=91. The Howe Truss Type.=—The truss shown in Fig. 20 is the skeleton
of the Howe truss, to which reference has already been made. The
inclined web members are all in compression, while the vertical web
members are all in tension. In the Howe truss all compression members
are composed of timber. It has the disadvantage of subjecting the
longest web members to compression. It thus makes the truss, if built
all in iron or steel, heavier and more expensive than the trusses of
the Pratt type. As in the preceding case, the moving train or load is
supposed to pass across the bridge from _B_ to _A_. Also, as before,
the + sign indicates tension and the - sign compression. The greatest
stresses, given in the tabulated statement below, can be computed or
checked by the method of moments in this case, precisely as in the
preceding.
_Stress in c₁_ = -(¹/₇ + ²/₇) _W_ sec _a_ = -³/₇ _W_ sec _a_.
_Stress in P₄_ = -(¹/₇ + ²/₇ + ³/₇) _W_ sec _a_ = -⁶/₇ _W_ sec _a_;
” ” P₃_ = -(_¹⁰/₇ W + Wʹ + W₁_) sec _a_;
” ” P₂_ = -(_¹⁵/₇ W + 2Wʹ + 2W₁_) sec _a_;
” ” P₁_ = -3(_W + Wʹ + W₁_) sec _a_.
_Stress in T₃_ = + (_¹⁰/₇ W + W₁_) sec _a_;
” ” T₂_ = + (_¹⁵/₇ W + Wʹ + 2W₁_) sec _a_;
” ” T₁_ = + (_3W + 2Wʹ + 3W₁_) sec _a_.
_Stress in L₁_ = + 3(_W + Wʹ +W₁_) tan _a_;
” ” L₂_ = + 3(_W + Wʹ + W₁_) tan _a_+2(_W + Wʹ + W₁_) tan _a_
= + 5(_W + Wʹ + W₁_) tan _a_;
” ” L₃_ = + 5(_W + Wʹ + W₁_) tan _a_+(_W + Wʹ + W₁_) tan _a_
= + 6(_W + Wʹ + W₁_) tan _a_;
” ” L₄_ = _Stress in L₃._
_Stress in U₁_ = _- Stress in L₁_
” ” U₂_ = _- ” ” L₂_;
” ” U₃_ = _- ” ” L₃_.
It will be noticed in the cases of Figs. 19 and 20 that upper and lower
chord panels in the same lozenge or oblique panel have identically
the same stresses, but with opposite signs. For instance, in Fig. 20
the stress in _U₂_ is equal in amount to that in _L₂_; and the same
observation can be made in reference to the stresses in _U₂_ and _L₄_
of Fig. 19. This must necessarily always be the case in trusses having
vertical web members.
In making computations for these forms of trusses it is very essential
to observe where the first counter-member, as _c₁_, must be used. These
counter-members may be omitted if the proper main web members near the
centre of the span are designed to take both tension and compression.
=92. The Simple Triangular Truss.=—The truss shown in Fig. 21, in which
all the web members have equal inclination to a vertical line, is
sometimes called the Warren Truss, although that term has also been
applied specially to this type of truss so proportioned as to make the
depth just equal to the panel length. As before, the moving train is
supposed to pass over the bridge from _B_ toward _A_, while the + sign
represents tension and the - sign compression. The greatest stresses
are the following.
[Illustration: FIG. 21.]
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