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# Total long term deflection of concrete beam/slab ?

## Total long term deflection of concrete beam/slab ?

(OP)
Hello everyone,

Is the total deflection the sum of :
(a) Deflection due to short term loading with short term concrete modulus
(b) Deflection due to long term loading with long term concrete modulus
(Ee long term = E short term / (1+Creep Coefficient))
(c) Deflection due to shrinkage curvature.

In other words, is the total long term deflection equal to the sum of (a) +(b) + (c) above?
Or am I wrong ?

If anyone here is familiar with RAPT software, in their help manual section T.7.7.3
it says as follows:
The curvatures used by RAPT for calculating deflections are calculated in Detailed Flexural Reinforcement using the four following load and modulus combinations:

1)Short Term Load (A) with Short Term Concrete Modulus
2)Permanent Load (B) with Short Term Concrete Modulus
3)Permanent Load (B) with Long Term Concrete Modulus plus shrinkage curvature

Long-term deflection
The deflection that will be measured (from zero datum) after all long-term effects. Note that it is not the summation of the initial and incremental deflections. Deflections are calculated from the sum of combinations (from T.7.7.3).
3 + (1 - 2)

Which I don't understand why we need to subtract the deflection due to 2).

Many thanks

### RE: Total long term deflection of concrete beam/slab ?

The short term loads "contains" the permanent load. So if you do not subtract out the deflection due to 2 you have double-counted the permanent load and therefore over-estimated your deflections.

### RE: Total long term deflection of concrete beam/slab ?

The owner/creater of Rapt is also on the forums, I am sure he will give you the answers you are looking for.

### RE: Total long term deflection of concrete beam/slab ?

Actually, it should be 1 + (3-2) (same result) as the permanent cases are simply used to determine the creep and shrinkage effects.

### RE: Total long term deflection of concrete beam/slab ?

(OP)
Hi Rapt,

If I understand correctly, the software adds the relevant curvatures and then calculate the deflection based on the "final" curvature for total long term deflection. My question is : would it be the same if we calculate the deflection for each curvature separately then combine those deflections later to get the final deflection ?

Thank you
NTCONLINE

### RE: Total long term deflection of concrete beam/slab ?

Depends on what you mean by each curvature?

If you are using RAPT, then it is as it is. Why are you using the RAPT manual if it is not for use of RAPT, in which case your question is irrelevant.

The RAPT manual is copyright material for RAPT users!

### RE: Total long term deflection of concrete beam/slab ?

(OP)
Hi Rapt,

I am trying to develop my own Excel spreadsheet to calculate the deflection based on moment curvature area method and tension stiffening based on Eurocode procedure. My calculation did not give me sensible result for long term deflection. Thus, I wanted to find out where I made mistakes and make sure if my overall calculation procedure was correct. I did some google search and and had led me to RAPT manual online.

### RE: Total long term deflection of concrete beam/slab ?

I suppose I will now have to put RAPT users through the inconvenience of having to have a password to access it, to avoid its indiscriminate use.

People might think anything that Google can give them access to is free. It is not! RAPT users pay good money for the right to use RAPT software and manuals. They are not a free source for non RAPT users!

### RE: Total long term deflection of concrete beam/slab ?

NTConline, it is common to calculate the short-term/long-term/shrinkage deflections separately and then add them for the total deflection, as opposed to adding the curvatures then working out only the final deflection.

If I've understood your description of the RAPT procedure, the two are equivalent anyway.

### RE: Total long term deflection of concrete beam/slab ?

(OP)
Hi Steveh49,

I did also come to the same conclusion by experiment. Either way led to the same result. After that, I had a look again at the moment-area method and realised deflection is just a linear function of curvature (M/EI = 1/R). Thus,either calculating the short-term/long-term/shrinkage deflections separately and then add them for the total deflection, or adding the curvatures then working out only the final deflection are, mathematically, the same.

This discussion has provided me more confident in calculating the total long term deflection. Thank you all for your help!
Regards
NTConline

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