What is the slope at the end of a simply supported beam of span 2 m carrying a load of 5 kg per unit length over the entire span?
Try it first: pick an option, then read the explanation.
Correct answer: B. 5/(3EI)
Asked in SSC JE 02/03/2017 (Morning)
Detailed Explanation
For a simply supported beam with a UDL over the whole span, the slope at each support is wL³/24EI.
\[ \theta = \frac{wL^3}{24EI} = \frac{5\times2^3}{24EI} = \frac{40}{24EI} = \frac{5}{3EI} \]
Why “5/(3EI)” Is Correct
The end slope is 5/(3EI) (in kg and m units).
Why the Other Options Are Wrong
- A. 1/(16EI): 1/16EI uses the central-point-load coefficient without the load values.
- C. 1/(3EI): 1/3EI is five times too small.
- D. 1/(20EI): 1/20EI has no basis.
Key Point
Simply supported UDL: θend = wL³/24EI.
Key Concepts for Students
- Central point load: θend = WL²/16EI.
- Maximum deflection: 5wL⁴/384EI.
- Write the answer in the same units as the data.
Practice more: this is question 34 in Slope and Deflection MCQs – Part 3. Try the whole set and check every answer instantly.