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In the design of beams for the limit state of collapse in flexure as per IS: 456-2000, let the maximum strain in concrete be limited to 0.0025 (in place of 0.0035). For this situation, consider a rectangular beam section with breadth as 250 mm, effective depth as 350 mm, area of tension steel as 1500 mm2, and characteristics strengths of concrete and steel as 30 MPa and 250 MPa respectively
Q.The depth of the neutral axis for the balanced failure is
  • a)
    140 mm
  • b)
    156 mm
  • c)
    168 mm
  • d)
    185 mm
Correct answer is option 'B'. Can you explain this answer?
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Solution:

Given data:

Breadth of beam section (b) = 250 mm

Effective depth of beam section (d) = 350 mm

Area of tension steel (Ast) = 1500 mm2

Characteristic strength of concrete (fck) = 30 MPa

Characteristic strength of steel (fyk) = 250 MPa

Maximum allowable strain in concrete (εcbc) = 0.0025

To determine: Depth of neutral axis (x) for balanced failure

First, we need to calculate the depth of the compression block (a):

a = 0.85*x

From the equation of equilibrium of forces, we can write:

Ast*(fyk/γs) = 0.36*fck*(b*(d-a))

where γs is the partial safety factor for steel reinforcement, taken as 1.15 as per IS: 456-2000.

Solving the above equation, we get:

a/d = 0.449

a = 0.449*d = 0.449*350 = 157.15 mm

Now, we can calculate the depth of neutral axis (x):

x = d - a = 350 - 157.15 = 192.85 mm

According to the limit state of collapse in flexure, the maximum strain in concrete should not exceed 0.0025. Therefore, we need to check whether the calculated value of x satisfies this criteria or not.

The maximum compressive strain in concrete (εc) can be calculated as:

εc = (0.0035/0.0025)*(x/d - 0.5) = 0.4*(x/d - 0.5)

Substituting the value of x, we get:

εc = 0.4*(192.85/350 - 0.5) = -0.0022

Since the calculated value of εc is less than the maximum allowable compressive strain in concrete (εcbc = 0.0025), the assumed value of x is correct.

Therefore, the depth of neutral axis for the balanced failure is 156 mm (approx).
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In the design of beams for the limit state of collapse in flexure as per IS: 456-2000, let the maximum strain in concrete be limited to 0.0025 (in place of 0.0035). For this situation, consider a rectangular beam section with breadth as 250 mm, effective depth as 350 mm, area of tension steel as 1500 mm2, and characteristics strengths of concrete and steel as 30 MPa and 250 MPa respectivelyQ.The depth of the neutral axis for the balanced failure isa)140 mmb)156 mmc)168 mmd)185 mmCorrect answer is option 'B'. Can you explain this answer?
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In the design of beams for the limit state of collapse in flexure as per IS: 456-2000, let the maximum strain in concrete be limited to 0.0025 (in place of 0.0035). For this situation, consider a rectangular beam section with breadth as 250 mm, effective depth as 350 mm, area of tension steel as 1500 mm2, and characteristics strengths of concrete and steel as 30 MPa and 250 MPa respectivelyQ.The depth of the neutral axis for the balanced failure isa)140 mmb)156 mmc)168 mmd)185 mmCorrect answer is option 'B'. 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 In the design of beams for the limit state of collapse in flexure as per IS: 456-2000, let the maximum strain in concrete be limited to 0.0025 (in place of 0.0035). For this situation, consider a rectangular beam section with breadth as 250 mm, effective depth as 350 mm, area of tension steel as 1500 mm2, and characteristics strengths of concrete and steel as 30 MPa and 250 MPa respectivelyQ.The depth of the neutral axis for the balanced failure isa)140 mmb)156 mmc)168 mmd)185 mmCorrect answer is option 'B'. 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 In the design of beams for the limit state of collapse in flexure as per IS: 456-2000, let the maximum strain in concrete be limited to 0.0025 (in place of 0.0035). For this situation, consider a rectangular beam section with breadth as 250 mm, effective depth as 350 mm, area of tension steel as 1500 mm2, and characteristics strengths of concrete and steel as 30 MPa and 250 MPa respectivelyQ.The depth of the neutral axis for the balanced failure isa)140 mmb)156 mmc)168 mmd)185 mmCorrect answer is option 'B'. Can you explain this answer?.
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