ponts A and D.

15 Shear Dagram Moment Dagram 5b. Locate the pont at whch pure bendng occurs (dstance from pont A) and determne the maxmum tensle stress. (6 ponts) On the cross- secton shown n the pcture below, locate where the maxmum tensle stress occurs. You may use b = 8 cm and h = 16 cm. (2 ponts)

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17 ME 270 Fnal Exam Equatons Sprng 2013 Normal Stress and Stran σ F A σ y My I ε σ E L L ε ε ε ε y y ρ FS σ σ Shear Stress and Stran τ V A τ ρ Tρ J τ Gγ G E 2 1 γ δ L π 2 θ For a rectangular crosssecton, τ y 6V h Ah 4 y τ 3V 2A Second Area Moment I y 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 x V 0 p d M x M 0 V d Buoyancy F =ρgv B Flud Statcs p=ρgh ( ) F = p Lw eq avg Belt Frcton T T L S = e µβ Dstrbuted Loads F eq xf eq = L 0 = L ( ) w x dx 0 Centrods x x= = xda c da y ( ) x w x dx x A = c A y= In 3D, x= y da c da y A c A x V c V Centers of Mass xɶ = xɶ = x ρda cm ρda yɶ = x ρa cm ρa yɶ = y ρda cm ρda y ρa cm ρa

18 Sprng 2013 Fnal Exam Answers 1A. Defntons 1B. T AD = 30-60y +20kN M o = j N-m 1C. P = 49.5N 1D. Zero-Force Members: FB, BH, HC 2A. F gd = 1400 lbs 2 A = m Compresson x = m 2B. o θ = C. σ = ps -6 ε = x 10 n/n Contradctng 2D. T = 40N-m 2 2 outer = 1,821,624 N/m nner = 1,518,020 N/m 3A. FBDs 3B. F D = 41.0 kn 3C. F O = 116 kn 3D A = x 10 m 4A. Dagram 4B. F eq = 1560 lb d = ft 4C. FBDs 4D. N A = lbs 4E. N A = 325 lbs Yes 4F. F B = j lbs

19 5A. A x = 0 A y = 1500N D y = 1500N 5B. x 2 N σ = 6,591,796.9 M