Ultimate bending strength of timber beams

Abstract

The current design method of calculating bending strength of timber beams is based on elastic theory, that is, on working stress approach. The elastic theory does not hold true beyond the proportional limit of stress and thus does not describe the actual behavior of timber beams in the inelastic range up to failure. The broad objective of this study is to develop a rational approach of evaluating the ultimate bending strength of timber beams. The scope of the research is to cover various sizes of clear beams and of beams with strength reducing characteristics such as knots. An ultimate bending strength theory for timber beams is developed. The theory predicts the ultimate moment capacity of the beam using compressive and tensile strength values of the beam material obtained from direct tests on small clear specimens. A comprehensive experi mental program is carried out to verify the theory. Tests were conducted on some two hurdred and fifty-five (255) eastern spruce and Douglas-fir beams. Beams of five different sizes were subjected to central and third-point loading. Good agreement is observed between the theory and experimental results. Tests were also performed on some one thousand and nine hundred (1900) small specimens matched with the beams to determine direct compressive and tensile strengths of the test material. The ultimate tensile strength of the test material is observed tQ be two to three times the ultimate compressive strength. The actual behavior of the test beams is investigated by measuring strain at various levels along the beam depth. A linear variation of the strain distributi.on is observed along the depth for all stages of loading up to failure. It is observed that, at the proportional limit in bending as obtained from the load-deflection curve, the neutral axis is aporoximately at the center of beam depth. Beyond the proportional limit, the neutral axis shifted gradually towards the tension side, and at ultimate load, the movement of the neutral axis ranged between five to fifteen percent of the beam depth. The proporti ona 1 1 imit 5.;tress in bending is not si gni fi cantly affected by the depth of the beam. For beams subjected to third-point loading, this stress is equal to the ultimate compressive strength of the beam material obtained from direct tests . But for centrally loaded beams, the proportional limit stress in bending is about eleven percent greater than the corresponding value for similar beams loaded at third-span points . The maximum tensile stress developed at the extreme fiber of a beam at failure is statistically less than the ultimate strength in direct tension obtained from tests on small size standard soecimens. The actual value is dependent on the depth of the beam and is smaller as the depth is increased. The effect of method of loading of the beam on maximum tensile stress at failure is found to be the same as the effect on the prooortional limit-stress. The difference between both methods of loading is about eleven percent. An empirical fonnula relatinq the maximum tensile stress at failure in a beam to its size is derived . It is observed that the presence of knots influenced the type of failure of the beam. Beams containing small knots failed in a compressiontension sequence, while beams with relatively large knots near the edge of the tension zone failed in tension without any compression failare. The 1 oad-defl ecti on and 1 oad strain curves of the beams with 1 a rge knots xxvii indicated that the flexural behavior of these beams is elastic up to fa i lure . To account for the weakeninq effect of knots on compressive ·and tensile strengths in a beam, correlation equations between the strength and size and location of knots, are obtained. The concept presented in this thesis has the advantage that the ultimate moment capacity of a given timber beam for both elastic and inelastic behaviors, could be predicted from two known mechanical oroperties of the beam material, and it is simple to apply .~