I am looking for practical references to show me how to find modulus of elasticity in UHPC.
When working with a non-linear material, there is a difference between the Tangent modulus (the slope of the stress/strain curve at a point) and the Secant modulus (the slope of the straight line joining the point to the origin).
Use the Tangent modulus when looking at the effects of changing the stress by a small amount., and the Secant modulus when looking at the effects of applying the whole stress.
Secant modulus generalises to the "Secant modulus from one stress to another": it becomes the slope of the line joining one point on the stress/strain curve to another, and is used when looking at the effects of changing the stress by an amount which cannot be considered "small" (so the Tangent modulus cannot be used).
I do agree with Roger that in the elastic limit, modulus of elasticity is simply the slope of the stress-strain line. Considering the non linear curve, there are to methods for calculating the modulus of elasticity either tangent modulus or the secant modulus,
For immediate load test of concrete specimen under the uni axial load, you can draw the stress and strain diagram of concrete. Draw the initial tangential line from the origin. Then measure the slop of the line which is the EC. Usually this line is tangential to the stress-strain curve nearly up to 0.45f'c.
Hi Mohammad Ali
The modulus of elasticity is one of the most important elastic properties of concrete since it impacts the serviceability and performance of concrete structures. The elastic modulus of concrete is closely related to the properties of the cement paste and stiffness of mix aggregates.
The stress-strain chart for concrete is a combination of stress-strain figures for the raw materials used to make concrete and the stress-strain figure of paste. The stress- strain figure for both materials and paste may be liner but the combination of them makes the concrete MOE figure pattern non-linear.
There are different methods available for determining MOE using stress-strain chart. however, the static chord method (CS line in the attached image) is the most commonly method used .
A list of the other methods using for the calculation MOE is listed as follows:
1- MOE calculation based on the introduced formula and fcm such as MOE=5000× √fcm or MOE=22×(fc/10)^0.3 or MOE=0.043×ρ^1.5 x √(fcm ) if fcm≤40 MPa
MOE=0.024×ρ^1.5×( √(fcm )+0.12) if fcm>40 MPa
where fc is characteristic strength, fcm is mean compressive strength and ρ is unit weight of concrete.
2- Secant modulus which is the slope of line OS in the attached image
3- Tangent modulus which is the slope of line TT’ in the attached image
4- Dynamic modulus which is the slope of line OD in the attached image
The stress-strain chart can be plotted by either performing test in accordance with the Australian Standard AS 1012.17 or other types of appropriate methods. If you need more details about the start and end points of each tangent line in the image please let me know.
ref : EN 1992-1-1 : 3.1.5 (2)
De modulus of elasticity is defined as the strain at a stress of 0.4 mean compressive strength divided by 0.4 mean compressive strength.
(mean compressive strength = characteristic compressive strength + 8 mPa)
The modulus of elasticity is defined as the tensile strength to the strain at linear region of stress-strain curve which is dependent on the standard method that is used for tension test. It is usually mentioned the procedure for calculating the Young's modulus and tensile strength in the applicable standard method such as ASTM D638 (tension testing method for plastics). If you want to compare some of the materials it is better to calculate the modulus at a certain and safe region of elastic strain.
In the case of the slope of line how to give the unit. Slope of any line is always very small value.
I am agree with Asif Jalal. If modulus of elasticity is the slope of stress-strain curve, then its value is very small & what would be its unit. Can I directly measure elastic modulus by dividing strain rate at break with tensile strength of the specimen?
I think the the young modulus is derived from the slope of stress/strain graph.
Stress is force/area
Strain is deformation in length
Hence it will be pascals/micron or newtons/micron
Correct me if i m wrong
Please academians share me some information about the strain at which the Tensile Modulus should be calculated for non-linear strain-stress with some constants?
Hello Mengistu, take a point 0.2% of Young Modulus and draw a line parallel from the origin equal to the young modulus.
If we want initial tangent modulus we draw a line from the origin point in the stress-strain graph and find the slope of that line. If you are looking for secant modulus select two points in the linear portion of graph and find the difference of those stress points and corresponding strains.The ratio of these differences gives secant modulus.
According to Hooke's law,
Stress is directly propotional to Strain below propotional limit(NOT elastic limit which indicates recovery of material to original shape after removal of stress or load which occurs after propotional limit.
Stress = Young's Modulus * Strain
the Slope of LINEAR PORTION OF stress vs strain curve yiels Young's Modulus.
Young's Modulus is Synonmous with Cohesive Strength which the materials elastically resists with respect to external force before plastic deformation ensues.
thanks & regards,
g. sudhakar
Can anyone please guide how to precisely get Young's modulus value as a slope from the stress-strain curve of a nanofiber mat in the origin software? and what does it mean to linear fit stress-strain curve over 0.5-1% strain range?
Any lead to this matter will be highly appreciated.
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