Cracking failure of a curved laminated lumber might occur due to transverse stress under a curvature-decreasing bending moment. From both safety and cost perspectives, it is essential to understanding the failure moments and failure modes of curved laminated lumber. While the existing equation to calculate the transverse stress of a curved laminated lumber under a bending moment applied in most literatures is approximate and may cause considerable errors when the initial curvature of beam is small. This is detrimental to the design of curved laminated timber. To solve this problem, we proposed a new equation of bending moment Mc at which the cracking failure is initiated. Mc calculated from this new equation is accurate and larger than Mc-approx calculated from the existing approximate equation. We also derived a novel equation to calculate the minimum ch (cminh) below which cracking failure will not occur. Besides, a novel equation to calculate the critical ch (ccrih) which represents equal opportunities for cracking and bending failure of the beam to occur was further derived. The model proposed in this article are valuable and practical in the design of curved laminated lumber.
To exert our model to practice, the equations derived in this paper are applied to literature data (Wood handbook, 1999) and the results showed that hardwoods have statistically significantly larger average values of three parameters, Mc, cminh and ccrih, than softwoods which means hardwoods are more resistant to cracking failure than softwoods. This information is quite useful since lots of laminated lumber for building or furniture are made of hardwoods in Asia.