#HELICAL GEAR DESIGN EQUATIONS SERIES#

N = total design load on the staircase (kN/m 2) M vs = Vertical moment at supports= k 3nR 2 2 H = Horizontal redundant force at midspan = k 2nR 2 M o = Redundant moment acting tangentially at the midspan = k 1nR 2 2 Radial horizontal shear V h = HcosОё - (6) Vertical shear V n = nR 1ОёcosП• вЂ“ HsinОёsinП• - (5) Torsion T = (M osinОё вЂ“ HR 2ОёcosОёtanП• + nR 1 2sinОё вЂ“ nR 1R 2Оё)cosП• + HR 2sinОёsinП• - (3)ДЄxial force N = -HsinОёcosП• вЂ“ nR 1ОёsinП• - (4) Vertical moment M y = M ocosОё + HR 2ОёtanП•sinОё вЂ“ nR 1 2(1 вЂ“ cosОё) - (2) Horizontal moment M n = M o sinОёsinП• вЂ“ HR 2ОёtanП•cosОёsinП• вЂ“ HR 2sinОёcosП• + nR 1sinП•(R 1sinОё вЂ“ R 2Оё) - (1)

#HELICAL GEAR DESIGN EQUATIONS SERIES#

They used computer program to solve those complicated equations and constructed a series of design charts to provide the values of the coefficients.ДЇig 2: Geometry and internal stresses in helical staircase They proposed some simple equations for design purpose with the provision of using coefficients in the equations. Santathadaporn and Cusens (1966) worked further on helicoidal stair slabs to simplify the design process. The two redundants at mid-span are the horizontal shear H and the vertical moment M o.Д¬usens and Trirojna (1964) carried out a test on half scaled fixed ended helical staircase and confirmed the equilibrium equations derived by Morgan. By selecting the redundant at mid-span and using the principle of symmetry, all but two of the redundants become zero. Morgan (1960) and Scordelis (1960) presented the analysis of the longitudinal elastic axis of the helical beam as a three-dimensional structure indeterminate to the sixth degree. The method reduces the problem to that of a horizontal bow girder, which fails to take into account the inherent structural strength of a helical beam. Furthermore, helical staircases can sometimes be idealised as a fixed ended curved beam for the purposes of design due to their complexity.Д«ergman (1956) proposed an approximate solution to helical staircases called the in-plane beam solution. Fig 1: Internal stresses in a helical staircaseДespite the existence of the six internal stresses at any section in a helical staircase, they are usually designed for the horizontal bending moment only.

Helical gear design equations