A one way slab has effective span 3·6 m and is 150 mm thick. The live load expected on it is 3 kN/m². What are the design shear and loads for checking serviceability respectively ?
- A18·225 kN, 6·75 kNCorrect
- B16·225 kN, 5·75 kN
- C18·225 kN, 7·75 kN
- D15·225 kN, 8·75 kN
Solution
Concept
Factored shear and unfactored load for serviceability
Formula
Vu = wu L / 2; wu = 1.5 (DL + LL)
Step-by-step solution
1. Dead load = 0.150 × 25 = 3.75 kN/m². 2. Serviceability load = 3.75 + 3.0 = 6.75 kN/m (per metre width). 3. Factored load wu = 1.5 × 6.75 = 10.125 kN/m. 4. Design shear Vu = 10.125 × 3.6 / 2 = 18.225 kN.
Explanation
The shear force is computed with the factored load, while deflection is checked under the unfactored (characteristic) load.
Why the other options are wrong
The other pairs do not equal 18.225 kN and 6.75 kN.
Shortcut
Serviceability uses 1.0 (DL + LL); strength uses 1.5.
Common mistake
Using the factored load for serviceability.
Correct answer: A) 18·225 kN, 6·75 kN