ME 270 Fall 2013 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. Slvers 8:30-9:30am B. Hylton 2:30-3:20pm J. Jones 11:30am-12:20pm J. Sepel 12:30-1:20pm M. Murphy 9:00-10:15am E. Nauman 9:30-10:20 am K. L 1:30-2:20pm J. Jones Dstance Learnng Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Total
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): PROBLEM 1 (20 ponts) Prob. 1 questons are all or nothng. 1(a) n overhead lamp s held n statc equlbrum by cable C and horzontal sprng B. Gven the sprng constant s k=300 N/m and the net deformaton of the sprng s 0.453m, determne the magntude of the tenson n cable C and the weght of the lamp. (4pts) T = C Lamp (2 pts) W = (2 pts) 1(b) Bar BC s loaded at C wth one force and one couple as shown. Determne the equvalent force-couple system at. Express your soluton n vector form. (Hnt Ths s not a statc equlbrum problem.) (4pts) (F ) = (2 pts) eq eq (M ) = (2 pts)
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): 1(c) Bar O s loaded wth a sngle force as shown and s held n statc equlbrum by a bult-n support at O. Determne the reactons at O due to ths loadng. (4pts) F = O M = O (2 pts) (2 pts) 1(d) The fnk truss s loaded as shown. Identfy all zero-force members by placng a zero over that member. (4pts)
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): 1(e) The 15 wedge shown s beng removed by force P. On the fgures provded, complete the free body dagram of the crate and wedge. Wrte the x and y-equlbrum equatons for the wedge. ssume frcton exsts on all nterfaces (, B and C). Leave the frcton forces generc (.e., f, f B, f C ) DO NOT SOLVE THE EQUTIONS. (4pts) C 1 pt 1 pt F x = 0 = (1 pt) F = 0 = (1 pt) y
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): PROBLEM 2 (20 ponts) Gven: Rod B s loaded at ts mdpont wth a vertcal force PC 72 lb. The weght of the rod s neglgble. It s held n place at by a ball and socket jont. t B, the rod rests aganst a smooth wall n the x-z plane, and s held n place by a cable (BD) whch s parallel to the x- axs. Fnd: a) On the fgure provded, draw a complete free body dagram. (5 pts) b) Wrte the poston vector from to B, and the poston vector from to C. (3 pts) c) Determne the tenson n cable BD, and the force from the smooth wall at B. Gve your answers n vector form. (8 pts) d) Determne the reactons from the ball and socket jont at. Gve your answer(s) n vector form. (4 pts) Free Body Dagram
ME 270 Fall 2013 Fnal Exam NME (Last, Frst):
ME 270 Fall 2013 Fnal Exam Name (last, frst) Problem #3 Fall 2013 Fnal Jont C NME (Last, Frst): The structure s subjected to a 80kp (80,000 lb) load as shown. The mass of the members s neglgble when compared to appled load. BD s a two-force member. support pn at Jont makes contact wth the jont on two sdes (double shear pn). B 4 ft B F F D 80 kp 3 ft C y D 80 kp 6 ft x 12 ft The modulus of elastcty (E) s 10x10 6 ps (10x10 3 ks) for all members, ncludng the pn at. Posson s Rato for all members, ncludng the pn at. The cross-sectonal area of member BD s 0.5 n 2. The jont at s supported on two sdes by a pn wth a crosssectonal area of 0.5 n 2. Please place your answers n the box provded. Remember unts! Coordnate axs s provded for ths problem. LL steps of your work must be shown to earn credt. a. The free-body dagrams for the entre structure s provded, please complete the free-body dagram for the exploded structure (3 ponts) on the fgure provded. b. Determne the reactons at and F (3 ponts) c. Determne the magntude of the shear force V and the shear stress τ on the support pn at (3 ponts). d. Determne the shear stran on the Pn at (3 Ponts) e. Determne the load carred by member BD and crcle whether t s n tenson or compresson (3 ponts) f. Determne the axal stress σ BD n member BD (3 ponts) g. Determne the axal stran ε x n BD (2 ponts) x y F y a. C C B B D D 80 kp x y F F y b. x = y = F y =. c. V = τ =. d. γ = e. Load BD tenson or compresson (crcle one) f. σ BD g. ε x n member BD
ME 270 Fall 2013 Fnal Exam NME (Last, Frst):
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): PROBLEM 4 (20 ponts) 4(a) cantlevered structure s loaded as shown, wth F = 100 N. Calculate the nternal forces and moments, n vector form, at cut. coordnate system s provded on the fgure. (4 pts) FBD 4(b) leather worker s punchng a square hole n a leather strap. The punch cross-secton s 5mm by 5mm. The leather strap s 2 mm thck. If the leather worker apples a 5 N force to the punch, calculate the average shear stress n the leather. (3 pts)
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): 4(c) cantlevered shaft s loaded as shown. Secton B s a sold alumnum shaft wth dameter d. Secton BC s a hollow steel shaft wth an outer dameter d and wall thckness 0.1*d. Let d = 6 nches and T = 10 ft-kps. Calculate the polar moment of area and maxmum torsonal stress n the hollow regon of the shaft (BC). Then, usng the provded values, calculate the maxmum torsonal stran n the shaft. (6 pts) B BC Polar Moment of rea (J) 127.23 n 4 Maxmum Torsonal Stress ( ) 2.83 ks Modulus of Rgdty (G) 3.8 x 10 3 ks 11.2 x 10 3 ks Torsonal Stran ( )
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): 4(d) Setup but do not ntegrate the equaton for the 2nd moment of area of the cross-secton shown below, rotatng about the gven axs, x. (3 pts) 4(e) Usng the method of composte parts, calculate the 2nd moment of area of the cross secton shown below, rotatng about the gven axs, x. Both cross-bars have the same length and thckness. (4 pts)
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): ME 270 Fall 2013 Problem 5. (20 pts). 5a. The beam gven below s supported by a pn and roller. Determne the reactons at ponts and D and wrte them n the space provded below. Note that the beam cross secton s rectangular, wth a base of 200 mm and a heght of 400 mm. 5 kn/m 4 kn-m B 1m 4 kn 2m (Draw Free Body Dagrams used for part 5a here): C 1m D (2 pts) Reacton at pont (WRITE NSWER HERE): (2 pts) Reacton at pont D (WRITE NSWER HERE):
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): ME 270 Fall 2013 Problem 5 Contnued 5b. For the beam gven n part a above, draw the shear force and bendng moment dagram n the space provded. (9 pts). 5 kn/m 4 kn-m B 4 kn 1m 2m 1m C D Shear Force V(x) Bendng Moment M(x)
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): ME 270 Fall 2013 Problem 5 Contnued 5c. Locate the pont where pure bendng occurs as the dstance from pt. (2 pts) Locaton of pure bendng measured from (WRITE NSWER HERE): 5d. What s the maxmum magntude of bendng moment that occurs n the beam. (2 pts). Maxmum bendng moment (WRITE NSWER HERE) : 5e. For the locaton found n part c, determne the maxmum axal stress due to bendng. (3 pts). Maxmum axal stress (WRITE NSWER HERE):
ME 270 Fall 2013 Fnal Exam NME (Last, Frst):
ME 270 Fall 2013 Fnal Exam NME (Last, Frst):
ME 270 Fnal Exam Equatons Fall 2013 ME 270 Fall 2013 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 = 2 1 + ϑ γ = δ s L s = π 2 θ For a rectangular crosssecton, τ(y) = 6V h2 h 2 4 y2 τ max = 3V 2 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 Belt Frcton T T L S e 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
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): Fall 2013 ME 270 Fnal nswers 1. T C = 157 N W Lamp = 78.5 N 1B. (F eq ) = 25 + 43.3j lb (M eq) = 520 lb-ft 1C. F O = -80 + 60j N O M = 460k N-m 1D. Zero Force Members: BP, CP, CO, CN, DN, EM, ON, & NE. 1E. F = 0 = -P + f + f cos 15 - N sn 15 X o B B F = 0 = -N + N cos 15 + f sn 15 y 2. Free Body Dagram o B B 2B. r B = 4-7j + 9k ft r C = 2-35j + 4.5k ft o o 2C. N = 28 lb j T = -16 lb 2D. F = 16-28j + 72k lb 3. Free Body Dagram 3B. x = -80 kp 3C. V = 100 kp 3D. γ = 0.026 n/n 3E. Load BD 120 kp Tenson 3F. BD 3G. x = 240 ks y = -60 kp n member BD s 0.024 n/n = 100 ks F y = 60 kp 4. F = (160 + 120j) N M = (360k) N-m 4B. VG = 0.125 MPa 4C. γ max = 0.000745
ME 270 Fall 2013 Fnal Exam NME (Last, Frst): 4D. 4E. 3 4 3 - x 4 - y 4 2 3 3 4 3 2 I x = 0 y dydx or 0 0 (3 - x) dxdy 0 4 I = 1365.6 n x 4 5. FBD Reacton at pont : 9j kn Reacton at pont D: 5j kn 5B. Shear force bendng moment dagram 5C. Locaton of pure bendng measured from : x = 2m or 2m from pt 5D. Maxmum bendng moment: 11.5 kn-m 5E. Maxmum axal stress: 2.156 MPa