The trussed stringer is not a true truss, and the stresses cannot be accurately determined by the methods used for trusses, because the stresses in the members depend upon the deflection of the beam as a member of a truss and as a beam also. The exact solution is very complicated. An approximate solution can be made as follows: In Fig. 2S5, if load P is applied over the center strut as shown, then If the load P is applied uniformly over the whole length of ab, then the stresses are approximately as follows: The beams ad and db are however subjected to bending stress clue to the load acting directly on the beam between the unsupported points bending stress can be found approximately from the formula f — My in which y = Half the depth of the beam. I The bending moment may be taken as * P X ab.
The beam must be proportioned so as to provide for the direct stress plus the stress due to bending, without exceeding the allowable fiber stress of the timber.
In Fig. 2S6, if a load P is applied over each of the struts, the stress es can be determined approximately as follows: If the load 2 P is applied uniformly over the whole length ab, then the stresses are approximately as follows: The load at e and f can be taken approximately as P; then before; and if I is the moment of inertia of the beam, the bending Mg stress in ac — in which y = ", Depth of the beam; the bending Mmay be taken ass P X ab. The beam must be proportioned so that
the combined bending and direct stress shall not exceed the safe fiber stress for the timber.
Owing to the fact that the actual distribution of stress in trussed stringers is uncertain, and the methods of determining these stresses only approximate, a factor of safety of not less than 5 should be used. The detail of the connection of the rods with the end of the beam is shown in Fig. 2S7. Sometimes a single rod going between a hori zontal beam made of two timbers, is used; and sometimes where two rods are used, these are placed outside of the timber. A detail which will avoid boring through the timber is preferable. The plate at the end must be large enough to distribute the stress without exceeding the safe compression value of the timber used; for hard pine, this should be 1,000 pounds per square inch. The plate should be thick enough to provide for the shearing stress on the metal, and the bending stress induced by the pull of the rod on the unsupported portion of the plate.
It is important to have the center lines of the members intersect at the center of the bearing, as otherwise considerable additional bend ing stress will be caused, owing to the eccentricity.