Reliability Design of Lumber Floor Beams

Abstract

A designer is faced with difficult task of balancing the two competing demands of safety and economy. In an attempt to achieve the optimum balance, a designer is frustrated by many uncertainties. Quantities as structural loads material strength and material stiffness are not constant but instead vary over some range. The traditional devices employed in the face of these variations is to apply factor of safety, based on experience and judgment. In this study a reliability design method for lumber floor (single member) subjected to dead and live loads is presented in which the two limit states of strength (MOR) and deflection (MOE) , are considered. The developed method is in a Load and Resistance Factor Design (LRFD) format this method gives the designer better control over the probability of failure of lumber floor beams while retaining much of the simplicity of current design procedures. The load and resistance factors used for design are obtained from equations in the form: exp (α β V) where α is a constant, β target reliability index and V the coefficient of variation of the appropriate variable. The examples considered in this study demonstrate that the use of the equations results in floor beams having actual reliability index nearly equal to the target reliability index Probability-based values of dead load, live load. modulus of rupture and modulus of elasticity are discussed. Reasonable probability distributions for the above variables are adopted in order to be used in the development of the new method. Probability of failure calculations by the methods of second moment evaluation and numerical integration are discussed A computer program which performs reliability analysis by numerical integration is described. Numerical integration is selected for use in the development of proposed design method.