Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

550 CHAPTER 19 Structural Idealization

Eq.(19.11)reducesto

qs=−

Sy

Ixx

∑n

r= 1

Bryr+qs,0 (i)

inwhich

Ixx= 2 ( 200 × 302 + 250 × 1002 + 400 × 1002 + 100 × 502 )=13.86× 106 mm^4

Equation(i)thenbecomes

qs=−

10 × 103

13.86× 106

∑n

r= 1

Bryr+qs,0

thatis,

qs=−7.22× 10 −^4

∑n

r= 1

Bryr+qs,0 (ii)

“Cutting”thebeamsectioninthewall23(anywallmaybechosen)andcalculatingthe“basic”shear
flowdistributionqbfromthefirsttermontheright-handsideofEq.(ii),wehave

qb,23= 0

qb,34=−7.22× 10 −^4 ( 400 × 100 )=−28.9N/mm

qb,45=−28.9−7.22× 10 −^4 ( 100 × 50 )=−32.5N/mm

qb,56=qb,34=−28.9N/mm(bysymmetry)

qb,67=qb,23=0(bysymmetry)

qb,21=−7.22× 10 −^4 ( 250 × 100 )=−18.1N/mm

qb,18=−18.1−7.22× 10 −^4 ( 200 × 30 )=−22.4N/mm

qb,87=qb,21=−18.1N/mm(bysymmetry)

Takingmomentsabouttheintersectionofthelineofactionoftheshearloadandthehorizontalaxisof
symmetryandreferringtotheresultsofEqs.(19.7)and(19.8),wehave,fromEq.(16.18),

0 =[qb,81× 60 × 480 + 2 qb,12( 240 × 100 + 70 × 240 )+ 2 qb,23× 240 × 100

− 2 qb,43× 120 × 100 −qb,54× 100 ×120]+ 2 × 97200 qs,0

Substitutingtheprecedingvaluesofqbinthisequationgives

qs,0=−5.4N/mm

thenegativesignindicatingthatqs,0actsinaclockwisesense.