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A beam of rectangular cross-section (b x d) is subjected to a torque T. What is the maximum torsional stress induced in the beam (b < d and α is a constant)?
- a)T/αb2d
- b)T/αbd2
- c)T/αbd
- d)T/bd
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A beam of rectangular cross-section (b x d) is subjected to a torque T...
Torsion constant of a rectangular section of width b and depth d (b < d) may be expressed as,
J = b3d
J = b3d
For T, L and / sections torsion constant,
where bi and di are the dimensions of each of the component rectangles into which the section may be divided.
Torsional shear stress for rectangular section
Torsional shear stress for rectangular section
For T, L and / sections torsional shear stress may be calculated for each component rectangle by considering them subjected to torsional moment,
Most Upvoted Answer
A beam of rectangular cross-section (b x d) is subjected to a torque T...
X d)?
The maximum torsional stress induced in a beam of rectangular cross-section (b x d) subjected to a torque T can be calculated using the following formula:
τmax = (T / J) * (d / 2)
where τmax is the maximum torsional stress induced in the beam, T is the applied torque, J is the polar moment of inertia of the cross-section, and d is the depth (or height) of the rectangular cross-section.
The polar moment of inertia of a rectangular cross-section can be calculated as:
J = (bd^3) / 3
Substituting this into the formula for τmax, we get:
τmax = (3T / bd^3) * (d / 2)
Simplifying, we get:
τmax = (3T / 2bd^2)
Therefore, the maximum torsional stress induced in the beam is proportional to the applied torque and inversely proportional to the product of the beam's width and the square of its depth.
The maximum torsional stress induced in a beam of rectangular cross-section (b x d) subjected to a torque T can be calculated using the following formula:
τmax = (T / J) * (d / 2)
where τmax is the maximum torsional stress induced in the beam, T is the applied torque, J is the polar moment of inertia of the cross-section, and d is the depth (or height) of the rectangular cross-section.
The polar moment of inertia of a rectangular cross-section can be calculated as:
J = (bd^3) / 3
Substituting this into the formula for τmax, we get:
τmax = (3T / bd^3) * (d / 2)
Simplifying, we get:
τmax = (3T / 2bd^2)
Therefore, the maximum torsional stress induced in the beam is proportional to the applied torque and inversely proportional to the product of the beam's width and the square of its depth.
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