User:Eml4500.f08.a-team.melvin/Lecture 17

Meeting 17: Friday, 26 September 2008, EML4500
ΣFx = 0, ΣFy = 0, ΣM A = 0 (sum of moments trivial)

Q: How about ΣM B ?



3D explanation

ΣM B  = BA X F

ΣM B  = BA' X F

for A' on linen of action of F

BA = BA + AA'

M B  = (BA + AA') X F

M B  = BA X F + AA' X F

where = AA' X F = 0

Back to 3-Bar Truss:

Node A is in equilibrium : ΣF i  = 0 from i=0 to i=3

Σ i M Bi  = Σ i BA' i  X F i 

A' i = any point on the line of action of F i 

Σ i M Bi  = Σ i BA' i  X F i 

Σ i M Bi  = BA X Σ i F i  = 0 - meaning ΣM B is useless, still only 2 useful equations.



K 33 = K(1) 33 + K(2) 11 + K(3) 11

K 34 = K(1) 34 + K(2) 12 + K(3) 12

HW: Fill out the rest!