Question

Which statement best describes the role of carryover factors in the Moment Distribution Method?

• A. Carryover factors distribute moments from one end of a member to the other
• B. Carryover factors redistribute moments from fixed ends to free ends
• C. Carryover factors account for the effects of support conditions on adjacent members
• D. Carryover factors adjust support reactions to match applied loads

Hint:

In the Moment Distribution Method:

• Distribution factors determine how an unbalanced moment at a joint is shared among the members connected to that joint.
• Carryover factors determine the moment induced at the far end of a member when a moment is applied at the near end, reflecting the stiffness and continuity of the members and thus the effect of support conditions.

Answer 1

The Correct Option is C

Step 1: Understand the Moment Distribution Method.
The Moment Distribution Method, developed by Hardy Cross, is an approximate method of structural analysis for indeterminate beams and frames. It is an iterative displacement method that involves distributing unbalanced moments at joints until equilibrium is achieved. Key concepts include distribution factors and carryover factors.
Step 2: Define Carryover Factor.
When a moment is applied at one end of a beam member, a portion of that moment is "carried over" to the other end of the member. The carryover factor represents the ratio of the induced moment at the far end to the applied moment at the near end. For a prismatic member with uniform cross-section, fixed at the far end and hinged at the near end, the carryover factor is +1/2.
Step 3: Relate carryover factors to support conditions and adjacent members.
The primary role of carryover factors is to reflect how moments are transferred from one end of a member to the other due to the rotation (or lack thereof) at the joint where moments are balanced. This transfer of moments directly impacts the moments developed in adjacent members and thus implicitly accounts for the influence of support conditions (like fixed or continuous ends) on the moment distribution throughout the structure.
Step 4: Evaluate the given options.
Option 1: Carryover factors distribute moments from one end of a member to the other. While carryover factors do relate moments between ends, their primary role is not merely "distribution" in the sense of balancing at a joint, but rather the transfer of a portion of a fixed-end moment or applied moment to the other end. This statement is less precise than option 3 regarding the role in the method's overall objective of accounting for support conditions.
Option 2: Carryover factors redistribute moments from fixed ends to free ends. This is incorrect. Moments are not redistributed from fixed ends to free ends in this manner.
Option 3: Carryover factors account for the effects of support conditions on adjacent members. This statement accurately describes the comprehensive role of carryover factors. They ensure that the moments transferred to adjacent members are consistent with the stiffness and end conditions of those members, which in turn reflects the overall support conditions of the structure.
Option 4: Carryover factors adjust support reactions to match applied loads. Carryover factors are directly related to moments, not support reactions, although moments will eventually lead to reactions. Their immediate role is not about adjusting reactions but about moment distribution. The final answer is $\boxed{\text{3}}$.