--- title: "Design procedure of steel purlin" subject: "Design of Steel and Timber Structure" chapter: 8 key: "semester_6/design_of_steel_and_timber_structure:purlin-design-procedure" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/purlin-design-procedure site: BCT Engineering --- # Design procedure of steel purlin Design of Steel and Timber Structure · Chapter 8: Design of Roof Trusses - Asked in: 2078 Chaitra, 6 marks; 2073 Magh, 5 marks (asked 2 times) - Video: [Design of I section purlin | Design of purlin | Design of purlin in steel structure](https://www.youtube.com/watch?v=agOhq23leAk) — Civil learning online - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/purlin-design-procedure - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-8 ## Question Describe the design procedure of steel purlins in roof truss. ## Short answer Steel purlin design as simply supported beam under biaxial bending from dead, live, and wind loads resolved normal and parallel to roof. Compute bending moments Mz and My, select trial section, check Mz/Mdz + My/Mdy ≤ 1, shear capacity, deflection limits, and uplift case with sag rods. Use IS 800:2007 load combinations. ## Answer 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. ```text truss truss |<----- L ----->| |==== purlin ====| sag rod at mid-span ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How are the vertical (gravity) loads treated when designing a purlin on an inclined rafter? A. Resolved into w cos(alpha) normal to the roof and w sin(alpha) parallel to the roof B. Applied entirely normal to the roof C. Applied entirely along the roof slope D. Ignored for the minor axis; only wind is resolved Answer: A. Gravity loads are inclined to the purlin's principal axes, so they give a normal component w cos(alpha) and a tangential component w sin(alpha); wind already acts normal to the roof. (Key point: Resolving loads) 2. What do sag rods do in a purlin design, and how do they enter the calculation? A. They increase the major-axis moment Mz by reducing L B. They restrain the purlin in the plane of the roof, so My uses the reduced span L' (e.g. L/2 for one rod at mid-span) C. They carry the wind uplift directly to the truss D. They are used only to connect the purlin to the rafter Answer: B. Sag rods carry the tangential component, so the minor-axis moment is My = w_t L'^2/8 with L' the span between sag rods. (Key point: Role of sag rods) 3. Which combination is checked for wind uplift, and what extra check does it need? A. 1.5(DL + LL), with a shear check B. 1.2(DL + LL + WL), with a deflection check C. 0.9DL + 1.5WL, with lateral-torsional buckling since the bottom flange is in compression D. 1.5DL only, with a bearing check Answer: C. Under uplift the net load reverses, putting the unrestrained bottom flange in compression, so LTB capacity must be checked. (Key point: Uplift combination) 4. What is the simplified strength check for a purlin under biaxial bending? A. Mz + My <= Md B. Mz/Mdy + My/Mdz <= 1 C. Mz/Mdz <= 1 only, since My is small D. Mz/Mdz + My/Mdy <= 1 Answer: D. Bending about both axes is combined through the sum of the utilisation ratios, which must not exceed 1. 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