The ratio of stiffness of a member meeting at a structural joint to the sum of the stiffness of all members meeting at that joint is known as:
Distribution factor
Structural Joint Stiffness Ratio
The question asks about a specific ratio related to the stiffness of structural members connected at a joint. This ratio compares the stiffness of one particular member at the joint to the combined stiffness of all members connected at that same joint.
Let's look at the options provided and understand what each term represents in structural analysis:
- Distribution factor: This is a factor used in methods like Moment Distribution. It represents the proportion of the total resisting moment at a joint that is taken by a particular member connected to that joint. Mathematically, it is defined as the ratio of the stiffness of the member to the sum of the stiffness of all members meeting at the joint.
- Carryover factor: This is another factor used in Moment Distribution. It represents the proportion of a moment applied at one end of a member that is carried over to the other end. For prismatic members in typical frames, the carryover factor is often 0.5.
- Stiffness ratio: While related to stiffness, this is not a standard term used to define the specific ratio mentioned in the question. Stiffness itself is a property of a member, representing its resistance to deformation.
- Distribution moment: This is not a factor but rather the moment distributed to a specific member at a joint during methods like Moment Distribution. It is calculated by multiplying the distribution factor of the member by the unbalanced moment at the joint.
Based on the definitions, the ratio of the stiffness of a member meeting at a structural joint to the sum of the stiffness of all members meeting at that joint is precisely the definition of the Distribution factor.
The formula for the distribution factor (\(DF\)) for a member AB at joint A is given by:
\[DF_{AB} = \frac{K_{AB}}{\sum K_A}\]
Where:
- \(K_{AB}\) is the stiffness of member AB at joint A.
- \(\sum K_A\) is the sum of the stiffnesses of all members connected at joint A.
Therefore, the term that correctly describes this ratio is the Distribution factor.
Important Questions from Methods of Structural Analysis
A surface structure has:-
A single bay single storey portal frame has a hinged left support and fixed right support. It is loaded with a uniformly distributed load of w/m length on the beam. Which one of the following statements is true with regard to the deformation of the frame? Assume all the members have equal length.
In the structural analysis, the unit load method used is:
Who proposed the Theorem of Reciprocal Deflection?
Which method can be used to analyse the two or three dimensional members?
