Losses of Pre-stress_I-Beam & T-Beam

Dear Viewers,

Good-Day to everybody. Hope, you all are well. Lets Start today's Lesson.
At my last article I was talking about "Losses of Pre-stress". According to this topic I am going to start my today's article.
Hope already you have read my last article about "Losses of Pre-Stress",

http://seasoft022.blogspot.com/2013/06/losses-of-pre-stress.html

In this article, I described briefly about Losses of Pre-stress, Classification of Losses of Pre-stress, Significance of Losses of Pre-stress and Necessary Formulas for calculating Losses of Pre-stress in case of "Pre-tensioned Pre-stress Beam & Post-tensioned Pre-stress Beam".
I gave two (02) examples also at my previous article about "Estimating the Losses of Pre-stress in case of both Pre-tensioned & Post-tensioned Pre-stress Beam". But those examples regarding about a simple rectangular pre-stress beam.
Now I am going to present to you "Estimating the Losses of Pre-stress in case of Pre-stress I-Beam & T-Beam".

Our necessary formulas are same, please review these necessary formulas again,

Losses of Pre-stressing Force in case of Pre-tensioned Pre-stress beam:

Losses due to Elastic Shortening, Δf_s = nf_c,

Losses due to Creep, Δf_s = (C_c-1)nf_c,

Losses due to Shrinkage, Δf_s = E_sδ_s,

Losses due to Steel Relaxation, Δf_s = 5% of f_i,

Losses of Pre-stressing Force in case of Post-tensioned Pre-stress beam:

Losses due to Elastic Shortening, Δf_s = 0.5nf_c,

Losses due to Creep, Δf_s = (C_c-1)nf_c,

Losses due to Shrinkage, Δf_s = E_sδ_s,

Losses due to Anchor Slip, Δf_s = (Δ_a E_s)/L,

Losses due Friction, Δf_s = (f₂-f₁) = (f_i-f₁),

Losses due to Steel Relaxation, Δf_s = 5% of f_i,

_{Now Lets Start,}

_{At First , Estimating the Losses of Pre-stress for a Post-Tensioned Pre-stress I-Beam,}

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Now, Estimating the Losses of Pre-stress for a Pre-Tensioned Pre-stress T-Beam,

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Dear Viewers,

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Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Losses of Pre-stress

Losses of Pre-stress:

In pre-stressed concrete application, the most important variable is the Pre-stressing Force. In the early days, it was observed that the pre-stressing force does not stay constant, but reduces with time. Even during pre-stressing of the tendons and the transfer of pre-stress to the concrete member, there is a drop of the pre-stressing force from the recorded value in the jack gauge. The various reductions of the Pre-stressing Force are termed as the Losses in Pre-stress.

Classification of Losses of Pre-stress:

The Losses of Pre-stress Force are broadly classified into two groups,

            ------Immediate Losses of Pre-stress,

            ------Time-dependent Losses of Pre-stress.

Immediate Losses of Pre-stress:

The immediate losses occur during pre-stressing of the tendons and the transfer of pre-stress to the concrete member. The losses due to elastic shortening of the member, friction at the tendon-concrete interface and slip of the anchorage are the immediate losses

Time-Dependent Losses of Pre-stress:

The time-dependent losses occur during the service life of the pre-stressed member. The losses due to the shrinkage and creep of the concrete and relaxation of the steel are the time-dependent losses.

Figure-01 indicates the Classification of Losses of Pre-stress,

Figure-01: Classification of Losses of Pre-stress

Generally the following types of Losses of Pre-stress are used in everywhere in the world, these are,

      ------Elastic shortening of concrete,

      ------Losses due to creep of concrete,

      ------Losses due to shrinkage of concrete,

      ------Losses due to Steel Relaxation,

      ------Losses due to anchorage take-up,

      ------Frictional Loss,

      ------Losses due to bending moment of the member,

Significances of Losses of Pre-stress:

The total analysis and design of a pre-stressed concrete tendon at each significant stages of loading gather with appropriate material properties for that one in the life history of the structure. The most common stages are as follows,

Immediately following transfer of pre-stress force to the concrete section stresses are evaluated from a measure of behavior.

At service load after all losses of pre-stress have occurred and a long-term effective pre-stress level has been reached, stresses are checked again as a measure of behavior and sometimes of strength.

Why do we estimate effective pre-stress force of pre-stressed concrete?

The effective pre-stress is the initial losses of pre-stressing force. Now while the initial pre-stress can be measured and applied accurately- the losses that we assumed, since it is difficult to generalize the amount of loss of pre-stress, because it is dependent on so many factors, the properties of steel, curing & moisture conditions, magnitude and time of application of pre-stressing force, the process of pre-stressing etc. Each of these factors are themselves variable and there is no definite method to accurately express them, besides other types of losses can occur too. Hence the effective pre-stress is estimated based on practical data & experiments.

Importance of Loss Estimation of Pre-stressed Concrete:

All the pre-stressing design is made considering the effective pre-stress (which is the initial losses of the pre-stressing force) during preparing the span. So it is very essential to estimate the magnitude of the total losses of pre-stress. Since it leads to the value of effective pre-stressing force needed for designing.

The accurate determination of losses is more important for some structures than other. The more accurate and detailed the technique of predicting losses, the more specific is the input information needed.

The percentage of loss in case of Post-tensioned beam increase, if the number of tendon is increased:

If there is only a single tendon in a Post-tensioned member, the concrete shortens as that tendon is jacked against the concrete. But if there is more than one tendon and the tendons are stressed one by one, then the pre-stress is gradually applied to the concrete. As a result the tendon that is first tensioned would suffer the maximum amount of loss due to the shortening of concrete by the application of pre-stress from all other tendons.

Formulas:

Losses of Pre-stressing Force in case of Pre-tensioned Pre-stress beam:

            Losses due to Elastic Shortening, Δf_s = nf_c ,

            Losses due to Creep, Δf_s = (C_c-1)nf_c ,

            Losses due to Shrinkage, Δf_s = E_sδ_{s ,}

            Losses due to Steel Relaxation, Δf_s = 5% of f_{i ,}

Losses of Pre-stressing Force in case of Post-tensioned Pre-stress beam:

            Losses due to Elastic Shortening, Δf_s = 0.5nf_c ,

            Losses due to Creep, Δf_s = (C_c-1)nf_c ,

            Losses due to Shrinkage, Δf_s = E_sδ_{s ,}

            Losses due to Anchor Slip, Δf_s = (Δ_a E_s)/L ,

            Losses due Friction, Δf_s = (f₂-f₁) = (f_i-f₁) ,

            Losses due to Steel Relaxation, Δf_s = 5% of f_{i ,}

_{Now, Using the above formulas, I am going to present two examples about Losses of Pre-stress to all of my viewers.}

_{The basic question of these two examples are same but One example is for Pre-tensioned Pre-stress Concrete Beam and the Other one is for Post-tensioned Concrete Beam.}

_{So that, by the mathematical example here we will try to calculate the amount of Losses in case of both Pre-tensioned and Post-tensioned Concrete.}

At first the basic question is,
A Pre-stress Beam of rectangular cross-section of 23 cm X 47 cm is tensioned with a cable of 20 wires of 7 mm diameter. The cable of circular cross section in with an  eccentricity 16 cm at the mid span and zero at the supports. The total span is 20 m long. The wires are initially stressed to 850 N/sq. mm.
Find the corresponding Losses of Pre-stress if this Pre-stress Beam is Pre-tensioned or Post-tensioned.

At first, we will solve this above mathematical problem in case of Pre-tensioned Pre-stressed Concrete Structures,

Already we know the required formulas for losses of pre-tensioned pre-stressed concrete which is,

            Losses due to Elastic Shortening, Δf_s = nf_c ,

            Losses due to Creep, Δf_s = (C_c-1)nf_c ,

            Losses due to Shrinkage, Δf_s = E_sδ_{s ,}

            Losses due to Steel Relaxation, Δf_s = 5% of f_{i ,} 

So lets start,

The following Page-01 to Page-05 indicates the solution of the above mathematical problem when the structure is Pre-tensioned Pre-stressed Concrete Structure,

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Now, we will solve this above mathematical problem in case of Post-tensioned Pre-stressed Concrete Structures,

Already we know the required formulas for losses of post-tensioned pre-stressed concrete which is,

            Losses due to Elastic Shortening, Δf_s = 0.5nf_c ,

            Losses due to Creep, Δf_s = (C_c-1)nf_c ,

            Losses due to Shrinkage, Δf_s = E_sδ_{s ,}

            Losses due to Anchor Slip, Δf_s = (Δ_a E_s)/L ,

            Losses due Friction, Δf_s = (f₂-f₁) = (f_i-f₁) ,

            Losses due to Steel Relaxation, Δf_s = 5% of f_{i ,}

So lets start,

The following Page-01 to Page-07 indicates the solution of the above mathematical problem when the structure is Post-tensioned Pre-stressed Concrete Structure,

Page-01: Post-tensioned Pre-stressed Concrete Structures,
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Discussion:

The amount of Losses reduces in case of Post-tensioned Pre-stressed Concrete Beam than Pre-tensioned Pre-stressed Concrete Beam.