The quantity _Z÷P_ is the stress produced in the member by a unit load applied at the joint or point where the deflection is desired. Again, _S÷A_ is the stress per unit of area, i.e., intensity of stress, in the member considered by the actual dead and moving loads. For brevity let these be written _Z S_ --- = _z_ and --- = _s_; _P A_ then _zsl_ _w_ = ------. (43) _E_ If the influence of every member of the truss is similarly expressed, the value of the total deflection produced by the dead and moving loads will be _zsl_ _w_ = ∑ ------. (44) _E_ The sign of summation ∑ indicates that the summation is to extend over all the web and chord members of the truss. =111. Application of Method for Deflection to Triangular Frame.=—Before applying those equations to the case of Fig. 29 it is best to consider a simpler case, i.e., that of the triangular frame shown in Fig. 18. The reactions are _l₂ l₁_ _R_ = --- _W_ and _Rʹ_ = --- _W_. (45) _l l_ The stresses in the various members are: _l₁_ In _CB_, _S_ = ---- _W_ sec α. _l_ _l₂_ ” _CA_, _S_ = ---- _W_ sec β. _l_ _l₂ l₁_ ” _AB_, _S_ = --- _W_ tan β = --- _W_ tan α. _l l_ Also: _CB = h_ sec α; area of section = _A₁_. _CA = h_ sec β; ” ” ” = _A₂_. _AB = l_; ” ” ” = _A₃_. In this instance it is simplest to take _P = W_. Equation (44) then gives ( _l₁² h_ sec³ α _l₂² h_ sec³ _β_ _w_ = (----- ---------- + ----- ------------- ( _l² A₁ l² A₂_ _l₂² l_ tan² _β_ ) _W_ + ---- ------------) ------. (46) _l² A₃_ ) _E_ Let it be supposed that _l_ = 25 feet = 300 inches; _h_ = 8 feet 4 inches = 100 inches; _l₂_ = 16 feet 8 inches = 200 inches and _l₁_ = 100 inches; tan β = 1; sec β = 1.414; sec α = 2.24; _W_ = 10,000 pounds. If the bars are all supposed to be of yellow-pine timber, there may be taken _E_ = 1,000,000 pounds; _A₁_ = 10″ × 12″ = 120 square inches; _A₂_ = 10″ × 10″ = 100 square inches; _A₃_ = 10″ × 12″ = 120 square inches. The insertion of these quantities in equation (46) gives the deflection _w_ = .01042 + .01253 + .01111 = 0.034. (47) Equation (47) is so written as to show the portion of the deflection due to each member of the frame.