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Two shafts are connected by means of a flange coupling to transmit torque of 25 N-m. The flanges of the coupling are fastened by four bolts of the same material at a radius of 30 mm. What is the size of bolts if the allowable shear stress for the botl material is 30 MPa?
  • a)
    M 4
  • b)
    M 8
  • c)
    M 12
  • d)
    M 16
Correct answer is option 'A'. Can you explain this answer?
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Given data:
Torque transmitted (T) = 25 N-m
Radius (r) = 30 mm
Allowable shear stress (τ) = 30 MPa

To find: Size of bolts required

Solution:
1. Calculation of shear stress:
The torque transmitted by the coupling is resisted by the bolts. The shear stress developed in the bolts can be calculated using the formula:

τ = T/(2A)
where A is the area of the bolt cross-section.

In this case, there are four bolts, so the total area of cross-section is:

A = 4 × π/4 × d^2/4
where d is the diameter of the bolt.

Substituting the given values, we get:

τ = 25/(2 × 4 × π/4 × 0.03^2) = 17.48 MPa

The allowable shear stress is given as 30 MPa. Therefore, the bolts are safe for the given torque.

2. Selection of bolt size:
The size of the bolt can be selected based on the shear area required to withstand the given torque. The shear area (As) can be calculated using the formula:

As = T/(τ × d)
where d is the diameter of the bolt.

Substituting the given values, we get:

As = 25/(30 × 10^6 × d) = 0.83 × 10^-6 m^2

The standard sizes of bolts are available in the market. From the available sizes, the closest size which fulfills the shear area requirement can be selected. The closest size is M4 bolt, which has a shear area of 0.785 × 10^-6 m^2.

Therefore, the required bolt size is M4.

Answer: Option A (M4)
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Two shafts are connected by means of a flange coupling to transmit torque of 25 N-m. The flanges of the coupling are fastened by four bolts of the same material at a radius of 30 mm. What is the size of bolts if the allowable shear stress for the botl material is 30 MPa?a)M 4b)M 8c)M 12d)M 16Correct answer is option 'A'. Can you explain this answer?
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