{ -(_⁶/₇W + ½Wʹ_) sec _a_, or _Stress in P₄_ = { +(_⁶/₇W - ½W′_) sec _a_; ” ” P₃_ = { -(_¹⁰/₇W + 1½W′ + W₁_) sec _a_, or { +(_³/₇ W - 1½Wʹ - W₁_) sec _a_; ” ” P₂_ = -(_¹⁵/₇ W + 2½Wʹ + 2W₁_) sec _a_; ” ” P₁_ = -(_3W + 3½ Wʹ + 3W₁_) sec _a_. { +(_¹⁰/₇W + ½Wʹ + W₁_) sec _a_, or _Stress in T₃_ = { -(_³/₇W - ½Wʹ - W₁_) sec _a_; ” ” T₂_ = +(_¹⁵/₇W + 1½W′ + 2W₁_) sec _a_; ” ” T₁_ = +(_3W + 2½Wʹ + 3W₁_) sec _a_. _Stress in L₁_ = + 3(_W + Wʹ + W₁_) tan _a + ½W′_ tan _a_; ” ” L₂_ = _Stress in L₁_ + (_5W + 5Wʹ + 5W₁_) tan _a_ = + 8(_W + Wʹ + W₁_) tan _a + ½Wʹ_ tan _a_; ” ” L₃_ = _Stress in L₂_ + 3(_W + Wʹ + W₁_) tan _a_ = + 11 (_W + Wʹ + W₁_) tan _a + ½Wʹ_ tan _a_; ” ” L₄_ = _Stress in L₃_ + (_W + Wʹ + W₁_) tan _a_ = + 12 (_W + Wʹ + W₁_) tan _a + ½Wʹ_ tan _a_. _Stress in U₁_ = -6(_W + Wʹ + W₁_) tan _a_; ” ” U₂_ = -6(_W + Wʹ + W₁_)tan _a_ - 4(_W + Wʹ + W₁_) tan _a_ = -10(_W + Wʹ + W₁_) tan _a_; ” ” U₃_ = -10(_W+ Wʹ+ W₁_) tan _a_ - 2(_W + Wʹ + W₁_) tan _a_ = -12(_W + Wʹ + W₁_) tan _a_. The chord stresses may be checked or found by the method of moments, precisely as in the case of Fig. 19. If, for instance, it is desired to determine the stresses in the upper chord member _U₂_, moments must be taken about the lower-chord panel-point 5, and about the upper-chord panel-point _d_ for the lower-chord stress in _L₄_. Taking moments about those points, results given in equations (31) and (32) will at once follow, which it will be observed are identical with the values previously found for the same members. (_3W + 3½ W′ + 3W₁_)._2p_ - 2_W′p_ - (_W + W₁_)_p_ _Stress in U₂_ = - ------------------------------------------------- _d_ = -10(_W + W′ + W₁_) tan _a_. (31) (_3W + 3½ W′ + 3W₁_)._3½ p_ - 3(_W + W₁_)._1½p - 3W′.2p_ _Stress in L₄_ = + ------------------------------------------------------- _d_ = + 12(_W + W₁ + W′_) tan _a_ + ½_W′_ tan _a_. (32) =93. Through- and Deck-Bridges.=—These simple trusses have all been taken as belonging to the “through” type, i.e., the moving load passes along their lower chords. It is quite common to have the moving load pass along the upper chords, in which cases the bridges are said to be “deck” structures. The general methods of computation are precisely the same whether the trusses be deck or through. It is only necessary carefully to observe that the application of the methods of analysis depends upon the position of each panel-load as it passes across the structure. [Illustration: Fig. 22.]