Purlins are basically a flexural member in which transverse load act, in case of purlins the moments from both the axis occur as a result purlins are needed to be designed for biaxial moment. So we need to check the bending moment carrying capacity against both the axisand then we have to check the interaction formula so that the purlin is designed and these purlins are basically connects the transverse members in the roof structure to support the roof sheets and other materials and these purlins are placed on the rafter.
Let me show a picture through which we can see, that if this is a roof truss then trusses are connected with this purlin member, these are the purlin members and these purlin members are placed on the rafter. If you see these purlins are inclined and generally channel or angle sections are used for purlins because the weight is very less. So how the channel sections are placed as purlins, were discussed in lecture video and are shown in the following figure.
Now for purlin design we need to know what are the load coming into picture.
So if we see for an example say for channel section if we see here that load is basically two type one is the wind load ( H) which are acting perpendicular to the roof. Another load is acting vertically downward i.e. self-weight ( P ). Codal provision says that we should design purlin as an continuous beam because purlins are connected to the truss members in different places.So the moment can be calculated as,Mu=P ' L/10 and Mv=H ' L/10Mu = maximum bending moment about u-u axis.Mv = maximum bending moment about v-v axis.P’ = gravity loads acting along v-v axis, including sheeting, self-weight of purlins, LL &snow loads = H +Pcosθ .H’ = loads acting along u-u axis, including wind loads= Psinθ❑ L = span of the purlin, i.e.c/c distance of adjacent trussesMuu=(H+Pcosθ )L/10Mvv=(Psinθ )L/10
For biaxial moment of channel and I-sections the interaction formula is given byMuMdu+MvMdv≤1.0Where,Mdu = design bending moment about u-u axisMdv = design bending moment about v-v axis
Purlins are subjected to bi-axial bending. A trial section may be obtained arbitrarily or theexpression given by Gaylord et al. (1992) as follows:Zp Z=MZ γm0f y +My γm0f y ×2.5× bdfWhere,Zpz = required plastic section modulusMy= factored bending moment about y-y axisMz = factored bending moment about z-z axisfy = Yield stress of the materiald = depth of the section
bf = width of the sectionWe have to assume certain d and bf value initially and on the basis of that we can find out Zpzvalue and once we find out Zpz value we can find out a particular section say channel section,or I section, or angle section.So after knowing the actual d and bf we can again find out what is the actual requirement Zpzand whether it is satisfying that or not,
Design procedures for channel/I section purlin:1. The span of the purlin is taken as c/c distance of adjacent trusses2. The gravity loads P and wind loads H are computed. The component of these loads inthe direction parallel & perpendicular to the sheeting are determined. These loads aremultiplied with partial safety factor for loads as per Table 4 of the code for variousload combinations3. The maximum B.M. (Mz or Muu and My or Mvv) and S.F. (Fz and Fy) using the factoredloads are determined
4. The required value of plastic section modulus of the sectionmay be determined by using the following equationZp, reqd=MZ γm0f y +My γm0f y ×2.5× bdfwhereMy= Factored bending moment about y-y axisMz = Factored bending moment about z-z axisfy = Yield stress of steelγm0 = Partial safety factor = 1.10d = Depth of the trial sectionbf = Width of the trial section
5. Check for the section classification as per Table 2: IS 800: 2007 .6. Check for shear capacity of the section for both z and y axes taken as (Moris & Plum1996)Vdy=f y√3 γm0 Avy and V dz=f y√3γm0 AvzAvz=D tw and Avy=2bf tfwhereD = height of the sectiontw= thickness of the webbf = breadth of the flangetf = thickness of the flange
7. Compute the design capacity of the section in both the axes usingMdz=Zpz f yγm0≤ 1.2Zezf yγm0Mdy=Zpy f yγm0≤ 1.2Zey f yγm08. Check for local capacity using the interaction formulaMZMdz+MyMdy≤ 1.09. Check whether deflection is under permissible limits (l/180) as per Table 6, IS 800:2007.
Design of Angle Section Purlins:The following procedure is adopted for the design :1. The vertical and the wind loads are determined. These loadsare assumed to be normal to roof truss.2. The maximum bending moment is computed.Mu=w L210∨W L10where L = span of purlinw = uniformly distributed loadW = concentrated load at centroid
3. The required section modulus is calculated byZp, reqd=M1.33 ×0.66×f y4. Assuming the depth = 1/45 of the span and width = 1/60 of the span, a trial section ofangle purlins is arrived by.The depth and width must not be less than the specified values to ensure the deflectioncriteria.5. A suitable section is then selected for the calculated value of leg lengths of angle section.The modulus of section provided should be more than modulus of section calculated.So for purlin we have seen that generally we use either channel section, I section or anglesection and most commonly we use channel or angle. So the design criteria for channelsections are discussed, similarly the design criteria for angle section to use as a purlinmember are also discussed. In next class we will go through one example to understand howto design the purlin section, thank you.
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