# Solution to Problem 332 | Flanged bolt couplings

**Problem 332**

In a rivet group subjected to a twisting couple T, show that the torsion formula τ = Tρ/J can be used to find the shearing stress τ at the center of any rivet. Let J = ΣAρ^{2}, where A is the area of a rivet at the radial distance ρ from the centroid of the rivet group.

# Solution to Problem 331 | Flanged bolt couplings

**Problem 331**

A flanged bolt coupling consists of six ½-in. steel bolts evenly spaced around a bolt circle 12 in. in diameter, and four ¾-in. aluminum bolts on a concentric bolt circle 8 in. in diameter. What torque can be applied without exceeding 9000 psi in the steel or 6000 psi in the aluminum? Assume G_{st} = 12 × 10^{6} psi and G_{al} = 4 × 10^{6} psi.

# Solution to Problem 330 | Flanged bolt couplings

**Problem 330**

Determine the number of 10-mm-diameter steel bolts that must be used on the 400-mm bolt circle of the coupling described in Prob. 328 to increase the torque capacity to 14 kN·m

# Solution to Problem 329 | Flanged bolt couplings

**Problem 329**

A torque of 700 lb-ft is to be carried by a flanged bolt coupling that consists of eight ½-in.-diameter steel bolts on a circle of diameter 12 in. and six ½-in.-diameter steel bolts on a circle of diameter 9 in. Determine the shearing stress in the bolts.

# Solution to Problem 328 | Flanged bolt couplings

**Problem 328**

A flanged bolt coupling consists of eight 10-mm-diameter steel bolts on a bolt circle 400 mm in diameter, and six 10-mm-diameter steel bolts on a concentric bolt circle 300 mm in diameter, as shown in Fig. 3-7. What torque can be applied without exceeding a shearing stress of 60 MPa in the bolts?

# Solution to Problem 327 | Flanged bolt couplings

**Problem 327**

A flanged bolt coupling consists of ten steel ½-in.-diameter bolts spaced evenly around a bolt circle 14 in. in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 6000 psi.

# Solution to Problem 326 | Flanged bolt couplings

**Problem 326**

A flanged bolt coupling consists of ten 20-mm-diameter bolts spaced evenly around a bolt circle 400 mm in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 40 MPa.

# Flanged bolt couplings

In shaft connection called flanged bolt couplings (see figure), the torque is transmitted by the shearing force P created in he bolts that is assumed to be uniformly distributed. For any number of bolts n, the torque capacity of the coupling is

# Solution to Problem 325 Torsion

**Problem 325**

The two steel shaft shown in Fig. P-325, each with one end built into a rigid support have flanges rigidly attached to their free ends. The shafts are to be bolted together at their flanges. However, initially there is a 6° mismatch in the location of the bolt holes as shown in the figure. Determine the maximum shearing stress in each shaft after the shafts are bolted together. Use G = 12 × 10^{6} psi and neglect deformations of the bolts and flanges.