ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 1 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 36 Lab-05 Angle Problems

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 2 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Problem  Cables AB & AC attached to Tree Trunk and fastened to Stakes in the Ground  Given Cable Tension T AC = 3.6 kN  Find Components of Force exerted by cable AC on the Tree The Space Angles θ x, θ y, θ z for Cable AC

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 3 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 4 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 5 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 6 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 7 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Tree Prob by MATLAB >> TAC = 3.6; >> Fyv = -TAC*sind(45) Fyv = >> Fh = TAC*cosd(45) Fh = >> Fzv = Fh*cosd(25) Fzv = >> Fxv = -Fh*sind(25) Fxv = >> TACv = [Fxv Fyv Fzv] TACv = >> uAC = TACv/TAC uAC = >> Qxyz = acosd(uAC) Qxyz =

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 8 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Problem  Given the Geometry of the Steel FrameWork as Shown  Given EF & EG are Cables Pt-E is at MidPt of BC Tension in Cable EF is 330N  Find Angle Between EF and BC Projection on BC of the force exerted by Cable EF at Pt-E

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 9 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics û EF û BC û EF

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 10 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 11 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 12 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics I-Beam Prob by MATLAB >> B = [ ]; F = [1 0 0]; C = [ , -12]; >> E = [16/2 ( )/2 -6] E = >> EFv = F-E EFv = >> BCv = C - B BCv = >> EFm = norm(EFv) EFm = 11 >> BCm = norm(BCv) BCm = >> uEF = EFv/EFm uEF = >> uBC = BCv/BCm uBC = >> Qceg = acosd(dot(uEF,uBC)) Qceg =

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 13 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Problem  Given Geometry as Shown BungiCord PC with Tension of 30N Distance OP = 120 mm  Find Angle Between PC and OA Projection on OA of the force exerted by the BungiCord PC at Pt-P

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 14 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 15 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics =

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 16 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics û OA |û| û OA

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 17 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Bungi Prob by MATLAB >> OAm = norm([ ]) OAm = 360 >> OPm = 120; >> Ratio = OPm/OAm Ratio = >> A = [ ] A = >> P = Ratio*A P = >> C = [ ] C = >> PCv = C-P PCv = >> OAv = A; >> PCm = norm(PCv) PCm = >> OAm = norm(OAv) OAm = 360 >> Qcpa = acosd(dot(PCv,OAv)/(PCm*OAm)) Qcpa = >> uPC = PCv/PCm uPC = >> Tpcv = 30*uPC Tpcv = >> FOAproj = 30*cosd(Qcpa) FOAproj =

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 18 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Problem  Given Geometry as Shown –Angle OAB is 90° Tension in Cable BC is 5.3 kN T BC = 5.3 kN

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 19 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Problem T BC = 5.3 kN  Find The Angle, θ, Between the Cable and Pipe BA The Components of F BC (cable force acting at Pt-B) that are || and  to Pipe BA

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 20 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 21 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics −

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 22 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 23 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics

ENGR-36_Lab-05_Fa07_Lec-Notes.ppt 24 Bruce Mayer, PE Engineering-36: Vector Mechanics - Statics Pipe Prob by MATLAB >> TBC = 5.3; % in kN >> A = [ ]; C = [ ]; >> B = [ *sind(30) 1200*cosd(30)] B = 1.0e+03 * >> BAv = A-B BAv = 1.0e+03 * >> BCv = C-B BCv = 1.0e+03 * >> BAm = norm(BAv) BAm = 1200 >> BCm = norm(BCv) BCm = e+03 >> Qabc = acosd(dot(BAv,BCv)/(BAm*BCm)) Qabc = >> Fpar = TBC*cosd(Qabc) Fpar = >> Fper = TBC*sind(Qabc) Fper =