Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

552 CHAPTER 19 Structural Idealization

WeshallillustratethemethodbyapplyingittoExample19.3.InFig.19.7,theshearloadof4.8kN
is applied to the face of the section which is seen when a view is taken along thezaxis toward the
origin.Thus,whenconsideringunitlengthofthebeam,wemustensurethatthissituationisunchanged.
Figure 19.13 shows a unit (1mm, say) length of beam. The change in bending moment between the
front and rear faces of the length of beam is 4.8×1kNmm, which produces a change in boom load
givenby(seeEq.(15.18))

Pr=

4.8× 103 × 200

48 × 106

× 300 =6N

Thechangeinboomloadiscompressiveinbooms1and2andtensileinbooms3and4.
Equation (19.12), and hence Eq. (19.13), is based on the tensile load in a boom increasing with
increasingz.Ifthetensileloadhadincreasedwithdecreasingz,theright-handsideoftheseequations
wouldhavebeenpositive.Itfollowsthatinthecasewhereacompressiveloadincreaseswithdecreasing
z,asforbooms1and2inFig.19.13,theright-handsideisnegative;similarlyforbooms3and4,the
right-handsideispositive.Thus,

q 12 =−6N/mm

q 23 =− 6 +q 12 =−12N/mm

and

q 34 =+ 6 +q 23 =−6N/mm

Fig.19.13

Alternative solution to Example 19.3.