Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

3.4 Torsion of a Narrow Rectangular Strip 81

solutionincreasesass/tdecreases.Therefore,inordertoretaintheusefulnessoftheanalysis,afactor
μisincludedinthetorsionconstant;thatis,

J=

μst^3

3

Values ofμfor different types of section are found experimentally and quoted in various references
[Refs.3,4].Weobservethatass/tapproachesinfinity,μapproachesunity.
The cross section of the narrow rectangular strip of Fig. 3.9 does not remain plane after loading
butsufferswarpingdisplacementsnormaltoitsplane;thiswarpingmaybedeterminedusingeitherof
Eqs.(3.10).Fromthefirstoftheseequations

∂w

∂x

=y

dθ

dz

(3.30)

sinceτzx=0(seeEqs.(3.27)).IntegratingEq.(3.30),weobtain

w=xy

dθ

dz

+constant (3.31)

Sincethecrosssectionisdoublysymmetricalw=0atx=y=0,sothattheconstantinEq.(3.31)is
zero.Therefore

w=xy

dθ

dz

(3.32)

andthewarpingdistributionatanycrosssectionisasshowninFig.3.10.

Fig.3.10

Warping of a thin rectangular strip.