Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

4.3 Applications of the Principle of Virtual Work 105

Hence,

θA=

W

2 EIL

{[

L

x^2

2

−

x^3

3

]L/ 2

0

−

1

3

[

(L−x)^3

]L

L/ 2

}

fromwhich

θA=

WL^2

16 EI

Example 4.6
CalculatetheverticaldeflectionofthejointBandthehorizontalmovementofsupportDinthetruss
showninFig.4.12(a).Thecross-sectionalareaofeachmemberis1800mm^2 andYoung’smodulus,E,
forthematerialofthemembersis200000N/mm^2.

Thevirtualforcesystems—thatis,unitloads—requiredtodeterminetheverticaldeflectionofBand
thehorizontaldeflectionofDareshowninFig.4.12(b)and(c),respectively.Therefore,iftheactual
verticaldeflectionatBisδB,vandthehorizontaldeflectionatDisδD,h,theexternalvirtualworkdone
bytheunitloadsis1δB,vand1δD,h,respectively.Theinternalactualandvirtualforcesystemscomprise
axialforcesinallthemembers.

Fig.4.12

Deflection of a truss using the unit load method.