GATE CE 2020 Set 2 — Question 53
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Structural Engineering → RC Fundamentals & Beams → Limit State Method
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Question
The cross-section of the reinforced concrete beam having an effective depth of is shown in the figure (not drawn to the scale). The grades of concrete and steel used are M35 and Fe550, respectively. The area of tension reinforcement is . It is given that corresponding to proof stress, the material safety factor is and the yield strain of Fe550 steel is .
As per IS 456:2000, the limiting depth (in mm, round off to the nearest integer) of the neutral axis measured from the extreme compression fiber, is __________.
Correct answer
220 to 224
Solution
The limiting depth of the neutral axis () for a singly reinforced section is determined by the strain compatibility at the limit state of collapse in flexure. It is given by the formula:where:
is the yield strain of the steel reinforcement.
is the effective depth of the beam.Given:
Yield strain of Fe550 steel,
Effective depth, Substituting the values into the formula:Rounding off to the nearest integer, the limiting depth of the neutral axis is .
is the yield strain of the steel reinforcement.
is the effective depth of the beam.Given:
Yield strain of Fe550 steel,
Effective depth, Substituting the values into the formula:Rounding off to the nearest integer, the limiting depth of the neutral axis is .
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