## Modulus of Elasticity of Concrete Solution

STEP 0: Pre-Calculation Summary
Formula Used
Elastic Modulus of concrete for mix design = 5000*(Characteristics Compressive Strength of Concrete)^0.5
Ecmd = 5000*(fck)^0.5
This formula uses 2 Variables
Variables Used
Elastic Modulus of concrete for mix design - (Measured in Pascal) - Elastic Modulus of concrete for mix design is defined as the ratio of the applied stress to the corresponding strain.
Characteristics Compressive Strength of Concrete - (Measured in Pascal) - Characteristics compressive strength of concrete the strength of the concrete below which not more than 5% of the test results are expected to fall.
STEP 1: Convert Input(s) to Base Unit
Characteristics Compressive Strength of Concrete: 20.01 Newton per Square Millimeter --> 20010000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Ecmd = 5000*(fck)^0.5 --> 5000*(20010000)^0.5
Evaluating ... ...
Ecmd = 22366269.246345
STEP 3: Convert Result to Output's Unit
22366269.246345 Pascal -->22.366269246345 Megapascal (Check conversion here)
22.366269246345 Megapascal <-- Elastic Modulus of concrete for mix design
(Calculation completed in 00.016 seconds)
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RV COLLEGE OF ENGINEERING (RVCE), BENGALURU
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## < 7 Mix Design Calculators

Modulus of Rupture of rectangular sample in three-point bending

## Modulus of Rupture of rectangular sample in three-point bending

Formula
"f"_{"3ptr"} = (3*"F"_{"f"}*"L")/(2*"B"*("T"^2))

Example
"84.375MPa"=(3*"80N"*"180mm")/(2*"100mm"*("1.6mm"^2))

Calculator
LaTeX
Modulus of Rupture of Concrete Threepoint bending = (3*Load at fracture point*Length of section)/(2*Width of Section*(Average Section Thickness^2))
Modulus of Rupture of rectangular sample in four-point bending

## Modulus of Rupture of rectangular sample in four-point bending

Formula
"f"_{"4ptr"} = ("F"_{"f"}*"L")/("B"*("T"^2))

Example
"56.25MPa"=("80N"*"180mm")/("100mm"*("1.6mm"^2))

Calculator
LaTeX
Modulus of Rupture of Concrete Fourpoint bending = (Load at fracture point*Length of section)/(Width of Section*(Average Section Thickness^2))
Gel-Space Ratio for Complete Hydration

## Gel-Space Ratio for Complete Hydration

Formula
"GS" = (0.657*"C")/((0.319*"C")+"Wo")

Example
"1.568019"=(0.657*"10kg")/((0.319*"10kg")+"1000mL")

Calculator
LaTeX
Gel Space Ratio = (0.657*Mass Of Cement)/((0.319*Mass Of Cement)+Volume Of Mixing Water)
Volume of products of hydration per unit of dry cement

## Volume of products of hydration per unit of dry cement

Formula
"Vp" = ("V"_{"hc"}/"V"_{"cah"})

Example
"22.22222mm³"=("70mL"/"3.15g/mL")

Calculator
LaTeX
Volume of Solid Products of Hydration = (Volume of Hydrated Cement/Absolute Volume of Dry Cement actually Hydrated)
Target Mean Strength for Mix Design

## Target Mean Strength for Mix Design

Formula
"f'"_{"ck"} = "fck"+(1.65*"σ")

Example
"20MPa"="20MPa"+(1.65*"2")

Calculator
LaTeX
Target Average Compressive Strength = Characteristic compressive strength+(1.65*Standard Deviation of distribution)
Volume of Empty Capillary Pores

## Volume of Empty Capillary Pores

Formula
"Vec" = ("V"_{"cp"}-"V"_{"wcp"})

Example
"4mL"=("8mL"-"4mL")

Calculator
LaTeX
Volume of Empty Capillary Pores = (Volume of Capillary Pores-Volume of Water Filled Capillary Pores)
Modulus of Elasticity of Concrete

## Modulus of Elasticity of Concrete

Formula
"E"_{"cmd"} = 5000*("f"_{"ck"})^0.5

Example
"22.36627MPa"=5000*("20.01N/mm²")^0.5

Calculator
LaTeX
Elastic Modulus of concrete for mix design = 5000*(Characteristics Compressive Strength of Concrete)^0.5

## Modulus of Elasticity of Concrete Formula

Elastic Modulus of concrete for mix design = 5000*(Characteristics Compressive Strength of Concrete)^0.5
Ecmd = 5000*(fck)^0.5

## What is the value of elasticity of concrete?

The modulus of elasticity of concrete is relatively constant at low stress levels but starts decreasing at higher stress levels as matrix cracking develops. The elastic modulus of the hardened paste may be in the order of 10-30 GPa and aggregates about 45 to 85 GPa.

## How to Calculate Modulus of Elasticity of Concrete?

Modulus of Elasticity of Concrete calculator uses Elastic Modulus of concrete for mix design = 5000*(Characteristics Compressive Strength of Concrete)^0.5 to calculate the Elastic Modulus of concrete for mix design, Modulus of Elasticity of Concrete is defined as the ratio of the applied stress to the corresponding strain. It demonstrates the ability of concrete to withstand deformation due to applied stress and also its stiffness (the ability of concrete to deflect elastically). Elastic Modulus of concrete for mix design is denoted by Ecmd symbol.

How to calculate Modulus of Elasticity of Concrete using this online calculator? To use this online calculator for Modulus of Elasticity of Concrete, enter Characteristics Compressive Strength of Concrete (fck) and hit the calculate button. Here is how the Modulus of Elasticity of Concrete calculation can be explained with given input values -> 22.36627 = 5000*(20010000)^0.5.

### FAQ

What is Modulus of Elasticity of Concrete?
Modulus of Elasticity of Concrete is defined as the ratio of the applied stress to the corresponding strain. It demonstrates the ability of concrete to withstand deformation due to applied stress and also its stiffness (the ability of concrete to deflect elastically) and is represented as Ecmd = 5000*(fck)^0.5 or Elastic Modulus of concrete for mix design = 5000*(Characteristics Compressive Strength of Concrete)^0.5. Characteristics compressive strength of concrete the strength of the concrete below which not more than 5% of the test results are expected to fall.
How to calculate Modulus of Elasticity of Concrete?
Modulus of Elasticity of Concrete is defined as the ratio of the applied stress to the corresponding strain. It demonstrates the ability of concrete to withstand deformation due to applied stress and also its stiffness (the ability of concrete to deflect elastically) is calculated using Elastic Modulus of concrete for mix design = 5000*(Characteristics Compressive Strength of Concrete)^0.5. To calculate Modulus of Elasticity of Concrete, you need Characteristics Compressive Strength of Concrete (fck). With our tool, you need to enter the respective value for Characteristics Compressive Strength of Concrete and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know