Page 532 - Aircraft Stuctures for Engineering Student

12.7 Stiffness matrix for a uniform beam 513

L
4
- dunit length

wL -
- - - wL
-
-
wL
wL
wL
wL
wL
4 4 4 4 4 4 8
W
w
w W
2 2 3 3 4 4
-
128 I28
Fig. 12.8 Idealization of a beam supporting a uniformly distributed load.
complicated and therefore time consuming will be the analysis. Figure 12.8 shows a
typical idealization of a beam supporting a uniformly distributed load. Details of
the analysis of such beams may be found in Martin4.
Many simple beam problems may be idealized into a combination of two beam-
elements and three nodes. A few examples of such beams are shown in Fig. 12.9. If
we therefore assemble a stiffness matrix for the general case of a two beam-element
system we may use it to solve a variety of problems simply by inserting the appro-
priate loading and support conditions. Consider the assemblage of two beam-
elements shown in Fig. 12.10. The stiffness matrices for the beam-elements 1-2 and
2-3 are obtained from Eq. (12.44); thus

Fig. 12.9 Idealization of beams into beam-elements.