Equivalent Nodal ForcesDA P P E N D I X

The equivalent nodal (or joint) forces for different types of loads on beam elementsare shown in Table D–1.

d Problems

D.1 Determine the equivalent joint or nodal forces for the beam elements shown in FigurePD–1.

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Figure PD–1

Table D–1 Single element equivalent joint forces f0 for different types of loads

f1y m1 Loading case f2y m2

1.�P2

�PL8

�P2

PL

8

2.�Pb2ðLþ 2aÞ

L3

�Pab2L2

�Pa2ðLþ 2bÞL3

Pa2b

L2

3. �P �að1� aÞPL �P að1� aÞPL

4.�wL2

�wL2

12

�wL2

wL2

12

5.�7wL20

�wL2

20

�3wL20

wL2

30

6.�wL4

�5wL2

96

�wL4

5wL2

96

(Continued )

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Table D–1 (Continued )

f1y m1 Loading case f2y m2

7.�13wL32

�11wL2

192

�3wL32

5wL2

192

8.�wL3

�wL2

15

�wL3

wL2

15

9.�Mða2 þ b2 � 4ab� L2Þ

L3

Mbð2a� bÞL2

Mða2 þ b2 � 4ab� L2ÞL3

Mað2b� aÞL2

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