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A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.?
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A load of 1000 KN is applied to a reinforced concrete column of 600 mm...
Stress in Concrete and Steel in a Reinforced Concrete Column
Given:
- Load applied = 1000 kN
- Diameter of the column = 600 mm
- Diameter of the steel rods = 40 mm
- Modulus of elasticity of concrete (Ec) = 15 MPa
- Modulus of elasticity of steel (Es) = 200 GPa
Calculating Stress in Concrete:
The stress in the concrete can be calculated using the formula:
Stress (σc) = Load / Area
Calculating Area of the Column:
The area of the column can be calculated using the formula:
Area = π * (diameter / 2)2
Substituting the given values:
Area = π * (600 mm / 2)2 = 282,743.34 mm2
Converting the area to square meters:
Area = 282,743.34 mm2 * (1 m / 1000 mm)2 = 0.28274 m2
Substituting the Values:
Stress (σc) = 1000 kN / 0.28274 m2 = 3.539 MPa
Therefore, the stress in the concrete is 3.539 MPa.
Calculating Stress in Steel:
The stress in the steel can be calculated using the formula:
Stress (σs) = Load / Area
Calculating Area of Steel Rods:
The area of one steel rod can be calculated using the formula:
Area = π * (diameter / 2)2
Substituting the given values:
Area = π * (40 mm / 2)2 = 1256.64 mm2
Converting the area to square meters:
Area = 1256.64 mm2 * (1 m / 1000 mm)2 = 0.001257 m2
Substituting the Values:
Since there are four steel rods, the total area of steel is:
Total Area = 4 * 0.001257 m2 = 0.005028 m2
Stress (σs) = 1000 kN / 0.005028 m2 = 198,542 MPa
Therefore, the stress in the steel is 198,542 MPa.
Summary:
- The stress in the concrete is 3.539 MPa.
- The stress in the steel is 198,542 MPa.
- The concrete and steel experience different levels of stress due to their different modulus of elasticity values. The steel, being much stiffer than the concrete, carries most of the load, resulting in a higher stress. This is the principle behind the use of reinforced concrete, where the steel reinforcement
Given:
- Load applied = 1000 kN
- Diameter of the column = 600 mm
- Diameter of the steel rods = 40 mm
- Modulus of elasticity of concrete (Ec) = 15 MPa
- Modulus of elasticity of steel (Es) = 200 GPa
Calculating Stress in Concrete:
The stress in the concrete can be calculated using the formula:
Stress (σc) = Load / Area
Calculating Area of the Column:
The area of the column can be calculated using the formula:
Area = π * (diameter / 2)2
Substituting the given values:
Area = π * (600 mm / 2)2 = 282,743.34 mm2
Converting the area to square meters:
Area = 282,743.34 mm2 * (1 m / 1000 mm)2 = 0.28274 m2
Substituting the Values:
Stress (σc) = 1000 kN / 0.28274 m2 = 3.539 MPa
Therefore, the stress in the concrete is 3.539 MPa.
Calculating Stress in Steel:
The stress in the steel can be calculated using the formula:
Stress (σs) = Load / Area
Calculating Area of Steel Rods:
The area of one steel rod can be calculated using the formula:
Area = π * (diameter / 2)2
Substituting the given values:
Area = π * (40 mm / 2)2 = 1256.64 mm2
Converting the area to square meters:
Area = 1256.64 mm2 * (1 m / 1000 mm)2 = 0.001257 m2
Substituting the Values:
Since there are four steel rods, the total area of steel is:
Total Area = 4 * 0.001257 m2 = 0.005028 m2
Stress (σs) = 1000 kN / 0.005028 m2 = 198,542 MPa
Therefore, the stress in the steel is 198,542 MPa.
Summary:
- The stress in the concrete is 3.539 MPa.
- The stress in the steel is 198,542 MPa.
- The concrete and steel experience different levels of stress due to their different modulus of elasticity values. The steel, being much stiffer than the concrete, carries most of the load, resulting in a higher stress. This is the principle behind the use of reinforced concrete, where the steel reinforcement
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A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.?
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A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.?.
A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A load of 1000 KN is applied to a reinforced concrete column of 600 mm diameter which has four steel rods of 40 mm diameter embedded in it. Determine the stress in the concrete and steel. Take E for concrete 15 MPa and steel 200 GPa.?.
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