Page 526 - Aircraft Stuctures for Engineering Student

12.6 Matrix analysis of space frames 507

giving
Fx,l = - Fx,2 - FY,2 = W

Fy,l = 0
Fy,3 1 Fy>2 = - W
Fy,3 = w
Finally, the forces in the members are found from Eqs (12.32), (vii) and (viii)
AE
s12 = t[l 01 = - w (compression)
AE
s13 = l1 = 0 (as expected)

L -.__ ." - ..1-- 1 I-T .r
-
mdic%sn-tz statically indeterminate frameworks
The matrix method of solution described in the previous sections for spring and pin-
jointed framework assemblies is completely general and is therefore applicable to any
structural problem. We observe that at no stage in Example 12.1 did the question of
the degree of indeterminacy of the framework arise. It follows that problems
involving statically indeterminate frameworks (and other structures) are solved in
an identical manner to that presented in Example 12.1, the stiffness matrices for
the redundant members being included in the complete stiffness matrix as before.

-" %". ",
Matrix anal)

The procedure for the matrix analysis of space frames is similar to that for plane pin-
jointed frameworks. The main difference lies in the transformation of the member
stiffness matrices from local to global coordinates since, as we see from Fig. 12.5,
axial nodal forces and have each now three global components cy.;, Fv,i,
Fz,i and Fx,j, Fy,j, Fz,j respectively. The member stiffness matrix referred to global
coordinates is therefore of the order 6 x 6 so that [ICii] of Eq. (12.22) must be
expanded to the same order to allow for this. Hence
ui v; w; uj vj wj
1 0 0 -1 0 0
0 0 0 0 0 0
- AE
[K..] = ~ 0 0 0 0 0 0 (12.33)
" L
- 1 0 0 1 0 0
0 0 0 0 0 0
0 0 0 0 0 0