Abstract
The design formula now used for wooden built-up beams are almost empirical one and, therefore, in applying these formula the form and the construction of beams are considerably limited. In this paper the theoretical formula for the rigidity and the strength of built-up beams are obtained, which consist of two or more parallel chords connected by several connectors (dowers, bolts, nails with or without wooden blocks, or blocks glued together). For the sake of theoretical treatment the beam is substituted by a frame consisting of main chord members and several connecting members perpendicular to the chords, all joints being rigid. The effective rigidity coefficient k of the connecting members is assumed according to the construction and the form of the connectors, and the method of computing k-values is developed. The deformation and the stresses of the beam are computed in consideration of the fact that they are due to both the flexure of each member, and the deformation of main chord members. The rigidity of the built-up beams is shown by the effective flexural rigidity (EJ)_e, and the formula for the ratio ζ=(EJ)_e/Σ(EJ_1) are given. (EJ_1 means the rigidity of each chord member.) The maximum allowable load of the beam depends upon the strength of the connecting parts or the strength of the main chord itself. The formula for the stresses of each part under any load are given. Using the upper formula the specification of A.I.J. are examined and the limit of application of this specification is discussed.
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