Write the node equations for the nodes 1 and 2 of the model of the oak beam sketched in Figure 2-32.






The model of the round beam is such that axial symmetry is assumed so that a

hemispherical section will suffice for nodes. In Figure 2-32 the node numbering scheme

follows the pattern of number 1 is in the center, 2, 3, and 4 are radially outward to the

outside surface. Then on a 22.5º rotation numbers 5, 6, and 7 occur. On the next 22.50

rotation numbers 8, 9, and 10 occur. Continuing in this pattern there are three nodes at

every 22.5º rotation for the first 28 nodes. On the next hemisphere axially parallel to the

first hemisphere node number 29 will be on the center position with numbers 30. 31.

And 32 outward. Again at a 22.5º rotation numbers 33, 34, and 35 occur. Continuing, the

pattern is such that nodes on the hemisphere parallel to the succeeding hemisphere will

have a number of the previous node plus 28. Thus, node 2 will be adjacent to nodes 29,

axially, and also to nodes 3, 5, and 1. This model is sketched. Node 1 has nine (9)

adjacent radial nodes; 2, 5, 8, 11, 14, 17, 20, 23, and 26. Node 1 also has an adjacent

node on the axis, number 29. This model is sketched.





Physics & Space Science

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