Modulus of elasticity of concrete, E is calculated using:
Understanding Modulus of Elasticity of Concrete
The modulus of elasticity, often denoted as E, is a fundamental material property that describes its stiffness. In simpler terms, it tells us how much a material will deform elastically under stress. For concrete, the modulus of elasticity is an important parameter used in structural analysis and design calculations, especially when determining deflections and deformations under load.
Factors Affecting Concrete Modulus of Elasticity
The modulus of elasticity of concrete is influenced by several factors, including:
- The strength of the concrete (higher strength generally means higher modulus).
- The type of aggregate used.
- The age of the concrete (modulus increases with age).
- The mix proportions.
- The curing conditions.
Standard Formula for Modulus of Elasticity
For standard concrete used in design, codes often provide empirical formulas to estimate the short-term static modulus of elasticity based on the characteristic compressive strength. The characteristic compressive strength of concrete is denoted by \(f_{ck}\).
Based on common standards and practices in structural engineering, the short-term static modulus of elasticity (\(E\)) for concrete is widely calculated using the following formula:
\[\rm{E = 5000\sqrt{f_{ck}}}\]
where:
- \(E\) is the short-term static modulus of elasticity of concrete in MPa.
- \(f_{ck}\) is the characteristic compressive strength of concrete at 28 days in MPa.
Analyzing the Given Options
We are given several options for calculating the modulus of elasticity of concrete, E:
- Option 1: \(\rm{E = 5000\sqrt{f_{ck}}}\)
- Option 2: \(\rm{E = 500\sqrt{f_{ck}}}\)
- Option 3: \(\rm{E = 50\sqrt{f_{ck}}}\)
- Option 4: \(\rm{E = 5\sqrt{f_{ck}}}\)
Comparing these options with the standard formula used for calculating the modulus of elasticity of concrete, we can see that Option 1 matches the widely accepted empirical relationship.
Conclusion
The modulus of elasticity of concrete, E, is calculated using the formula \( \rm{E = 5000\sqrt{f_{ck}}} \), where \( f_{ck} \) is the characteristic compressive strength of the concrete.
| Option | Formula | Correctness |
|---|---|---|
| 1 | \( \rm{E = 5000\sqrt{f_{ck}}} \) | Correct |
| 2 | \( \rm{E = 500\sqrt{f_{ck}}} \) | Incorrect |
| 3 | \( \rm{E = 50\sqrt{f_{ck}}} \) | Incorrect |
| 4 | \( \rm{E = 5\sqrt{f_{ck}}} \) | Incorrect |
Revision Table: Concrete Modulus of Elasticity
| Concept | Description | Formula |
|---|---|---|
| Modulus of Elasticity (E) | Measure of concrete stiffness, resistance to elastic deformation under stress. | \( \rm{E = 5000\sqrt{f_{ck}}} \) (Short-term static) |
| Characteristic Compressive Strength (\(f_{ck}\)) | Concrete cube strength at 28 days, used as a parameter in the formula. | - |
Additional Information on Concrete Properties
While \( \rm{E = 5000\sqrt{f_{ck}}} \) gives the short-term static modulus of elasticity, the actual modulus can vary. Factors like long-term loads (creep) and dynamic loads can affect the effective modulus. Design codes often provide adjustments or different values for specific applications.
Other important properties of concrete include:
- Compressive Strength: Resistance to crushing under compression.
- Tensile Strength: Resistance to pulling apart (much lower than compressive strength).
- Creep: Time-dependent deformation under sustained load.
- Shrinkage: Volume reduction due to loss of moisture.
Understanding these properties is crucial for the safe and efficient design of concrete structures.
Important Questions from Introduction
In the following table, the left column contains the names of standard graph algorithms and the right column contains the time complexities of the algorithms. Here, n and m are number of vertices and edges, respectively. Match each algorithm with its time complexity.
List I List II Standard graph algorithms Time complexities A. Bellman‐Ford algorithm I. O(m*log n) B. Kruskal’s algorithm II. O(n 3) C. Floyd‐Warshall algorithm III. O(n*m) D. Topological sorting IV. O(n + m) Choose the correct answer from the options given below :
How many cards must be selected from a standard deck of 52 cards to guarantee that at least three hearts are present among them?
Match List 1 with List 2 and choose the correct answer from the code given below:
List I
(Graph Algorithm)
List II
(Time Complexity)
a) Dijkstra’s algorithm
i) Θ(E log E)
b) Kruskal’s algorithm
ii) Θ(V 3)
c) Floyd-Warshall algorithm
iii) Θ(V 2)
d) Topological sorting
iv) Θ(V + E)
Where V and E are the number of vertices and edges in graph respectively.
The solution of recurrence relation: T(n)=2T(sqrt(n)) + lg(n) is
In how many types can R.C.C. be classified into?
