Civil Engineering Reference
In-Depth Information
mm to cut the three members HC, IC and GJ and using the method of sections to
calculate the corresponding member forces. Having obtained
F
GJ
we can consider
the equilibrium of joint G to calculate
F
GI
and
F
GF
. Hence
F
FI
and
F
FH
follow by
considering the equilibrium of joint F; the remaining unknown member forces follow.
Note that obtaining
F
GJ
by taking the section mm allows all the member forces in the
right-hand half of the truss to be found by the method of joints.
The method of sections could be used to solve for all the member forces. First we
could obtain
F
HC
,
F
IC
and
F
GJ
by taking the section mm and then
F
FH
,
F
FI
and
F
GI
by
taking the section nn where
F
GJ
is known, and so on.
4.11 S
PACE
T
RUSSES
The most convenient method of analysing statically determinate stable space trusses
(seeEq. (4.2)) is that of tension coefficients. In the case of space trusses, however, there
are three possible equations of equilibrium for each joint (Eq. (2.11)); the moment
equations (Eq. (2.12)) are automatically satisfied since, as in the case of plane trusses,
the lines of action of all the forces in the members meeting at a joint pass through
the joint and the pin cannot transmit moments. Therefore the analysis must begin at
a joint where there are no more than three unknown forces.
The calculation of the reactions at supports in space frames can be complex. If a space
frame has a statically determinate support system, a maximum of six reaction com-
ponents can exist since there are a maximum of six equations of overall equilibrium
(Eqs (2.11) and (2.12)). However, for the truss to be stable the reactions must be ori-
entated in such a way that they can resist the components of the forces and moments
about each of the three coordinate axes. Fortunately, in many problems, it is unnec-
essary to calculate support reactions since there is usually one joint at which there are
no more than three unknown member forces.
E
XAMPLE
4.6
Calculate the forces in the members of the space truss whose
elevations and plan are shown in Fig. 4.24.
In this particular problem the exact nature of the support points is not specified so that
the support reactions cannot be calculated. However, we note that at joint F there are
just three unknown member forces so that the analysis may begin at F.
The first step is to choose an axis system and an origin of axes. Any system may be
chosen so long as care is taken to ensure that there is agreement between the axis
directions in each of the three views. Also, any point may be chosen as the origin of
axes and need not necessarily coincide with a joint. In this problem it would appear
logical to choose F, since the analysis will begin at F. Furthermore, it will be helpful to
sketch the axis directions on each of the three views as shown and to insert the joint
coordinates on the plan view (Fig. 4.24(c)).
