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Unformatted text preview: 10Ch10.qxd 9/27/08 7:32 AM Page 809 809 SECTION 10.4 Method of Superposition Method of Superposition
P The problems for Section 10.4 are to be solved by the method of superposition.
All beams have constant flexural rigidity EI unless otherwise stated. When
drawing shear-force and bending-moment diagrams, be sure to label all critical
ordinates, including maximum and minimum values. B A MA
RA Problem 10.4-1 A proposed cantilever beam AB of length L carries a a concentrated load P acting at the position shown in the figure.
Determine the reactions RA, RB , and MA for this beam. Also, draw the
shear-force and bending-moment diagrams, labeling all critical ordinates. b
L Solution 10.4-1 Propped cantilever beam
Select RB as redundant. OTHER REACTIONS (FROM EQUILIBRIUM) EQUILIBRIUM RA RA P RB MA Pa RBL
MA RELEASED STRUCTURE AND FORCE-DISPLACEMENT RELATIONS Pb
2L3 (3L2 Pab
2L2 b2) (L + b) ; SHEAR-FORCE AND BENDING-MOMENT DIAGRAMS COMPATIBILITY
dB (dB)1 (dB)2 dB
2L3 (3L 0 a) RBL3
3EI a) ; 2 0 RB ...
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- Fall '11