Influence Line

Influence Line:

Assume,

Here AB is a simply-support beam. 1 kip load is applied downward on the point A.We will get an upward reaction value (noted as R_A) at Point A because of applied 1 kip downward load.

Now when that 1 kip downward load is moved from Point A to Point B then this load (1 kip) will act all points on the beam AB & we will get a different reaction value of R_A each time while 1 kip load will move on the different points of beam AB (Point A to Point B). By adding these all reaction values of R_A, we will get a straight line. This straight line will known to us as Influence Line for R_A that is IL for R_A.

Now by the same way, we apply that 1 kip vertically downward load at Point B at first. We will get an upward reaction value (noted as R_B) at point B. Now move this load from Point B to Point A. We will get a different reaction value of R_B each time while 1 kip load will move on the different points of beam AB (Point B to Point A). By adding these all reaction values of R_B, we will get a straight line. This straight line will known to us as Influence Line for R_B that is IL for R_B.

Example-01:

Draw Influence Line for R_A and R_B.

Solution:

IL of R_A:

Now at first put 1 kip load downward at point A and then move this 1 kip load from Point A to Point B, we get,

When 1 kip load at first on the Point A then reaction of A that is R_A=1, RB=0, because total applied load is resisted by R_A.

Now when 1 kip is started to move from Point A to Point B and at last will rest on Point B then R_A=0 and R_B=1.

Now if we want to draw the influence line for R_A, then we get the following structure,

When 1 kip load rest upon Point A then R_A=1 and when 1 kip load rest upon Point B then R_A=0.

But as the definition of Influence Line, we need to add all reaction values which we will get from all points upon AB, during moving of 1 kip downward load from Point A to Point B. But here we have added reaction values only when 1 kip load rests at starting point and Ending Point.

Now we will calculate different reaction values of R_A from different points on beam AB.

At first consider the 1 kip load rests at Point C which is located at a distance 2 feet from point A.

Then,

∑M_A= 1*2 – R_B*10 = 0

So, R_B = 0.2 kip,

∑F_Y= R_A – 1 + 0.2 = 0

So, R_A= 0.8 kip.

Now consider the 1 kip load rests at Point D which is located at a distance 5 feet from point A.

Then,

∑M_A= 1*5 – R_B*10 = 0

So, R_B = 0.5 kip,

∑F_Y= R_A – 1 + 0.5 = 0

So, R_A= 0.5 kip.

Though 1 kip load is applied at middle point of AB then R_A will be half of applied load and R_B will be another half of applied load that means the summation of R_A & R_B will be the equal value of the applied load.

Now consider the 1 kip load rests at Point E which is located at a distance 8 feet from point A.

Then,

∑M_A= 1*8 – R_B*10 = 0

So, R_B = 0.8 kip,

∑F_Y= R_A – 1 + 0.5 = 0

So, R_A= 0.2 kip.

Now put all these reaction values of R_A and plot them on a Plain Graph Paper, which values we have already calculated by applying 1 kip load at Point C, D & E.

After plotting them on a Plain Graph Paper we get IL of R_A which is similar with the previous, by this experiment we can take decision that,

To find IL of any Simply Supported Beam we need to find only two reaction values at Starting Point & at Ending Point, we need not find any more reaction values at any other point on the BEAM.

IL for R_{B :}

When 1 kip load at first on the Point B then reaction of B that is R_B=1, R_A=0, because total applied load is resisted by R_B.

Now when 1 kip is started to move from Point B to Point A and at last will rest on Point A then R_B=0 and R_A=1.

So IL of R_B will be as follows,

We need not calculate different reaction values of R_B from different points on beam AB, because IL will be same (it is already proved for R_A)

Pre-stressed Concrete Structures (04)

Dear Viewers,
Hello & Good-Day to everyday. Hope all of you are well with a very very happy & fresh mind.
Today I am going to explain you about some Mathematical Problem based of Three (03) concepts of Pre-stressed Concrete Structures.

At my this Blog, I have already explained about the theoretical term of Three (03) Concepts of Pre-stressed Concrete Structures which you can review by

http://seasoft022.blogspot.com/2013/05/pre-stressed-concrete-structures-02.html

Now I will explain you these Three (03) Concepts of Pre-stressed Concrete Structures with Mathematical Problem & Solution.
So, Lets start,

Before starting the mathematical problem & solution at first lets review the three (03) concepts of Pre-stressed Concrete Structures again shortly.

There are Three (03) Concepts Pre-stressed Concrete Structures, these are as follows,

1^st concept: Pre-stressing to transform concrete into elastic material,

2^nd concept: Pre-stressing for combination of high strength steel to high strength concrete,

3^rd concrete: Pre-stressing to achieve load balancing.

Now we have considered a Mathematical Problem. This Mathematical Problem which will be solved by using Three (03) Concepts of Pre-stressed Concrete Structures.
So, the Question of our desire Mathematical Problem is as follows,

Question: A Pre-stressed Concrete Beam of 12" x 36" has a simple span of 30' and is loaded by a uniform load of 3.27 kip/ft including its own weight. The Pre-stressing Tension is located at an eccentrically of e=8" and produce an effective prestress of 350 kip.

Compute fiber stresses in the concrete at mid-span section.

Solution: Now lets go to solve this mathematical problem at first by using 1st concept of Pre-stressed Concrete Structures,
Picture-01 & Picture-02 indicates the mathematical solution by using the 1st Concept of Pre-stressed Concrete Structures,

1st Concept of Pre-stressed Concrete Structures, Page 01 of 02
By Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Picture-01: Mathematical Solution by using the 1st Concept of Pre-stressed Concrete Structures (Page 01 of 02)

1st Concept of Pre-stressed Concrete Structures, Page 02 of 02
By Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Picture-02: Mathematical Solution by using the 1st Concept of Pre-stressed Concrete Structures (Page 02 of 02)

Now, solve the same mathematical problem by using 2nd Concept of Pre-stressed Concrete Structures,
Picture-03, Picture-04 & Picture-05 indicates the mathematical solution by using the 2nd Concept of Pre-stressed Concrete Structures,

2nd Concept of Pre-stressed Concrete Structures, Page 01 of 03
By Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Picture-03: Mathematical Solution by using the 2nd Concept of Pre-stressed Concrete Structures (Page 01 of 03)

2nd Concept of Pre-stressed Concrete Structures, Page 02 of 03
By Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Picture-04: Mathematical Solution by using the 2nd Concept of Pre-stressed Concrete Structures (Page 02 of 03)

2nd Concept of Pre-stressed Concrete Structures, Page 03 of 03
By Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Picture-05: Mathematical Solution by using the 2nd Concept of Pre-stressed Concrete Structures (Page 03 of 03)

At Last, Solve the same mathematical problem by using 3rd Concept of Pre-stressed Concrete Structures,
Picture-06 & Picture-07 indicates the mathematical solution by using the 3rd Concept of Pre-stressed Concrete Structures,

3rd Concept of Pre-stressed Concrete Structures, Page 01 of 02
By Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Picture-06: Mathematical Solution by using the 3rd Concept of Pre-stressed Concrete Structures (Page 01 of 02)

3rd Concept of Pre-stressed Concrete Structures, Page 02 of 02
By Engr. Snehashish Bhattacharjee (Tushar), seasoft022.blogspot.com

Picture-07: Mathematical Solution by using the 3rd Concept of Pre-stressed Concrete Structures (Page 02 of 02)

Now lets analyze these Three (03) types of solutions of a same mathematical problem.

Analyze:
*** At first process (1st Concept), there is no extra method to solve this problem.
*** At second process (2nd Concept), there is consideration about compression & tension force,
*** At the third & last process (3rd concept), moment will be calculated by using unbalanced load (Upward Uniform Load from Pre-stressing Force-Download Uniform Load), so that this moment (133.425 kip-ft) will be called unbalanced moment.
*** We can understand that the result of all of these solutions will be more or less same.

Cold Joint (Part-02)

How Cold Joints forms in concrete:

A Cold Joint is the intersection between the end of one concrete pour and the beginning of a new pour. The basic rule is to try to avoid Cold Joints by pouring straight through until the job is finished. The Cold Joint is a weak area and could allow the entry of water. If it must be done, inserting reinforcing bars in the fresh concrete of the fresh concrete of the old pour will tie in the new pour more effectively.
Figure-01 indicates how can a Cold Joint will form in a Concrete Slab,

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

Figure-01: Cold Joint in a Concrete Slab

Cold Joints are formed primarily between two batches of concrete where the delivery and placement of the second batch has been delayed and the initial placed and compacted concrete has started to set. The full knitting together of the two batches of concrete under vibration to form a homogeneous mass is therefore not possible, unlike the compaction of two fresh workable batches of concrete. This could be a potential plane of weakness. Cold joints, unlike cracks that form in hardened concrete through tensile restraint, are not gaps in the concrete but merely seams containing no appreciable void structure. They are usually linear, closely joined and bonded. However, there is a danger of small voids in areas where the concrete is not fully compacted, as with any concrete pour.
Figure-02 indicates the formation of a Cold Joint in a Concrete Slab,

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

Figure-02: Cold Joint forms in a Concrete Slab

Problems associates with Cold Joint:

A cold joint is an undesirable discontinuity between layers of concrete that occurs when one layer of concrete is allowed to harden before the rest of the concrete is poured in what is meant to be a single, solid mass. The discontinuity occurs between the layers due to the inability of the freshly poured, wet concrete to intermix with and bind properly to the hardened concrete. Such a discontinuity is often the result of logistical issues such as a contractor’s work schedule or an unexpected material shortage.

Figure-03 indicates undesirable continuous layer of Cold Joint which caused discontinuity between two concrete layer,

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

 Figure-03: Undesirable continuous layer of Cold Joint & discontinuity between two concrete layer

Problems associated with cold joints range from the relatively minor to the very serious. At the less serious end of the spectrum, a cold joint may result in a visually unappealing discontinuity, called a cold joint line, that is visible on the surface once the concrete has hardened. This kind of aesthetic defect may simply be concealed rather than repaired.

------A more serious problem associated with a cold joint is the possibility of moisture intrusion into the concrete section. If water settles in a cold joint, it may lead to degradation of the concrete under certain environmental conditions. For example, as water expands when it freezes and then contracts when it melts, water trapped in a cold joint may cause cracking or erosion of the material. Moisture may also damage other things beyond the concrete mass if it is able to seep all the way through it.

Figure-04 indicates water absorption into old concrete section during new concrete portion is poured,

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

Figure-04: Effect of water absorption on the new poured section

Additionally, a cold joint is an area of compromised strength. Concrete is notable for its high strength under compression, but it is much weaker under tension. A cold joint is even weaker under tension, and it is susceptible to shearing at the discontinuity.

Whenever possible, cold joints should be avoided in concrete construction by completing the entire pour for a given section in one session. This allows the entire section to harden in a continuous, solid mass. If this is not possible, several steps can be taken to mitigate the more serious problems.

Specialized waterproofing joint sealant may be applied to the joint to make it watertight, thereby protecting against potentially damaging moisture intrusion. A special surface preparation may be applied to the hardened layer before applying a fresh layer of concrete. This will strengthen the bond between the two layers. Another way to increase the strength of the cold joint is to insert reinforcing bar, or re-bar, into the first layer before pouring the next layer. This will better help tie them together and increase the tensile strength of the joint. It is also sometimes possible to locate the weakened joint in an area that is not critical to supporting a large load.

Repairing of Cold Joints:

Repairing of Cold Joints While Pouring Cement:

------ Mix the concrete from the earlier portion of the pour with the fresh concrete, if possible. Use a concrete vibrator to work the two sections into a single mix of concrete as much as possible. How hard, or setup, the first pour of concrete has become will determine if this is possible. If successful, this blending of the two concrete pours will provide the strongest slab that is the least likely to crack.

Figure-05 indicates concreting process to avoid/repair Cold Joint,

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

Figure-05: Concreting process to avoid/repair Cold Joint 

------Place reinforcing rods between the first portion of the slab and the new pour. If the second portion of the pour will be more than two or three hours after the first portion the re-bar should be set in the first portion while it is still wet. After the second portion of the concrete is poured, the re-bar serves as a connection between the two slabs. The week joint of the cold slab may still crack, but with the re-bar connecting the two portions of the slab, the cement will not shift and form a displaced fracture of the cement.

Trowel the cement as smoothly as possible over the cold joint. Cold joints often remain visible after all the concrete has cured due to differences in the color of the concrete.

Figure-06 indicates the re-bar process to repair/avoid Cold Joint,

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

Figure-06: Re-bar process to repair/avoid Cold Joint

Repairing of Cold Joints in Cured Slabs:

Repair small cracks at cold joints with thin mix or a concrete crack sealant. Closing and sealing the cracks prevents water from entering the crack and causing damage through freeze and thaw cycles.

Cut out bigger cracks using a concrete saw. This becomes necessary if the small crack has deteriorated over time and is causing breakage of the concrete, resulting in an open crevice with unstable concrete on the edges. Cut the concrete back far enough so both edges of the opening are high quality cement.

Figure-07 indicates how cracks form because of Cold Joint & how it can be removed,

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

Figure-07: How cracks form because of Cold Joint & how it can be removed

Cold Joint (Part-01)

Hello, Good-Day to Everybody.

Today I will tell you about a topic which is frequently seen in practical life of a Civil Engineer but rarely read at your books, but in practical life usually it can be seen always.

Now, I am going to explain you about “Cold Joint”.

------ Engr.Snehashish Bhattacharjee (Tushar).

Cold Joint:

A Cold Joint is a plane of weakness in concrete caused by an interruption or delay in the concreting operations. It occurs when the first batch of concrete has begun to set before the next batch is added, so that the two batches do not intermix properly. Sometimes Cold Joints occur because of emergency interruptions & delays and sometimes because of the work stoppage at the end of the day, but they can also occur from poor consolidation.

Figure-01 indicates a cross section of a road with cold joint,

Figure-01: Cold Joint

To prevent or avoid Cold Joint in walls, beams and other structural components it is necessary to place concrete in layers about 18 inches deep and intermix each layer with the previous one by using a vibrator. Placement of concrete should begin in the corners and work toward the center. When slabs are placed the concrete should be placed against the preceding batch and not dumped in an individual pile. On sloping grades the work should proceed uphill. In hot weather a retarding admixture may be needed to slow the setting time.

Cold Joint is simply a joint of concrete pour which is usually seen in construction field, which will happen naturally for long length structures with a slope such as long length span of a bridge, long length slab of a building structures etc.

For Example,

Suppose we have a long span of 38 meter of a Flyover and we are unable to pour concrete the total span at a time. Now see the following figure,

Figure-02 which indicates how can Cold Joint forms in concrete in practical life,

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

 Figure-02: Cold Joint forms in concrete (at practically)

Now let’s analyze this Figure-02. From this Figure-02, there are two Piers and a 38 m span is in between them. The distance between Pier-A & Pier-B is 38 m. This is a Cast-In-Situ Span. So, we need to cast this span at site. It is needed to be remembered that there is a slope between two piers, the slope is downward from Pier-A to Pier-B.

Now, what will be the concreting process of this Cast-In-Situ span?

At first let’s start our concreting process from Pier-A. Our destination is to concrete pour up to 13 m from Pier-A. This 13 m is not any fixed distance, actually there is a slope between two Pier (downward slope from Pier-A to Pier B), that’s why at the time of concreting when concrete was in liquid state, it behaves like water & wanted to go to downward. Because of more amount of liquid material will create a free flow & will want to go downward. It causes the damage/not proper quality of casting process.

So that, we need to stop at a distance (here is 13 m, just say). Then after casting at Pier-A, now we will go to the other side at Pier-B, here we will do concreting process at the distance 13 m also from Pier-B.

So, we have completed concreting process 13 m from Pier-A & 13 m from Pier-B (total 13 m+13 m=26 m), other 12 m (38 m-26 m=12 m) in between is not be filled up yet by concrete. Now when we re-back to start our concreting process at the last 12 m space then the new concrete pour will go to create a bond with the concrete which we have already concreted (26 m). The concreting process which is already completed (13 m from Pier-A & 13 m from Pier-B) going to be hardened and already become hard than new concrete pour (12 m space). Here bonding between the new concrete pour and old concrete pour not be happened properly and create a weak point as a joint which we have called “Cold Joint”.

Actually Cold Joint is not acceptable in case of any concreting process. Any Engineer does not like/appreciate Cold Joint, but in some situation Cold Joint is performed where we can’t do anything.

For Example, in this situation (Figure-02), we have nothing to avoid Cold Joint because,

        ---This is a span with long length so that we could not continue concreting process simultaneously,

       ---There is a slope so that we could not pour the concrete continuously, because concrete is in liquid state which behaves like water and want to go downward automatically during concreting time, so quality can’t be maintained properly, so that we have a distance limitation.

        ---Here, It will be helpful for us to do concreting process at last 12 m space because concreting at the other two sides (Pier-A & Pier-B) have already done & it become hardened during the last casting process at last 12 m space, so that concrete could not go anywhere from its own place.

Different types of Cold Joint:

Cold Joint can be forms in concrete in Vertical & Horizontal both direction also,

Figure-03 indicates Vertical Cold Joint forms in concrete,

Figure-03: Vertical Cold Joint

Figure-04 indicates Horizontal Cold Joint forms in concrete,

Figure-04: Horizontal Cold Joint

How can we avoid Vertical and Horizontal Cold Joint:

Assume that any foundation contractor is not able to pour all of the concrete for a foundation at once, leaving vertical and horizontal cold joints. They can prepare the surface of the concrete after the first pour by,

By using epoxy bonding agents named Anti-Hydro mixtures:

---They can use a concrete additive called Anti-Hydro. It’s available in one-gallon jugs and five-gallon cans at most builder supply stores for about $13 per gallon. Mix one part Anti-Hydro to three parts clean water, and add enough fresh (not old, lumpy, or partially hydrated) Type I Portland cement to make a thick, rich slurry, or "Slush Coat." Apply this mixture liberally with a stiff brush to the clean cold joint immediately before you pour. If they are on a big pour and the slurry has started to set up by the time they get to it, just brush on more. This will result in a strong, continuous bond.

---Anti-Hydro increases the percentage of hydration in concrete without affecting its chemical composition, resulting in a denser, harder, stronger, and more waterproof material. It also accelerates the rate of hydration, so it has many uses with all Portland cement-based products.

---There are also many different Epoxy Bonding Agents available from a variety of manufacturers (including Anti-Hydro). The better quality epoxies are expensive, but are supposed to provide a joint at least as strong as the concrete.

By using Extra Reinforcement method:

If anyone have extra reinforcement that extends out of the cold joint 30 to 40 bar diameters (at least 15 inches for #4 bar, 19 inches for #5 bar), he can tie in the rest of this re-bar and continue the pour.

What an Civil Engineer will do to avoid Cold Joint at present instantly in the construction field:

Any Civil Engineer do not like cold joint, but Cold Joint happens. If engineer know they have got another one coming in the construction field, here are several things they can do,

---Try to avoid cold joints in the middle of the wall, where the loads are high.

---Let the re-bar run 2 to 3 feet out of the concrete at the joint so you can tie into it when you continue the pour.

---If there is not already re-bar in place where an engineer stop the pour, put some in before the concrete begins to set.

To Be Continued...... ...... ...... ...... ...... ......