Moment distibution (stiffness factor modifications) for a frame

In summary, the homework equations connect A to D by a hinge, but at the bottom of CD, it is not restrained by A. At the top of AB, sideways movement of B is resisted by the joint at A. In the beam BC, vertical movement at B is resisted by the combination of the rigidity of BCE and constraints at D and E. C cannot move up or down because of D. B can only move left or right because of E. At the bottom of CD, sideways movement of C is not restrained by A.
  • #1
fonseh
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2

Homework Statement


For the KAb and KCD , they are connected by the same method ... At B and C , we can see that they are connected by the same method , although i am not sure it's fixed or pinned .

Homework Equations

The Attempt at a Solution


I assume they are fixed at B and C , so i agree that KAB is 4EI / L for far end fixed case . So , i think KCD should be 4EI / L as well .
 

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  • #2
fonseh said:
far end fixed
Aren't the "far ends" A and D? One is fixed and one is pinned.
 
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  • #3
haruspex said:
Aren't the "far ends" A and D? One is fixed and one is pinned.

B and C are fixed ? How do we know that ? It's not stated in the question
 
  • #4
fonseh said:
B and C are fixed ? How do we know that ? It's not stated in the question
No, not B and C; A and D. As I read it, the stiffness factor at one end of a beam depends on whether the far end (other end) is fixed or only pinned. That makes intuitive sense to me.
A, B and C are fixed, so for the interactions at B and C:
AB is 4 because A is fixed
BC is 4 at each end because the other end is fixed
CD is 3 because D is pinned
CE is 3 because E is pinned
 
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  • #5
haruspex said:
BC is 4 at each end because the other end is fixed
Which end is fixed ? B or C ?
 
  • #6
fonseh said:
Which end is fixed ? B or C ?
Both are "fixed". (I think this just means it's a rigid joint, not a hinge.)
But hey, I'm only inferring all this from the text.
 
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  • #7
haruspex said:
Both are "fixed". (I think this just means it's a rigid joint, not a hinge.)
But hey, I'm only inferring all this from the text.
You just assume they are fixed ? So , for this type of question , we just assume they are always fixed ?? Since the author didnt show how's the connection at B and C
 
  • #8
fonseh said:
You just assume they are fixed ? So , for this type of question , we just assume they are always fixed ?? Since the author didnt show how's the connection at B and C
I'm not sure how you were supposed to know. They certainly look rigid in the drawing, but then so do D and E.
 
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  • #9
S
haruspex said:
I'm not sure how you were supposed to know. They certainly look rigid in the drawing, but then so do D and E.
Since they look ' rigid' , so they are assumed to be fixed at B and C ?
 
  • #10
fonseh said:
S

Since they look ' rigid' , so they are assumed to be fixed at B and C ?
I might have it...

The question of "far end fixed" is to do with sideways flexing at the "near end" being inhibited by the far end.
At the top of CD, sideways movement of C is not resisted by the joint D since that is a hinge.
At the top of AB, sideways movement of B is resisted by the joint at A.
In the beam BC, vertical movement at B is resisted by the combination of the rigidity of BCE and constraints at D and E. C cannot move up or down because of D. The rigidity of BCE then inhibits vertical movement at B.
Similarly, vertical movement at C is resisted by the combination of the rigidity of BCE and constraints at AB and E. B cannot move up or down because of A.

Hope that makes sense.
 

FAQ: Moment distibution (stiffness factor modifications) for a frame

What is moment distribution method?

The moment distribution method is a structural analysis technique used to solve indeterminate frames, commonly used in civil engineering. It involves distributing the moments at the joints of a frame until equilibrium is achieved, taking into account the stiffness of each member.

What are stiffness factors in moment distribution?

Stiffness factors in moment distribution refer to the modification factors applied to the stiffness of each member in order to account for the distribution of moments at the joints. These factors are usually calculated based on the relative stiffness of each member and the degree of indeterminacy of the frame.

How is moment distribution different from other analysis methods?

Moment distribution differs from other analysis methods, such as the slope-deflection method, in that it takes into account the stiffness of each member in distributing moments at the joints. This allows for a more accurate analysis of indeterminate frames and can be more efficient for larger and more complex structures.

What are the advantages of using moment distribution?

Moment distribution offers several advantages, including its accuracy in solving indeterminate frames, its ability to handle complex structures, and its efficiency in terms of computational time and effort. It also provides a visual representation of the distribution of moments, making it easier to understand and analyze the behavior of a structure.

What are the limitations of moment distribution?

Moment distribution has some limitations, such as its inability to handle certain types of supports, such as settlements or rotations. It also assumes that the frame is rigid and that there is no change in member stiffness due to loading. Additionally, it may not provide accurate results for structures with significant axial deformations or those with highly non-linear behavior.

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