The value of the ordinates, at the quarter span of the influence line diagram for the midspan bending moment of a simply supported beam is 0.5 m. If the span of the beam is doubled, then what will be the ordinates at the midspan of the influence line?
- A2.0 mCorrect
- B1.0 m
- C0.5 m
- DNone of the above.
Solution
Concept
Midspan bending moment influence line
Formula
Ordinate at x (x ≤ L/2) = x/2; maximum at midspan = L/4
Step-by-step solution
1. For a unit load at x from the left support, Mmid = x/2 (x ≤ L/2). 2. At the quarter span x = L/4: ordinate = L/8 = 0.5 m, so L = 4 m. 3. For a span of 2L = 8 m, the midspan ordinate = 8/4 = 2.0 m.
Explanation
The influence line for the midspan bending moment is a triangle with maximum ordinate L/4 at midspan. The quarter-span ordinate is half of that, L/8.
Shortcut
Midspan ordinate = L/4; quarter-span ordinate = L/8.
Common mistake
Mixing this up with the influence line for the bending moment AT the quarter point, whose maximum ordinate is 3L/16.
Correct answer: A) 2.0 m