Structural Analysis Methods II: Structural Systems - Mechanics of Structures: Variational and Computational Methods - page 287

FIGURE 5.23
Results for Example 5.5.

for each element i . Direct nodal loads are not introduced at the element level. Rather, they
are inserted in the assembled global stiffness equations.
Tables 4.2 and 4.4 provide general expressions for the components of the loading vector
p i 0 . For example, for a beam element with a uniformly distributed load of magnitude p 0 ,
this vector appears as (Table 4.2)

1
− / p 0 6

p i 0 = (5.96)

1
/

2

6

If the displacements and forces are referred to a local coordinate system, then Eq. (5.95)
would appear as

− p i 0 = k i p i v i

(5.97)

As expected, the coordinate transformation matrix T i

can be used to move from local to

global coordinates and vice versa. Thus,

p i 0 k i T i ,

p i T iT p i , k i T iT p i 0 T iT

= = =

(5.98)