If the far end of the member is fixed, the stiffness of the beam with usual notation is
- A2EI/l
- B3EI/l
- C4EI/lCorrect
- D5EI/l
Solution
Concept
Flexural stiffness of beam with fixed end
Formula
k = 4EI/L
Step-by-step solution
1. Flexural stiffness of a member is defined as the moment required to produce a unit rotation at a given end. 2. When the far end of a prismatic member of length l is fixed, applying a unit rotation at the near end induces a moment M = 4EI/l. 3. Therefore, the rotational stiffness of the member with a fixed far end is 4EI/l. Answer: C
Explanation
Bending stiffness represents the moment required to produce a unit rotation at a given joint. When the far end of a structural member is fixed, it offers higher resistance to rotation, resulting in a rotational stiffness value of 4EI/l. If the far end were hinged, the stiffness would instead be reduced to 3EI/l.
Why the other options are wrong
A) 2EI/l represents carry-over moment terms, not the fixed far-end flexural stiffness. B) 3EI/l is the flexural stiffness when the far end is hinged or simply supported. D) 5EI/l is not a standard formula for beam end stiffness.
Shortcut
Stiffness of a beam with far end fixed = 4EI/L (far end hinged = 3EI/L).
Common mistake
Confusing the stiffness for a fixed far end (4EI/l) with the stiffness for a hinged/simply supported far end (3EI/l).
Correct answer: C) 4EI/l