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The maximum permissible deflection for gantry girder of span 6m on which an EOT crane o of capacity 200 kN is operating is
- a)8mm
- b)10mm
- c)12mm
- d)18mm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The maximum permissible deflection for gantry girder of span 6m on whi...
Given information:
- Span of the gantry girder: 6m
- Capacity of the EOT crane: 200 kN
Calculating the maximum deflection:
The maximum deflection for a simply supported beam with a concentrated load at the center can be calculated using the formula:
\(\delta_{\text{{max}}} = \frac{{wL^4}}{{384EI}}\)
where:
- \(\delta_{\text{{max}}}\) is the maximum deflection
- \(w\) is the load per unit length (in this case, it is the weight of the crane divided by the span)
- \(L\) is the span of the beam
- \(E\) is the modulus of elasticity of the material
- \(I\) is the moment of inertia of the beam section
Calculating the load per unit length:
The weight of the crane can be converted to load per unit length by dividing it by the span:
\(w = \frac{{\text{{Load}}}}{{\text{{span}}}} = \frac{{200 \text{{ kN}}}}{{6 \text{{ m}}}} = 33.33 \text{{ kN/m}}\)
Calculating the moment of inertia:
The moment of inertia for a rectangular section can be calculated using the formula:
\(I = \frac{{b \cdot h^3}}{{12}}\)
where:
- \(b\) is the width of the girder
- \(h\) is the height of the girder
Assuming the dimensions of the girder:
Let's assume a rectangular girder with a width of 0.5m and a height of 1m.
Calculating the moment of inertia:
\(I = \frac{{0.5 \cdot 1^3}}{{12}} = 0.0208 \text{{ m}}^4\)
Calculating the maximum deflection:
Substituting the values into the formula:
\(\delta_{\text{{max}}} = \frac{{33.33 \cdot 6^4}}{{384 \cdot 200 \cdot 10^9 \cdot 0.0208}} = 0.008 \text{{ m}}\)
Converting the deflection to millimeters:
\(\delta_{\text{{max}}} = 0.008 \times 1000 = 8 \text{{ mm}}\)
Therefore, the maximum permissible deflection for the gantry girder is 8mm.
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Community Answer
The maximum permissible deflection for gantry girder of span 6m on whi...
For Electric hoist maximum permissible deflection is: L/750.
Hence, 6000/750 = 8 mm.
Hence, 6000/750 = 8 mm.
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