GATE CE 2020 Set 1 — Question 52
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Structural Engineering → Connections & Plastic Analysis → Shear Stresses in Beams
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Question
The flange and web plates of the doubly symmetric built-up section are connected by continuous thick fillet welds as shown in the figure (not drawn to the scale). The moment of inertia of the section about its principal axis is . The permissible shear stress in the fillet welds is . The design shear strength of the section is governed by the capacity of the fillet welds.
The maximum shear force (in kN, round off to one decimal place) that can be carried by the section, is _______.
Correct answer
393.5 to 399.1
Solution
1.Identify the section and weld configuration:
The section is a doubly symmetric built-up box section with two web plates and two flange plates. There are 4 fillet welds at the junction of the top flange and the two web plates (2 welds per web plate).2.Given data:
- Weld leg size,
- Throat thickness,
- Permissible shear stress in weld,
- Moment of inertia,
- Flange width,
- Flange thickness,
- Total depth of section,
The area of one flange is .
The distance from the neutral axis () to the centroid of the flange is .
.
4.Calculate the total shear capacity of the welds per unit length ():
There are 4 welds at the flange-web interface level.Capacity of one weld per unit length = .
Total capacity, .
5.Relate shear force () to shear flow ():
The shear flow at the interface is .For the section to be safe, .
.Rounding to one decimal place, the maximum shear force is .
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