P01: Calculate the modulus of elasticity Ec for each case shown in table: E,=33w¹ √√, psi E=0.043w¹5 √√, MPa Density 180 pcf 160 pcf 145 pcf 2550 kg/m³ 2400 kg/m³ 2300 kg/m³ f'c 5000 psi 4000 psi 3000 psi 45 MPa 40 MPa 25 MPa
P01: Calculate the modulus of elasticity Ec for each case shown in table: E,=33w¹ √√, psi E=0.043w¹5 √√, MPa Density 180 pcf 160 pcf 145 pcf 2550 kg/m³ 2400 kg/m³ 2300 kg/m³ f'c 5000 psi 4000 psi 3000 psi 45 MPa 40 MPa 25 MPa
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Subject is Reinforced Concrete Design
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### P01: Calculate the Modulus of Elasticity \( E_c \) for Each Case Shown in the Table:
#### Formula for Calculating Modulus of Elasticity:
For units in psi (pounds per square inch):
\[ E_c = 33w^{1.5} \sqrt{f'_c} \text{ psi} \]
For units in MPa (megapascals):
\[ E_c = 0.043w^{1.5} \sqrt{f'_c} \text{ MPa} \]
#### Data Table:
The table below lists the density and compressive strength values for various cases:
| Density | \( f'_c \) |
|----------------|----------------|
| 180 pcf | 5000 psi |
| 160 pcf | 4000 psi |
| 145 pcf | 3000 psi |
| 2550 kg/m³ | 45 MPa |
| 2400 kg/m³ | 40 MPa |
| 2300 kg/m³ | 25 MPa |
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#### Explanation of the Table:
- **Density**: This column provides the density values in pounds per cubic foot (pcf) for the first three cases and in kilograms per cubic meter (kg/m³) for the last three cases.
- **\( f'_c \)**: This column indicates the compressive strength of the material in pounds per square inch (psi) for the first three cases and in megapascals (MPa) for the last three cases.
To calculate the modulus of elasticity \( E_c \) for each case, use the provided formulas and corresponding units for density and compressive strength.
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### P01: Calculate the Modulus of Elasticity \( E_c \) for Each Case Shown in the Table:
#### Formula for Calculating Modulus of Elasticity:
For units in psi (pounds per square inch):
\[ E_c = 33w^{1.5} \sqrt{f'_c} \text{ psi} \]
For units in MPa (megapascals):
\[ E_c = 0.043w^{1.5} \sqrt{f'_c} \text{ MPa} \]
#### Data Table:
The table below lists the density and compressive strength values for various cases:
| Density | \( f'_c \) |
|----------------|----------------|
| 180 pcf | 5000 psi |
| 160 pcf | 4000 psi |
| 145 pcf | 3000 psi |
| 2550 kg/m³ | 45 MPa |
| 2400 kg/m³ | 40 MPa |
| 2300 kg/m³ | 25 MPa |
---
#### Explanation of the Table:
- **Density**: This column provides the density values in pounds per cubic foot (pcf) for the first three cases and in kilograms per cubic meter (kg/m³) for the last three cases.
- **\( f'_c \)**: This column indicates the compressive strength of the material in pounds per square inch (psi) for the first three cases and in megapascals (MPa) for the last three cases.
To calculate the modulus of elasticity \( E_c \) for each case, use the provided formulas and corresponding units for density and compressive strength.
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