Consider the following statements: 1.The distribution factor for fixed and pin support is zero since any moment is resisted by an equal and opposite moment within the support and no balancing is required. 2.In the case of pinned supports, the distribution factor is equal to 1.0 since 100% of any applied moment must be balanced and a carry-over of 1/2 × the balancing moment transferred to the remote end at the internal support. Which of the above statements is/are correct?
- A1 only
- B2 onlyCorrect
- CBoth 1 and 2
- DNeither 1 nor 2
Solution
Concept
In moment distribution, DF = 0 at a fixed end and DF = 1 at a pinned (free) end.
Formula
DF = kmember / Σk at the joint; fixed end DF = 0; pinned end DF = 1; carry-over factor = 1/2
Step-by-step solution
1. Fixed support: its stiffness is infinite. It takes any unbalanced moment itself. So DF = 0. 2. Pinned support: the support gives no rotational resistance. So the full moment must be balanced by the member. DF = 1.0. 3. Statement 1 says DF is zero for both fixed and pin supports. This is wrong for the pin support. 4. Statement 2: at a pin, 100% of the moment is balanced and half is carried over to the far internal joint. This is correct. 5. So only statement 2 is correct.
Explanation
A fixed support resists all moment itself, so its distribution factor is zero. A pinned end cannot hold any moment, so the whole moment is released (DF = 1). Half of this balancing moment is carried over to the far end. Statement 1 wrongly puts pin supports with fixed supports.
Why the other options are wrong
A and C: statement 1 is wrong, because DF at a pin support is 1, not 0. D: statement 2 is a correct description of the pinned end.
Shortcut
Fixed end: DF = 0. Pinned/free end: DF = 1.
Common mistake
Thinking all supports have DF = 0. Only fixed supports do.
Correct answer: B) 2 only