Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

Problems 475

Ans. α=51.9◦,σz,max=101N/mm^2.

Fig. P.15.8

P.15.9 A uniform beam is simply supported over a span of 6m. It carries a trapezoidally distributed load with
intensityvaryingfrom30kN/mattheleft-handsupportto90kN/mattheright-handsupport.Findtheequationof
thedeflectioncurveandhencethedeflectionatthemidspanpoint.Thesecondmomentofareaofthecrosssection
ofthebeamis120× 106 mm^4 andYoung’smodulusE=206000N/mm^2.

Ans. 41mm(downward).

P.15.10AcantileveroflengthLandhavingaflexuralrigidityEIcarriesadistributedloadthatvariesinintensity
fromw/unitlengthatthebuilt-inendtozeroatthefreeend.Findthedeflectionofthefreeend.

Ans. wL^4 /30EI(downward).

P.15.11Determinethepositionandmagnitudeofthemaximumdeflectionofthesimplysupportedbeamshownin
Fig.P.15.11intermsofitsflexuralrigidityEI.

Ans. 38.8/EImdownwardat2.9mfromleft-handsupport.

Fig. P.15.11

P.15.12DeterminetheequationofthedeflectioncurveofthebeamshowninFig.P.15.12.Theflexuralrigidityof
thebeamisEI.