# Method of consistant deformations

• jmf322
In summary, the conversation discusses the analysis of an indeterminate structure with a degree of indeterminacy of 2. The structure has two spring supports and a fixed support, and the method of consistent deformations will be used. There is a question about the contribution of the springs, with one being vertical and the other horizontal, attached to the same joint. The main concern is whether there may be a greater degree of indeterminacy not being accounted for. The system is expected to have a degree of indeterminacy of 2, and a picture of the structure will be posted for further clarification.

#### jmf322

I am analyzing an indeterminate structure with a degree of indeterminacy of 2(i think).

It is a frame with two spring supports and a fixed support. (and external loadings). I am required to use method of consistant deformations.

My question is about the springs. I would like to verify they contribute only one degree of indeterminacy each. One is in the vertical(moves up and down) and the other is horizontal(moves left and right). They are attached to the same joint.

So I am assuming three primary structures: Externally loaded structure, redundant as a unit force in the vertical, and redundant as a unit force in the horizontal.

I've noticed that the horizontal-spring stiffness has units (Force*Length)/radians, and the vertical-spring stiffness has units Force/Length.

My main concern is there may be a greater degree of indeterminacy i am not taking into account? Do these springs contribute more redundants than I am assuming? I hope I have been specific enough without a picture of the structure.

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According to what you've described, the system should have a degree of indeterminacy equal 2, as you said.

I would like to see a picture anyway.

radou - thanks for the quick reply, i am attempting the problem with three primary structures and two compatability equations(two degrees of indeterminacy)

cyclovenom - i'll post a picture shortly.

## What is the Method of Consistent Deformations?

The Method of Consistent Deformations is a structural analysis technique used to determine the internal forces and deformations in a structure under loading conditions. It is based on the principle of equilibrium and compatibility, and it assumes that the structure deforms in a consistent manner throughout.

## How is the Method of Consistent Deformations different from other structural analysis methods?

The Method of Consistent Deformations differs from other methods, such as the slope-deflection method or moment distribution method, in that it considers the compatibility of deformations throughout the structure, rather than focusing on individual elements or joints.

## What are the steps involved in using the Method of Consistent Deformations?

The steps involved in using the Method of Consistent Deformations are: 1) setting up the structural model, 2) applying loading conditions, 3) calculating the fixed-end moments and member stiffness, 4) determining the fixed-end displacements, 5) calculating the member forces and deformations, and 6) checking for equilibrium and compatibility.

## What are the advantages of using the Method of Consistent Deformations?

The advantages of using the Method of Consistent Deformations include: 1) it is a more accurate and realistic method compared to other techniques, 2) it can handle complex structural systems with multiple loading conditions, 3) it provides a better understanding of the behavior of the structure, and 4) it can be used for both determinate and indeterminate structures.

## What are the limitations of the Method of Consistent Deformations?

Some limitations of the Method of Consistent Deformations include: 1) it can be time-consuming and tedious for large and complex structures, 2) it requires a good understanding of structural mechanics, and 3) it may not provide accurate results for structures with highly non-linear behavior.