Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

532 CHAPTER 18 Combined Open and Closed Section Beams

sothat

q 03 =−1.04s 3 (v)

andq 3 =−104N/mminthewall03.Itfollowsthatforequilibriumofshearflowsat3,q 3 ,inthewall
34,mustbeequalto−138.5− 104 =−242.5N/mm.Hence,

q 34 =−69.0× 10 −^4

∫s^4

0

2 ( 75 −s 4 )ds 4 −242.5

whichgives

q 34 =−1.04s 4 +69.0× 10 −^4 s^24 −242.5 (vi)

Examination of Eq. (vi) shows thatq 34 has a maximum value of−281.7N/mm ats 4 =75mm; also,
q 4 =−172.5N/mm.Finally,thedistributionofshearflowinthewall94isgivenby

q 94 =−69.0× 10 −^4

∫s^5

0

2 (− 125 )ds 5

thatis,

q 94 =1.73s 5 (vii)

ThecompletedistributionisshowninFig.18.3.

Fig.18.3

Shear flow distribution in beam of Example 18.1 (all shear flows in N/mm).