Introduction to Aircraft Structural Analysis (Elsevier Aerospace Engineering)

20 CHAPTER 1 Basic Elasticity

Fig.1.14

Solution of Example 1.3 using Mohr’s circle of stress.

ThenumericalsolutionsofEq.(iii)correspondingtothegivenvaluesofσx,σy,andτxyaretheprincipal
stressesatthepoint,namely

σ 1 =200N/mm^2 (given)σII=−160N/mm^2

Having obtained the principal stresses, we now use Eq. (1.15) to find the maximum shear stress,
thus,

τmax=

200 + 160

2

=180N/mm^2

ThesolutionisrapidlyverifiedfromMohr’scircleofstress(Fig.1.14).FromthearbitraryoriginO,
OP 1 andOP 2 aredrawntorepresentσx=160N/mm^2 andσy=−120N/mm^2 .ThemidpointCofP 1 P 2
isthenlocated.OB=σ 1 =200N/mm^2 ismarkedout,andtheradiusofthecircleisthenCB.OAisthe
requiredprincipalstress.PerpendicularsP 1 Q 1 andP 2 Q 2 tothecircumferenceofthecircleareequalto
±τxy(toscale),andtheradiusofthecircleisthemaximumshearstress.

1.9 Strain..................................................................................................

Theexternalandinternalforcesdescribedintheprevioussectionscauselinearandangulardisplace-
mentsinadeformablebody.Thesedisplacementsaregenerallydefinedintermsofstrain.Longitudinal