Two shafts are connected by means of a flange coupling to transmit tor...
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)
Two shafts are connected by means of a flange coupling to transmit tor...
Two pulleys, one 450 mm diameter and the other 200 mm diameter, on parallel shafts
1.95 m apart are connected by a crossed belt. Find the length of the belt required and
the angle of contact between the belt and each pulley.
What power can be transmitted by the belt when the larger pulley rotates at 200 rev/min, if the maximum permissible tension in the belt is 1 KN, and the coefficient of friction between the belt and pulley is 0.25?
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