GATE CE 2020 Set 1 — Question 54
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Structural Engineering → Slabs, Columns & Prestressed → Prestressed Concrete Beams
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Question
A simply supported prismatic concrete beam of rectangular cross-section, having a span of , is prestressed with an effective prestressing force of . The eccentricity of the prestressing tendon is zero at supports and varies linearly to a value of at the mid-span. In order to balance an external concentrated load of applied at the mid-span, the required value of (in mm, round off to the nearest integer) of the tendon, is ________.
Correct answer
39 to 41
Solution
According to the load balancing concept, the upward force exerted by the prestressing tendon should balance the downward external load.For a linear (triangular) tendon profile with eccentricity at mid-span and zero at supports, the upward concentrated force () exerted by the tendon at mid-span is given by:
Given:
Effective prestressing force,
Span of the beam,
External concentrated load at mid-span, Setting :
The required value of is .
Given:
Effective prestressing force,
Span of the beam,
External concentrated load at mid-span, Setting :
The required value of is .
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