NOTATION 



A Area 



ij Symbol defined by a matrix (see Appendix A) 



ds Differential distance along shear element 



dx, dy, dz Differential distances along x-, y-, 2-axes, respectively 



E Local Young's modulus of elasticity 



El Flexural rigidity of beam 



Eg Reference modulus of elasticity 



E-(y,z) Known stress functions (i = 1, 2, 3) 



G Local modulus of elasticity in shear 



G- (y,s) Known stress functions which are linear homogeneous functions of 



F^(y,z){i = 1,2, 3) 



GJe 

 hi 



^- 



e Areal polar moment of inertia of a cross section about its shear center 



KAG Shear rigidity 



k Effective area factor 



E 

 k' k — 



A'j, A'2J A'o Temporary unknown constants used to derive equations 



M^, M , M Bending moments about the x-, y-, and s-axes, respectively; positive when the 

 vector representing them is in the positive coordinate direction 



M , M, Bending moments about the y-, s-axes, respectively; positive when the vector 



representing them is in the positive coordinate direction 



M^ Bending moments about a longitudinal axis passing through the center of shear; 



positive when the vector representing it is in the positive coordinate direction 



q Shear flow 



s Arc length along shear element 



t Thickness 



Torsional 



rigidity 





GiGj 



Equals 



dA 



Functions 



of /,^. 



