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A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is?
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A singly reinforced concrete beam of 25 cm width and 70 cm effective d...
Solution:
Given data:
Width of the beam (b) = 25 cm
Effective depth of the beam (d) = 70 cm
Area of steel reinforcement (Ast) = 18.75 cm2
Modular ratio (m) = 15
The depth of the neutral axis can be found out by using the following formula:
Ast / (b x d) x m = (0.87fy / fy + 0.48)
where, fy is the characteristic strength of steel reinforcement.
Calculation:
Substituting the given values in the above formula, we get:
18.75 / (25 x 70) x 15 = (0.87fy / fy + 0.48)
On solving this equation, we get:
fy = 415.8 N/mm2
Now, substituting fy in the above formula, we get:
18.75 / (25 x 70) x 15 = (0.87 x 415.8 / 415.8 + 0.48)
On solving this equation, we get:
Depth of neutral axis (x) = 34.4 cm
Therefore, the depth of neutral axis of the given singly reinforced concrete beam is 34.4 cm.
Explanation:
The neutral axis is the axis of the beam where the tensile and compressive stresses are equal to zero. In a singly reinforced concrete beam, the steel reinforcement is provided only on the tension side of the beam. The depth of the neutral axis depends on the area of steel reinforcement, modular ratio, characteristic strength of steel reinforcement, and the compressive strength of concrete.
In this problem, we have calculated the depth of the neutral axis by using the formula for singly reinforced concrete beam.
Given data:
Width of the beam (b) = 25 cm
Effective depth of the beam (d) = 70 cm
Area of steel reinforcement (Ast) = 18.75 cm2
Modular ratio (m) = 15
The depth of the neutral axis can be found out by using the following formula:
Ast / (b x d) x m = (0.87fy / fy + 0.48)
where, fy is the characteristic strength of steel reinforcement.
Calculation:
Substituting the given values in the above formula, we get:
18.75 / (25 x 70) x 15 = (0.87fy / fy + 0.48)
On solving this equation, we get:
fy = 415.8 N/mm2
Now, substituting fy in the above formula, we get:
18.75 / (25 x 70) x 15 = (0.87 x 415.8 / 415.8 + 0.48)
On solving this equation, we get:
Depth of neutral axis (x) = 34.4 cm
Therefore, the depth of neutral axis of the given singly reinforced concrete beam is 34.4 cm.
Explanation:
The neutral axis is the axis of the beam where the tensile and compressive stresses are equal to zero. In a singly reinforced concrete beam, the steel reinforcement is provided only on the tension side of the beam. The depth of the neutral axis depends on the area of steel reinforcement, modular ratio, characteristic strength of steel reinforcement, and the compressive strength of concrete.
In this problem, we have calculated the depth of the neutral axis by using the formula for singly reinforced concrete beam.
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A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is?
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A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is?.
A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A singly reinforced concrete beam of 25 cm width and 70 cm effective depth is provided with 18.75 cm2 steel. If the modular ratio (m) is 15, the depth of the neutral axis, is?.
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