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Definition of Under Reinforced Section And Over Reinforced Section

2019-09-21T09:01:00.000-07:00

Definition of Under Reinforced Section And Over Reinforced Section


Definition of Under Reinforced Section And Over Reinforced Section

Under-Reinforced Beam Section

If less amount of steel used in the section than that of a balance section is called under reinforced section. In such condition the stress the stress in steel will reaches its concrete remain below the permissible stress. Under such condition the beam will fails due to over stress in the steel. The steel provided in the beam is such that steel reach the limiting values of strain prior to concrete. This results in yielding of the steel and the steel could yield till it attains the ultimate strain at which point it breaks. It is important to notice that it is the yielding stain that is considered as failure strain in steel and not the ultimate fracture strain. The steel still has to undergo strain hardening, softening and then fracture. In under reinforced section, the depth of actual Na is less than the critical Na.

i.e.; Na<Nc.

Reinforced concrete beam sections in which the steel reaches yield strain at loads lower than the load at which the concrete reaches failure strain is called under-reinforced sections.

Every singly reinforced beam should be designed as under-reinforced sections because this section gives enough warning before failure.

Yielding of steel in under-reinforced beam section does not mean the structure has failed, as when steel yields, excessive deflection and cracking in beam will occur before failure which gives enough time to occupants to escape before the section fails.

The failure in under-reinforced beam section is due to the concrete reaching its ultimate failure strain of 0.0035 before the steel reaches its failure strain which is much higher 0.20 to 0.25.

Under Reinforced Section And Over Reinforced Section

Over Reinforced Section

Reinforced concrete beam sections in which the failure strain in concrete is reached earlier than the yield strain of steel is reached, are called over-reinforced beam sections.

In an over reinforced section, the percentage of steel provided is greater than the balanced section. So, the actual neutral axis shifts downward i.e., n>n_c. In this section, stress in concrete reaches its permissible value while steel is not fully stressed. Concrete is brittle and it fails by crushing suddenly. As steel is not fully utilized, the over reinforced section is uneconomical (steel is much costlier than concrete). The various features of over reinforced s section are:

(i) Concrete is fully stressed while steel is not (i.e., the stress in concrete is at its permissible value σ_cbc but stress in steel is less than σ_st).

(ii) The actual neutral axis is below the critical neutral axis i.e., n > n_c.

(iii) The percentage of steel is more than the balanced section, so the section is uneconomical.

(iv) Sudden failure.

If more steel used in the section than that of a balance section is called over reinforce section. The steel is not fully stressed to its maximum permissible tensile stress, which the comprehensive stress in concrete at extreme fiber reaches its maximum permissible value in this case the beam will fails initially due to over stress in concrete.So, in over reinforced section, the depth of actual Na is greater than the critical Na.

i.e.; Na > Nc

Xumax Equation: Xumax / 0.0035 = d-xumax / (0.87fy/Es + 0.002),,,

Classifications of Aggregates According to Shape

2019-09-21T00:01:00.000-07:00

Classifications of Aggregates According to Shape

Classification of Aggregates Based on Shape

The practical shapes of aggregates influence the properties of fresh concrete more than those of hardened concrete. Depending upon the particle shape the aggregate may be classified as rounded, irregular or partly rounded, angular or flaky.

We know that aggregate is derived from naturally occurring rocks by blasting or crushing etc., so, it is difficult to attain required shape of aggregate. But, the shape of aggregate will affect the workability of concrete. So, we should take care about the shape of aggregate. This care is not only applicable to parent rock but also to the crushing machine used.

Aggregates are classified according to shape into the following types

Rounded aggregates
Irregular or partly rounded aggregates
Angular aggregates
Flaky aggregates
Elongated aggregates
Flaky and elongated aggregates

Rounded Aggregate

rounded aggregate

The aggregate with rounded particles (river or seashore gravel) has minimum wide ranging from 32 to 33 percent. It gives minimum ratio of surface area to the volume; the requiring minimum cement paste to make good concrete. The only disadvantages that the interlocking between its particles is less and hence the development of the bond is poor, making it unsuitable for high strength concrete and pavement.

Irregular Aggregate

irregular aggregate

The aggregate having partly rounded particles (pitsand and gravel) has higher percentage of voids ranging from 35 to 38. It requires more cement paste for a given workability. The interlocking between particles, through better than that obtained with the rounded aggregate is inadequate for high strength concrete.

Angular Aggregate

angular aggregate

Aggregate with sharp, Angular and rough particles (crushed rock) has a maximum percentage of voids ranging from 30 to 40. The interlocking between the particles is good, thereby providing a good Bond. The aggregate requires more cement paste to make workable concrete of high strength than that required by rounded particles. The angular aggregate is suitable for high strength concrete and pavement subjected to tension.

Flaky and And Elongated Aggregates

Flaky and And Elongated Aggregates

An aggregate termed flaky when its least dimension(thickness) is less than three- fifth of its mean dimension. The mean dimension of aggregate is the average of sieve size through which the particles pass and are retained, respectively. The particle is said to be elongated when it greatest dimension (length) is greater than nine-fifth of its mean dimension.

The angularity of aggregate effects of workability or stability of the mix which depend on the interlocking of the particles. The elongated and flaky particles also adversely affect the durability of concrete as they tend to be oriented in one plane with water and air wire forming underneath. The presence of these particles should be restricted to 10 to 15%. This requirement is particularly important for or crushed fine aggregate since the material made this content flatter and more elongated particle. The angularity of the aggregate can be estimated from the proportion of voids in a sample compacted as prescribed in IS: 2386(part-1)-1963. The higher the angularity number the more angular is the aggregate. The elongation index of an aggregate is defined as the percentage by weight of particles present in whose greatest dimension(length) is greater than nine-fifth of their mean dimension.

Classification of Aggregates According to Size

2019-09-20T21:31:00.000-07:00

Classification of Aggregates as per Size

What is an Aggregate?

Aggregates are the important constituents of the concrete which give body to the concrete and also reduce shrinkage. Aggregates occupy 70 to 80 % of total volume of concrete. So, we can say that one should know definitely about the aggregates in depth to study more about concrete. The size of aggregates used in concrete range from few or more down to a few microns. The maximum size of the aggregate may vary, but in each case, it is to be so graded that the particles of different size fractions are incorporated in the mix in appropriate proportions. The particle size distribution is called the grading of the aggregate according to size the aggregate is classified as: fine aggregate, coarse aggregate and all in aggregate.

aggregate

Fine Aggregate :-

It is the aggregate most of which passes through a 4.75 mm IS and contains only that much coarser material as is permitted by the specification sand is generally considered to have a lower size limit of about 0.07 mm. Material between 0.06 mm and 0.002 mm is classified as silt, and still smaller particles are called clay. The soft Deposit consisting of sand silt, clay in about equal proportions is termed loam. The fine aggregate may be one of the following types:

1) natural sand that is the fine aggregate resulting from natural disintegration of Rock and for that which has been deposited by stream and glacial agencies,

2) crushed stone sand that is the fine aggregate produced by crushing hard stone or

3) craft Travels and that is the fine aggregate produced by crushing natural gravel.

According to size, the aggregate may be described as coarse, medium and fine sands. Depending upon the particle size distribution IS: 383-1970 has divided the fine aggregate into four grading zones. The grading zones become progressively finer from grading zone 1 grading zone 4.


fine aggregate

Fine aggregate	Size variation
Coarse Sand	2.0mm – 0.5mm
Medium sand	0.5mm – 0.25mm
Fine sand	0.25mm – 0.06mm
Silt	0.06mm – 0.002mm
Clay	<0.002

Coarse Aggregate:-

Aggregates most of which are written on the 4.75 mm IS sieve and content only that much of fine materials as is permitted by the specification are termed coarse aggregates. The coarse aggregate may be one of the following types;

1) crushed gravel for stone obtained by the crushing of gravel for hard stone,

2) uncrushed gravel or stone resulting from the natural disintegration of rock, or

3) partially crossed gravel or stone obtained as a product of the bleeding of the above two types.

The graded coarse aggregate is described by its nominal size, i.e. 40 mm, 20 mm,16 mm, and 12.5 mm, etc. For example, a graded aggregate of nominal size 12.5 mm means and aggregate most of which passes the 12.5 mm IS sieve. Since the aggregates are formed due to natural disintegration of rocks or by the artificial crushing of rock
or gravel, they derive many of their properties from the parent rocks. These properties are chemical and mineral composition, petrographic description, specific gravity, hardness, strength, physical and chemical stability, pore structure, and color. Some other properties of the aggregates not possessed by the parent rock are particle shape and size, surface structure, absorption, etc. All these properties may have a considerable effect on the quality of concrete in fresh and hardened states.

coarse aggregate

Coarse aggregate	Size
Fine gravel	4mm – 8mm
Medium gravel	8mm – 16mm
Coarse gravel	16mm – 64mm
Cobbles	64mm – 256mm
Boulders	>256mm

All-in-aggregate:-

Sometimes combined aggregates are available in nature comprising different fraction of fine and coarse aggregates, which are known as all-in-aggregate. In such cases adjustments often become necessary to supplement the grading by addition of respective size fraction which may be deficient in the aggregate. Like coarse aggregate, the all-in-aggregate is also described by its nominal size. The all-in-aggregates are not generally used for making high quality concrete.

Single-Size-Aggregate:-

Aggregates comprising particles falling essentially within a narrow limit of size fraction are called single-size-aggregates. For example, a 20 mm single- size-aggregate means in aggregate most of which passes through a 20 mm IS sieve and the major portion of which is retained in a 10 mm IS sieve.

Definition of Shear Force And Bending Moment

2019-09-04T11:33:00.004-07:00

Definition of Shear Force And Bending Moment

shear and moment

Image:-Google

SHEAR FORCE:-The shear force (briefly written as S.F.) at the cross-section of a beam may be defined as the algebraic sum of all the forces on either side of the section.

Shear stress
Common symbols	$τ$
SI unit	pascal
Derivations from other quantities	$τ = F / A$


A shearing force is applied to the top of the rectangle while the bottom is held in place

BENDING MOMENT:-The bending moment (briefly written as B.M.) at the cross-section of a beam may be define as the algebraic sum of the forces on either side of the section.A bending moment is the reaction induced in a structural element when an external force or moment is applied to the element causing the element to bend.The most common or simplest structural element subjected to bending moments is the beam.

computing the bending moment in a beam

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How do I design isolated rectangular footing as per practical considerations?

2019-09-04T10:33:00.000-07:00

How do I design isolated rectangular footing as per practical considerations?

footing

DEFINITION:-

A concrete support under a foundation that rests in solid ground and is wider than the structure supported. Footings distribute the weight of the structure over the ground. A footing or a shallow foundation is placed immediately below the lowest part of the superstructure.Foundation may be broadly classified under two heads :shallow foundation and Deep foundation .According to Terzaghi, a foundation is shallow if it is depth is equal to or less than its width. In the case of deep foundations, the depth is equal to or greater than the width. Apart from deep strip, rectangular or square foundations, other common forms of deep foundations are : pier foundation,pile foundation and well foundation. The shallow foundations are of the following types: spread footing (or simply, footing), strap footing,combined footing, and mat or raft footing.

Types of Isolated footing:-

(i) Pad footing

(ii) Stepped footing

(iii) Sloped footing

Shapes of Isolated footing:-

(i) Square footing

(ii) Rectangular footing

(iii) Circular footing.

Image:- www.chegg.com

CALCULATION OF FOOTING SIZE:-

Ø Footing Size Calculation of Column :

Axial load of column = 635.74 kn
Considering 10% additional load including in the footing = 635.747 x 1.1 = 699.321 kn.
Bearing capacity of soil = 120 kn/m2
So, Area of footing = 699.321 / 120 = 5.827 m2
Let, The ratio of B to L = 250/400 = 5/8
Now, (5/8L) x L = 5.827 or, L=3m & B = 2m

1.DESIGN CONSTANT:

For M20 concrete and Fe 415 steel,
xu,max/d = 0.479 ; Ru = 2.716

2. CALCULATION OF FOOTING SIZE:

Load in column W=635.74kN Let would be equal to 10% w=63.574Kn
Taking bearing capacity of soil 120 kn/m2
So, area of footing=(635.74+63.574)/120 m2=5.83 m2
Let ratio of B to L=25/40=5/8
So, 5/8L*L=5.83 or L=3m and B=2m
Now net upward pressure Po=635.74/(2*3)=106kN/m2

3. DESIGN OF SECTION:

Bending moment M1 about section X-X is
M1 = {(P0*B)*(L-a) 2}/8 = {(106*2)*(3.0-0.4)2}/8 =179.14 kn-m=179.14*106 N-mm
M1u = 1.5M1 = 1.5*179.14*106 = 268.71*106 N-mm
So, d=√ (M1u/Ru*B) =√ {268.71*106/ (2.716*2000)} =222.41mm =225 mm
Keep d=225 mm and total depth = 291 mm,
Providing uniform thickness for the entire footing.
Now bending moment about section Y-Y is
M2 = {(P0*L)*(B-b)2}/8 ={(106*3)*(2.0-0.25)2}/8 *106 N-mm =121.73*106 N-mm
M2u = 1.5*M2 m= 1.5*121.73*106 = 182.6*106 N-mm
Thus, M2u<M1u so effective depth found above has to be checked for shear.

4. CHECK FOR SHEAR:

Ø Depth on the basis of one way shear
Shear force along section AB is
V=P0B {(L-a)/2-d} =106*2{(3.0-0.4)/2-0.001d}*103 = 212000(1.3-0.001d) N/m
Vu =1.5v = 318000(1.3 – 0.001d) N/m
τ
v
=Vu/Bd =318000(1.3 – 0.001d) /2000d =159(1.3-0.001d)/d N/mm2
Assuming under reinforced section with P=0.3%, we get τ
c
=0.384 N/mm2 and for M20 concrete also k=1 So Permissible shear stress = 1* 0.384 = 0.384 N/mm2
Equating this to the equation we get
0.384 = 159(1.3-0.001d)/d from which d = 380 mm
For the two way action or punching shear action along ABCD
Perimeter ABCD =2{(a + d) + (b + d)} = 2{(0.4+0.38) + (0.25+0.38)} = 2.82m = 2820 mm
Area ABCD = {(a + d) + (b + d)} = {(0.4+0.38)*(0.25+0.38)} = 0.4914 m2
So, punching shear = 1.5*106*[(2*3)-0.4914] = 875.87 kn
τ
v
={(875.87*1000)/(2820*380)} = 0.817 N/mm2
Allowable shear stress τ
c
is
τ
c
= 0.25√fck = 0.25√20 = 1.118 N/mm2
Ks = {0.5+ (o.25/0.4)} = 1.125 however adopt maximum Ks =1
So, ksτ
c
= 1*1.118 = 1.118 N/mm2
This is more than τ
v
= 0.817 N/mm2 Hence safe from punching shear
Now taking depth = 450 mm so, d= (450-60-6) = 384mm providing effective cover = 60 mm in one direction and other direction d = (384-12) =372 mm using 12 mm Ф bar.

5. DESIGN FOR REINFORCEMENT:

Area Ast1 of long bars calculated for moment M1u is
Ast1 = (0.5fck/fy)[1-√{1-(4.6M1u/fckBd12)}]Bd1
= (0.5*20/415)[1-√{1-(4.6*268.71*106/20*2000*3842)}]*2000*384
= 2052.98 mm2
Hence number of 12mm Ф bars = [2052.98/ (π/4)122] = 18 no.
The area Ast2 of short bars calculated for M2u is
Ast2 =(0.5fck/fy)[1-√{1-(4.6M2u/fckLd22)}]Ld2
=(0.5*20/415)[1-√{1-(4.6*182.6*106/20*2000*3722)}]*2000*372
=1396.47 mm2
Ø Hence number of 12mm Ф bars = [1396.47/ (π/4)122] = 12 no.

6. CHECK FOR DEVELOPMENT LENGTH:

Development length Ld = 47 = 564 mm
Providing 60 mm side cover, length available ½[B-b]-60 = ½[2000-250] =815 mm
This is greater than Ld.
Hence it is OK.

Design of isolated footing

What Is Bar Bending Schedule?

2019-09-02T09:09:00.001-07:00

What Is Ber Bending Schedule?

What is Bar Bending Schedule:-

Bar Bending schedule is commonly referred to as BBS Bar bendingschedule (or schedule of bars) is a list of reinforcement bars, and given rcc work item, and is presented in a tabular form for easy visual reference .We also calculate all materials and making a tables. This tables have all the needed particulars of bars-like no of item, bars. Diameter of bars, no each type of bar, etc. And this table is provide total quantity of bar and this information is a great help in preparing an estimate of quantities.

How to prepare a BBS?

Necessary Columns

· Bar number/Bar Mark Reference

· Bar shape

· Diameter

· Spacing

·         Length of bar

·         Cutting Length

·         Number of bars

NOTE :

Extra bar for L hook= 6ø

For Round hook=9ø

For cranked bar(45®)=0.42d(d=depth of section)

Cranked(30®)=0.27d

Formula:

§ Total length of vertical bar = floor height (1,2,3) + height of ground level + L_d + overlap length.

BAR BENDING SCHEDULE

What is the difference between under reinforced section and over reinforced section?

2019-09-02T00:47:00.002-07:00

What is the difference between under reinforcement section and over reinforcement section?


difference between under and over reinforce section

Under Reinforce Section

i.e.; Na<Nc.

Over Reinforce Section

If more steel used in the section than that of a balance section is called overreinforce section. The steel is not fully stressed to its maximum permissible tensile stress, which the comprehensive stress in concrete at extreme fiber reaches its maximum permissible value in this case the beam will fails initially due to over stress in concrete.So, in over reinforced section, the depth of actual Na is greater than the critical Na.

i.e.; Na > Nc

Xumax Equation: Xumax / 0.0035 = d-xumax / (0.87fy/Es + 0.002),,,

value of Xumax and Mlimit

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Definition of Under Reinforced Section And Over Reinforced Section

Definition of Under Reinforced Section And Over Reinforced Section

Under-Reinforced Beam Section

i.e.; Na<Nc. Reinforced concrete beam sections in which the steel reaches yield strain at loads lower than the load at which the concrete reaches failure strain is called under-reinforced sections.

Over Reinforced Section

Over Reinforced Section

Classifications of Aggregates According to Shape

Classification of Aggregates Based on Shape

The practical shapes of aggregates influence the properties of fresh concrete more than those of hardened concrete. Depending upon the particle shape the aggregate may be classified as rounded, irregular or partly rounded, angular or flaky.

Aggregates are classified according to shape into the following types

Rounded Aggregate

Irregular Aggregate

Angular Aggregate angular aggregate

Flaky and And Elongated Aggregates

Classification of Aggregates According to Size

Classification of Aggregates as per Size

What is an Aggregate?

Fine Aggregate :-

Coarse Aggregate:-

coarse aggregate

Single-Size-Aggregate:-

Aggregates comprising particles falling essentially within a narrow limit of size fraction are called single-size-aggregates. For example, a 20 mm single- size-aggregate means in aggregate most of which passes through a 20 mm IS sieve and the major portion of which is retained in a 10 mm IS sieve.

Definition of Shear Force And Bending Moment

Definition of Shear Force And Bending Moment

Image:-Google

How do I design isolated rectangular footing as per practical considerations?

How do I design isolated rectangular footing as per practical considerations?

DEFINITION:-

Types of Isolated footing:-

Shapes of Isolated footing:-

CALCULATION OF FOOTING SIZE:-

What Is Bar Bending Schedule?

What Is Ber Bending Schedule?

What is Bar Bending Schedule:-

How to prepare a BBS?

Formula:

What is the difference between under reinforced section and over reinforced section?

What is the difference between under reinforcement section and over reinforcement section?

Under Reinforce Section

Over Reinforce Section

i.e.; Na<Nc.

Reinforced concrete beam sections in which the steel reaches yield strain at loads lower than the load at which the concrete reaches failure strain is called under-reinforced sections.

Angular Aggregate

angular aggregate