Column MS) under plates, which is 

 defined as 1/2 (12k 'tAs) = 6.0 ® (s) (l2) , 

 represents the division of the plate effec- 

 tive tension area, one-half being assigned 

 to the node at each end. This division is 

 effected in Columns ©-(S) under nodes; 

 then the net node area is computed in node 

 Column (9) •* Plate Columns (u) and (15) 

 are used as Columns (?) , (9). and (27) of 

 Table 4, Sheet 2, in carrying out the calcu- 

 lations for the distribution of y- and z-shear. 

 Compute y from 1(2) • (D /S (?) . Because 

 of symmetry, "z = 0.** Compute Columns 

 (iW— (16) for nodes as indicated. Bending 

 parameters are calculated on Sheet 1; the 

 factor of 2 is for symmetry and 144 is to 

 change from square inches to square feet. 



To compute the shear parameters, 

 first find a tree; that is, a set of plates so 

 that one and only one path exists between 

 every two nodes (see section Shear and 

 Torsion in Appendix A. 2). The tree chosen 

 consists of all the plates except 5 and 9 

 (see Figure 1). For y-shear. Columns (2) 

 and (3) of Sheet 2, Table 4, represent all 

 nodes further from the root (node 1) than 

 the plate in question. The [T..] matrix 



discussed in Shear and Torsion of Appendix A. 2 is applicable to these columns; in particular, 

 see Equation [14]. Considering Plate 2, it is seen that shear flows from nodes 3, 4, and 5 



Figure 2 - Sample Problem 

 3 



Shear Flow X 10 per Unit V 

 Shear Flow X 10^ per Unit V 

 Shear Flow X 10^ per Unit M 



1/ft 

 1/ft 

 1/ft^ 



The numbers in Figure 2 give the shear flows in the 

 plates corresponding to the following conditions: 



v, = i, 



v. = o, 



M, = 



(top numbers) 



V„ = 0, 



Vz=l' 



M^ = 



(middle numbers) 



v, = o, 



v, = o, 



M^ = l 



(bottom numbers) 



The scales are indicated under the caption. The nu 

 come from Sheet 2, Col. (s); Sheet 2, Col. (28); and 

 Sheet 3, Col. (8)of Table 4' respectively. 



* us) represents one-half the effective area of each plate employed in Columns fb), (t), and Ts) at the top of 

 the sheet in determining total node areas. Hence, the factor of 1/2 is introduced in calculating QJ) (bottom). 

 The assignment to proper nodes is carried out by entering values from US) (bottom) in appropriate spaces under 

 (6), ( t) , and (s) (top). For example, for Plate 7, which corrects nodes 6 and 8. one-half the effective area is 



12.0 (Column uS) , bottom). This value is entered as "Plate Area" once at node 6 iCs) top) and once at node 8 

 ((6^ top). Whether a particular number is entered under Columns \6), (t), or (s) is of no significance. Effective- 

 ness k'=k-g- = PK, Column (s). Plate thickness (inches) t = PT, Column (?). Plate length (feet) As = 

 Column 6.2) . 6 = 1/2 x 12 converts inch feet to square inches. Columns (4) and (Sj were arbitrarily chosen as 

 sample problem input data. They were used only as indicated in calculating the entries of Columns (l3) , (l^ . 



**See Figure 3. 



11 



