# Slope deflections method analysis of beam

• fonseh
In summary, the conversation discusses the need to consider two conditions when analyzing a beam - when the beam curves downwards and when it curves upwards. The difference between these two cases is that the author assumes a clockwise direction as positive in both scenarios. The conversation also brings up the question of whether considering the second case where the beam curves upwards is necessary, as the first case already shows a downward curve. The conversation also touches on the concept of relative linear displacement and why only one scenario is considered rather than both. Overall, the need to consider both cases is still unclear and requires further explanation.
fonseh

## Homework Statement

why we need to consider 2 conditions , the beam curve downwards ( as in 11-3) and beam curve upwards ( as in 11-4) ?
What's the difference between 2 cases ?

I notice that in both cases , the author assume clockwise as positive
here are the 3 consecutive pages of notes

## The Attempt at a Solution

I think the second cases where the curve curve upwards is unnecessary because we can see that the curve curve downwards (U shape) in the first photos .

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why for the relative linear dispalcement , we just have to consider one scenario only , namely consider the case where the member B is displaced relative to A ? Why we don't have to consider the case where the member A is displaced relative to B ?

Is there anything wrong with these cases ?

Can someone explain it ?
Or we need to consider 2 cases ( where the curve curve upwards and curve downwards) because it is a must to do so ? The beam will curve like this one if we superimpose 2 graph ? The red part represent the shape of graph , while the black line represent the beam

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## 1. What is the slope deflection method?

The slope deflection method is a structural analysis technique used to determine the displacements and moments of a beam subjected to various loading conditions. It involves calculating the slope and deflection at different points along the beam and using them to find the bending moments and shear forces at those points.

## 2. How is the slope deflection method different from other analysis methods?

The slope deflection method is different from other analysis methods, such as the moment distribution method, because it takes into account the actual stiffness of the beam at different points instead of assuming a constant stiffness throughout the beam. This makes it a more accurate and precise method of analysis.

## 3. What are the advantages of using the slope deflection method?

One of the main advantages of the slope deflection method is its ability to handle complex loading conditions, such as distributed and concentrated loads, as well as moments and settlements. It also allows for the analysis of non-prismatic and continuous beams. Additionally, it can provide more accurate results compared to other methods.

## 4. What are the limitations of the slope deflection method?

One limitation of the slope deflection method is that it can be time-consuming and tedious to apply, especially for more complex structures. It also requires the use of advanced mathematical equations and may not be suitable for manual calculations. Additionally, it may not be accurate for structures with large deflections or non-linear behavior.

## 5. Are there any practical applications of the slope deflection method?

Yes, the slope deflection method is commonly used in the design and analysis of buildings, bridges, and other structures. It allows engineers to accurately predict the behavior of a structure under different loading conditions and ensure its safety and structural integrity. It is also used in the evaluation and retrofitting of existing structures.

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