## Step-by-Step Solution ### **Given Data** - **Steel Sheet:** .42 Zincalume - **Purlin:** Z 15012 - **Purlin Spacing:** 400 mm (.4 m) center-to-center - **Purlin Span:** 2 m (between rafters) - **Rafter:** 200UB29.8 - **Rafter Span:** 3 m (between supports) - **To Find:** (a) Line load \( Q \) on Purlin (b) Line load \( Q \) on Rafter --- ### **Step 1: Load on Purlin (\( Q_{purlin} \))** The load on a purlin consists of the weight of the roof sheeting it supports. The **tributary width** for each purlin is the distance to the next purlin (center-to-center spacing), which is \( .4 \) m. #### **a. Find Mass of .42 Zincalume Sheet** Typical mass for .42 mm Zincalume roofing: - **Approx. \( 4.3 \) kg/m²** (You can confirm with manufacturer data, but this is typical.) #### **b. Convert to kN/m²** \[ 1\, \text{kg} = 9.81\, \text{N} \] \[ 4.3\, \text{kg/m}^2 = 4.3 \times 9.81\, \text{N/m}^2 = 42.18\, \text{N/m}^2 = .0422\, \text{kN/m}^2 \] #### **c. Area Supported by One Purlin per Meter Length** - The purlin "sees" a strip of roofing \( .4 \) m wide per meter length. #### **d. Line Load on Purlin (\( Q_{purlin} \)):** \[ Q_{purlin} = \text{Roof Load Intensity} \times \text{Tributary Width} \] \[ Q_{purlin} = .0422\, \text{kN/m}^2 \times .4\, \text{m} = .01688\, \text{kN/m} \] **Final Answer (a):** \[ \boxed{Q_{purlin} = .0169\, \text{kN/m}} \] (Rounded to four significant figures) --- ### **Step 2: Load on Rafter (\( Q_{rafter} \))** The rafter supports the purlins. Each purlin acts as a **point load** on the rafter. However, for the **line load** on the rafter, we sum the distributed weight of all purlins (including the roof sheet they support) over the length of the rafter. #### **a. Tributary Width per Rafter** - Distance between rafters = **3 m** #### **b. Load per Square Meter** - The roof sheeting is \( .0422\, \text{kN/m}^2 \). #### **c. Line Load on Rafter (\( Q_{rafter} \)):** \[ Q_{rafter} = \text{Roof Load Intensity} \times \text{Tributary Width} \] \[ Q_{rafter} = .0422\, \text{kN/m}^2 \times 3\, \text{m} = .1266\, \text{kN/m} \] **Final Answer (b):** \[ \boxed{Q_{rafter} = .127\, \text{kN/m}} \] (Rounded to three significant figures) --- ## **Summary of Answers** (a) **Line load on Purlin:** \[ \boxed{.0169\, \text{kN/m}} \] (b) **Line load on Rafter:** \[ \boxed{.127\, \text{kN/m}} \] --- **Note:** - These calculations assume the roof sheeting is the only load. For design, include self-weight of purlins/rafters, insulation, imposed loads, etc., as required by codes. - If you have project-specific sheet weight, use that value instead of the typical value.