Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

15.3 Deflections due to Bending 451

SolutionofEq.(vii)gives

z=1.35a

sothatthemaximumdownwarddeflectionis,fromEq.(vi),

EIv=

1

8

W(1.35a)^3 −

W

6

(0.35a)^3 −

5

8

Wa^2 (1.35a)

thatis,

vmax(downward)=−

0.54Wa^3

EI

In a similar manner, it can be shown that the maximum upward deflection lies between D and F at
z=3.42aandthatitsmagnitudeis

vmax(upward)=

0.04Wa^3

EI

Analternativemethodofdeterminingthepositionofmaximumdeflectionistoselectapossiblebay,
setv′=0forthatbay,andsolvetheresultingequationinz.Ifthesolutiongivesavalueofzthatlies
withinthebay,thentheselectioniscorrect;otherwise,theproceduremustberepeatedforasecondand
possiblyathirdandafourthbay.Thismethodisquickerthantheformerifthecorrectbayisselected
initially;ifnot,theequationcorrespondingtoeachselectedbaymustbecompletelysolved,aprocedure
clearlylongerthandeterminingthesignoftheslopeattheextremitiesofthebay.

Example 15.10
DeterminethepositionandmagnitudeofthemaximumdeflectioninthebeamofFig.15.21.

Fig.15.21

Deflection of a beam carrying a part span uniformly distributed load.