Exam 2 Solution - COE 2001: STATICS Lot/J i. H ] FALL 2010...

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Unformatted text preview: COE 2001: STATICS Lot/J i. H ] FALL 2010 NAME: 5% “rib” The exam is closed book and closed notes. Scientific calculators are allowed. No mp3 players, cell phones, laptops, etc. Linearly doeument all steps and show all supporting work. Answers given without supporting work will be given zero credit. Write legibly and box all final answers. HONOR STATEMENT: 1 have read and strictly abided by all conditions set forth in the Georgia Tech Honor Code and thus have neither given nor received assistance of any type regarding the content or solution of the problems in this examination, nor will I discuss the content with other students until the exam has been graded and returned. SIGNATURE: l Georgialime‘ftfiflnfitce “ @iiTechrmceflcogJy Problem 1 15 pts a. Suppose a 3D support has the following characteristics: free to translate in the y—direction and rotate about the m— and y—axes. Which reaction components (F:,Fy,Fz,JiIIm,fi/Iy,M:} are present at this support? (5 pts) PX Fa A E b. A beam of length L has a distributed load according to a function f(:c) on the interval 0 < a: < L. Give the mathematical expressions for (i) the resultant force, F,., as well as (ii) the location of the resultant, $1.. Explain in a few words each what these expressions mean/accomplish. (5 pts) L FF: jfixflx N Am wasn- FCe> ’00—— D swwirroru 0F ForLcE L I >4 Hid/ix 3 b {V CEM’fi—Ofb 5F figs)ch 0N xé(0/L) Vex c. List and draw the three cases when a set of forces and moments may be replaced by a single force resultant. (5 pts) C 0N CUE-(LEM Co PLAN/NL- P/J MLLEL 3% ,7 /9 ” Jifl Problem 2 25 ts The following 3D pipe is fistupported at point B. Compute all six fixed end support reactions at B clue to three orthogonal forces applied at A. 300N\ Ix” v Kg iii: €44» gob : Z2: F7 +— 3’00 : ZFZ; Fé — lb?) : 2AM“: Ax*100(?>'?oo(q)=0 Ag: H05 N'rH 3‘73 ” A7 “P 900*) — [M(£): A7: 4w» N'm Z/Hzg 1 A? + 9’06?) ‘ he (0 = 0 fl} : ~2200 N’». Problem 3 30 9135 For the following system, compute the magnitude of the single force resultant, FT, and its location, 93¢. On the range 0 < 59 < 10, the force function is given by q($) = —4-3in %) - 5 lb/ft. On the range 10 < a: < 16, the function linearly decreases to a value of 0 lb/ ft. Clearly indicate/label any superposition assumptions you invoke. Note: the negative signs in tins equation indicate that the force is oriented downward. $0 ‘94” (E7 L'ra’fELTD/ ll FEEL: (fl-FELL :: ’7f_L{(.-/f: " (“lug '5 Fr; gm ; ht" 79‘. ‘l‘ El; >921 (—7{H()(5)+—(~15>(h.> ” r : 5.16 1C+ 3%? ’7" - 40%! ——~_____________ Problem 3 Alt Solution 30 9’05 For the following system, compute the magnitude of the single force resultant, FT, and its location, 221,. On the range 0 < a: < 10, the force function is given by (1(a) = —4-sin("5—$) — 5 lb/ft. On the range 10 < m < 16, the function linearly decreases to a value of 0 lb/ft. Clearly indicate/label any superposition assumptions you invoke. Note: the negative signs in this equation indicate that the force is oriented downward. K‘? I'Hré‘cr'nw 1;“ i \ :3“ _\_. f“ + as?“ l I 1 ‘3? 9:: \\ T\ T Fame, + FEM-1 + F.9sz Fr; 47.7.? (m) » rz.27(7J) a 1.!(t'L) {S H .— /— , 5.01 I a; Problem 4 30 Hts The following 3D system consists of a triangular plate located on the X Yaplane. The plate is supported at A by a vertical (Z —direction) roller and by a hinge at B that is free to rotate about the Y—axis. Assume that the dimensions of the hinge are much smaller than the length of the plate such that all effects at B effectively act at the origin. The plate has a total weight of —1000k N. a. Overlay a free body diagram onto the figure below and label all forces/ moments. b. Solve for all support reactions. A Roller Triangularplate (support in Z—dz'rection) in X Y-plane A2: 8 2F»! = K: = D Z : = O FE:,4?+E?..Iooo=o 32 :657/v ZAX : AK” — lboo (c) = 0 ARK :1000 Nut, 33’: N r14 \| ...
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This note was uploaded on 09/12/2011 for the course COE 2001 taught by Professor Valle during the Spring '08 term at Georgia Institute of Technology.

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Exam 2 Solution - COE 2001: STATICS Lot/J i. H ] FALL 2010...

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