Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

476 CHAPTER 15 Bending of Open and Closed, Thin-walled Beams

Ans. v=−

1

EI

(

125

6

z^3 −50[z−1]^2 +

50

12

[z−2]^4 −

50

12

[z−4]^4 −

525

6

[z−4]^3 +237.5z

)

Fig. P.15.12

P.15.13Auniformthin-walledbeamABDofopencrosssection(Fig.P.15.13)issimplysupportedatpointsBand
Dwithitswebvertical.ItcarriesadownwardverticalforceWattheendAintheplaneoftheweb.
Deriveexpressionsfortheverticalandhorizontalcomponentsofthedeflectionofthebeammidwaybetween
thesupportsBandD.ThewallthicknesstandYoung’smodulusEareconstantthroughout.

Ans. u=0.186Wl^3 /Ea^3 t,v=0.177Wl^3 /Ea^3 t.

Fig. P.15.13

P.15.14AuniformcantileverofarbitrarycrosssectionandlengthlhassectionpropertiesIxx,Iyy,andIxywithrespect
tothecentroidalaxesshowninFig.P.15.14.Itisloadedinthevertical(yz)planewithauniformlydistributedload
of intensityw/unit length. The tip of the beam is hinged to a horizontal link which constrains it to move in the
verticaldirectiononly(providedthattheactualdeflectionsaresmall).Assumingthatthelinkisrigidandthatthere
arenotwistingeffects,calculate:

(a) theforceinthelink;

(b) thedeflectionofthetipofthebeam.