Design procedure of steel purlin

A purlin is a beam spanning between roof trusses that carries the roof sheeting and transfers the loads to the truss panel points. Its design is done as a beam under bi-axial bending (IS 800:2007).

Procedure

1. Spacing and span. Span $L$ = truss spacing (usually 4 to 6 m). Purlin spacing $s$ along the rafter is fixed by the roofing sheet (e.g. 1.2 to 1.8 m for GI/AC sheets) so that purlins sit at the truss panel points.
2. Loads per metre of purlin.
   • Dead load: weight of sheeting $\times s$ + self-weight of the purlin (assumed, then revised).
   • Live load (IS 875 Part 2): $0.75 - 0.02(\alpha - 10)$ kN/m² on plan for roof slopes above 10° (minimum 0.4 kN/m²), applied on the plan projection $s\cos\alpha$.
   • Wind load (IS 875 Part 3): $p_d = (C_{pe} - C_{pi})p_z$ acting normal to the roof, $\times s$.
3. Resolve vertical loads into components normal to the roof ($w\cos\alpha$) and parallel to the roof ($w\sin\alpha$). Wind acts normal to the roof.
4. Load combinations (IS 800 Table 4): $1.5(DL + LL)$, $1.2(DL + LL + WL)$, $1.5(DL + WL)$, and uplift $0.9DL + 1.5WL$ (check the reversal of stress).
5. Bending moments. $M_z = w_nL^2/8$ (simply supported; $wL^2/10$ if continuous). $M_y = w_t\,(L')^2/8$ about the minor axis, where $L'$ is the span between sag rods (a sag rod at mid-span gives $L' = L/2$).
6. Select a trial section (ISMB, ISLB, channel or angle) from $Z_{pz,req} = M_z\gamma_{m0}/f_y$ (add about 20 to 30% for the minor-axis moment).
7. Classification and capacity. $M_{dz} = Z_{pz}f_y/\gamma_{m0}$ and $M_{dy} = Z_{py}f_y/\gamma_{m0}$ (each not more than $1.2Z_ef_y/\gamma_{m0}$); check lateral-torsional buckling for the uplift case when the bottom flange is in compression.
8. Interaction (biaxial bending). $\dfrac{M_z}{M_{dz}} + \dfrac{M_y}{M_{dy}} \le 1$ (cl. 9.3.1, simplified).
9. Shear $V \le V_d = A_vf_y/(\sqrt3\gamma_{m0})$.
10. Deflection under unfactored loads, limit span/150 for elastic (GI) sheeting and span/180 for brittle (AC) sheeting (Table 6).
11. Sag rods and connections. Provide sag rods (12 to 16 mm) at mid-span or third points to carry the tangential component, and cleat angles (with two bolts) to connect the purlin to the rafter; check the bolts for shear.

   truss           truss
    |<----- L ----->|
    |==== purlin ====|   sag rod at mid-span