Equivalent Nodal Forces [PDF]

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APPENDIX



D



Equivalent Nodal Forces



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



d



Problems D.1



Determine the equivalent joint or nodal forces for the beam elements shown in Figure PD–1.



Figure PD–1



752



Table D–1



Single element equivalent joint forces f0 for different types of loads



f1y



m1



1.




P 2



2.



Loading case



f2y



m2




PL 8




P 2



PL 8




Pb 2 ðL þ 2aÞ L3




Pab 2 L2




Pa 2 ðL þ 2bÞ L3



Pa 2 b L2



3.




P




að1
aÞPL




P



að1
aÞPL



4.




wL 2




wL 2 12




wL 2



wL 2 12



5.




7wL 20




wL 2 20




3wL 20



wL 2 30



6.




wL 4




5wL 2 96




wL 4



5wL 2 96



(Continued ) 753



754 Table D–1 (Continued )



f1y



m1



7.




13wL 32



8.




wL 3



9.




Mða 2 þ b 2
4ab
L 2 Þ L3



Loading case



f2y



m2




11wL 2 192




3wL 32



5wL 2 192




wL 2 15




wL 3



wL 2 15



Mbð2a
bÞ L2



Mða 2 þ b 2
4ab
L 2 Þ L3



Mað2b
aÞ L2