Analysis of Deflection of a Fixed Ridge Beam due to Pressure Applied on the Beam

D.S.Rodrigo, H.M.N.Sewwandi

The roof is a major component in building and housing construction and also it is the identity of the building or house. This study is focused on kingpost and beam joinery in gable roof types that commonly used in hotel entrances, cabanas, summerhouses, greenhouses and assembly halls in temples. For this study, the simplest structure of king post which is the structure that only the kingpost connects to the horizontal beam is used and mortise and tenon joinery is used to connect beam and king posts; the kingpost is used as a mortise element and beam is used as a tenon element. Therefore the ridge beam is a fixed which is supported at both free ends and is restrained against rotation and vertical movement. The study is considered the jack wood beam which has the length 198 inches (16.5 feet= 5.03m), 11 jack wood rafters that have the length 144 inches (12 feet) and two jack wood kingpost trusses that have kingposts with the length 44 inches (3.8 feet). Generally, carpenters in Sri Lanka use 8-11 feet as the range of standard distance between king post trusses. In this study, an attempt will be made to investigate the deformation of a ridge beam of under pressure exerted by rafters, tiles and kingpost trusses and from that to detect the optimum distance between kingpost trusses that can be used to design the king post beam joinery more effective way. Euler-Bernoulli Beam theory and Fourier series were the mathematical tools, which was used in the study. The shape of a deflected beam can be described by the Euler-Bernoulli Differential Equation. The results showed that the minimum deflection values have occurred at the standard range that used by carpenters. By examined those results, the optimum range for distance between kingpost trusses is 8-11 feet and when considering this range minimum deflection values have occurred around 9 - 9.5 feet. The results obtained from this study can be used to design the king post beam joinery more effective way.

https://dx.doi.org/10.31873/IJEAS.5.6.09