Draft

13.2CurvedSpaceStructures 223

Figure13.11:Geometryof CurvedStructurein Space

24 Theweakbendingaxisis normalto bothNandS, andthus itsunitvectoris determined

from

w=ns (13.33)

13.2.1.2 Equilibrium

25 For theequilibriumequations,we considerthefreebodydiagramof Fig. 13.12anapplied

loadPis actingat pointA. Theresultant forcevectorFandresultant moment vectorM

actingonthecutsectionBaredeterminedfromequilibrium

F= 0; P+F= 0; F=P (13.34-a)

M

B

= 0; LP+M= 0; M=LP (13.34-b)

whereLis thelever armvectorfromBtoA.

26 TheaxialandshearforcesN; VsandVwareallthreecomponents of theforcevectorFalong

theN; S, andW axesandcanbe foundby dotproductwiththeappropriateunitvectors:

N = F
n (13.35-a)

Vs = F
s (13.35-b)

Vw = F
w (13.35-c)