We have looked into the compressive strength and relevant you know issues related to compressive

strength, in the previous lecture. Now, we should look into other mechanical properties,

and today we shall look into tensile strength, fatigue strength and impact abrasion resistance

of concrete right.

So, tensile strength we will look into first tensile strength of concrete and the general

outline of our discussion today would be tensile strength. Now, we look to tensile strength

in 2 different ways; one is called flexural strength other is split test. We will describe

this and this relationship, with compressive strength that is what we look into. Then individually,

we will look into fatigue strength, impact resistance of concrete and abrasion and bond

strength.

Now, let us see where why do we need at all the tensile strength of concrete, you see

concrete generally we exploit its properties, in such a manner we exploit in such a manner

that we rely mostly on its compressive strength. And list on its tensile strength, because

we know that it is weak in tension. And therefore, we put reinforcement in reinforced concrete

structures or we blister them for that purpose. So, that it can withstand certain amount of

tensile loading however, in some cases we may have to still rely on the tensile strength

of concrete. The examples are for example, we have shrinkage

cracks comes in you know shrinkage cracks to arrest those shrinkage cracks or shear

cracks or differential movement cracks or cracks due to any other reason. So, whenever

such cracks come in to resist such cracking, we have to rely on the tensile strength of

concrete in many cases. Now, there are examples: where these are certain structures are designed

for tensile strength of concrete for example, dam under earthquake excitations, pavement

slabs, airport runways. These are designed on the basis of tensile strength direct or

flexural tensile strength as the case may be.

Therefore, we got to know the tensile strength and it can be seen that tensile strength can

be related to compressive strength, because as we have understood from the failure mechanism

of concrete in compression; after all even in uni axial compression concrete fails in

tension. So, there can be some sort of empirical relationship a correlation might exist between

the 2 and they in fact they, really do exist and we relate it that way.

So, that can be understood from the failure envelope of concrete, you know if you remember

we talked about bi axial testing of concrete. So, when we look into the bi axial. For example:

if this axis shows the tension in a given x direction and this is tension in the y direction,

in other direction bi axial situation we are looking at. This is the compression and this

is also compression right. So, this is the neutral point where there

is no stress this side is a tension this side is a compression. So, if I call this plus

I call this minus. This is the compression tension in the y axis and compression in the

y axis goes along this direction. This gives us the failure enevelope; that means, at this

point when there is only 1 compression it is a combination of load, because I am it

is a bi axial loading situations and failure envelopes shows under bi axial condition how

concrete fails. Now, this 1 would mean; this point would mean

that I have compression along this x axis up to this point and then there is no tension

or compression along the other direction. So, this point presents uni axial compression

and you can see this value is 8k where, k is this value. Now, what does this value represents

this value represents uni axial tensile strength along y direction and this is same as the

uni axial tensile strength along this direction, because here the stress is along x direction

0 whereas, in y direction it is k. So, this envelope represents a failure envelope

when you have combination of tensile and compressive load on both directions; it is a bi axial

situation both the direction; that means, you might have compression along this direction.

In the other direction you might have tension or compression. So, that is the bi axial you

know bi axial situation. For example this is your sample if you have compression. So,

and may be tension along this direction or you might have compression along this direction

or you might have tension. So combinations of this situation.

So, this point represents no tension compression along this direction; however, you have a

pure tension along this direction along this direction. So, uni axial tension and this

value is k this value is also k and this rectangular. In fact, under combination when you have bi

axial tension that is also is you know this is k and k both together fails here. So, if

this is k uni axial compression is eight k. Similarly, along this direction when there

is no stress on the other direction, when there is no stress in x direction only y direction

I have pure compression this is eight k. So, compressive strength is 8 time of 8 times

of tensile strength and therefore, there seems to be a relationship. You know it is 8 times

8 times the compressive strength as shown by this failure envelope study experimental

study. So, there is some relationship between the compressive strength and tensile strength.

This will be further we will look into such relationship.

Now, how do we test for tensile strength how do we test for tensile strength? It is difficult

to measure tensile strength directly, because the specimens you know initially they were

tried like this initially, 1 would you know people have tried breaker test what is called

breaker test. You have you have samples you have samples and like this, samples like this

like mortar concrete breaker test you know and this is the sample this is the sample

would look like this and you will grip this here and grip this here and try to pull. Now,

what would happen in such situation. This gripping was really proper and the failure

would always take place along this direction along the grip itself. You know because of

satisfactory gripping was difficult and therefore, direct tensile strength was difficult to measure.

You know it is quite difficult. So, this test is not now relied upon by any code or any

within, rather indirect methods are used for measurement of tensile strength of concrete.

For example we after all most of the cases, we rely you know tensile strength of concrete

is required possibly under flexure under bending under bending you know if you may recall under

the bending situations, when a beam is loaded you know in some form it bends and the bottom

is under tension. So, when I reinforce concrete bomb beam or

any beam is bending the bottom is under tension and therefore, flexural tension is an important

property that we would like to know. So, one of the ways is to test a beam and this test

is known as modulus of rupture test. We will look into that test in more details

in a short while. A second way to test is through what is known as split tension test

and it is also an indirect. So, there are no direct test there are 2 types of test,

one you call as modulus of rupture test which is nothing but strength in flexure and second

one is split tension test.

Let us see the first 1 first the modulus of rupture test. This is what the it, would look

like you know this is what the modulus of specimen would look like.

For example you will have 2 point loading commonly used is 2 point loading. This is

1 point this is another point and this points are if this length is 3d. This distance is

d as you can see this is d. So, you have 2 roller supports here such that, it is simply

supported and you have the load coming from the top of it a single point through the single

point you know you might be loading it like this using a single point P whereby, it will

get divided to P by 2 and P by 2 again by roller you are ensuring that it is actually

point load. So, this is point load point load and point

support and point support. So, purely simply supported system, with 2 point loading this

is depth is d this is b okay. Usually 10 by 10 you know by 50 centimeter is used in IS

code 10 by 10 by 50 with this being 40 here of course, it could be 4d or 5d. So, this

is about 13 in case of Indian standard situation of IS I mean 16. So, 13 into 13.3 and overall

is 50 meter 50 centimeter is a overall span. So, this is a simply supported these are supporting

rollers supporting rollers. This allows for rotation. So, makes it purely

simply supported there is no restraint here no horizontal reactions will be available

only vertical reactions, P by 2 will be available. So, you can see that P load you know P by

2 P by 2 uniform load is applied here and P by 2 P by 2 reactions would be obtained

here and if you look at its bending movement diagram this will look something like this,

because we are interested in finding out how much will be load carrying capacity right.

So, this is the bending movement diagram as you know, because P by 2 here P by 2 here

the reactions would be P by 2 P by 2 and the bending movement diagram, would look like

this because P by 2 it will be 0 here simply supported system. It will be 0 here because

it is a simply supported system you know it will it will be it will be it will be 0 here,

because it is a simply supported system and as you can see the bending movement maximum

would be P 2 by P 2 into l by 3 because this is P 2 P by 2 and this distance is l by 3.

So, maximum bending movement is P by 2 into l by 3 and same thing from here if you calculate

out. So, maximum bending movement will be P by P l by 6 and how do you find out the

bending stress, you find it out as f equals to M over Z and P l over b d square you know

this is what will come. Because, we know the Z for this section would

be Z for this section would be b d cube by 12 for rectangular section, we are using of

course, b and d in general terms, but usually they are same. So, 10 centimeter, 10 centimeter

you know both are taken as same. In any case it is b d cube by 12 as you know for a rectangular

section the high inertia moment of inertia is b d cube by 12 divided by d by 2, because

we are interested in the maximum extreme fibre test. So, this is d by 2. So, b d cube by

12 divided by 2 would result in b d square by 6 and P l by 6.

So, finally, the extreme fiber stress would be given as P l by b d square. So, if you

know the P and the failure P max, if you know the P where P is the overall load applied

at this point P is the overall load applied at this point. So, if you know P then the

modulus of rupture will be the flexure tensile strength will be given by P l by b d square

this we also call as modulus of rupture. Now, you see 2 things 1 must notice from here.

First of all shear force in this zone would be 0 shear force is 0 no shear force, in this.

So, if you draw a shear force diagram you know a shear force diagram you will be possibly

draw it something like this shear force diagram. So, there is no shear force her no shear force,

in this zone it is pure bending pure flexure also this is spanning over a distance of d

the bending maximum bending movement is spanning over a spanning over a you know distance of

d. Now, we could have also used single point loading. So, if you use single point loading;

obviously, shear force would not have been 0 in any part of the section not only that

the maximum bending movement, would have been there only in 1 place in 1 point 1 single

point. Now, failure could take place in that point

or may not take place in this point that would depend upon whether, there is an there is

a weak point at just below the load or not. If the weak point is somewhere else, it will

fails there. So, which means the probability it will depend upon probability of finding

the weak point at the maximum load you know just below that load point-point where load

has been applied. Now, this tends to give you much higher strength as we shall see.

So, that is not the best way to it that is why most of the code adopt this there is since,

you can eliminate out shear from here, shear force from here you know shear force from

here and also this is pure this is bending here and you have a span. So, 2 point loading

is preferred over 1 point loading.

And you can see that in fact, people have tried to do the test with 2 point loading

and 1 point loading and 1 point loading tends to give you always higher load 1 point loading

always tends to give you higher load right. So, single point loading gives you always

higher apparent tensile strength, flexural strength whereas, 2 point loading gives you

apparently low tensile strength okay. So, this is 1 kind of test that, we do and this

test we call as modulus of rupture test. Now, this test you know if you remember that, we

assume a specific kind of stress distribution in the calculation when, we have used the

linear elastic bending theory actually.

We have assume as stress distribution rectangular stress distribution simple triangular stress

distribution you know triangular stress distribution. We have assumed a triangular stress distribution

and calculate calculating out f equals to P l by b d square you know that, we have calculated

out because we have used M by Z equals to f etcetera. If you remember that uses a triangular

stress distribution, because we are assuming the linear behavior of the material, but in

actual concrete the behavior is something this is your concrete beam at the failure

the stress diagram is something like this, in the compression and tension zone, it is

something like this and this value is actually lower than what we have calculated what we

have calculated. So, we can see that we have estimated the

tensile strength as this, but actually it is this much smaller. So, we are over estimating

even the flexural tensile strength, because we are using the modulus of rupture; which

is calculated on the basis of triangular stress distribution triangular stress distribution

in compression as well as in tension and therefore, we are going to estimate. This is 1 problem;

a second problem not a problem really because we understand this. So, it is not a problem,

but this is the actual you know this is the deviation from the reality.

A second aspect is that in such tests this extreme fiber is subjected to maximum stress

whereas all other points. This point the neutral axis let us say all other points here

is subject to lesser stress than this. So, now this is the only point which is subjected

to maximum stress. Now, supposing I have you know this there is some strong points here

it is not the weak plane is not here. So, this fiber the crack does not propagate the

crack of course, the crack would propagate I mean; we can see the other direction the

crack would propagate like this. So, the crack does not propagate or it gets

stuck somewhere, by an aggregate or something of that kind then it will again tend to give

you higher load. The volume of the concrete, which is subjected to the tensile stress is

relatively less because this is subjected to maximum rest all are subjected to lesser

and lesser stress whereas, this side is purely in compression. So, this is another reason

why modulus of rupture would tend to actually over estimate. So, over estimate the strength.

So, you can see that this is true strength is somewhere here and calculated strength

is bigger.

So, 2 point loading therefore, summarizing this discussion just now, I have talked about

2 point loading ensures pure bending without shear in the central 1 third span 2 point

loading produces maximum moment, between the loads, thus more area is exposed to maximum

bending moment than 1 point loading hence lower apparent modulus of rupture. So, when

we compare between 2 point loading and 1 point loading we find 2 point loading gives us lower

apparent modulus of rupture. But, calculation of modulus of rupture triangular

stress distribution, actual stress differs some other point; we will discuss again little

bit more later on. Hence forth it has been observed that modulus of rupture is greater

than the next test, I will talk about that is called split tension test or direct tension

results, if they are they are available, but as I told you it is difficult to obtain direct

tensile strength result. So, in any case MOR gives you higher value than split tension

test well.

Tensile strength split tension related to modulus of rupture and this is what it shows.

If you can see or notice this you see this is tensile strength is 1 modulus of rupture

is 2. It is 2 and this is if they recall you would have got a 45 degree line, but what

actually getting is vertical line. So, therefore, vertical line is you know slope of this much

slope which means; that actually modulus of rupture always predicts the tensile strength.

Let us see the other test which is most popular and commonly used, it is called split tension

test and it would look like this. You have a cylindrical specimen or can be cube also

as we shall see later. So, in this cylinder cylindrical specimen you apply load along

this direction to a simple plate sort of thing and like, in case of in case of MOR test we

use specimen size is 10 centimeter by 10 centimeter by 50 centimeter with 40 centimeter being

the central portion you know which, where we apply the between the supports 40 centimeter.

In this case, we use this dimension is usually 15 or 150 millimeter 150 millimeter that is

15 centimeter and this length is usually 300 mm. So, 1 is to cylinder that we have been

talked about that, we have been talking about that is what we use and apply load a kind

of a point load this is the cross section loading cross section and you apply load here.

So, 1 can look into the stress where small element there from theory of elasticity, we

will come to that. So, when you apply load like this what happens

is the this along this vertical diameter tensile stresses act as shown here tensile stresses

very little portion, it is not tensile stresses acts here and it splits along this direction

splits. Simply this will become 2 pieces something like this 1 portion and it splits into other

portion. So, you will have cylinder gets splitted when you apply load like this when you apply

load like this and that is why you call it split cylinder test. This also used for rocks

is also called sometime Brazilian test or Brazilian split cylinder test and is been

very popular for concrete now, for determination of tensile strength right.

Now, let us look into the split test. This is the typical stress distribution across

the across the across the diameter you know this axis shows 0 to D. So, this is the diameter

of the specimen, this is the diameter of the specimen 0 to D and if you look at it this

side beyond this point this point beyond this point compression we are calling it positive

and tension is negative. So, only over a small height you have compression

acting, but majority of the section which is about you know you can see D by 12 or even

less than D by 12 is where compression is acting on both sides, but majority of the

portion, it is actually tensile stresses is acting and it is actually by an large uniform

tensile stress. So, from theory of elasticity 1 can calculate

out this uniform stress and this stress uniform stress is given as 2 P over pi L D where,

P is the load that is been applied on the specimen you know P is the load P is the load

that has been applied on to the specimen right over a thin plate or used in a thin plate

basically usually a plastic sheet or something through which the load is applied a thin plate

or thin sheet through which it is applied. So, tensile stress is given as tensile stress

therefore, will be given as 2 P maximum load that you can apply divided by pi L D.

So, this stress this is you can see that this is 1 pi L D minus 1 stress is you know stress

multiplied by pi L D by 2 P that equals to 1 which means stress is equal to 2 P by pi

L D. So, it is nearly constant at 2 P over pi L D, and you calculate out the tensile

strength from this value you can calculate out the tensile strength from this value.

So, this is what is called split tension test.

It can be done on cubes also it can be done on cubes also IS 500 and IS 500 and 16 allows

it to do it on cubes or any other code allows you to do it on cubes. And this is how it

is applied on a cube as well and the formula here is of course, slightly different it is

twice P by pi d square, because we are calling this as d this dimension as d.

So, it is 2 p over pi d square 2 p over pi d square again this is validated from theory

of elasticity that you will have a tensile stress. Physically you can understand where

you are applying compressive load, it will have a tendency to go away and just, because

your point load just below the load there is a high you know relatively higher tension.

And since concrete fails in tension this tension causes splitting of the either the cylinder

or the cube and you can find out the strength from this.

Now, again let us compare these 2 tests least volume is subjected to maximum tension in

modulus of rupture test followed by split followed by direct test; how it is. In modulus

of rupture test if you see the portion where tension is applied is the bottom portion and

then if you assume a stress diagram you know you assume a stress diagram of this kind you

assume a stress diagram of this kind. So, maximum something like this something like

this maximum tensile stress is here all other portions tensile stresses are not maximum.

They are less and the volume is only not even the half you know half volume through which

you are actually applying the stress tensile stress bottom half top half is in compression.

So, volume of concrete which is subjected to tensile stress is in the in the central

span or where you have actually, maximum bending movement. You have very little volume very

little volume which is subjected to actually tensile stress and that only the bottom portion

has got maximum rest all are less than that. Now, you come to split you have split say

in case of split cylinder test, you have some portion where tensile stresses are acting

and this portion corresponds to about we said we have seen that this is D by about twelve

on this side where it will not be acting and D by twelve on this side on which it will

be compressive D by 12 on which it will be again compressive. So, you see the full section

is again not subjected to direct tensile stress whereas, when you have a direct specimen direct

tensile stress full section is subjected to direct tensile stress.

So, maximum tension you know volume is least volume is subjected to maximum tension in

MOR followed by split followed by direct and this result, in this is the result why you

have you know lower strength you know that is MOR gives you higher value than split than

the direct. Also we said earlier that non uniform stress distribution in moment of I

mean; in case of modulus of rupture test in non uniform stress distribution because bottom

has maximum all other places it is less. So, it is non uniform stress distribution.

In case of modulus of rupture where the maximum tensile stress the bending tensile stress

is at the bottom fiber other fibers above the bottom fibers, they are at lesser stress

this is what happens, in case of bending you know physically we can understand this when

something is bending the bottom fiber is elongated most followed by the possibly the next fiber

above it and so on so forth and at the neutral axis the fiber is not at all elongated and

if you go beyond, it above the fibers are actually compressed.

So, if you look at it there is a non uniform stress distribution in case of modulus of

rupture test the flexure test bottom is actually, at maximum stress and the neutral axis is

at no stress in between the stress varies. We are assuming it varies linearly although

in actual failure condition it does not vary linearly, but in any case it is non uniform

distribution. So, since it is non uniform distribution also in case of split only the

central portion there is uniform distribution other portion there is less and this can impede

the propagation of crack. So, when cracks are forming the portions where

stresses are less they may not allow the crack to propagate and they together with the issue

that least volume is subjected to maximum tension all other points that we have mentioned.

So, far and that is all confirms that modulus of rupture you know theoretically, modulus

of rupture should be greater than split tension tensile strength tensile strength and then

direct tensile strength you know direct tension strength.

Strength determines through direct test should be the least strength determined to split

is somewhat greater than that and tensile strength determined to modulus of rupture

is still greater than that right. Few more points crushed aggregate exhibit better modulus

of rupture than rounded aggregate because of bond and moisture condition also has some

influence. It is interesting crushed aggregate, because of the bond you know, in case of modulus

of rupture the crack has to start from the bottom and then propagate upward.

As the P increases the load increases the bending stress increases the bending movement

increases and the bending stresses increases. The crack has to propagate from the bottom

towards the centre the neutral axis upward. Now, here if the bond aggregate provides better

bond if the aggregate provides better bond you know and then the crack cannot propagate

and it has been observed that the crushed aggregate shows better modulus of rupture

value than the rounded aggregate. This may not be true for others.

The moisture condition also has got some influence on modulus of rupture. Now, you remember when

we talked about moisture influence of moisture on moisture on influence of moisture on compressive

strength we said the compressive strength actually, reduces when moisture content is

high. In a saturated specimen the strength would be lower than the dry specimen and it

has been attributed to dilation of the cohesion force. Because moisture would get adsorbed

in the gel structure, in the gel phases and this will dilate you know it will create distance

between the gel or inter layer distance will increase resulting in lesser cohesion reduction

in cohesion and this reduction in cohesion results in lowering of the strength.

So, moist specimen in case of compressive strength compressive strength of concrete

moist specimen shows lower apparent strength whereas, dry 1 shows higher, but in case of

tensile strength I mean; we are talking of the flexural tensile strength it shows higher

I made some passing remark in the last lecture; when we are talking about the effect of moisture

content on strength of concrete compressive strength of concrete, but we see here it is

other way round. And if you remember we mentioned at that time as well that the tensile strength

becomes you know, in case dry that tensile strength is lower the reason is it is actually

causes some shrinkages cracks. So, initially already, because of drying there

will be some shrinkages cracks. So, when you start applying load this shrinkage cracks

will help you know they the possibly initiation of crack will start from may even start from

such shrinkage cracks. Well shrinkage cracks also shrinkage may affect the interfacial

transition zone. So, shrinkage cracks due to drying have been attributed to improvement

in strength by moisture you know by saturation. In case of compression if you moist specimen

shows lower strength here a moist specimen shows modulus of rupture and moist specimen

shows higher strength that because a dry specimen will have some amount of shrinkage cracks

and that may lower down the strength result in modulus of rupture.

But this influence is not seen in case of other 2 that is direct tensile test and test

for you know another is the split cylinder test. In split test we do not see this and

this diagram shows us this behavior as we can see you see in case of splitting test

splitting test both direct wet and dry is shown by this line. And which is showing least

which is showing actually, least compared to all 3 splitting well wet and dry both are

same. But, you can see there is a difference and

this difference of course, increases as we go towards the higher strength concrete you

know in tnpa concrete shows much higher difference compared to let us say, 30 or 20 MPa while

difference is less low if you go to flexure you know the modulus of rupture. This is the

modulus of rupture test this is the dry specimen and this is the wet specimen you know this

is the dry specimen this is the wet specimen and wet specimen shows higher strength and

this is parallel these 2 are parallel and of course, these 2 are much higher than both

of them. So, and this difference is also increases

with either of this as the strength increases. So, these strengths are higher you know these

strengths are higher and wet shows higher compared to dry and this difference is this

is this is since this is more or less same irrespective to the strength and this difference

had been attributed to shrinkage of concrete due to drying. So, when you dry shrinkage

takes place resulting in some shrinkage cracks at various places including the interfacial

transition zone and that is why the strength is lower.

So, that is what it is the influence of moisture and also aggregate do you know influence the

strength of the aggregate do influence the strength of the aggregate also influence the

strength of the you know concrete. Now, if you look at the relationship of f c with f

t if you look relationship of a f c with f t that is compressive strength with tensile

strength we said there should exist a relationship between f c and f t, because we have seen

in the failure envelope of bi axial under bi axial stresses in case of concrete the

compression you know compressive strength is eight times that of tensile strength. So,

there must be some relationship existing between the 2. So, empirical relationship has been

attempted and compressive strength versus flexural strength is something like this sort

of relationship has been observed something like this sort of relationship has been observed

and if 1 looks into a more elaborate diagram 1 would see that in case of splitting tension

test these are the results much more actually. so many,, so many test that are for various

size of aggregate for various m s a right. And this is the modulus of rupture test and

this is a split tension test for you know this diagram is for split tension test.

This is the modulus of rupture test for various kind of aggregate size etcetera m s a various

m s a these values are given and modulus of rupture again shows lower value sorry, modulus

of rupture again shows higher value split tension test shows lower value. So, relationships

do exist between f c and f t, because this is compressive test f c and this is f t. So,

there is relationship exist between both f c and f t in flexure as well as direct split

as well as split tension test; however, for design purposes we cannot distinguish all

that because we have to use 1 of them.

So, in case of in case of design we use specific value which has given in code. There are several

sort of relationships are available. In fact, several factors affect this relationship these

factors are something like aggregate type age curing condition water cement ratio.

So, various sort of even some sort of relatively more elaborate relationship has been suggested,

but in the research level of course, in the code level a simple relationship or most of

the codes adopt fairly simple relationship at the moment simply relates the compressive

strength, with the tensile strength through formula something of this kind you know f

t is proportional f t is related to k f c, by this compressive strength a power n and

this is the this f stands for strength this tensile strength this is compressive strength.

So, tensile strength is related to some constant multiplied by compressive strength to the

power some n and if you look at it the IS code values IS code, gives you this value

equals to this case to point seven and n is taken as 0.5 when f c and f t both are in

MPa when both are in MPa. In IS code of course, all this you know this when both of these

are in Mpa f c and f t in MPa then k is 0.7 and n is equals to 0.5.

So, this is the value 0.5 this is the value suggested by the code for design purpose other

codes also suggest similar values and similar sort of relationship although there can be

more elaborate relationship based on water cement ratio curing condition age and aggregate

type, because we have seen that aggregate type may affect this it does affect this relationship

depending upon what relationship you are talking about right. So, this is the design relationship

irrespective of how we measure about purposes for calculation purposes this is what is used.

So, this is the idea regarding tensile strength of concrete.

Let us look into now what is called fatigue what is fatigue well, in case of concrete

we will define it in 2 different ways later on, but in general first define when you have

repeated loading material fails at load lower than the static strength. The failure load

being lower with number of reputations you know for example, supposing, I have a load

I repeat go you know I start from a load and increase the load and bring it down.

So, I go cyclically increase the apply the load somewhere I go up and go down. So, 0

to some load and something like this. So, I repeat this loads cyclically go up and go

down in any manner you know I go up and go down. Now, it after certain repetitions the

specimen or material will fail, but if I apply let us say: static load then in 1 cycle it

fails static load 1 cycle it fail and that is what is static strength static strength

that is what you call it static all static ultimate strength.

Now, if I apply repeated loading then after certain number of repeated loading the material

will fail and at that time the load need not be the ultimate load it can be lower. So,

this load required to fail the material depends upon the number of cycles, I have applied

more the number of cycles it will fail it lesser and lesser load this is a relationship.

This is a relationship called s and n relationship strength versus number of cycles relationship.

So, more the number of cycles it will fail at much lesser load you know this value at

lower of lesser of as well. This sort of situation is referred to as fatigue

failure, when you have repetitive loading it does not it need not when if you not go

to the ultimate static failure load you are operating at let us say, somewhat lower load

and you repeat go to that load come back 0 it or go even negative whatever, it is you

repeat cyclically you go increase the load come back increase the load and come back

you will find that the material fails even though you have never each other static ultimate

failure load. This is the phenomenon of fatigue, but in

concrete of course, this is something else also happen we shall see first in few minutes

time. So, that is called fatigue failure. Now, steel has a fixed endurance limit. An

endurance limit is that many number of cycles beyond which, if you go on increasing the

number of cycle the fatigue load would not or fatigue strength would not reduce that

is called endurance limit repetition beyond which the fatigue strength remains constant.

We shall see through a diagram the same thing, but concrete does not have a fixed endurance

limit right it does not have a fixed endurance limit.

So, let us see this through a figure may this will make things or more clear something like

this you know the year on this side is the number of cycles this is called an s n curve

right. This n is the number of cycle usually, plotted in log scale and this is the strength,

but we are talking in terms of ratio of fatigue strength to short term static strength.

Static strength is when you have just applied the load once and it has failed that I called

as static strength and this is 1 is you know this is like 1 cycle this will be 1, but when

you have you know cycle increasing when you have lesser values. So, fatigue this is the

ratio of fatigue strength to static strength and you can see in case of steel, in case

of mild steel this decreases you know as I increase the number of repetition number of

cycles, but a point comes beyond, which it does not decrease further this point is nothing,

but the endurance limit and we have a fixed endurance limit clear cut defined well defined.

Endurance limit in case of mild steel, which is about which will give you fatigue strength

of about 0.5 of the static strength. So, its 50 percent of the static strength right. So,

if you are if you expect fatigue load in case of structure, we can you can actually deduce

down your static strength by some value, in which you should be operating of course depending

upon the situation. Now, we look to concrete in tension it is

something like this and there is no there is no sign of any where, actually there is

a endurance limit and in compression also it reduces down and fatigue compressive strength

will be somewhat this. So, what you do we define it with respect to 1 million cycles

10 to the power 6 cycles what we say fatigue compressive strength of concrete is defined

with respect to 1 million cycle that is the strength which it can withstand after 1 million

cycle you know. If you have n is equals to 10 to the power

6 the corresponding strength s what you call as a fatigue compressive strength fatigue,

tensile strength is similarly defined as the same 1 million cycle. So, when I have 1 million

cycle the strength that can it can actually withstand that is what a fatigue tensile strength

is alright. So, this is what we have in case of concrete when we apply cyclic or repetitive

loading now in concrete.

I said that there can be 2 types of fatigue behavior you know 1 is sustained load, it

is not need be repetitive loading, but you have sustained load near the static strength

under increasing load and this causes failure you know very slow rate of loading you have

just load applied load near the near the near the static strength and its failure.

So, this is called static fatigue or creep rupture this is this is a special thing to

concrete we call it creep rupture or static fatigue. Now, you see fatigue is nothing,

but you are applying repetitive load. So, when you apply this repetitive load at a very

slow rate very slow rate you know such that, frequency of application cycles per second

is very small very small you know then such very slow rate of loading that situation shows

you static that situation shows you what is called static fatigue or creep rupture. The

other case I just mentioned was repeated cyclic loading or simple fatigue as you understand.

This is static fatigue this diagram shows you static fatigue. For example normal rate

of loading as we have we know that 100 and 40 kg per centimeter square per minute that

is what about 3 minutes, we go to failure and this is about ultimate short term strength,

but if I go at a faster rate very faster rate I will get still higher strength, but if I

slow down this rate, I have reached the ultimate short term strength you know in 2 minutes

then my strength reduces. I still reduce it down ion 3 days I fail the

specimen and I reach here and if I do the same thing in 50 days I will reach there.

So, increasing the test duration right that is decreasing the rate of loading results

in this kind of a this kind of a failure, you know failure at the strain increases you

know failure at the stress strain curve actually, this side is a strain and this side is a strength

or you know rather strength to strength to strength stress to strength ratio. So, failure

actually increases and your failure load therefore, also reduces.

So, you can see that this is you know in 50 days if I try to fail it, I fail it the failure

strain is much higher now much higher and I have an envelope. This is called static

fatigue static fatigue failure or creep rupture envelope.

So, this is the envelope if you increase it, still further more days it does not increase

beyond that it will be the failure strain you know failure strain might increase, but

the load does not increase. So, this is the envelope. So, as you go on increasing the

duration test duration it fails at lower load somewhat lower load somewhere around 0.75

of the actually you know 0.75 of the of the normal short term static strength and if you

increase the rate of loading then it fails at much higher load.

This is what we call at it in other words you know is you are applying the load once

in 50 days, in this case you know once in 3 days once in 2 minutes once in 3 minutes

etcetera. So, this is static fatigue behavior static fatigue behavior of concrete and there

are similar curve of the similar kind, which you can see that when we have again supposing

I subject the concrete specimen to 0.3 of the static strength and just keep it for long

period of time what I will find out after thirty years the strain will be increased

like this. So, this is the limiting strength after 30

years beyond that there is no increase in strength similarly, if I load it to 0.6 of

the static strength, I get something like this you know the strain after 30 years and

so on so forth and it matches static fatigue failure and envelope matches strain. So, the

strain that that strain that concrete specimen attains depends upon the load and this envelope

seems to match again. So, this also gives static fatigue static

fatigue failure envelope you know with respect to usual short term strength. So, static fatigue

failure is actually very slow rate of loading you find that very slow rate of loading. You

apply load once in very long time and you find that it fails at much lower load. This

is something due to creep phenomena which is which is occurring. In fact, creep is very

closely related to fatigue in case of concrete. I mentioned to you creep sometime, in 1 of

the previous lectures that creep is a time dependent deformation you keep the load deformation

will increase. So, that is what is the phenomena is creep

and this is related to the static fatigue is related to creep phenomena and even in

general creep of concrete even cyclic creep can be cyclic fatigue can be related to secondary

creep phenomena of concrete. So, this is right this is static fatigue.

Now, let us see cyclic fatigue you see, if you apply load to the concrete specimen if

you apply repetitive load to the concrete specimen, then what will happen you apply

go to that place that is maximum not the maximum load, but some some loads some MPa may be

some percentage of static strength ultimate strength and release the load it does not

come back to its original position. That is, because lot of cracking micro cracking

takes place in concrete we shall see that later on again when we look into the stress

strain diagram of concrete micro cracking occur and which will not close down. So, therefore,

there is certain amount of energy lost in creating those new surfaces certain amount

of strain energy has been absorbed there. So, it does not come back. Now, there is a

hysteresis as we call it and then again; if I go on repeating after 675 cycle I will find

that hysteresis is relatively hysteresis is you know is reduced hysteresis has reduced.

So, alternating load will have hysteresis 675 and will have hysteresis and if I go on

increasing further, I find this area between the hysteresis loss the energy lost in the

hysteresis is less, because this was larger area this is smaller area and this is still

smaller area and you know smaller areas actually after twenty four thousand cycles you find

the hysteresis is very minimum, but you go on increasing this number of cycles you know

and strain also increases of course, permanent strain there will be some permanent strains

here. So, strain increases and here the strain starts

increasing at a very faster rate and hysteresis also starts increasing before failure. So,

this dark line shows increasing load this 1 shows the return load.

So, there is hysteresis losses and hysteresis losses reduces with number of cycles, but

near the failure when large number of cycles have been applied the hysteresis loss will

be still will become higher and strains will increase at a very faster rate strains will

increase at a very faster rate. So, that is the behavior of fatigue behavior you know

fatigue behavior of concrete.

Now, some 1 can what kind of load it can withstand is under fatigue is given by what is known

modified Goodmans diagram modified Goodmans diagram you know. So, that is that shows the

range of stress to cause failure after 1 million cycles that is what is called that is what

fatigue is, because we are define fatigue strength of concrete with respect to 1 million

cycle, because we do not have a specific clearance limit. So, we have defined it with respect

to 1 million cycles the load or the you know load which under repetitive loading it can

with stand. So, 1 million cycle that is what we call as

fatigue strength of concretes. So, this modified Goodmans diagram gives you various cases.

For example this line it starts from it starts from this 45 degree line, which is the base

line 45 degree line 45 degree line is the base line this is base line actually and this

line represents this point beyond this point; it represents the minimum tensile stress this

represents the maximum compressive stress right line and this line represent uni axial

tension this line represent uni axial tension and compression and this line represent flexural

tension and compression. This is uni axial compression. Now, let us

see how this diagram is read. For example you will have as your cyclic loading would

be always based upon static loading. So, you will have some initial stress over

that the cyclic loading will be applied you know where this fatigue loading is important

like bridges where, there is a static load. And over it, there are some amount of cyclic

load comes or similar many other structures where, repetitive load can come off shore

structures or many other structures you know where in off structures waves can come and

hit repetitively, but you have repeatedly, but you have a static stress already repeated

load or the cyclic load gets superimposed over it.

So, Goodmans diagram deals with such situation say case A you consider the A is this line

you have some amount of static stress, which is tensile because this side is the tension

and this side is the compression. So, already nearly about point 1 tensile stress is existing

then from that if you apply further uni axial tension you can go up to this. This line represents

the limits of uni axial tension. So, it touches here this is the minimum tensile stress line.

So, point 1 you know point 1 you just draw a line. So, this is the minimum stress line

from here it can, if you are trying to find out how much is the tensile cyclic tensile

load of a static strength it will have in terms of tension load this would be given

by this. For example if this was 0.2 of the ultimate tensile load. If you have applied,

then this much you could have gone under fatigue superimposed cyclic fatigue load would be

this much the range this range is 0.5, in this particular case supposing you had 0.2

here and you could have gone here. So, this would have been again 0.4 or may

be slightly less than 0.4 or something of that kind. So, you could have gone up to 0.4

over 0.2 you can apply still cyclically 0.4 tensions 0.4 of the static strength and that

is the fatigue load. So, this part of the through this you know this is the minimum

tensile stress. So, minimum tensile stress here is point 1 and under uni axial tension

we can go to this line this line is the maximum limit that gives you the maximum limit; that

means, you can have when you have a initial stress of point 10 percent of the ultimate

tensile strength. Then you can go to about 0.6 of the ultimate

tensile strength repeatedly for 10 to the power 6 number of cycles, then it will fail

only after 10 to the power number of 6 cycles it will fail. So, you can see that how I use

this how 1 uses this diagram similarly, you go to B line B. Now, this is for maximum compressive

stress that has been applied. Now, this is the maximum compressive stress that has been

applied right from this; if I want to go to the uni axial tension and compression the

compressive stress that has been applied. Now, from this I want to go to uni axial tension;

that means, I am reversing I am reversing the stresses right I am reversing the stresses.

So, I can reverse the stress to about 0.5, I can reverse the compression you know reverse

this stress to 0.4 or 0.5 whatever, is 0.4 also and this repetition can takes place for

10 to the power 6 cycles before failure. Similarly, look at C flexural compression

C starts from here C are this line right. So, flexural compression is flexural tension

compression is this curve. So, C is here from here, I can go up to this and I can recycle

this cycle this for 10 to the power 6. So, this is point 1 here from 1 flexural compression

I can go to this value and I can recycle this for ten to the power 6 number of cycles before

failure. So, if I want to find out how much I can apply

the stress this I can find out from Goodmans diagram look at D uni axial compression and

uni axial compression. So, its starting point is here uni axial compression, in this curve

uni axial compression and I can go to maximum compression this much; that means, I can cycle

over this portion, I can start from point 1 this is nearly about point 1 and go to about

point five or. So, 0.5 or therefore range is 0.4 you see the range is 0.4. So, I can

cycle over this. So, using Goodmans diagram I can actually I can Goodmans diagram I

can find out what is the fatigue strength of concrete. So, modified Goodmans diagram

is used in this 1.

Next one is impact strength well. This is another issue important 1 impact strength

of concrete, it has been observed that lower the water cement ratio you know impact strength

depends upon aggregate type a strong aggregate would; obviously, show higher impact. For

example some sort of you know angular aggregate this is granite this is gravel.

So, it depends upon aggregate type. A stronger aggregate can absorb a lot of energy and it

can be impact strength can be related to compressive strength you know number of now, how is this

measured number of its rebound is applied and number of rebound number of rebound beyond;

which there will be no rebound that is called you know is a measure of the impact strength.

And this increases as my you know, this increases with the compressive strength number of rebound

required to come to number of required to come to come to you know no rebound situation.

That is an impact strength lower MSA improves impact strength lower water stored lower water

stored concrete. This value is lowered when you have water stored in water, but, if it

is dry it is somewhat higher. Then next we can look into the last aspect of this impact

is nothing,

But actually means of very fast rate of loading. So, when you have very fast rate of loading

the impact strength is generally higher than, the compressive strength that 1 can understand.

So, rate of loading when it is very high that corresponds to impact strength and actually

strength can be 200 percent higher right; last is the abrasion resistance and this also

can be related to the compressive strength of concrete.

You see as the water cement ratio decreases as the water cement ratio decreases, as the

water cement ratio decreases as the water cement ratio decreases the powder that is

formed under grinding that is a measure of abrasion.

There are 3 different tests and all test you know like 1 test is you have disc, in which

you grind and the powder that is formed under grinding; that is called that is the measure

of impact resistance higher powder forms means; lower the impact resistance. So, as you increase

the water cement ratio impact resistance reduces, impact resistance reduces right.

Last is the bond strength and bond strength of concrete again, can be related to compressive

strength like this, bond strength of concrete can be related to compressive strength like

this. You know, in this manner you can relate it to the compressive strength like higher

the compressive strength, bond strength increases.

This for plane bars this for deformed bars. So, summarizing the whole, we have looked

into the tensile strength, fatigue strength, impact resistance, and bond strength of concrete.

This impact and resistance and bond strength there is not much you know the factors affecting

are not understood. However, they can all be related to tensile strength of I mean,

compression strength of concrete. So, almost all other strength properties of concrete

can be related to compression compressive strength and that is what, I think with that

we can summarize.