A one-way slab has effective span of 3·6 m and is 150 m thick (printed as in the paper; 150 mm). The live load expected on it is 3 kN/m². What is the load for checking serviceability ?
- A14·4 kN
- B6·75 kNCorrect
- C0·75 kN
- D16·40 kN
Solution
Concept
Serviceability loads are unfactored (characteristic) loads
Formula
ws = self-weight + live load (partial safety factor = 1.0)
Step-by-step solution
1. Self-weight of the slab = 0.150 × 25 = 3.75 kN/m². 2. Live load = 3 kN/m². 3. Serviceability load = 3.75 + 3 = 6.75 kN/m (per metre width). (Factored load for strength would be 1.5 × 6.75 = 10.1 kN/m.)
Explanation
For serviceability limit states (deflection, cracking) the unfactored loads are used. So the load on a 1 m strip is dead load plus live load = 6.75 kN/m.
Why the other options are wrong
The other values do not equal 3.75 + 3. The factored load (10.125) is not used for serviceability.
Shortcut
Serviceability: γf = 1.0. Strength: γf = 1.5.
Common mistake
Using the factored load 1.5 × 6.75.
Correct answer: B) 6·75 kN