Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

5.4Application to the Solution of Statically Indeterminate Systems 125

Example 5.3
Calculatetheloadsinthemembersofthesinglyredundantpin-jointedframeworkshowninFig.5.9.
The members AC and BD are 30mm^2 in cross section, and all other members are 20mm^2 in cross
section.ThemembersAD,BC,andDCareeach800mmlong.E=200000N/mm^2.

From the geometry of the framework ABD̂=̂CBD= 30 ◦; therefore, BD=AC= 800

√

3mm.
ChoosingCDastheredundantmemberandproceedingfromEq.(5.16),wehave

1

E

∑k

i= 1

FiLi

Ai

∂Fi

∂R

=0(i)

FromTable5.3,wehave

∑k

i= 1

FiLi

Ai

∂Fi

∂R

=− 268 +129.2R= 0

Hence,R=2.1Nandtheforcesinthemembersaretabulatedincolumn⑦ofTable5.3.

Fig.5.9

Framework of Example 5.3.

Table 5.3Tension positive

① ② ③ ④ ⑤ ⑥ ⑦

Member L(mm) A(mm^2 ) F(N) ∂F/∂R (FL/A)∂F/∂R Force(N)

AC 800

√

33050 −

√

3 R/ 2 −

√

3 / 2 − 2000 + 20

√

3 R 48.2

CB 800 20 86.6+R/ 21 / 2 1732 + 10 R 87.6

BD 800

√

330 −

√

3 R/ 2 −

√

3 / 220

√

3 R −1.8

CD 800 20 R 140 R 2.1

AD 800 20 R/ 21 / 210 R 1.0

=− 268 +129.2R