Effect of Increase in Swayload on Unsymmetrically Loaded Portal Frame Structure at Lekki Using Slope Deflection Method

Abstract

This research work involves the study on the effect of increase in lateral load by 0.5kN on the slopes (θ), linear displacement (∆), Xmax and the bending moments of an unsymmetrically loaded portal frames structures with uniform flexural rigidity (E.I = constant) using the slope deflection method, also the results was obtained and represented graphically. In this study, the discussion will be restricted to one story building under differential settlement and also the analysis will be carried out on an unsymmetrical loaded portal frame structure using the slope deflection method of analysis. The slope B (θB) decreases positively as the lateral load increases by 0.5kN while slope C (θC) increases negatively as the sway load increases. The linear displacement (∆) increases negatively as the sway load increases while the Xmax, Mmax, MAB, MBA andMCB increases positively as the sway load increases by 0.5kN. MDC decreases negatively as the sway load increases by 0.5kN. The proposed method of analysis offers a number of relative simple expressions from which the lateral sway, slopes, Xmax values and the bending moments can be easily calculated for the portal frame structure under increase in lateral loads that is saving time and attractive for use in preliminary design and studying structures subjected to dynamic loads. The present analysis describes the relation between the increase in lateral load on linear displacements, slopes, Xmax values and the bending moments of the portal frame structure. The maximum sway depends mainly in the contribution of the increase in lateral load, bending moment and the slope of the portal frame structure, the bending moment in columns and the beams which represent the contribution of the moment of inertia of columns, beams and their cross sectional areas. The contribution of the normal forces in the portal frame is approximately equal to zero which represent the contribution of the cross sectional area of the portal frame. The great advantages of the slope deflection method of analysis are the determination of the lateral sway by using hand calculations only (without the use of computer computations) or by using simple spread sheet program {Excel program}. Slope deflection equation was derived for one storey residential building under collapse due to sideway or linear displacement. The dead loads and live loads were applied as uniformly distributed load on beam and sway force on column of the portal frame. This research work will serve as a useful interactive material for teaching structural engineering students and a valuable tool for practicing structural engineers.