Assuming the truss members only bear axial loads, the following set of 10 equations can be determined: -АВ cos (z/3) + AС + А, 3D0 -AB sin(t/3) + Ay = 0 АВ cos(1/3) — ВС cos (п/3) — ВD %3D 0 AB sin(t/3) + BC sin(t/3) = W/2 -АС + ВС сos(т/3) — CD cos(1/3) + СE3D0 -BC sin(r/3) – CD sin(t/3) = 0 BD + CD cos(t/3) – DE cos(t/3) = 0 CD sin(t/3) + DE sin(r/3) = W/2 DE cos(r/3) – CE = 0 -DE sin(t/3) + Ey = 0
Assuming the truss members only bear axial loads, the following set of 10 equations can be determined: -АВ cos (z/3) + AС + А, 3D0 -AB sin(t/3) + Ay = 0 АВ cos(1/3) — ВС cos (п/3) — ВD %3D 0 AB sin(t/3) + BC sin(t/3) = W/2 -АС + ВС сos(т/3) — CD cos(1/3) + СE3D0 -BC sin(r/3) – CD sin(t/3) = 0 BD + CD cos(t/3) – DE cos(t/3) = 0 CD sin(t/3) + DE sin(r/3) = W/2 DE cos(r/3) – CE = 0 -DE sin(t/3) + Ey = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How would you put those equations into a matrix? Like A=xb
Transcribed Image Text:Assuming the truss members only bear axial loads, the following set of 10 equations can be determined:
-AB cos(t/3) + AC+ Ax = 0
-AB sin(t/3) + Ay = 0
АВ cos(t/3) — ВС cos (п/3) — ВD %3D0
AB sin(t/3) + BC sin(t/3) = W/2
-AC + BC cos(T/3) – CD cos(t/3) + CE = 0
-BC sin(t/3) – CD sin(t/3) = 0
BD + CD cos(t/3) – DE cos(T/3) = 0
CD sin(t/3) + DE sin(t/3) = W/2
DE cos(t/3) – CE = 0
-DE sin(t/3) + Ey = 0
|
%3D
where AB, AC, BC, etc. are the axial forces carried by the members, W is the weight of the fuel-filled
rocket, Ax and Ay are the x- and y- components of the reaction force at joint A, and Ey is the reaction force
at joint E, and angles are in units of radians. The axial stress in each member of the truss will be o =
force)/(cross-sectional area).
(axial
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