lecture notes4

Idealized stress-strain curve:

ST

RE

SS

fd

Design Curve

Idealized Curve

For concrete in member

A B

σo = fmax fmax = 0.67 fck

fck

Idealized Curve

Actual Curve

fd = 0.67 fck / 1.5

= 0.446 f

σmax = fck

σ

Stress-Strain Relationship (For Concrete) Lecture – 4

31/07/2012

0.001 0.002 0.003

STRAIN

0.0035

Design Curve= 0.446 fck

εo εmaxε

Various investigator have proposed different shape and expressions for an idealized curve in

place of the actual stress-strain curve for concrete under axial compression

ε=strain at any point

σ=stress at any point

ε0= strain at which parabolic part ends (Limit of Elasticity=0.002as per IS code

σo= idealized maximum stress corresponding to ε0

Idealized stress-strain curve:

ST

RE

SS

fd

Design Curve

Idealized Curve

For concrete in member

A B

σo = fmax fmax = 0.67 fck

fck

Idealized Curve

Actual Curve

fd = 0.67 fck / 1.5

= 0.446 f

σmax = fck

σ

0.001 0.002 0.003

STRAIN

0.0035

Design Curve= 0.446 fck

εo εmaxε

The effect of size and shape of test specimen with that of actual structural member in

flexure is taken into account.

Partial safety factor of 1.5 is applied to get the design curve

Stress-Strain Relationship (For Steel)

Reinforcing steel consists of bars, usually circular in cross section.

These are, at present, available in three different grades:

Fe250

Fe415

Fe500

Here, Fe refers to ferrous metal

Number refers to the specified guaranteed yield stress in N/mm2.

Types of Reinforcement:Types of Reinforcement:

Based on physical and mechanical properties such as:

1. Ductility

2. Yield strength

Following three types of steel reinforcements are used in RC construction:

Plain round bar of mild steel

Deformed bars of high grade steel

Types of Reinforcement:Types of Reinforcement:

Based on physical and mechanical properties such as:

1. Ductility

2. Yield strength

Following three types of steel reinforcements are used in RC construction:

Plain round bar of mild steel

Deformed bars of high grade steel

Steel wire fabrics

1. Plain Round bars of Mild-Steel

They are usually of mild steel (grade Fe250)

conforming to IS: 432

They have a well defined yield point giving

yield stress of 250N/mm2

Excellent ductility with percentage elongation at failure not less

than 23%

Guaranteed weldabilityGuaranteed weldability

10 20 27

ST

RE

SS

30

Idealized Stress- Strain Curve for Steel

Upper Yield Point

Lower Yield Point

Actual Curve

Breaking Stress

Maximum Stress

1.5 10 20 27

STRAIN (%)

30

Stress – Strain curve for mild steel specimen

For mild steel, the stress is proportional to strain up to yield point.

Thereafter rate of increase of strain is more than of stress, reaching the maximum stress.

The necking continues to form with reduction of stress and increase in strain.

Finally the test specimen breaks.

For the purpose of analysis an idealized curve is drawn in place of actual stress-strain curve.

1.5

0.001 0.002 0.003

ST

RE

SS

STRAIN (%)

0.0035

fy

STRAIN (%)

Stress – Strain curve for HYSD Bars

HYSD bars do not show a definite yield point….

Therefore, to obtain the yield stress of HYSD bar it is subjected to tension test

Following procedure should be followed:

1. Plot the stress-strain graph from reading of load taken corresponding to elongation.

2. Draw a initial tangent from the origin to the stress-strain curve.

3. At a strain of 0.002, draw a straight line parallel to initial tangent.

4. The y-coordinate of the point where it cuts the stress-strain curve represent the yield

stress of HYSD bar.

0.001 0.002 0.003

ST

RE

SS

0.0035

fy

0.001 0.002 0.003

STRAIN (%)

0.0035


As the name indicates the high yield strength of deformed bars have much high yield point.

But the yield point is not well defined.

The bars are either hot rolled from steel billets or by cold working.

In the cold working process the bars having deformation are cold twisted.

Twisting is continued till the strains are in the elasto-plastic range and then unloaded.

The high strength deforms bars shall conform to IS: 1786.

0.001 0.002 0.003

ST

RE

SS

STRAIN (%)

0.0035

fy

STRAIN (%)


These bars have following advantages:

Because of the high yield strength the quantity of steel required in RC work is reduced.

Since the difference in its cost compared to mild steel is marginal there is reduction in the

overall cost of RC construction.

HYSD bar have very good bond with concrete than mild steel so that they may be placed

without end hook and resulting in saving in steel.

By cold working the strength of the bar is increased in a radially symmetrical pattern.

Each bar is severely tested for defects.

0.001 0.002 0.003

ST

RE

SS

STRAIN (%)

0.0035

fy

STRAIN (%)


These bars have following disadvantages:

With increase in stress level the cracking tendency increases.

So, for Fe550 or higher grade of steel it becomes necessary to use high grade concrete.

Due to reduction in percentage of tension steel, the design shear strength of concrete is

reduced.

0.001 0.002 0.003

ST

RE

SS

STRAIN (%)

0.0035

fy

Codal Provisions & Design Criteria:

For HYSD bars the stress is proportional to a strain upto a stress of 0.8fy

Thereafter the curve is nonlinear.

It attains the yield stress at a strain of 0.002+fy/Es

Here, the first part of 0.002 is an inelastic strain and the later part is an elastic strain.

The inelastic strain of 0.002 is added to the elastic strain so that there is sufficient yielding of

steel before failure.

Applying partial safety factor of steel as 1.15, the design stress, fyd=fy/1.15 = 0.87fy is adopted

STRAIN (%)


0.001 0.002 0.003

ST

RE

SS

STRAIN (%)

0.0035

fy

STRAIN (%)


Codal Provisions & Design Criteria:

Thus, the design stress-strain curve is linear upto design stress of 0.87fy/1.15.

And nonlinear till it reaches a value fy/1.15 at a strain of 0.002+0.87fy/Es

The modulus of elasticity of steel is taken equal to 2,00,000N/mm2 or in short 2E5 Mpa

Characteristic Strength and Characteristic Load

The structure is normally designed to provide safety against collapse...

The failure occurs when the load acting on the structure exceed its strength.

Thus, the load and the strength of material become the two basic design parameters which

decide the safety of the structure.

Since both these factors are totally independent of each other,

Hence, they need separate treatment in the process of determination of safety

Each of the above factors have hardly ever a constant value.

Value is prone to variation and that is its characteristic value.Value is prone to variation and that is its characteristic value.

Since collapse of a structure is related to simultaneous occurrence of overload and

understrength,

The value to be assigned to the load has to be that value which has minimum acceptable

probability of not being exceeded during the life time of the structure.

And the material strength has to be that value which has maximum reliability.

“The characteristic strength of material is that value of material strength below which not

more than a minimum acceptable percentage (5% as per IS Codes) of test results are

expected to fail”

Characteristic Strength and Characteristic Load

“The characteristic strength of material is that value of material strength below which not

more than a minimum acceptable percentage (5% as per IS Codes) of test results are

expected to fail”

It means that characteristic strength has 95% reliability

OR

There is only 5% probability of actual strength being less than the characteristic strength.

The characteristic value of quantity to variation is obtained from frequency distribution curve

Frequency distribution curve…

lecture notes4

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