U , U , U^ Displacements of cross section of beam along x-, y-, and s-axes, respectively; 



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



U^, V , U^ Displacements of cross section along x-, y-, and s-axes, respectively; positive 

 when the vector representing them is in the positive coordinate direction 



U y, U 2 Displacements of cross section of beam along y-, s-axes, respectively; positive 



when the vector representing them is in the positive coordinate direction 



V , V , V Forces acting on positive side of cross section of beam (i.e., portion of beam 



on -X side of section) along x-, y-, and s-axes, respectively; positive when the 

 vector representing them is in the positive coordinate direction 



V Force acting on positive side of cross section of beam (defined as for V^) along 

 i^-axis; positive when the vector representing it is in the positive coordinate 

 direction 



V , V Force acting on positive side of cross section of beam (defined as for V and 



V , respectively) along y- and J-axes, respectively; positive when the vector 

 representing them is in the positive coordinate direction 



W, W Strain energy and strain energy per unit length, respectively 



X, y, s Coordinates of a right-hand rectangular Cartesian coordinate system (see 



or Figure 3); y, s are also the positions of the neutral axis in x-, y-, s-coordinate 



X, y, 3 system 



X, y, i Position of the shear center in x-, y-, s-coordinate system 



Aa;, Ay, As Length of segment along x-, y-, and s-axes, respectively 



Rotations of cross section of beam about x-, y-, s-axes, respectively 



Rotations of cross section of beam about x-, y-, s-axes, respectively 



Rotations of cross section of beam about x-, y-, s-axes, respectively 



^x' -y 



a a 

 ■^X' y 



^7 



Stress components in rectangular coordinate system defined as the force per unit 

 area acting on a face perpendicular to the z-axis and in the ^-direction 



{i = X, y, s; j = x, y, s) 



fj. Mass per unit length of beam 



r^ , 9 9 1/2 



r: Equals {a^ + t^D 



Subscript i in test denotes node numbers unless otherwise indicated; thus y-, 

 3 ., A; are the coordinates and corresponding area for i'^ node. 



