The elastic constants to be used are:* 



EA =E Sk^A. 



O . 11 



EI = E 2k:(y. -y)2A. 



yy o. i^^i '^ ' 1 



EI,^ = E Sk:(y. -y) (z. -Y)A. 

 EI ^ =E 2kr(z, -I)2a. 



ZZ O. 1^1 / 1 



These numbers are calculated by the computer, and in the output statement: 



EA 

 Structure Area = — — 



Eo 



Y EL Axis** =y 



Z EL Axis** = z" 



YY Flexibility = E I /E(I I - I ^ ) 

 o yy "^ yy zz yz ' 



YZ Flexibility --E I /E(I I -I 2) 



•; o yz ^yyzz yx' 



ZZ Flexibility =E I /E(I I - I 2) 



'' ozz ^ yy zz yz' 



These latter equations are not independent of materials and effectiveness. The values of 

 I , I , I^z are obtained from the equations for EI , etc., given previously in which k^ 

 accounts for effectiveness and modulus at each node. 



For cross sections consisting of stringers and plates, assume the following in order 

 to calculate shear stresses (see Chapter 6 of Reference 8): 



1. All of the shear is carried in the plates (see Chapter 2 of Reference 7).T The plates 

 are thin, and the component of shear perpendicular to the surface of a plate must vanish; 

 hence, the shear stress r has a direction along the plate direction (i.e., if the plate has a 

 slope Az/Ay, then the condition for zero component of shear perpendicular to the surface of 

 the plate is a /a^ = Az/Ay). 'T Assume that the magnitude of the stress does not vary 

 across the thickness and call this magnitude t . 



(.^2^a2 +a2 ) 

 \^ xy xz ' 



*Note that A (=/ SA) is defined as part of the term EA which is defined as E Sk'A.. The term EA is 

 defined as a single unit, and E and A are not employed separately. Similarly, for subsequent equations. 



♦♦Coordinates of the elastic axis. 



jshear stiffness of a rod is small compared to that of a plate and is assumed to vanish. 



tfrhe projection of t along the y- and z-axis is equal to a and o respectively. 



53 



