GATE CE 2014 Set 2 — Question 41
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Structural Engineering → Stress, Strain & Beams → Thermal Stress
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Question
The beam of an overall depth mm (shown below) is used in a building subjected to two different thermal environments. The temperatures at the top and bottom surfaces of the beam are and respectively. Considering coefficient of thermal expansion () as per , the vertical deflection of the beam (in mm) at its mid-span due to temperature gradient is ________
Correct answer
2.38 to 2.45
Solution
The vertical deflection at the mid-span of a simply supported beam due to a linear temperature gradient is calculated based on the curvature induced by the temperature difference.
The curvature induced by a linear temperature gradient is given by:
Thus, the vertical deflection at mid-span is mm.
1.Identify the parameters:
- Total length of the beam, .
- Overall depth of the beam, .
- Temperature at the top, .
- Temperature at the bottom, .
- Temperature difference, .
- Coefficient of thermal expansion, .
The curvature induced by a linear temperature gradient is given by:
3.Calculate the mid-span deflection ():
For a simply supported beam with a constant curvature, the deflection at the mid-span is:Thus, the vertical deflection at mid-span is mm.
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