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A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will be
Correct answer is '1100'. Can you explain this answer?
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A beam of size 250 mm width and 460 mm effective depth is subjected to...
Calculation of limiting area of steel for a rectangular beam
Given data:
Width of beam = 250 mm
Effective depth of beam = 450 mm
Grade of concrete = M20
Grade of steel = Fe 415
Assuming the modular ratio as 280/3, the moment of resistance can be calculated using the following formula:
M.R. = 0.87*f_ck*b*d^2/3 + 0.33*f_y*(A_st)/100*(d - A_st/200)
Where,
f_ck = characteristic compressive strength of concrete
b = width of the beam
d = effective depth of the beam
f_y = characteristic strength of steel
A_st = area of steel required
Substituting the given values in the above formula, we get:
M.R. = 0.87*20*250*450^2/3 + 0.33*415*(A_st)/100*(450 - A_st/200)
M.R. = 0.13875*10^9 + 1.385*A_st - 0.00413*A_st^2
The limiting value of M.R. is obtained when the second derivative of the above equation is zero. Solving for A_st, we get:
A_st = 1077 mm^2
Therefore, the limiting area of steel for a rectangular beam of 250 mm width and 450 mm effective depth with M20 concrete and Fe 415 steel is 1077 mm^2.
Given data:
Width of beam = 250 mm
Effective depth of beam = 450 mm
Grade of concrete = M20
Grade of steel = Fe 415
Assuming the modular ratio as 280/3, the moment of resistance can be calculated using the following formula:
M.R. = 0.87*f_ck*b*d^2/3 + 0.33*f_y*(A_st)/100*(d - A_st/200)
Where,
f_ck = characteristic compressive strength of concrete
b = width of the beam
d = effective depth of the beam
f_y = characteristic strength of steel
A_st = area of steel required
Substituting the given values in the above formula, we get:
M.R. = 0.87*20*250*450^2/3 + 0.33*415*(A_st)/100*(450 - A_st/200)
M.R. = 0.13875*10^9 + 1.385*A_st - 0.00413*A_st^2
The limiting value of M.R. is obtained when the second derivative of the above equation is zero. Solving for A_st, we get:
A_st = 1077 mm^2
Therefore, the limiting area of steel for a rectangular beam of 250 mm width and 450 mm effective depth with M20 concrete and Fe 415 steel is 1077 mm^2.
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A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will beCorrect answer is '1100'. Can you explain this answer?
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A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will beCorrect answer is '1100'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will beCorrect answer is '1100'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will beCorrect answer is '1100'. Can you explain this answer?.
A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will beCorrect answer is '1100'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will beCorrect answer is '1100'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A beam of size 250 mm width and 460 mm effective depth is subjected to limit state moment of 146 kNm. If M 20 grade concrete and Fe 415 steel are used, the area of steel required will beCorrect answer is '1100'. Can you explain this answer?.
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