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Crack Control of R.C. Slabs Using Simplified Rules

Cracking is the partial or complete separation of a section into two or more parts as a result of fracture. In concrete sections, cracking occurs when the tensile stress exceeds the tensile strength of the concrete. Due to the inherent weakness of concrete in tension, it is bound to crack easily and more often than not, steel reinforcements are used for crack control.

Cracking can occur in concrete in a plastic or hardened state. Autogenous shrinkage, differential settlement, drying shrinkage, thermal stresses, chemical reactions, imposed restraints, corrosion of reinforcement, poor construction techniques, construction overloads, errors in design and detailing, and externally applied loads are all potential causes of cracking in concrete.

Cracking is considered a serviceability limit state problem in reinforced concrete design. Reinforced concrete slabs are prone to cracking because they are predominantly subjected to flexural stresses. Therefore, crack control using reinforcements is very important in the design of reinforced concrete slabs. The serviceability limit states covered by Eurocode 2 are;

– Stress limitation (section 7.2)
– crack control (section 7.3) and
deflection control (section 7.4)

According to clause 7.3.1 of EN 1992-1-1:2004, the general considerations in the control of cracking in a building are as follows;

  • (1)P Cracking shall be limited to an extent that will not impair the proper functioning or durability of the structure or cause its appearance to be unacceptable.
  • (2) Cracking is normal in reinforced concrete structures subject to bending, shear, torsion or tension resulting from either direct loading or restraint or imposed deformations.
  • (3) Cracks may also arise from other causes such as plastic shrinkage or expansive chemical reactions within the hardened concrete. Such cracks may be unacceptably large but their avoidance and control lie outside the scope of this Section.
  • (4) Cracks may be permitted to form without any attempt to control their width, provided they do not impair the functioning of the structure.
  • (5) A limiting calculated crack width, wmax, taking into account the proposed function and nature of the structure and the costs of limiting cracking, should be established.

In Eurocode 2 cracking is controlled in the following ways:

Minimum areas of reinforcement Cl 7.3.2 & Exp (7.1)
• Limiting crack widths.

wkmax is determined from Table 7.1N (in the UK from Table NA.4)

These limits can be met by either:
– ‘deemed to satisfy’ rules (Cl. 7.3.3)
– direct calculation (Cl. 7.3.4) – design crack width is wk
Note: slabs ≤ 200 mm depth are okay if As,min is provided.

A little consideration will however show that the deemed to satisfy rules are more handy and applicable for all design purposes. A solved example on application of deemed to satisfy rules is presented in this post.

Worked Example on the Crack Control of RC Slab

Let us consider a simply supported slab in a proposed office building. The thickness of the slab is 150 mm, and the dead load on the slab gk = 5.6 kN/m2, and the live load qk is 3 kN/m2. The area of steel required is 698 mm2/m, and the area of steel provided is 753 mm2/m. (T12@150mm). Verify if the slab meets the cracking requirement according to Eurocode 2 limiting the crack width to 0.3mm.

Solution

In order to use Tables 7.2N or 7.3N of EC2, we need to determine the service stress in the bars by;

Service stress/Ultimate stress = [(Gk + ψ2Qk,1)/(γGGk + γQQk,1)] × (1/δ)
ψ2 = 0.3 (see the table below for combination factors)

Actionψ0ψ1ψ2
Category A: domestic, residential 0.70.50.3
Category B: office area0.70.50.3
Category C: congregation areas0.70.50.6
Category D: shopping area0.70.70.6
Category E: storage areas1.00.90.8
Category F: traffic area, ≤ 30 kN0.70.70.6
Category G: office area, 30 – 160 kN0.70.50.3
Category H: roofs00
Snow load: H ≤ 1000m a.s.l.0.50.20
Wind loads on buildings0.50.20

γG = 1.35
δ = 1.0
Service stress/Ultimate stress = (5.6 + 0.3 × 3)/(1.35 × 5.6 + 1.5 × 3) = 0.5389

The stress in the reinforcement under quasi-permanent loading is given by;
σs = 0.5389 × 0.87fyk × (As,req / As,prov) = 0.5389 × 0.87 × 460 × (698/753) = 199.94 Mpa

From Tables 7.2 and 7.3 of EC2;

crack%2Bcontrol

From table, maximum bar size = 25 mm
Maximum bar spacing = 250 mm

Therefore the size of the reinforcement spacing of the rebars is sufficient to limit the cracking of the slab to 0.3 mm.

Thank you for visiting Structville today.


Question of the Day (01/06/2018)

QUESTION%2BOF%2BTHE%2BDAY%2B3


Structville daily questions
From now henceforth, Structville will be publishing daily questions on different aspects of civil engineering. You are expected to enter your response in the comment section. At the end of every week, exceptional participants will stand a chance to win some gifts. This exercise is open to participants all over the world. Happy new month to you all.


Today’s Question
What is the deflection at point 2 of a structure if diagram (a) is the bending moment due to externally applied load, and (b) is the bending moment due to vertically applied virtual load at point 2? (The main bending moment diagram is obtained from equation of the form, wl2/2)

Thank you for participating in exercise today, remember to enter your answer in the comment section. The main aim of this exercise to stimulate knowledge of structural analysis on the internet in a fun and exciting way. We are always happy to hear from you, so kindly let us know how you feel about Structville.

E-mail: info@structville.com
WhatsApp: +2347053638996

You can also visit Structville Research for downloads of civil engineering materials.

STRUCTVILLE REINFORCED CONCRETE DESIGN MANUAL
We have this very affordable design manual available…

final%2Bfront%2Bcover

Do you want to preview the book, click PREVIEW
To download full textbook, click HERE

Question of the Day (30/05/2018)

question%2Bof%2Bthe%2Bday%2B2


Structville daily questions
From now henceforth, Structville will be publishing daily questions on different aspects of civil engineering. You are expected to enter your response in the comment section. At the end of every week, exceptional participants will stand a chance to win some gifts. This exercise is open to participants all over the world.


Today’s Question
For the  frame loaded as shown above, which of the options is the most likely bending moment diagram considering linear elastic response.

Thank you for participating in exercise today, remember to enter your answer in the comment section. The main aim of this exercise to stimulate knowledge of structural analysis on the internet in a fun and exciting way. We are always happy to hear from you, so kindly let us know how you feel about Structville.

E-mail: info@structville.com
WhatsApp: +2347053638996

You can also visit Structville Research for downloads of civil engineering materials.

STRUCTVILLE REINFORCED CONCRETE DESIGN MANUAL
We have this very affordable design manual available…

final%2Bfront%2Bcover

Do you want to preview the book, click PREVIEW
To download full textbook, click HERE

Problems of Civil Engineering Consultancy in Nigeria

The wealth creation cycle in construction industry revolves around the political climate, economy, government policies, availability of resources, technology, and skilled manpower. Thousands of engineering graduates leave school in Nigeria each year, and the job opportunities are getting leaner by the day. If I may say, this trend is worse in structural engineering consultancy sector in Nigeria.


In Nigeria currently, construction and real estate companies are recruiting more civil engineering graduates than any other sector. The consultancy sector has been stagnant in terms of job creation recently.  There are a lot of explanations to this trend, and the idea is to keep fresh graduates abreast of the current position of the industry.

Current challenges of the consultancy sector;

(1) Inadequate Regulation
In the classroom, there appears to be a scale of fees for professionals in a building project, but out there in the field, there seems to be no professional standard. For instance in the structural design of buildings, it is not very clear whether we charge on the basis of number of floors, or area of  the building, or a percentage of the estimated total cost of the building. It appears every organisation has its own way of charging for designs in order to balance their book.

Also fresh graduates and students who have acquired design skills do not hesitate in collecting design jobs directly from architects and clients. With all these challenges of no basic control, the consultancy sector has become a haven of negotiation and bargaining power, instead of professional standard. However, it is important to point out that a few Grade ‘A’ consultancy firms still maintain their standards, and those who need them knows where to find them.

(2) Availability of Design Softwares
The availability of commercial softwares have improved speed, accuracy, and output of many consultancy firms. The negative aspect of it is that the demand for man power has significantly reduced. If a consultancy firm lands one design job per month, then they can comfortably make do with just one design engineer depending on the complexity of the jobs. With these softwares guaranteeing speed in output, engineers spend less time in generating working drawings and documents, thereby making organisations realise that they need fewer hands.


(3) In-house Designs
In order to save cost, most construction and real estate companies have resolved to carrying out their designs in-house by employing the services of a structural engineer. As a result of this, fewer jobs get to real consultancy firms, and the sector continues to suffer.

(4) Crowded Industry
The built environment sector in Nigeria is currently crowded with a lot of professionals offering the same services. In our society today, civil engineers are building, builders are building, architects are building, masons are building, and even quantity surveyors are building. In this case, anyone can easily obtain their working drawings from any source at the cheapest rate, work hard on obtaining COREN stamp, and all the way the building goes. If this issue is notaddressed, the consultancy sector will continue to suffer. This has led to many certified professionals into mediocrity in the bid to survive.

civil

(5) Lack of research and creativity
The conventional system of building in Nigeria has remained largely the same over a long period of time. The advances that have been made in materials science and technology rarely reflects in the construction projects executed in Nigeria. Innovation and creativity is what drives any industry, and if there are no new trends, we will remain stuck where we are. Engineers are encouraged to continue exploits in the areas of adaptation, research, sustainability, cost reduction, and improved technology. This is one of the ways consultancy can be revitalised.

(6) Insignificant Public Private Partnership (PPP)
In Nigeria, the construction industry is still largely financed by public funds, apart from the real estate sector that can be said to be shared equally. So for the industry to thrive, there is need for more public Private Partnership (PPP) initiatives to drive the industry forward. It is obvious the government cannot no longer do it alone due to huge capital requirements. This will have significant impact in the consultancy sector.

Eko Atlantic Nigeria1

Finally, I wish to encourage engineers to keep up the acts of hard work and professionalism in all their endeavours. Positive entrepreneurship geared towards service to humanity, research, development, sustainability, and enterprise is highly encouraged. Footprints on the sands of time are not made by sitting down. Nigeria is ours… God bless.


On the Bearing Capacity of Shallow Foundations

Bearing capacity is the maximum load a soil profile can withstand before undergoing excessive deformation and shear failure. It is the most popular and perhaps the most important information needed for the design of shallow foundations. The allowable bearing capacity of soil is used for the proper sizing of shallow foundations so that the load from the superstructure will not exceed the strength of the soil or lead to an excessive settlement.

If a load is applied gradually to a foundation, the settlement will increase. At a certain point when the load equals the bearing capacity of the soil, sudden failure of the soil supporting the foundation will take place. This sudden failure in which the failure surface will extend into the ground is known as ‘general shear failure‘.

When the soil supporting the foundation is of sand or clay soil of medium compaction, the failure surface of the soil will gradually extend outward from the foundation. When the applied load reaches the bearing capacity of the soil, the foundation movement will be accompanied by sudden jerks, and considerable movement will be required before the failure surface extends into the ground. This is generally referred to as ‘local shear failure‘, and the peak value of the load is not realised in this type of failure.

If the foundation is founded on loose soil, the failure surface will not extend into the ground surface. The load-settlement plot of this interaction will be steep and practically linear. Such failure is referred to as ‘punching shear failure‘.

types of foundation failure
Different types of bearing capacity failure

The methods of determining the ultimate bearing capacity of soils are;

  • General shear failure theory of Terzaghi
  • Theoretical solutions presented by Meyerhof, Hansen, and Vesic
  • Correlations from in-situ tests such as PLT, SPT, and CPT

Information needed for the evaluation of the bearing capacity of soil is obtained from site investigation. Laboratory study of undisturbed samples or in-situ soil tests can be done in order to obtain the shear strength parameters needed for the evaluation of the bearing capacity. Several correlations exist for relating in-situ soil properties from cone penetration test to bearing capacity of the soil.

Soil investigation is therefore one of the most important activities that must be carried out before the commencement of any construction project. In the soil test report, the geotechnical engineer is expected to state the strength of the soil at different layers, and ultimately recommend a suitable foundation. Some of the parameters used in describing the strength of a soil formation for the purposes of estimating the soil bearing capacity are the cohesion and the angle of internal friction of the soil.

In this article, we are going to present an example of how to determine the bearing capacity of soil using the general bearing capacity equation.

Background to the bearing capacity of shallow foundations

Terzaghi in 1943 extended the plastic failure theory of Prandtl to evaluate the bearing capacity for shallow strip footings. After the development of Terzaghi’s bearing capacity equation, several scholars such as Meyerhof (1951 and 1963), Vesic (1973), Hansen (1970), etc worked on this area and refined the solution to what is known as the general bearing capacity equation. This modification allowed for depth factor, shape factor, and inclination factors.

The modified general ultimate bearing capacity equation can be written as;

qu = c’FcsFcdFciNc + qFqsFqdFqiNq + 0.5FγsFγdFγiγBNγ

Where;
Fcs, Fqs, Fγs are shape factors which account for the shearing resistance developed along the surface in soil above the base of the footing
Fcd, Fqd, Fγd are depth factors to determine the bearing capacity of rectangular and circular footings
Fci, Fqi, Fγi are inclination factors to determine the bearing capacity of a footing on which the direction of load application is inclined at a certain angle to the vertical

Solved Example on the determination of bearing capacity

Let us determine the bearing capacity of a simple pad foundation with the following data;

Bearing capacity of shallow foundations

Depth of foundation Df = 0.9 m
Width of foundation B = 1.0 m
Effective cohesion of soil c’ = 12 kN/m2
Angle of internal friction φ’ = 27°
Unit weight of soil = 18.5 kN/m3

The water table is about 9 m below the surface

From table, we can determine the bearing capacity factors;

rtty
Bearing capacity factors culled from Das and Sobhan (2012)

Angle of internal friction φ’ = 27°
Nc = 23.94; Nq = 13.20; Nγ = 14.47

Fcs = 1 + (B/L)(Nq /Nc) = 1 + (1.0/1.0)(13.2/23.94) = 1.551
Fqs = 1 + (B/L)tanφ’  = 1 + (1.0/1.0)tan 27 = 1.509
Fγs = 1 + 0.4(B/L)  = 1 + 0.4(1.0/1.0) = 1.4

Fcd = 1 + 0.4(Df/B)  = 1 + 0.4(0.9/1.0) = 1.36
Fqd = 1 + 2tanφ'(1 – sin φ’)2(Df/B)  = 1 + 2tan27(1 – sin 27)2 (0.9/1.0) = 1.273
Fγd = 1.0

Since we are assuming vertical loads, take Fci = Fqi = Fγi = 1.0

q = (18.5 kN/m3 × 0.9 m) = 16.65 kN/m2

qu = c’FcsFcdFciNc + qFqsFqdFqiNq + 0.5FγsFγdFγiγBNγ
qu = (12 × 23.94 × 1.551 × 1.36 × 1.0) + (16.65 × 1.509 × 1.273 × 1.0 × 13.20) + (0.5 × 1.4 × 1.0 × 1.0 × 18.5 × 1.0 × 14.47) = 1215.55 kN/m2

Using a factor of safety (FOS) of 3.0
qallowable = qu /FOS = 1215.55/3.0 = 405.183 kN/m2

So with this, the allowable bearing capacity of the soil can be stated as 405 kN/m2

Question of the Day

Structville daily questions
From now henceforth, Structville will be publishing daily questions on different aspects of civil engineering. You are expected to enter your response in the comment section. At the end of every week, exceptional participants will stand a chance to win some gifts. This exercise is open to participants all over the world.


Today’s Question
For the compound frame loaded as shown above, find the bending moment just below point B under the action of the externally applied load. Assume linear elastic response.

Thank you for participating in exercise today, remember to enter your answer in the comment section. The main aim of this exercise to stimulate knowledge of structural analysis on the internet in a fun and exciting way. We are always happy to hear from you, so kindly let us know how you feel about Structville.

E-mail: info@structville.com
WhatsApp: +2347053638996

You can also visit Structville Research for downloads of civil engineering materials.

STRUCTVILLE REINFORCED CONCRETE DESIGN MANUAL
We have this very affordable design manual available…

final%2Bfront%2Bcover

Do you want to preview the book, click PREVIEW
To download full textbook, click HERE

Solution to Questions of the Week (4th week, May, 2018) and Winners

SOLUTIONS

Earlier this week, I started the daily questions program on Structville and I am happy for the kind of the reception the program has received. We are going to summarise the all questions asked last week, provide solution to the questions, and recognise those who participated.


Wednesday 23 May, 2018
We were asked to determine the equation that the two beams shown below have in common in their final state. The question has the conditions of assuming linear elastic response.

Structville%2BQuestion%2BChallenge

Solution
We can see that the difference in the beams is based on their support conditions. The first beam is simply supported, while the second beam is fully fixed at the supports. Under the action of the externally applied uniformly distributed load, the simply supported beam develops a maximum sagging moment of wL2/8 which occurs at the mid-span. However, the shear force at the support remains wL/2.

In the free state, the second beam develops a maximum sagging moment of wL2/8 which occurs at the mid-span, and a hogging fixed end moment of wL2/12 which occurs at the support. Now in the final state (combining free moment and fixed end moment), the maximum sagging moment becomes  wL2/8 wL2/12 = wL2/24 (at the midspan). But the shear force remains wL/2. So the correct answer is D.

Those who got the answer correct are:

  • Ogungbire Adedolapo
  • Palo Tuleja
  • Nitesh Mithapelli

Thursday, 24 May, 2018
We were required to determine the support reaction and bending moment at support C of the compound beam loaded as shown below;

STRUCTVILLE%2BCHALLENGE%2B2

Bending Moment at Support C
The bending moment at support C can be expressly determined by considering the cantilever moment from the concentrated load at the free end of the overhang.

MCR = -2 kN × 2m = -4 kN.m


Support Reaction at Support C
There are two easy ways of obtaining the vertical reaction at support C.
Since the values of the reaction at A and B are already given, we can easily sum up the vertical forces. (upward forces positive, downward forces negative)

Hence
 -2 – (6 × 4) – 2 + 1 + 34.6 – Cy = 0
Cy – 7.6 = 0
Cy = 7.6 kN (downwards)

On the other hand, we can take moment about point G just to the left. But Structville question is designed so that very simple approaches can be used to obtain the answers. So the correct answer is C.

The people that got the answers correct are as follows:

  • Ogungbire Adedolapo
  • Ovie Agbaga
  • Theodoros Gianneas
  • Subramanian Narayanan
  • Peter O.

Friday 25 May, 2018
In this one, we are required to obtain the bending moment just to the left of point E and the horizontal support reaction at support B.

QUESTION%2BOF%2BTHE%2BDAY%2BFRAME

To obtain the moment just to the left of node E, we have to carry out a very simple calculation. The support reaction at support A has already been provided.

Hence;
MGL = (2 × 4) – (2 × 42)/2 = – 8kNm
This is just as simple as that.


The horizontal support reaction can be readily obtained by summing up the horizontal forces. All forces pointing towards the right are taken as positive, while forces pointing towards the left is taken as negative.

Therefore;
4 kN – 7 kN + 4.875 kN – Bx = 0
1.875kN – Bx = 0
Bx = 1.875 kN

Therefore the correct answer is C.

The people that got the answer correct are;

  • Thaddeus Odinakachi Ekwugha
  • Ogungbire Adedolapo
Winner(s)
From the rules of the exercise, the winner for this week is Ogungbire Adedolapo (he got all three correct !!!). Mr. Adedolapo will receive special academic materials from Structville, and also, we will give him a one month data subscription for any network of his choice. Well done Mr. Adedolapo, and to all others who participated in the exercise. From my own point of view, this is neither a competition nor an exam, but just a way of teaching, learning, and discussing civil engineering on the internet.

My sincere appreciation also goes to all the people who commented on various social platforms. However for your response to be recognised specially, you must post it on this blog. Some people also commented on the blog anonymously. Thank you so much for your contributions. Let us look forward to this weeks questions. God bless.


Structville Question of the Day

QUESTION%2BOF%2BTHE%2BDAY%2BFRAME

Structville daily questions
From now henceforth, Structville will be publishing daily questions on different aspects of civil engineering. You are expected to enter your response in the comment section. At the end of every week, exceptional participants will stand a chance to win some gifts. This exercise is open to participants all over the world.


Today’s Question
For the compound frame loaded as shown above, find the bending moment just to the left of point E and the horizontal support reaction at support B assuming linear elastic response.

Thank you for participating in exercise today, remember to enter your answer in the comment section. The main aim of this exercise to stimulate knowledge of structural analysis on the internet in a fun and exciting way. We are always happy to hear from you, so kindly let us know how you feel about Structville.

E-mail: info@structville.com
WhatsApp: +2347053638996

You can also visit Structville Research for downloads of civil engineering materials.

STRUCTVILLE REINFORCED CONCRETE DESIGN MANUAL
We have this very affordable design manual available…

final%2Bfront%2Bcover

Do you want to preview the book, click PREVIEW
To download full textbook, click HERE

Design of Large Span Cantilever Structures

Large span cantilevers are delightful to everyone, but very challenging to engineers during design. This is because the engineer is battling with a lot of design factors, and he must guaranty the stability and good performance of the structure.

The most prominent issues in the design of reinforced concrete cantilever structures are;
(1) Excessive deflection and
(2) Balance of moment for stability

In this post, I am going to comment on some common design solutions to large span cantilevers. The simplest solutions are discussed below;

long%2Bspan%2Bcantilever

(1) Controlling deflection
For relatively shorter spans (say less than 1.5m), increasing the depth of the section or increasing the quantity of steel reinforcement looks like an express solution without very serious consequences. However as the span of the cantilever increases, increasing the depth will increase the design load and add to the design challenges. You may have to increase the compressive strength of the concrete (employing high strength concrete), and heavily reinforce the tension and compression zones of the section to assist in resisting deflection. On the other hand, you can try prestressing, and if your architect permits, the use of trusses to support the cantilever will provide a very fast and simple solution.


Furthermore, forming a web kind of design (like introducing grids) will improve the load distribution on the members, offer higher resistance, and ultimately bring about shallower sections. This is one of the most efficient ways of dealing with large span cantilevers. For improved aesthetics, the web can be adequately covered with finishes to make the whole arrangement look like one single section. See the example below where the use of multiple members have been used to approach a relatively large span cantilever problem.

IMG 20180508 092446

(2) Balance of moment for stability
For cantilever structures to stand, the moment generated at the fixed end must be balanced, otherwise equilibrium problem will ensue. If the cantilever structure has no backspan (discontinuous), then the foundation must be used to provide the balance needed, otherwise the structure will topple (EQU problem).  This also means that the column of the cantilever must be designed to resist heavy moment (STR problem). The exercise below has been presented to give you a little idea of what is being discussed. You can attempt the problem and place your solution in the comment section of this post.

Exercise
For the structure loaded as shown below, proportion the dimensions of base to counteract the moment from externally applied load. (Take width of base = 1.2 m, Unit weight of concrete = 24 kN/m3). Make all other necessary assumptions in your design. 
strucr

On the other hand, if the cantilever has a backspan (continuous), then the bending moment is distributed to all members meeting at that node, and column moment is alleviated to some extent. So we really do not need the base to help provide equilibrium, but the backspan of the structure and interaction with other members provide the balance needed. So we have mainly STR problem. The picture below shows a cantilever with a backspan. However, in some cases, the base will be required to assist in maintaining equilibrium.

back

There is a structural design challenge that is currently ongoing, and some Nigerian civil engineering students are carrying out a design on a structure that has many cantilevers that are spanning as long as 3 meters. We are all looking forward to the solutions that they will come up with. So let us anticipate.

To check out the nature of the competition, click HERE.

56d

Check out this beautiful cantilever structure below. Have you designed long span cantilever structures before? Kindly let us know how you approached it.

FGTTT


Structville Question of the Day (Thursday, 24/05/2018)

STRUCTVILLE%2BCHALLENGE%2B2

Structville daily questions
From now henceforth, Structville will be publishing daily questions on different aspects of civil engineering. You are expected to enter your response in the comment section. At the end of every week, exceptional participants will stand a chance to win some gifts. This exercise is open to participants all over the world.


Today’s Question
For the compound beam loaded as shown above, find the bending moment and support reaction at support C assuming linear elastic response.

Thank you for participating in exercise today, remember to enter your answer in the comment section. The main aim of this exercise to stimulate knowledge of structural analysis on the internet in a fun and exciting way. We are always happy to hear from you, so kindly let us know how you feel about Structville.

E-mail: info@structville.com
WhatsApp: +2347053638996

You can also visit Structville Research for downloads of civil engineering materials.

STRUCTVILLE REINFORCED CONCRETE DESIGN MANUAL
We have this very affordable design manual available…

final%2Bfront%2Bcover

Do you want to preview the book, click PREVIEW
To download full textbook, click HERE