A beam 3 m long, simply supported at its ends is carrying a point load W at its mid-span. If the slope at the ends of the beam does not exceed 1°, what is the deflection at the mid-span ?
- A17·45 mmCorrect
- B17·45 cm
- C19·45 mm
- D19·45 cm
Solution
Concept
Relation between end slope and central deflection
Formula
θ = WL²/16EI; δ = WL³/48EI ⇒ δ = θ L / 3
Step-by-step solution
1. θ = 1° = 0.017453 rad. 2. δ = θ L / 3 = 0.017453 × 3000 / 3 = 17.45 mm.
Explanation
The ratio of the central deflection to the end slope is L/3 for a central point load, independent of W, E and I.
Why the other options are wrong
17.45 cm and 19.45 cm are ten times too large, and 19.45 mm does not match θL/3.
Shortcut
δ = θL/3.
Common mistake
Mixing mm and cm.
Correct answer: A) 17·45 mm