Question:
Two shafts are said to have equal strength, if:
Two shafts are said to have equal strength, if:
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The strength of a shaft is defined by its ability to resist twisting. Therefore, two shafts are equal in strength when they can transmit the same maximum twisting moment (torque).
Updated On: Aug 7, 2026
- diameter of both the shafts is equal
- twisting moment of both the shafts is equal
- angle of twist of both the shafts is equal
- Material is same for both shafts
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
In mechanical design, the "strength" of a shaft refers to its capacity to transmit rotational energy (torque) without yielding or experiencing structural failure.
The strength is determined by the maximum shear stress developed in the shaft when subjected to a twisting moment.
Therefore, comparing the strengths of two shafts involves comparing their torque-carrying capacities.
Step 2: Detailed Explanation:
The torsional shear stress ($\tau$) developed in a solid circular shaft subjected to a torque or twisting moment ($T$) is given by the torsion equation:
\[ \frac{T}{J} = \frac{\tau}{R} \]
Where:
$J$ is the polar moment of inertia of the shaft's cross-section.
$R$ is the outer radius of the shaft.
Rearranging this equation to solve for the twisting moment:
\[ T = \tau \cdot \frac{J}{R} \]
The term $J/R$ is known as the polar section modulus ($Z_p$), which represents the geometric strength of the shaft's cross-section.
The maximum torque a shaft can safely transmit is:
\[ T = \tau_{\text{allowable}} \cdot Z_p \]
Two shafts are considered to have equal strength if they can safely transmit the same maximum twisting moment (torque) without exceeding their allowable shear stress limits.
Shafts with different diameters or made of different materials can still have equal strength if their geometry and material limits combine to allow the same maximum torque capacity.
Therefore, equal twisting moment is the defining criterion for equal strength.
Step 3: Final Answer
Two shafts have equal strength if their twisting moments are equal.
In mechanical design, the "strength" of a shaft refers to its capacity to transmit rotational energy (torque) without yielding or experiencing structural failure.
The strength is determined by the maximum shear stress developed in the shaft when subjected to a twisting moment.
Therefore, comparing the strengths of two shafts involves comparing their torque-carrying capacities.
Step 2: Detailed Explanation:
The torsional shear stress ($\tau$) developed in a solid circular shaft subjected to a torque or twisting moment ($T$) is given by the torsion equation:
\[ \frac{T}{J} = \frac{\tau}{R} \]
Where:
$J$ is the polar moment of inertia of the shaft's cross-section.
$R$ is the outer radius of the shaft.
Rearranging this equation to solve for the twisting moment:
\[ T = \tau \cdot \frac{J}{R} \]
The term $J/R$ is known as the polar section modulus ($Z_p$), which represents the geometric strength of the shaft's cross-section.
The maximum torque a shaft can safely transmit is:
\[ T = \tau_{\text{allowable}} \cdot Z_p \]
Two shafts are considered to have equal strength if they can safely transmit the same maximum twisting moment (torque) without exceeding their allowable shear stress limits.
Shafts with different diameters or made of different materials can still have equal strength if their geometry and material limits combine to allow the same maximum torque capacity.
Therefore, equal twisting moment is the defining criterion for equal strength.
Step 3: Final Answer
Two shafts have equal strength if their twisting moments are equal.
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