UPSC Exam > UPSC Questions > A rectangular beam reinforced on both sides i...
Start Learning for Free
A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18?
Most Upvoted Answer
A rectangular beam reinforced on both sides is 30cm wide and 55cm deep...
Given Data
- Width of the beam (b) = 30 cm
- Depth of the beam (d) = 55 cm
- Distance of steel from edges = 5 cm
- Limiting stress in concrete (f_c) = 5 N/mm²
- Limiting stress in steel (f_s) = 140 N/mm²
- Bending Moment (M) = 80 KN-m
- Modular Ratio (M) = 18
Effective Depth Calculation
- Effective depth (d) = Total depth - distance of steel from the edge
- d = 55 cm - 5 cm = 50 cm
Bending Moment Conversion
- Convert Bending Moment to N-mm:
- M = 80 KN-m = 80 × 10^3 × 1000 = 80,000,000 N-mm
Calculate Required Steel Area (A_s)
- Using the formula: M = f_s * A_s * (d - a/2)
- Where 'a' = depth of the neutral axis, for bending stress conditions, use:
- a = (f_c / (f_c + f_s/M)) * d
- Substituting values to find A_s, rearranging gives A_s = M / (f_s * (d - a/2))
Neutral Axis Depth Calculation
- For balanced sections, the neutral axis (a) can be approximated from:
- a = (f_c / (f_c + (f_s/M))) * d
- Using limiting stresses and effective depth, calculate 'a'.
Final Area of Steel Calculation
- Substitute back to find A_s:
- A_s = (80,000,000) / (140 * (50 - a/2))
Conclusion
- Calculate the value of A_s to determine the amount of steel required. Ensure that the calculated area meets the design requirements while adhering to the limiting stress values provided.
- Width of the beam (b) = 30 cm
- Depth of the beam (d) = 55 cm
- Distance of steel from edges = 5 cm
- Limiting stress in concrete (f_c) = 5 N/mm²
- Limiting stress in steel (f_s) = 140 N/mm²
- Bending Moment (M) = 80 KN-m
- Modular Ratio (M) = 18
Effective Depth Calculation
- Effective depth (d) = Total depth - distance of steel from the edge
- d = 55 cm - 5 cm = 50 cm
Bending Moment Conversion
- Convert Bending Moment to N-mm:
- M = 80 KN-m = 80 × 10^3 × 1000 = 80,000,000 N-mm
Calculate Required Steel Area (A_s)
- Using the formula: M = f_s * A_s * (d - a/2)
- Where 'a' = depth of the neutral axis, for bending stress conditions, use:
- a = (f_c / (f_c + f_s/M)) * d
- Substituting values to find A_s, rearranging gives A_s = M / (f_s * (d - a/2))
Neutral Axis Depth Calculation
- For balanced sections, the neutral axis (a) can be approximated from:
- a = (f_c / (f_c + (f_s/M))) * d
- Using limiting stresses and effective depth, calculate 'a'.
Final Area of Steel Calculation
- Substitute back to find A_s:
- A_s = (80,000,000) / (140 * (50 - a/2))
Conclusion
- Calculate the value of A_s to determine the amount of steel required. Ensure that the calculated area meets the design requirements while adhering to the limiting stress values provided.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18?
Question Description
A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18?.
A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18?.
Solutions for A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? defined & explained in the simplest way possible. Besides giving the explanation of
A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18?, a detailed solution for A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? has been provided alongside types of A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? theory, EduRev gives you an
ample number of questions to practice A rectangular beam reinforced on both sides is 30cm wide and 55cm deep the centres of steel are 5cm from the respective edges. If the limiting stresses in concrete and steel are 5N/mm² & 140N/mm² respectively determine the steel areas for a B.M of 80KN-m take M=18? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup