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A wooden beam of rectangular cross section 100mm × 200mm is formed by gluing two identical beams of square cross section. If the safe shear stress of the glue is 3 N⁄mm2, the safe shear strength
- a)30 kN
- b)40 kN
- c)50 kN
- d)60 kN
Correct answer is option 'B'. Can you explain this answer?
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A wooden beam of rectangular cross section 100mm × 200mm is formed by...
Maximum shear stress
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F = 40 × 103N
= 40 kN
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A wooden beam of rectangular cross section 100mm × 200mm is formed by...
Solution:
Given data:
Width of rectangular cross section = 100 mm
Height of rectangular cross section = 200 mm
Safe shear stress of glue = 3 N/mm²
To find:
Safe shear strength of glue
Approach:
1. Calculate the area of the rectangular cross-section.
2. Divide the area by 2 to get the area of the square cross-section.
3. Calculate the shear force acting on one square cross-section.
4. Multiply the shear force by 2 to get the total shear force acting on both square cross-sections.
5. Calculate the safe shear strength of glue using the formula: Safe shear strength = Safe shear stress x Area of glue joint.
Calculation:
1. Area of rectangular cross-section = Width x Height = 100 mm x 200 mm = 20000 mm²
2. Area of one square cross-section = Area of rectangular cross-section / 2 = 20000 mm² / 2 = 10000 mm²
3. Shear force acting on one square cross-section = Shear stress x Area of glue joint = 3 N/mm² x 10000 mm² = 30000 N
4. Total shear force acting on both square cross-sections = Shear force acting on one square cross-section x 2 = 30000 N x 2 = 60000 N
5. Safe shear strength of glue = Safe shear stress x Area of glue joint = 3 N/mm² x 10000 mm² = 30000 N = 40 kN (approx.)
Therefore, the safe shear strength of glue is 40 kN.
Given data:
Width of rectangular cross section = 100 mm
Height of rectangular cross section = 200 mm
Safe shear stress of glue = 3 N/mm²
To find:
Safe shear strength of glue
Approach:
1. Calculate the area of the rectangular cross-section.
2. Divide the area by 2 to get the area of the square cross-section.
3. Calculate the shear force acting on one square cross-section.
4. Multiply the shear force by 2 to get the total shear force acting on both square cross-sections.
5. Calculate the safe shear strength of glue using the formula: Safe shear strength = Safe shear stress x Area of glue joint.
Calculation:
1. Area of rectangular cross-section = Width x Height = 100 mm x 200 mm = 20000 mm²
2. Area of one square cross-section = Area of rectangular cross-section / 2 = 20000 mm² / 2 = 10000 mm²
3. Shear force acting on one square cross-section = Shear stress x Area of glue joint = 3 N/mm² x 10000 mm² = 30000 N
4. Total shear force acting on both square cross-sections = Shear force acting on one square cross-section x 2 = 30000 N x 2 = 60000 N
5. Safe shear strength of glue = Safe shear stress x Area of glue joint = 3 N/mm² x 10000 mm² = 30000 N = 40 kN (approx.)
Therefore, the safe shear strength of glue is 40 kN.
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A wooden beam of rectangular cross section 100mm × 200mm is formed by gluing two identical beams of square cross section. If the safe shear stress of the glue is 3 N⁄mm2, the safe shear strengtha) 30 kNb) 40 kNc) 50 kNd) 60 kNCorrect answer is option 'B'. Can you explain this answer?
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